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Transcript of Verification Manual
STAAD Foundation Advanced
V8i
Verification ManualDAA039800-1/0001
Last updated: 26 July 2011
Copyright InformationTrademark NoticeBentley, the "B" Bentley logo, STAAD Foundation are registered or nonregisteredtrademarks of Bentley Sytems, Inc. or Bentley Software, Inc. All other marks are theproperty of their respective owners.
Copyright Notice© 2011, Bentley Systems, Incorporated. All Rights Reserved.
Including software, file formats, and audiovisual displays; may only be used pursuant toapplicable software license agreement; contains confidential and proprietary information ofBentley Systems, Incorporated and/or third parties which is protected by copyright andtrade secret law and may not be provided or otherwise made available without properauthorization.
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Unpublished - rights reserved under the Copyright Laws of the United States andInternational treaties.
End User License AgreementsTo view the End User License Agreement for this product, review: eula_en.pdf.
Verification Manual — i
ii — (Undefined variable: Primary.ProductName)
Chapter 2
Table of Contents
Introduction 1Section 1 Australian Code (AS3600-2001[AMnd2004]) 31.1 General Isolated Foundation 1 3
1.2 General Isolated Foundation 2 6
1.3 General Combined Foundation 1 14
1.4 General Combined Foundation 2 16
Section 2 British Code (BS8110-1-1997) 232.1 General Isolated Foundation 1 23
2.2 General Isolated Foundation 2 26
2.3 General Isolated Foundation 3 32
2.4 General Isolated Foundation 4 38
2.5 General Isolated Foundation 5 44
2.6 General Isolated Foundation 6 53
2.7 General Isolated Foundation 7 62
2.8 General Combined Foundation 1 71
2.9 General Combined Foundation 2 77
2.10 Mat Combined Foundation 83
2.11 General Isolated Foundation with Eccentricity 88
Section 3 Canadian Code (CSA A23.3-2004) 993.1 CSA General Isolated Foundation 1 99
3.2 CSA General Isolated Foundation 2 105
3.3 CSA General Isolated Foundation 3 112
3.5 CSA Pilecap Foundation 1 115
3.4 CSA General Combined Foundation s1 122
Section 4 Indian Code (IS 456 -2000) 1254.1 IS General Isolated Foundation 1 125
4.2 IS General Isolated Foundation 2 129
4.3 IS General Isolated Foundation 3 133
4.4 IS General Isolated Foundation 4 138
4.5 IS General Isolated Foundation 5 140
4.6 IS General Isolated Foundations 6 145
4.7 IS General Isolated Foundation 7 150
Verification Manual — iii
4.8 IS Toolkit Combined 1 158
4.9 IS Toolkit Combined Foundation 2 164
4.10 IS Toolkit Combined Foundation 3 170
4.11 IS Toolkit Combined Foundation 4 176
4.12 IS Pilecap 1 182
4.13 IS Pilecap 2 189
4.14 IS Mat Combined Foundation 1 197
Section 5 United States Code (ACI 318 -2005) 2015.1 US General Isolated Foundation 1 201
5.2 US General Isolated Foundation 2 206
5.3 US General Isolated Foundation 3 211
5.4 US General Isolated Foundation 4 215
5.5 US General Isolated Foundation 5 220
5.6 US General Isolated Foundation 6 229
5.7 US General Isolated Foundation 7 233
5.8 US General Combined Foundation 1 241
5.9 US General Combined Foundation 2 247
5.10 US General Combined Foundation 3 253
5.11 US General Combined Foundation 4 258
5.12 US Pilecap Foundation 1 264
5.13 US Pilecap Foundation 2 271
5.14 US Pilecap Foundation 3 280
5.15 US Pilecap Foundation 4 287
5.16 US Mat Combined Foundation 1 295
5.17 US General Isolated Foundation with Sliding & Overturning 302
5.18 US General Isolated Foundation with Eccentric Loading 311
Section 6 Deadman Anchors (ACI 318 -2005) 3216.1 Deadman Guy Anchor US 1 321
6.2 Deadman Guy Anchor US 2 330
6.3 Deadman Guy Anchor US 3 338
6.4 Deadman Guy Anchor US 4 347
Section 7 Drilled Pier Foundations 3577.1 Drilled Pier Foundation 1 API 357
7.2 Drilled Pier Foundation 2 API 361
7.3 Drilled Pier Foundation 3 FHWA 366
iv — STAAD Foundation Advanced V8i
Chapter — 3
7.4 Drilled Pier Foundation 4 FHWA 371
7.5 Drilled Pier Foundation 5 VESIC 375
7.6 Drilled Pier Foundation 6 Vesic 380
Section 8 Plant Foundation 3858.1 Vertical Vessel Foundation 1 385
8.2 Vertical Vessel Foundation Design 394
8.3 Vertical Vessel Foundation Design 403
8.4 Vertical Vessel Seismic Load Generation 1 412
8.5 Vertical Vessel Seismic Load Generation 2 413
8.6 Vertical Vessel Seismic Load Generation 3 414
8.7 Vertical Vessel Seismic Load Generation 4 415
8.8 Vertical Vessel Seismic Load Generation 5 416
8.9 Vertical Vessel Seismic Load Generation 6 418
8.10 Vertical Vessel Seismic Load Generation 7 419
8.11 Vertical Vessel Seismic Load Generation 8 420
8.12 Vertical Vessel Seismic Load Generation 9 421
8.13 Vertical Vessel Wind Load Generation 1 422
8.14 Vertical Vessel Wind Load Generation 2 423
8.15 Vertical Vessel Wind Load Generation 3 424
8.16 Vertical Vessel Wind Load Generation 4 426
8.17 Horizontal Vessel Applied Loads 1 427
8.18 Horizontal Vessel Applied Loads 2 431
Section 9 Chinese Code (GB50007-2002) 4379.1 Cone Footing Design 437
9.2 PKPM Isolated Footing Design 445
9.3 Stepped Foundation Design 449
9.4 PKPM Stepped Footing Design 457
9.5 Combined Foundation 461
9.6 Pile Foundation Design 470
Section 10 Technical Support 485Index 487List of Figures & Tables 489Figures 489
Tables 493
Verification Manual — v
vi — (Undefined variable: Primary.ProductName)
Chapter 3
IntroductionThis document is intended to use as a hand calculation reference for STAAD FoundationAdvanced V8i (Release 6.0) verification problems. Verification Problems can be found underStart Page > Example > Verification.
Each section in this manual represents either specific design code (e.g., AS3600-2001) orparticular foundation type (e.g., Dead Man Anchor Guy Foundation). Hand calculation title(e.g., AS GEN ISO 1) indicates corresponding STAAD Foundation file name.
At end of each hand calculation a comparison table between hand calculations and programresults is provided for various output parameters like bearing pressure, overturning andsliding factor of safety, shear force, etc.
Verification Manual — 1
2 — (Undefined variable: Primary.ProductName)
Chapter 4
Section 1
Australian Code (AS3600-2001[AMnd 2004])1.1 General Isolated Foundation 1
1.1.1 Reference
1.1.2 ProblemDesign an isolated footing with the given data: Load Fy = 500 KN, fc = 25 MPa, fy = 450MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity of Soil = 110 KN/m2.Coefficient of friction =0.5, FOS against sliding =1.5, and FOS against overturning =1.5.Height of soil above footing = 500 mm, GWT is 200 mm from GL.
Surcharge= 10 KN/m2
Verification Manual — 3
Figure 1-1: Australian code General isolated foundation
1.1.3 SolutionApproximate area of footing required = 500/110 m2 = 4.545 m2
Assuming 2.4 m x 2.4 m x 0.400 m footing dimension,
Weight of footing = 2.4 x 2.4 x 0.400 x 25 KN = 57.6 KN
Weight of above soil = 2.4 x 2.4 x 0.500 x 18 KN = 51.84 KN
Reduction of Weight due to buoyancy = 2.4 x 2.4 x (0.500+0.400-0.200) x9.81 KN = 39.554 KN
Load due to surcharge = 2.4 x2.4 x 10 KN =57.6 KN
Therefore, total load on the footing = (500+57.6 +51.84+57.6 -39.554 ) KN= 627.486 KN
Maximum pressure = 627.486 /(2.4x2.4) = 108.94 KN/ m2
108.94 KN/m2 <110 KN/m2 (Hence safe)
Critical load case and the governing factor of safety forsliding
Along X Direction
Sliding force =0
4 — STAAD Foundation Advanced V8i
Chapter — 1
1.1 General Isolated Foundation 1
max Resisting force = µ x Total Service load on foundation
Total Service load on foundation = 627.486 KN
Hence Max possible Resisting Sliding force =0.5 x 627.486 = 313.74 KN
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation
Total Service load on foundation = 627.486 KN
Hence Max possible Resisting Sliding force =0.5 x 627.486 = 313.74 KN
Hence OK
Critical load case and the governing factor of safety foroverturning
WRT Z Direction
Overturning Moment =0
Max Resisting Moment = 0.5 x 2.4 x 627.486 = 752.98 KNm
Hence OK
WRT X Direction
Overturning Moment =0
Max Resisting Moment = 0.5 x 2.4 x 627.486 = 752.98 KNm
Hence OK
1.1.4 Comparison
Value of… ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure, KN/m2 108.94 108.63 NegligibleResisting force for sliding (x),KN
313.74 312.87 Negligible
Resisting Moment forOverturning (z), KNm
752.98 750.87 Negligible
Resisting force for sliding (z),KN
313.74 312.87 Negligible
Resisting Moment forOverturning (x), KNm
752.98 750.87 Negligible
Table 1-1: Australian verification example 1 comparison
Section 1 Australian Code (AS3600-2001[AMnd 2004])
1.1 General Isolated Foundation 1
Verification Manual — 5
1.2 General Isolated Foundation 21.2.1 Reference
1.2.2 ProblemDesign an isolated footing with the given data: Load Fy = 1,500 KN, Mz=50 KNm, Mx=50KNm, fc = 25 N/m2, fy = 450 N/m2m, Column Dimension = 300 mm x 300 mm, andBearing Capacity of Soil = 150 KN/m2. Coefficient of friction =0.5, FOS against sliding=1.5, and FOS against overturning =1.5 (Include SW for Factored Design)
Figure 1-2: Plan and Elevation
1.2.3 SolutionApproximate area of footing required = 1,500/150 m2 = 10.0 m2
Assuming 4.0 m x 4.0 m x 0.73 m footing dimension,
Tot Moment wrt Z =50 KNm
Tot Moment wrt X =50 KNm
Stress at four corners ( service condition)
σ1 = V/A – Mx/Zx + Mz/Zz
σ2 = V/A – Mx/Zx - Mz/Zz
6 — STAAD Foundation Advanced V8i
Chapter — 1
1.2 General Isolated Foundation 2
σ3 = V/A + Mx/Zx - Mz/Zz
σ4 = V/A + Mx/Zx + Mz/Zz
Tot Vertical Load on soil
Self wt of fdn = 4 m (4 m) (0.73 m) (25 KN/m3) = 292.0 KN
Column reaction load = 1,500 KN
Total Vertical load V = 1,792 KN
Zz = Z · X2/6 = 3.935 x 3.9352/6 =10.67 m3
Zx = Z · X2/6 = 3.935 x 3.9352/6 =10.67 m3
Mx= 50 KNm
Mz = 50 KNm
σ1 = V/A – Mx/Zx + Mz/Zz = 112 KN/m2
σ2 = V/A – Mx/Zx - Mz/Zz = 102.6 KN/m2
σ3 = V/A + Mx/Zx - Mz/Zz = 112 KN/m2
σ4 = V/A + Mx/Zx + Mz/Zz = 121.37 KN/m2
Max stress = 122 KN/m2 <150 KN/m2
Hence safe
Critical load case and the governing factor of safety forsliding
Along X Direction
Sliding force = 0
max Resisting force = µ x Total Service load on foundation =0.5 (1,792 KN) =896 KN
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation =0.5 (1,792 KN) =896 KN
Hence OK
Section 1 Australian Code (AS3600-2001[AMnd 2004])
1.2 General Isolated Foundation 2
Verification Manual — 7
Critical load case and the governing factor of safety foroverturning
Along X Direction
Overturning Moment =50 KNm
max resisting Moment = 0.5 · (4 m) · (1,972 KN) = 3,584 KNm
Hence FOS = 3,584/50 = 71.7 > 1.5
Hence OK
Along Z Direction
Overturning Moment =50 KNm
max resisting Moment = 0.5 · (4 m) · (1,972 KN) = 3,584 KNm
Hence FOS = 3,584/50 = 71.7 > 1.5
Hence OK
Factored Design
Axial Load = 292 KN + 1.4(1,500 KN) = 2,392 KN
MX =1.4 x 50 =70 KNm
MZ =1.4 x 50 =70 KNm
Check For Trial Depth against moment about Z Axis
Average Base Pressure along one edge = 156.07 KN/m2 (left end)
Average Base Pressure along other edge = 142.93 KN/m2 (right end)
Approximate Base Pressure at the left critical section = 150 KN/m2
Approximate Base Pressure at the right critical section = 149.01 KN/m2
Hence, the moment at the left critical section Mu (Left)
F = (156.07 + 150.0)/2 (1.85 m) (4 m) = 1,132.46 KN
LA = (150.0 + 2 · 156.07) (1.85 m) /[3(150.0 + 156.07)] = 0.932 m
Mu(left) = F · LA = 1,132.46 KN (0.932 m) = 1,055.4 KNm
Similarly, the moment at the right critical section Mu (Right):
F = (142.93 + 149.01)/2 (1.85 m) (4 m) = 1,080.2 KN
LA = (142.93 + 2 · 149.01) (1.85 m) /[3(142.93 + 149.01)] = 0.919 m
Mu(right) = F · LA = 1,080.2 KN (0.919 m) = 992.7 KNm
So max moment with respect to the Z axis, Mu(Z) = 1,056 KNm
8 — STAAD Foundation Advanced V8i
Chapter — 1
1.2 General Isolated Foundation 2
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (730 - 50 - 0.5 x 16) mm = 672 mm
m= fc/fy =0.0555
γ = 0.85 - 0.007(fc - 28) = 0.871 (Take γ = 0.85 per Clause 8.1.2.2
Kumax = 0.4 (Clause 8.1.3)
Ku = 0.34 · γ · (1 - 0.2 · γ) = 0.24
Rumax = 0.85 · fc · γ · Kumax · (1 - Kumax /2) = 3.891
Mumax = φ [Rumax · b · d2] = 5,622.7 KNm
Mu < MumaxHence OK
Check For Trial Depth against moment about X Axis
Average Base Pressure along one edge = 142.93 KN/m2(left end)
Average Base Pressure along other edge = 156.07 KN/m2 (right end)
Approximate Base Pressure at the left critical section = 149.01 KN/m2
Approximate Base Pressure at the right critical section = 150.0 KN/m2
Hence, the moment at the critical section Mu (left)
F = (142.93 + 149.01)/2 (1.85 m) (4 m) = 1,080.2 KN
LA = (142.93 + 2 · 149.01) (1.85 m) /[3(142.93 + 149.01)] = 0.919 m
Mu(right) = F · LA = 1,080.2 KN (0.919 m) = 992.7 KNm
Similarly, the moment at the right critical section Mu (Right):
F = (156.07 + 150.0)/2 (1.85 m) (4 m) = 1,132.46 KN
LA = (150.0 + 2 · 156.07) (1.85 m) /[3(150.0 + 156.07)] = 0.932 m
Section 1 Australian Code (AS3600-2001[AMnd 2004])
1.2 General Isolated Foundation 2
Verification Manual — 9
Mu(left) = F · LA = 1,132.46 KN (0.932 m) = 1,055.4 KNm
So max moment with respect to the X axis, Mu(X) = 1,056 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (730 - 50 - 0.5 x 16) mm = 672 mm
m= fc/fy =0.0555
γ = 0.85 - 0.007(fc - 28) = 0.871 (Take γ = 0.85 per Clause 8.1.2.2
Kumax = 0.4 (Clause 8.1.3)
Ku = 0.34 · γ · (1 - 0.2 · γ) = 0.24
Rumax = 0.85 · fc · γ · Kumax · (1 - Kumax /2) = 3.891
Mumax = φ [Rumax · b · d2] = 5,622.7 KNm
Mu < MumaxHence OK
Area of Steel Required along X dir
Calculation required steel for balanced section, Astx = 4,427 m2m
Minimum area of steel Astmin = 0.002 · b · d = 5,376 mm2
So, provided area of steel = 5,376 mm2
Area of Steel Required along Z dir
Calculation required steel for balanced section, Astx = 4,427 m2m
Minimum area of steel Astmin = 0.002 · b · d = 5,376 mm2
So, provided area of steel = 5,376 mm2
10 — STAAD Foundation Advanced V8i
Chapter — 1
1.2 General Isolated Foundation 2
Check for One-Way Shear
Along X Direction
Critical section for moment is at a distance, d, away from the face of column
Average Base Pressure along one edge = 142.93 kN/m2
Average Base Pressure along other edge = 156.07 kN/m2
Approximate Base Pressure at the left critical section = 156.07 + (142.93 - 156.07) ·1.178/4= 152.2 kN/m2
Approximate Base Pressure at the right critical section = 156.07 + (142.93 - 156.07) · (4 -1.178)/4 = 146.8 kN/m2
Hence, the SF at the left critical section:
F = (156.07 + 152.2)/2 (1.178 m) (4 m) = 726.3 kN
Shear at the right critical section:
F = (142.93 + 146.8)/2 (1.178 m) (4 m) = 682.6 kN
Critical shear is 727 kN
Developed shear stress, τv = 726.3 kN (103)/[4,000 (672)] = 0.44 N/mm2
τcmax = 0.2 · fc = 5 N/mm2
ß1 = 1.1(1.6 - d/1000) = 1.1(1.6 - 672/1,000) = 1.021
ß2 = 1
ß3 = 1
τc = φ · ß1 · ß2 · ß3. · [Ast · fc/(b · d)]1/3 = 0.75{1.021(1)(1)[5,376 · 25/(4,000 · 672)]1/3} = 0.282
N/mm2
Hence OK
Section 1 Australian Code (AS3600-2001[AMnd 2004])
1.2 General Isolated Foundation 2
Verification Manual — 11
Along Z Direction
Critical section for moment is at a distance, d, away from the face of column
Average Base Pressure along one edge = 142.93 kN/m2
Average Base Pressure along other edge = 156.07 kN/m2
Approximate Base Pressure at the left critical section = 156.07 + (142.93 - 156.07) · (4 -1.178)/4 = 146.8 kN/m2
Approximate Base Pressure at the right critical section = 156.07 + (142.93 - 156.07) ·1.178/4= 152.2 kN/m2
Hence, the SF at the left critical section:
F = (142.93 + 146.8)/2 (1.178 m) (4 m) = 682.6 kN
Shear at the right critical section:
F = (156.07 + 152.2)/2 (1.178 m) (4 m) = 726.3 kN
Critical shear is 727 kN
Developed shear stress, τv = 726.3 kN (103)/[4,000 (672)] = 0.27 N/mm2
τcmax = 0.2 · fc = 5 N/mm2
ß1 = 1.1(1.6 - d/1000) = 1.1(1.6 - 672/1,000) = 1.021
ß2 = 1
ß3 = 1
τc = φ · ß1 · ß2 · ß3. · [Ast · fc/(b · d)]1/3 = 0.75{1.021(1)(1)[5,376 · 25/(4,000 · 672)]1/3} =
0.282 N/mm2
Hence OK
Punching Shear
Punching Shear is checked on a perimeter 0.5 · d from the column face.
12 — STAAD Foundation Advanced V8i
Chapter — 1
1.2 General Isolated Foundation 2
Pm = 3,888 mm
Vmax = 2,251 kN
τv = Vmax/(Pm · d) = 2,251 kN (10)3/(3,888 mm · 672 mm) = 0.862 N/mm2
Punching shear stress capacity
τc = φ · [0.34 · √(fc)] = 0.7 · [0.34 · √(25)] = 1.19 N/mm2
τv < τc
Hence safe
Section 1 Australian Code (AS3600-2001[AMnd 2004])
1.2 General Isolated Foundation 2
Verification Manual — 13
1.2.4 Comparison
Value of… ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Corner Pressure, KN/m2 112
102.6
112
102.6
111.9
102.6
111.9
121.32
None
Resisting force for sliding,KN
896
896
895.6
895.6
None
Resisting Moment forOverturning, KNm
3,584
3,584
3,582.3
3,582.3
None
Shear Force (One-Way), KN 727
727
726
735
Negligible
Resisting Shear Stress (One-Way), N/mm2
0.284
0.284
0.284
0.284
None
Shear Force (Two-Way), KN 2251 2250 NoneResisting Shear Stress (Two-Way), N/mm2
1.19 1.19 None
Governing Flexural Moment,KNm
1,056
1,056
1,054
1,054
None
Resisting Flexural Moment,KNm
5,622
5,622
5,622
5,622
None
Reinforcement provided indesign, mm2
5,376 ea.way
5,376 ea. way None
Table 1-2: Australian verification example 2 comparison
1.3 General Combined Foundation 11.3.1 Reference
1.3.2 ProblemDesign a combined footing with the given data: Load Fy = 600 KN each column., fc = 25MPa, fy = 450 MPa, Column Dimension = 300 mm x 300 mm, Pedestal height-500 mm.and C/C column distance = 3,000 mm . Bearing Capacity of Soil = 105 KN/m2. Coefficientof friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
Ht of soil =450 mm. Depth of GWT=250 mm.
14 — STAAD Foundation Advanced V8i
Chapter — 1
1.3 General Combined Foundation 1
Figure 1-3: Plan and Elevation
1.3.3 SolutionApproximate area of footing required = 2(600)/115 m2 = 10.435 m2
Assuming 5 m x 2.8 m x 0.600 m footing dimension,
( left overhang=right overhang = 1 m)
Weight of footing = 5 (2.8) (0.600) (25) = 210 KN
Weight of pedestal=2(0.3)(0.3)(0.5)(25) = 2.25 KN
Weight of soil above footing = [5(2.8) - 2(0.3)(0.3)] · 0.450 · 18 = 111.9 KN
Reduction of Weight due to buoyancy = 5(2.8) · (0.45 + 0.6 - 0.25) · 9.81 KN = 109.9 KN
Therefore, total load on the footing = (2 · 600 + 210 + 2.25 + 111.9 - 109.9) KN = 1,414.3KN
Maximum pressure= 1,414.3 /(5 · 2.8) = 101.0 KN/ m2
101 KN/ m2 < 105 KN/m2 (Hence safe)
Critical load case and the governing factor of safety foroverturning
About Z Direction
Overturning Moment =0
Total Service load on foundation = 1,414.3 KN
Section 1 Australian Code (AS3600-2001[AMnd 2004])
1.3 General Combined Foundation 1
Verification Manual — 15
max resisting Moment = 5 m · 1,414.3 KN /2 =3,535.6 KNm
Hence OK
About X Direction
Overturning Moment = 0
max resisting Moment = 2.8 m · 1,414.3 KN /2 = 1,980 KNm
Hence OK
1.3.4 Comparison
Value of… ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure, KN/m2 101 101 NoneResisting Moment forOverturning (Z), KNm
3,535.8 3,535 None
Resisting Moment forOverturning (X), KNm
1,980 1,980 None
Table 1-3: Australian verification example 3 comparison
1.4 General Combined Foundation 21.4.1 Reference
1.4.2 ProblemDesign a combined footing with the given data: Load Fy = 600 KN and 550 KN on twocol., fc = 25 MPa, fy = 450 MPa, Column Dimension = 300 mm x 300 mm, Pedestalheight-500 mm. and C/C column distance=3000 mm . Bearing Capacity of Soil = 100KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning=1.5
16 — STAAD Foundation Advanced V8i
Chapter — 1
1.4 General Combined Foundation 2
Figure 1-4: Plan and Elevation
1.4.3 SolutionApproximate area of footing required = (600+550)/100 m2 = 11.5 m2
Assuming 5 m x 3 m x 0.500 m footing dimension,
( left overhang = right overhang = 1 m)
Weight of footing = 5 m · 3 m · 0.500 m · 25 = 187.5 KN
Weight of pedestal = 2(0.3)(0.3)(0.5)(25) = 2.25 KN
Therefore, total load on the footing = (600 + 550 + 187.5 + 2.25) KN = 1,339.8 KN
Pressure from axial load = 1,339.8 KN/(5 m · 3 m) = 89.3 KN/ m2
CG of foundation raft = 5/2= 2.5 m from left end
CG of load = (1 m · 600 KN + 4 m · 550 KN)/(600 KN + 550 KN) = 2.435 m
Eccentricity= 2.5 - 2.435 = 0.065 m
So Moment Mz = P · e = 1,150 KN (0.065 m) = 75 KNm
Zz = 3 · 52/6 = 12.5 m3
stress due to moment = M/Z = 75 KNm/12.5 m3 = 6 KN/m2
Stress at left end = P/A + M/Z = 89.3 + 6 = 95.3 KN/m2
Stress at right end = P/A - M/Z = 89.3 - 6 = 83.3 KN/m2
So, Maximum stress
95.3 KN/m2 < 100 KN/m2 (Hence safe)
Section 1 Australian Code (AS3600-2001[AMnd 2004])
1.4 General Combined Foundation 2
Verification Manual — 17
Critical load case and the governing factor of safety foroverturning
About Z Direction
Overturning Moment =0
max resisting Moment = 5 m (1,339.8 KN) /2 = 3,349.5 KNm
Hence OK
Wrt X Direction
Overturning Moment =0
max resisting Moment = 3 m (1,339.8 KN) /2 = 2,009.7 KNm
Hence OK
Check For Trial Depth
Moment About Z Axis (sagging)
Bending moment at critical section, Muz = 172 KNm
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (500 - 50 - 0.5 · 12) mm = 444 mm
m= fc/fy =0.0556
γ = 0.85 - 0.007 · (fc - 28) = 0.87
take γ = 0.85 ( Clause 8.1.2.2)
Kumax = 0.4 (Clause 8.1.3)
Ku = 0.34 ·γ · (1 - 0.2 · λ) = 0.34 · 0.85(1 - 0.2 · 0.85) = 0.24
Rumax = 0.85 · fc · γ · Ku · (1 - γ · Ku /2) = 0.85(25)(0.85)(0.24)(1 - 0.85 · 0.24/2) = 3.891N/mm2
Mumax = φ [Rumax · b · d2] =0.80 [3.891 N/mm2 · 3,000 mm · (444 mm)2]10-6 = 1,840
KNm
Muz < Mumax Hence OK
Moment About Z Axis (hogging)
Bending moment at critical section, Muz = 201 KNm
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (500 - 50 - 0.5 · 12) mm = 444 mm
m= fc/fy =0.0556
γ = 0.85 - 0.007 · (fc - 28) = 0.87
18 — STAAD Foundation Advanced V8i
Chapter — 1
1.4 General Combined Foundation 2
take γ = 0.85 ( Clause 8.1.2.2)
Kumax = 0.4 (Clause 8.1.3)
Ku = 0.34 ·γ · (1 - 0.2 · λ) = 0.34 · 0.85(1 - 0.2 · 0.85) = 0.24
Rumax = 0.85 · fc · γ · Ku · (1 - γ · Ku /2) = 0.85(25)(0.85)(0.24)(1 - 0.85 · 0.24/2) = 3.891N/mm2
Mumax = φ [Rumax · b · d2] =0.80 [3.891 N/mm2 · 3,000 mm · (444 mm)2]10-6 = 1,840
KNm
Muz < Mumax Hence OK
Moment About X Axis
Cantilever length = (3 - 0.3)/2 = 1.35 m
Bending moment at critical section, Mux = 107.34 N/mm2 (5 m) (1.35 m)2/2 =489.1 KNm
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (500 - 50 - 0.5 · 12) mm = 444 mm
m= fc/fy =0.0556
γ = 0.85 - 0.007 · (fc - 28) = 0.87
take γ = 0.85 ( Clause 8.1.2.2)
Kumax = 0.4 (Clause 8.1.3)
Ku = 0.34 ·γ · (1 - 0.2 · λ) = 0.34 · 0.85(1 - 0.2 · 0.85) = 0.24
Rumax = 0.85 · fc · γ · Ku · (1 - γ · Ku /2) = 0.85(25)(0.85)(0.24)(1 - 0.85 · 0.24/2) = 3.891N/mm2
Mumax = φ [Rumax · b · d2] =0.80 [3.891 N/mm2 · 5,000 mm · (444 mm)2]10-6 = 3,068
KNm
Mu < Mumax Hence OK
Area of Steel Required
Along X Direction (Bottom)
Astx = 1,083 mm2
Minimum area of steel Astmin = 0.002 · b · d = 2,664 mm2
Provided area = 2,664 mm2
Along X Direction (Top)
Astx = 1,268 mm2
Minimum area of steel Astmin = 0.002 · b · d = 2,664 mm2
Provided area = 2,664 mm2
Section 1 Australian Code (AS3600-2001[AMnd 2004])
1.4 General Combined Foundation 2
Verification Manual — 19
Along Z Direction (Bottom)
Therefore, Astz = 3,096 mm2
Minimum area of steel Astmin = 0.002 · b · d = 4,440 mm2
Provided area = 4,440 mm2
Figure 1-5: Graphs of combined strip footing internal forces
20 — STAAD Foundation Advanced V8i
Chapter — 1
1.4 General Combined Foundation 2
Check for One-Way Shear
Developed shear stress V = 299.5(10)3/(3,000 · 444) = 0.225 N/mm2
τcmax = 0.2 · fc = 5 N/mm2
ß1 =1.1(1.6-d/1000) = 1.2716
ß2 = 1
ß3 = 1
τc =ß1.ß2.ß3.(Ast.fc/b.d)1/3 = 0.488 N/mm2
Vumax = 299.5 KN
Developed shear stress, τv = 299.5(10)3/(3,000 · 444) = 0.225 N/mm2
τcmax = 0.2 · fc = 5 N/mm2
ß1 = 1.1(1.6 - d/1000) = 1.1(1.6 - 444/1,000) = 1.272
ß2 = 1
ß3 = 1
τc = φ · ß1 · ß2 · ß3. · [Ast · fc/(b · d)]1/3 = 0.7{1.272(1)(1)[2,664 · 25/(3,000 · 444)]1/3} = 0.328
N/mm2
Hence OK
Punching Shear
For Column One
Punching shear is checked on a perimeter 0.5 · d from the column face.
Two way shear = 777.8 KN
Pm = 4 · (300 mm + 444 mm) = 2,976 mm
τv = Vmax/(Pm · d) = 777.8 KN · 1000/(2,976 mm · 444 mm) = 0.589 N/mm2
τc = φ · [0.34 · √(fc)] = 0.7 · [0.34 · √(25)] = 1.19 N/mm2
τv < τc , Hence safe
For Column Two
Punching shear is checked on a perimeter 0.5d from the column face.
Two way shear= 713.4 KN
Pm = 2,976 mm
τv = Vmax/(Pm · d) = 713.4 KN · 1000/(2,976 mm · 444 mm) = 0.540 N/mm2
τc = φ · [0.34 · √(fc)] = 0.7 · [0.34 · √(25)] = 1.19 N/mm2
τv < τc , Hence safe
Section 1 Australian Code (AS3600-2001[AMnd 2004])
1.4 General Combined Foundation 2
Verification Manual — 21
1.4.4 Comparison
Value of… ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure, KN/m2 95.3
83.3
95.32
83.32
None
Governing Moment, KNm 172
201
489
167
201
512
Negligible
Resisting Moment, KNm 1,840
1,840
3,068
1,840
1,840
3,068
None
Shear Force (One-Way), KN 299.5 299.4 NoneShear capacity (One-Way),N/mm2
0.328 0.328 None
Shear Force (Two-Way), KN 777.8
713.4
777.8
713.4
None
Shear capacity (Two-Way),N/mm2
1.19 1.19 None
Resisting Moment forOverturning (Z), KNm
3,349 3,349 None
Resisting Moment forOverturning (X), KNm
2,010 2,010 None
Table 1-4: Australian verification example 4 comparison
22 — STAAD Foundation Advanced V8i
Chapter — 1
1.4 General Combined Foundation 2
Section 2
British Code (BS8110-1-1997)2.1 General Isolated Foundation 1
2.1.1 Reference‘Reinforced Concrete’ by T.J.Macgingley & B.S.Choo, Page 333 and Example: 11.1.
2.1.2 ProblemA column 400mm X 400mm carries a dead load of 800 kN and an imposed load of 300 kN.The safe bearing pressure is 200 kN/m2. Design a square base to resist the loads. Theconcrete is grade 35 and the reinforcement is grade 460.
Verification Manual — 23
2.1.3 SolutionFigure 2-1: Bending section considered
Figure 2-2: One way shear section considered
Figure 2-3: Two way shear section considered
24 — STAAD Foundation Advanced V8i
Chapter — 2
2.1 General Isolated Foundation 1
Size of base
Self-weight of footing = 2.5 x 2.5 x 0.5 x 25 = 78.125 kN.
Therefore, Service load = Dead load + Imposed load + Self weight
= (800 + 300 + 78.125) kN = 1178.125 kN.
Area required = 1178.125 / 200 m2 = 5.890625 m2.
Make the base 2.5 m x 2.5 m.
Moment Steel
Ultimate load = (1.4 x 800) + (1.6 x 300) = 1600 kN.
Ultimate pressure = 1600 / (2.5 x 2.5) = 256 kNm2
The critical section YY at the column face is shown in Figure 6.1.
MYY= 256 x (2.5 / 2 - 0.4 / 2) x 2.5 x 0.525 = 352.8 kNm.
Try an overall depth of 500 mm with 20 mm bars.
Effective depth = 500 – 40 – 20 – 10 = 430 mm.
Therefore z = 0.95d,
= 1976.31 mm2.
Minimum area of steel = 0.0015 x B x d = 0.0012 x 2500 x 430 = 1625 mm2 < AS (HenceSafe)
Let us provide 10 nos. 16 mm bars, AS = 2010.62 mm2.
One Way Shear
The critical section Y1 Y1 at d = 430 mm from the face of the column is shown in Figure 6.2.
Design shear force, VU = 256 x (2.5 /2 – 0.43 – 0.4 / 2) x 2.5 = 396.8 kN
Design shear stress, v = 396.9(10)3 / (2500 x 430) = 0.369 N/mm2
Now, vC1 = min(0.8 ,5) = 4.7328 N/mm2 > v (Hence Safe)
Section 2 British Code (BS8110-1-1997)
2.1 General Isolated Foundation 1
Verification Manual — 25
= 0.395 N / mm2 > v (Hence Safe)
Hence no shear reinforcement is required.
Punching Shear
Punching shear is checked on a perimeter 1.5d = 625.5 mm from the column face. Thecritical perimeter is shown in Figure 6.3.
Perimeter = 1690 x 4 = 6760 mm.
Shear = 256 x (2.52 – 1.692) = 868.8 kN.
v = 868 x 103 / (6760 x 430) = 0.3 N / mm2 < VC (Hence Safe).
Hence no shear reinforcement is required.
Spacing
We provided 10 nos. 16 mm bars, AS = 2010.62 mm2.
Spacing = (2500 - 40 x 2 - 16) / (10 -1) = 267.11 mm.
2.1.4 Comparison
Value of Reference Results STAAD FoundationResult Percent Difference
Effective Depth 430 mm 430 mm NoneGoverning Moment 352.8 KN-m 352.8 KN-m NoneArea of Steel 1976.31 1976.31 NoneShear Stress (One-Way) 0.369 N/mm2 0.369 N/mm2 NoneShear Stress (Two-Way) 0.3 N/mm2 0.3 N/mm2 None
Table 2-1: British verification example 1 comparison
2.2 General Isolated Foundation 22.2.1 Reference‘Reinforced Concrete’ by T.J.Macgingley & B.S.Choo, Page 340 and Example: 11.2.
2.2.2 ProblemThe characteristic loads for an internal column footing in a building are given in thefollowing table. The proposed dimensions for the column and base are shown in Figure6.4. The safe bearing pressure of soil is 150 kN / m2. The materials to be used in thefoundation are grade 35 concrete and grade 460 reinforcement.
Vertical Load (kN) Moment (KN m)Dead Load 770 78Imposed Load 330 34
Table 2-2: Table BS2.1 - Column loads
26 — STAAD Foundation Advanced V8i
Chapter — 2
2.2 General Isolated Foundation 2
Figure 2-4: Plan and Elevation
2.2.3 SolutionSelf-weight of footing = 0.5 x 3.6 x 2.8 x 24 = 120.96 kN.
Total axial load = 770 + 330 + 120.96 = 1220.96 kN.
Total moment = 78 + 34 = 112 kN-m.
Base area = 2.8 x 3.6 = 10.08 m2.
Section modulus = (I / y) = (1/12)BD3/(D/2) = 6.048 m3.
Maximum pressure = 1220.96/10.08 + 112/6.048 = 139.65 kN / m2 < 150 kN / m2 (HenceSafe).
Factored axial load = (1.4 x 770) + (1.6 x 330) = 1606 kN.
Factored moment = (1.4 x 78) + (1.6 x 34) = 163.6 kN-m.
Maximum pressure = 1606/10.08 + 163.6/6.048 = 186.38 kN / m2.
Minimum pressure = 1606/10.08 - 163.6/6.048 = 132.28 kN / m2.
Calculation of Reinforcement Along Shorter Span (X1- X1):
Average pressure for section X1X1 (as shown in Figure 6.5) = 159.33 kN / m2.
Moment (MY) = (159.33 x 1.175 x 3.6) x (1.175 / 2) = 395.955 kN-m.
Effective depth (d) = 500 – 40 – 10 = 450 mm.
0.015 < 0.156 (Hence Safe)
Section 2 British Code (BS8110-1-1997)
2.2 General Isolated Foundation 2
Verification Manual — 27
Therefore z = 0.95d,
= 2119.475 mm2.
The minimum area of steel = 0.13 x 3600 x 500 / 100 = 2340 mm2 > calculated area ofsteel.
Provide minimum steel.
Figure 2-5: Sections considered for bending in both directions
Calculation of Reinforcement Along Longer Span (Y1-Y1):
Pressure at section Y1 Y1 (as shown in Figure 6.5) = 162.7 kN / m2.
28 — STAAD Foundation Advanced V8i
Chapter — 2
2.2 General Isolated Foundation 2
Moment(MX) = (162.7 x 2.8 x 1.575)x(1.575 / 2)+(0.5 x 1.575 x (186.38 – 162.7) x 2.8)x(2/ 3 x 1.575) = 619.862 kN-m.
Effective depth (d) = 500 – 40 – 20 –10 = 430 mm.
0.034 < 0.156 (Hence Safe)
= 0.96d
Therefore z = 0.95d,
= 3472.334 mm2.
The minimum area of steel = 0.13 x 2800 x 500 / 100 = 1820 mm2 <
calculated area of steel. (Hence safe)
One Way Shear Along Section Y2-Y2:
The critical section Y2 Y2 at d = 430 mm from the face of the column is shown in Figure6.6.
Average pressure for the required section = 177.78 kN / m2.
Design shear force, VU = 177.78 x 2.8 x 1.145 = 569.96 kN
Design shear stress, v = =473.388 kN / m2
Now, vC1 = min(0.8 ,5) = 4732.8 kN / m2 > v (Hence Safe)
= 429.6 kN / m2.
Let us consider 1.5 times shear enhancement.
Vce = 1.5 x 429.6 = 644.4 kN/m2 > v (Hence safe)
Hence no shear reinforcement is required.
Section 2 British Code (BS8110-1-1997)
2.2 General Isolated Foundation 2
Verification Manual — 29
Figure 2-6: Sections considered for one-way shear in both directions
Along Section X2-X2:
The critical section X2X2 at d = 450 mm from the face of the column is shown in Figure6.6.
Average pressure for the required section = 159.33 kN / m2.
Design shear force, VU = 159.33 x 3.6 x 7.25 = 415.85 kN
Design shear stress, v = =256.698 kN / m2
Now, vC1 = min(0.8 ,5) = 4732.8 kN / m2 > v (Hence Safe)
30 — STAAD Foundation Advanced V8i
Chapter — 2
2.2 General Isolated Foundation 2
= 409.6 kN / m2.
Let us consider 1.5 times shear enhancement.
Vce = 1.5 x 409.6 = 614.4 kN/m2 > v (Hence safe)
Hence no shear reinforcement is required.
Punching ShearFigure 2-7: Section considered for punching shear
The punching shear will be calculated for an area outside the area enclosed by the rectangleat a distance 1.5d from the column face as shown in Figure 6.7.
Total pressure under the base = 2.8 x 3.6 x 132.28 + 0.5 x 3.6 x 2.8 x (186.38 – 132.28) =1606.05 kN.
Pressure under enclosed rectangle = (1.74)2 x 146.255 + 0.5 x (1.74)2 x (172.4 – 146.255) =482.38 kN
Punching shear force = 1606.05 – 482.38 = 1123.67 kN.
Critical perimeter = 1.74 x 4 = 6.96 m.
Punching shear stress = 1123.67 / (6.96 x 0.43) = 375.46 kN / m2.
Section 2 British Code (BS8110-1-1997)
2.2 General Isolated Foundation 2
Verification Manual — 31
2.2.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth (X-X) 430 mm 430 mm NoneEffective Depth (Y-Y) 450 mm 450 mm NoneGoverning Moment (My) 395.955 KN-m 395.943 KN-m NoneGoverning Moment (Mx) 619.862 KN-m 619.909 kN-m NoneArea of Steel (Along X-X) 2340.00 2340.00 NoneArea of Steel (Along Y-Y) 3472.2334 3472.2334 NoneShear Stress (One-Way) (Y1-Y1)
473.388 kN/m2 444.81 kN/m2 Negligible
Shear Stress (One-Way) (X1-X1)
256.698 kN/m2 256.698 kN/m2 None
Shear Stress (Two-Way) 375.46 kN/m2 375.44 kN/m2 None
Table 2-3: British verification example 2 comparison
2.3 General Isolated Foundation 32.3.1 Reference
2.3.2 ProblemDesign an isolated footing with the given data: Load Fy = 1500 KN, fc = 25 MPa, fy = 415MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity of Soil = 120KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning=1.5
32 — STAAD Foundation Advanced V8i
Chapter — 2
2.3 General Isolated Foundation 3
Figure 2-8: Plan and Elevation
2.3.3 SolutionApproximate area of footing required = 1500/120 m2 = 12.5 m2
Assuming 3.85 m x 3.85 m x 0.65 m footing dimension,
Weight of footing = 3.85 x 3.85 x 0.65 x 25 KN = 240.865 KN
Therefore, total load on the footing = (1500+240.865) KN = 1740.865 KN
Maximum pressure =1740.865/(3.85x3.85)=KN/ m2 = 117.45 KN/m2 <120 KN/m2 (Hencesafe)
Ultimate pressure =1500x1.4/(3.85x3.85) KN/m2 = 141.676 KN/m2
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation =0.5 x 1740.865 = 870.43 KN
Section 2 British Code (BS8110-1-1997)
2.3 General Isolated Foundation 3
Verification Manual — 33
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 3.85 x 1740.865 = 3351.1 KNm
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation =0.5 x 1740.865 = 870.43 KN
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 3.85 x 1740.865 = 3351.1 KNm
Hence OK
Check For Trial Depth
Moment About X Axis
Bending moment at critical section, Mux = 141.676 x 3.85 x1.775x1.775/2 = 859.26 KN-m
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (650-50-0.5 x 12) mm = 594 mm
K = = =0.0253 < 0.156
Hence safe
Moment About Z Axis
Bending moment at critical section, Muz = 141.676 x 3.85 x1.775x1.775/2 = 859.26 KN-m
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (650-50-0.5 x 12) mm = 594 mm
K = = 0.0253 < 0.156
Hence safe
34 — STAAD Foundation Advanced V8i
Chapter — 2
2.3 General Isolated Foundation 3
Area of Steel Required
Along X Direction
Z = d = 0.971 d>0.95d
So, Z= 0.95d
Therefore, Astx = = 3862.3 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 3253.25 mm2
Along Z Direction
Z = d = 0.971 d>0.95d
So, Z= 0.95d
Therefore, Astz = = 3862.3 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 3253.25 mm2
Check for One-Way Shear
Along X Direction
Percentage of steel pt = = 0.1689
Vumax = 141.676 x 3.85 x = 644.18 KN
Developed shear stress V = = 0.282N/mm2
Now allowable stress= Vc1 = = 4 N/mm2
V < Vc1, Hence Safe
V1 = 0.17 N/mm2
V2 = 1 N/mm2
Section 2 British Code (BS8110-1-1997)
2.3 General Isolated Foundation 3
Verification Manual — 35
V3 = 1 N/mm2
Vc = = 0.352 N/mm2
Vce = 0.704 N/mm2
So V < Vce , Hence Safe
Check for One-Way Shear
Along Z Direction
Percentage of steel pt = = 0.1689
Vumax = 141.676 x 3.85 x = 644.18 KN
Developed shear stress V = = 0.282N/mm2
Now allowable stress= Vc1 = = 4 N/mm2
V < Vc1, Hence Safe
V1 = 0.17 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.352 N/mm2
Vce = 0.704 N/mm2
So V < Vce , Hence Safe
Punching Shear
Punching shear is checked on a perimeter 1.5d = 891 mm from the column face.
Area within Critical Perimeter Am = 4.3347 m2
Vmax = 1485.87 KN
Critical perimeter Pm = 2 X ( b + h + 6 x d) = 8.328 m
Vm1 = Vmax/(Pm · d) = 0.3 N/mm2
36 — STAAD Foundation Advanced V8i
Chapter — 2
2.3 General Isolated Foundation 3
Now allowable stress= Vt1 = = 4 N/mm2
Vm1< Vt1 , Hence safe
V1 = 0.17 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.352 N/mm2
Vm1 < Vc, Hence safe
Bar Spacing
In the X Direction
No. of 12 mm bar = = 35
Spacing = = 110 mm
Spacing for 12 mm bar = 110 mm
In the Z Direction
No. of 12 mm bar = = 35
Spacing = = 110 mm
Spacing for 12 mm bar = 110 mm
Check For Development Length
Along x & Z direction
Max dia permitted =25 mm
ß = 0.5
Hence Fbu = ß x √fc =0.5 x 5 = 2.5
Ld = 0.95x fy x Ø / 4Fbu = 0.95x 415x25/4x2.5 = 985.6 mm
available length = 1725 mm
Hence OK
Section 2 British Code (BS8110-1-1997)
2.3 General Isolated Foundation 3
Verification Manual — 37
2.3.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth 594 mm 594 mm NoneBearing Pressure 117.45
KN/m2117.45 KN/m2 None
Ku 0.0253 0.0252 NegligibleGoverning Moment 859.26 KN-
m856.92 KN-m Negligible
Shear Force(One-Way) 644.18 KN 642.87 KN NegligibleShear Force(Two-Way) 1485.87 KN 1483.64 KN NegligibleSteel required 3862 m2m 3851 m2m 0.28% (
Negligible)Resisting force for sliding 870.43 KN 870.43 KN NoneResisting Moment forOverturning
3351.1 KNm 3351.1 KNm None
Table 2-4: British verification example 3 comparison
2.4 General Isolated Foundation 42.4.1 Reference
2.4.2 ProblemDesign an isolated footing with the given data: Load Fy = 2000 KN, fc = 25 MPa, fy = 415MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity of Soil = 100KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning=1.5 Soil cover above footing =500 mm
Plan and Elevation
38 — STAAD Foundation Advanced V8i
Chapter — 2
2.4 General Isolated Foundation 4
2.4.3 SolutionApproximate area of footing required = 2000/100 m2 = 20 m2
Assuming 5.3 m x 5.3 m x 0.75 m footing dimension,
Weight of footing = 5.3 x 5.3 x 0.75 x 25 KN = 526.687 KN
Weight of soil = 5.3 x 5.3 x 0.5 x 18 KN = 252.81 KN
Therefore, total load on the footing = (2000+526.687+252.81) KN = 2779.5 KN
Maximum pressure = 2779.5 KN/ (5.3 m x 5.3 m) KN/ m2 = 98.9 KN/m2 <100 KN/m2
(Hence safe)
Ultimate pressure = 1.4(2000 KN) / (5.3 m x 5.3 m)KN/m2 = 99.678 KN/m2
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation = 0.5 x 2779.5 = 1389.75 KN
Hence OK
Section 2 British Code (BS8110-1-1997)
2.4 General Isolated Foundation 4
Verification Manual — 39
Overturning Moment =0
max resisting Moment = 0.5 x 5.3 x 2779.5 = 7365 KNm
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation = 0.5 x 2779.5 = 1389.75 KN
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 5.3 x 2779.5 = 7365 KNm
Hence OK
Check for Trial Depth Against Moment
About X Axis
Bending moment at critical section, Mux = 99.68 x 5.3 x 2.5 x 2.5 / 2 = 1651 KN-m
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (750-50-0.5 x 16) mm = 692 mm
K = = =0.026 < 0.156
Hence safe
About Z Axis
Bending moment at critical section, Mux = 99.68 x 5.3 x = 1651 KN-m
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (750-50-0.5 x 16) mm = 692 mm
K = = =0.026 < 0.156
Hence safe
Area of Steel Required
Along X Direction
Z = d
40 — STAAD Foundation Advanced V8i
Chapter — 2
2.4 General Isolated Foundation 4
= 0.97 d>0.95d
So, Z= 0.95d
Therefore, Astx = = 6351.73 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 5167.5 mm2
Area of Steel Required along Z dir
Z = d
= 0.97 d>0.95d
So, Z= 0.95d
Therefore, Astz = = 6351.73 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 5167.5 mm2
Check for One-Way Shear
Along X Direction
Percentage of steel pt = = 0.173
Vumax = 99.68 x 5.3 x = 955.2 KN
Developed shear stress V = 955.2(103)/(5300 x 692) = 0.26N/mm2
Now allowable stress= Vc1 = = 4 N/mm2
V < Vc1, Hence Safe
V1 = 0.173 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.354 N/mm2
Vce = 0.708 N/mm2
So V < Vce , Hence Safe
Section 2 British Code (BS8110-1-1997)
2.4 General Isolated Foundation 4
Verification Manual — 41
Along Z Direction
Percentage of steel pt = = 0.173
Vumax = 99.68 x 5.3 x = 955.2 KN
Developed shear stress V = = 0.26N/mm2
Now allowable stress= Vc1 = = 4 N/mm2
V < Vc1, Hence Safe
V1 = 0.173 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.354 N/mm2
Vce = 0.708 N/mm2
So V < Vce , Hence Safe
Punching Shear
Punching shear is checked on a perimeter 1.5d = 1038 mm from the column face.
Area within Critical Perimeter Am = 5.645 m2
Vmax = 2237.3 KN
Critical perimeter Pm = 2 X ( b + h + 6 x d) = 9.504 m
Vm1 = Vmax/(Pm · d) = 0.345 N/mm2
Now allowable stress= Vt1 = = 4 N/mm2
Vm1< Vt1 , Hence safe
V1 = 0.173 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.354 N/mm2
42 — STAAD Foundation Advanced V8i
Chapter — 2
2.4 General Isolated Foundation 4
Vm1 < Vc, Hence safe
Bar Spacing
In the X Direction
No. of 16 mm bar = = 32
Spacing = = 165 mm
Spacing for 16 mm bar = 165 mm
In the Z Direction
No. of 16 mm bar = = 32
Spacing = = 165 mm
Spacing for 16 mm bar = 165 mm
Check For Development Length
Along X & Z direction
Max dia permitted =25 mm
ß = 0.5
Hence Fbu = ß x √fc =0.5 x 5 = 2.5
Ld = 0.95x fy x Ø / 4Fbu = 0.95x 415x25/4x2.5 = 985.6 mm
available length = 1725 mm
Hence OK
Section 2 British Code (BS8110-1-1997)
2.4 General Isolated Foundation 4
Verification Manual — 43
2.4.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth 692 mm 692 mm NoneBearing Pressure 98.9 KN/m2 98.75 KN/m2 NegligibleKu 0.026 0.026 NegligibleGoverning Moment 1651 KN-m 1647.74 KN-m NegligibleShear Force(One-Way) 955.2 KN 952.85 KN NegligibleShear Force(Two-Way) 2237.3 KN 2232.14 KN NegligibleSteel required 6352 m2m 6357.649 m2m NegligibleResisting force for sliding 1389.75 KN 1374.762 KN NegligibleResisting Moment forOverturning
7365 KNm 7148.63 KN Negligible
Table 2-5: British verification example 4 comparison
2.5 General Isolated Foundation 52.5.1 Reference
2.5.2 ProblemDesign an isolated footing with the given data: Load Fy = 1200 KN,Mz=80 KNm, fc = 25MPa, fy = 415 MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity ofSoil = 120 KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS againstoverturning =1.5
44 — STAAD Foundation Advanced V8i
Chapter — 2
2.5 General Isolated Foundation 5
2.5.3 SolutionApproximate area of footing required = 1200/120 m2 = 10 m2
Assuming 3.65 m x 3.65 m x 0.75 m footing dimension,
Tot Moment wrt Z =80 KNm
Stress at four corners ( service condition)
σ1 = V/A – Mx/Zx + Mz/Zz
σ2 = V/A – Mx/Zx - Mz/Zz
σ3 = V/A + Mx/Zx - Mz/Zz
σ4 = V/A + Mx/Zx + Mz/Zz
Tot Vertical Load on soil
Self wt of fdn = 3.65x 3.65x 0.75x25 = 249.8 KN
Dry wt of soil = 0
Col reaction load = 1200 KN
Tot Vertical load V = 1449.8 KN
Zz = Z.X2/6 = 3.65 x 3.652/6 =8.105 m3
Zx = X.Z2/6 = 3.65 x 3.652/6 =8.105 m3
Section 2 British Code (BS8110-1-1997)
2.5 General Isolated Foundation 5
Verification Manual — 45
Mx=0
Mz = 80 KNm
σ1 = V/A – Mx/Zx + Mz/Zz = 118.694 KN/m2
σ2 = V/A – Mx/Zx - Mz/Zz = 98.953 KN/m2
σ3 = V/A + Mx/Zx - Mz/Zz = 98.953 KN/m2
σ4 = V/A + Mx/Zx + Mz/Zz = 118.694 KN/m2
= 118.694 KN/m2 <120 KN/m2
Hence safe
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation =0.5 x 1449.8 = 724.9 KN
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 3.63x 1449.8 = 2645.885 KNm
Hence OK
Critical load case and the governing factor of safety foroverturning and sliding
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation =0.5 x 1449.8 = 724.9 KN
Hence OK
Overturning Moment =80 KNm
max resisting Moment = 0.5 x 3.63x 1449.8 = 2645.885 KNm
Hence FOS =2645.885/80 = 33.074
Hence OK
Check For Trial Depth
Moment About Z Axis
Force creating Moment= (139.922 +127.239) x 0.5 x 1.675 x 3.65 = 816.68 KN
Lever arm =(127.239 + 2 x 139.922) x 1.675/ 3x (139.922 + 127.239) = 0.8508 m
Moment = Fx LA = 694.84 KNm
46 — STAAD Foundation Advanced V8i
Chapter — 2
2.5 General Isolated Foundation 5
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (750-50-0.5 x 12) mm = 692 mm
K = = =0.016 < 0.156
Hence safe
Figure 2-9: Section considered for bending about the Z axis
Moment About X Axis
Force creating Moment= 126.103 x 1.675 x 3.65 = 770.97 KN
Lever arm = 1.675x 0.5 = 0.823 m
Moment = Fx LA =646.08 KNm
K = = =0.01481 < 0.156
Hence safe
Section 2 British Code (BS8110-1-1997)
2.5 General Isolated Foundation 5
Verification Manual — 47
Figure 2-10: Section considered for bending about the Z axis
Area of Steel Required
Along X Direction
Z = d = 0.983 d>0.95d
So, Z= 0.95d
Therefore, Astx = = 2594 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 3558.75 mm2
So, provided area of steel = 3558.75 mm2
Along Z Direction
Z = d = 0.97 d>0.95d
So, Z= 0.95d
Therefore, Astz = = 2412 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 3558.75 mm2
So, provided area of steel = 3558.75 mm2
48 — STAAD Foundation Advanced V8i
Chapter — 2
2.5 General Isolated Foundation 5
Check for One-Way Shear
Along X Direction
Percentage of steel pt = = 0.14
Vumax =1/2 x (139.922+132.479)x0.983 x 3.65 = 488.69 KN
Developed shear stress V = = 0.19N/mm2
Now allowable stress= Vc1 = = 4 N/mm2
V < Vc1, Hence Safe
V1 = 0.14 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.329 N/mm2
Vce = 0.658 N/mm2
So V < Vce , Hence Safe
Section 2 British Code (BS8110-1-1997)
2.5 General Isolated Foundation 5
Verification Manual — 49
Figure 2-11: Section considered for one-way shear along X direction
Along Z Direction
Percentage of steel pt = = 0.141
Vumax 126.103 x 0.983 x 3.65= 452.46 KN
Developed shear stress V = = 0.177 N/mm2
Now allowable stress= Vc1 = = 4 N/mm2
V < Vc1, Hence Safe
V1 = 0.141 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.329 N/mm2
Vce = 0.658 N/mm2
50 — STAAD Foundation Advanced V8i
Chapter — 2
2.5 General Isolated Foundation 5
So V < Vce , Hence Safe
Figure 2-12: Section considered for one-way shear along z direction
Punching Shear
Punching shear is checked on a perimeter 1.5d = 1038 mm from the column face.
Area within Critical Perimeter Am = 2.376 x 2.376 =7.68 m2
Vmax = 968.11 KN
Critical perimeter Pm = 2 X ( b + h + 6 x d) = 9.504 m
Vm1 = Vmax/(Pm · d) = 0.1472 N/mm2
Now allowable stress= Vt1 = = 4 N/mm2
Vm1< Vt1 , Hence safe
V1 = 0.14 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.329 N/mm2
Vm1 < Vc, Hence safe
Section 2 British Code (BS8110-1-1997)
2.5 General Isolated Foundation 5
Verification Manual — 51
Figure 2-13: Section considered for punching shear
Bar Spacing
In the X Direction
No. of 12 mm bar = = 32
Spacing = = 115 mm
Spacing for 12 mm bar = 115 mm
In the Z Direction
No. of 12 mm bar = = 32
Spacing = = 115 mm
Spacing for 12 mm bar = 115 mm
52 — STAAD Foundation Advanced V8i
Chapter — 2
2.5 General Isolated Foundation 5
Check For Development Length
Along X & Z direction
Max dia permitted =25 mm
ß = 0.5
Hence Fbu = ß x √fc =0.5 x 5 = 2.5
Ld = 0.95x fy x Ø / 4Fbu = 0.95x 415x25/4x2.5 = 985.6 mm
available length = 1725 mm
Hence OK
2.5.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth (mm) 692 692 NoneCorner Pressure (KN/m2) 118.69
98.95
98.95
118.69
118.69
98.95
98.95
118.69
None
Ku 0.01481
0.0156
0.0146
0.0158
Negligible
Governing Moment (KN-m) 646.08
694.84
643.82
692.8
Negligible
Shear Force ,One-Way (KN) 488.69
452.46
486.65
456.42
Negligible
Shear Force, Two-Way (KN) 968.11 961.62 NegligibleSteel required (mm2) 3558.75
3558.75
3558.75
3558.75
None
Resisting force for sliding(KN)
724.9
724.9
724.898
724.898
Negligible
Resisting Moment forOverturning (KN-m)
2645.8
2645.8
2645.8 Same
Table 2-6: British verification example 5 comparison
2.6 General Isolated Foundation 62.6.1 Reference
Section 2 British Code (BS8110-1-1997)
2.6 General Isolated Foundation 6
Verification Manual — 53
2.6.2 ProblemDesign an isolated footing with the given data: Load Fy = 1500 KN, Fx100 KN, fc = 25MPa, fy = 415 MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity ofSoil = 90 KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS againstoverturning =1.5
2.6.3 SolutionApproximate area of footing required = 1500/90 = 16.67 m2
Assuming 4.65 m x 4.65 m x 0.65 m footing dimension,
Tot Moment wrt Z =-0.65x100 =-65 KNm
Stress at four corners ( service condition)
σ1 = V/A – Mx/Zx + Mz/Zz
σ2 = V/A – Mx/Zx - Mz/Zz
σ3 = V/A + Mx/Zx - Mz/Zz
σ4 = V/A + Mx/Zx + Mz/Zz
Tot Vertical Load on soil
Self wt of fdn = 4.65x 4.65x 0.65x25 = 351.37 KN
54 — STAAD Foundation Advanced V8i
Chapter — 2
2.6 General Isolated Foundation 6
Dry wt of soil = 0
Col reaction load = 1500 KN
Tot Vertical load V = 1851.37 KN
Zz = Z.X2/6 = 4.65 x 4.652/6 =16.758 m3
Zx = X.Z2/6 = 4.65 x 4.652/6 =16.758 m3
Mx=0
Mz = -65 KNm
σ1 = V/A – Mx/Zx + Mz/Zz = 81.75 KN/m2
σ2 = V/A – Mx/Zx - Mz/Zz = 89.50 KN/m2
σ3 = V/A + Mx/Zx - Mz/Zz = 89.50 KN/m2
σ4 = V/A + Mx/Zx + Mz/Zz = 81.75 KN/m2
= 89.5 KN/m2 <90 KN/m2
Hence safe
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force =100 KN
max Resisting force = µ x Total Service load on foundation =0.5 x 1851.37 = 925.685 KN
Hence OK
Overturning Moment =65
max resisting Moment = 0.5 x 4.65x 1851.37 = 4304.43 KNm
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation =0.5 x 1851.37 = 925.685 KN
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 4.65x 1851.37 = 4304.43 KNm
Hence OK
Section 2 British Code (BS8110-1-1997)
2.6 General Isolated Foundation 6
Verification Manual — 55
Check For Trial Depth
Moment About Z Axis
Force creating Moment=1/2 x (102.552+97.472) x2.175x4.65 = 1011.5 KN
Lever arm =(97.472 + 2 x 102.552) x 2.175/ 3x (97.472+102.552) = 1.097m
Moment = Fx LA = 1109.62 KNm
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (650-50-0.5 x 12) mm = 594 mm
K = =0.027 < 0.156
Hence safe
Moment About X Axis
Force creating Moment= 97.122 x 2.175 x 4.65 = 982.27 KN
Lever arm =2.175 x 0.5 = 1.088 m
Moment = Fx LA =1068.71 KNm
K = =0.02606 < 0.156
Hence safe
56 — STAAD Foundation Advanced V8i
Chapter — 2
2.6 General Isolated Foundation 6
Area of Steel Required
Along X Direction
Z = d = 0.969 d > 0.95d
So, Z= 0.95d
Therefore, Astx = = 4890 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 3929.25 mm2
So, provided area of steel = 4890 mm2
Along Z Direction
Z = d = 0.97 d>0.95d
So, Z= 0.95d
Therefore, Astz = = 4706 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 3929.25 mm2
So, provided area of steel = 4706 mm2
Section 2 British Code (BS8110-1-1997)
2.6 General Isolated Foundation 6
Verification Manual — 57
Check for One-Way Shear
Along X Direction
Critical section for moment is at d dist from the face of column
Percentage of steel pt = = 0.178
Vumax =1/2 x (102.552+98.86)x1.581 x 4.65 = 740.36 KN
Developed shear stress V = 740.36 x1000/4650 x594 = 0.268N/mm2
Now allowable stress= Vc1 = = 4 N/mm2
V < Vc1, Hence Safe
V1 = 0.178 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.356 N/mm2
Vce = 0.712 N/mm2
So V < Vce , Hence Safe
58 — STAAD Foundation Advanced V8i
Chapter — 2
2.6 General Isolated Foundation 6
Along Z Direction
Critical section for moment is at d dist from the face of column
Percentage of steel pt = = 0.171
Vumax = 97.122 x1.58 x4.65= 714 KN
Developed shear stress V = 714 x1000/4650 x 594 =
= 0.258 N/mm2
Now allowable stress= Vc1 = = 4 N/mm2
V < Vc1, Hence Safe
V1 = 0.171 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.351 N/mm2
Vce = 0.702 N/mm2
So V < Vce , Hence Safe
Section 2 British Code (BS8110-1-1997)
2.6 General Isolated Foundation 6
Verification Manual — 59
Punching Shear
Punching shear is checked on a perimeter 1.5d = 1782 mm from the column face.
Area within Critical Perimeter Am = 2.082x2.082 =4.3347 m2
Vmax = 1679 KN
Critical perimeter Pm = 2 X ( b + h + 6 x d) = 8.328 m
Vm1 = Vmax/(Pm · d) = 0.3394 N/mm2
Now allowable stress= Vt1 = = 4 N/mm2
Vm1< Vt1 , Hence safe
V1 = 0.171 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.351 N/mm2
Vm1 < Vc, Hence safe
60 — STAAD Foundation Advanced V8i
Chapter — 2
2.6 General Isolated Foundation 6
Bar Spacing
In the X Direction
No. of 12 mm bar = = 44
Spacing = = 105 mm
Spacing for 12 mm bar = 155 mm
In the Z Direction
No. of 12 mm bar = = 42
Spacing = = 115 mm
Spacing for 12 mm bar = 115 mm
Check For Development Length
Along X & Z direction
Max dia permitted =25 mm
ß = 0.5
Hence Fbu = ß x √fc =0.5 x 5 = 2.5
Ld = 0.95x fy x Ø / 4Fbu = 0.95x 415x25/4x2.5 = 985.6 mm
available length = 1725 mm
Hence OK
Section 2 British Code (BS8110-1-1997)
2.6 General Isolated Foundation 6
Verification Manual — 61
2.6.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth 594 mm 594 mm NoneCorner Pressure 81.75
KN/m2
89.5 KN/m2
89.5 KN/m2
81.75KN/m2
81.74 KN/m2
89.5 KN/m2
89.5 KN/m2
81.74 KN/m2
None
Ku 0.02606
0.027
0.026
0.0269
None
Governing Moment 1068.71KNm
1109.62KNm
1065.83 KNm
1103.31 KNm
Negligible
Shear Force(One-Way) 740.36 KN
714 KN
736.98 KN
712 KN
Negligible
Shear Force(Two-Way) 1679 KN 1677 KN NegligibleSteel required 4890 m2m
4706 m2m
4959.354 m2m
4790.8 m2m
Negligible
Resisting force for sliding 925.68 KN
925.68 KN
925.68 KN
925.68 KN
None
Resisting Moment forOverturning
4304.43KNm
4304.43KNm
4304.43 KNm
4304.43 KNm
None
Table 2-7: British verification example 6 comparison
2.7 General Isolated Foundation 72.7.1 Reference
2.7.2 ProblemDesign an isolated footing with the given data: Load Fy = 1500 KN,Mz=Mx=50 KNm, fc =25 MPa, fy = 460 MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity ofSoil = 100 KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS againstoverturning =1.5
62 — STAAD Foundation Advanced V8i
Chapter — 2
2.7 General Isolated Foundation 7
Figure 2-14: Plan and Elevation
2.7.3 SolutionApproximate area of footing required =1500/100 m2 = 15 m2
Assuming 4.45 m x 4.45 m x 0.65 m footing dimension,
Tot Moment wrt Z =50 KNm
Tot Moment wrt X =50 KNm
Stress at four corners ( service condition)
σ1 = V/A – Mx/Zx + Mz/Zz
σ2 = V/A – Mx/Zx - Mz/Zz
σ3 = V/A + Mx/Zx - Mz/Zz
σ4 = V/A + Mx/Zx + Mz/Zz
Tot Vertical Load on soil
Self wt of fdn = 4.45x 4.45x 0.65x25 = 321.79 KN
Dry wt of soil = 0
Col reaction load = 1500 KN
Tot Vertical load V = 1821.79 KN
Section 2 British Code (BS8110-1-1997)
2.7 General Isolated Foundation 7
Verification Manual — 63
Zz = Z.X2/6 = 4.45 x 4.452/6 =14.686 m3
Zx = X.Z2/6 = 4.45 x 4.452/6 =14.686 m3
Mx= 50 KNm
Mz = 50 KNm
σ1 = V/A – Mx/Zx + Mz/Zz = 92KN/m2
σ2 = V/A – Mx/Zx - Mz/Zz = 85 KN/m2
σ3 = V/A + Mx/Zx - Mz/Zz = 92 KN/m2
σ4 = V/A + Mx/Zx + Mz/Zz = 98.81 KN/m2
= 98.81 KN/m2 <100 KN/m2 (Hence safe)
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation =0.5 x 1821.8 = 911 KN
Hence OK
Overturning Moment =50 KNm
max resisting Moment = 0.5 x 4.45x 1821.8 = 4053.5 KNm
Hence FOS=4053.5/50 = 81> 1.5
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation =0.5 x 1821.8 = 911 KN
Hence OK
Overturning Moment =50 KNm
max resisting Moment = 0.5 x 4.45x 1821.8 = 4053.5 KNm
Hence FOS=4053.5/50 = 81> 1.5
Hence OK
Check for Trial Depth Against Moment
About Z Axis
Avg Base Pressure at one edge=( 96.5149+106.047)/2 = 101.282 KN/m2
Avg Base Pressure at other edge=( 106.0473+115.5797)/2 = 110.814 KN/m2
64 — STAAD Foundation Advanced V8i
Chapter — 2
2.7 General Isolated Foundation 7
Force creating Moment= (110.814+106.37)/2 x 2.075x4.45 = 1002.72 KN
Lever arm = (106.37+2x110.814)x2.075/3x(106.37+110.814) m
Moment = Fx LA = 1047.85 KNm
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (650-50-0.5 x 12) mm = 594 mm
K = =0.027 < 0.156
Hence safe
About X Axis
Avg Base Pressure at one edge=( 96.5149+106.047)/2 = 101.282 KN/m2
Avg Base Pressure at other edge=( 106.0473+115.5797)/2 = 110.814 KN/m2
Force creating Moment= (110.814+106.37)/2 x 2.075x4.45 = 1002.72 KN
Lever arm = (106.37+2x110.814)x2.075/3x(106.37+110.814) m
Moment = Fx LA = 1047.85 KNm
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (650-50-0.5 x 12) mm = 594 mm
K = = 0.027 < 0.156
Hence safe
Section 2 British Code (BS8110-1-1997)
2.7 General Isolated Foundation 7
Verification Manual — 65
Area of Steel Required
Along X Direction
Z = d =<0.95d
= 0.969 d>0.95d
So, Z= 0.95d
Therefore, Astx = = 4165 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 3760 mm2
So, provided area of steel = 4165 mm2
Along Z Direction
Z = d
= 0.969 d>0.95d
So, Z= 0.95d
Therefore, Astz = = 4165m2m
Minimum area of steel Astmin = 0.0013 x B x D = 3760 mm2
66 — STAAD Foundation Advanced V8i
Chapter — 2
2.7 General Isolated Foundation 7
So, provided area of steel = 4165 mm2
Check for One-Way Shear
Along X Direction
Percentage of steel pt = = 0.158
Vumax =1/2 x (110.814+107.642)x1.481x4.45 = 719.87 KN
Developed shear stress V = 720x1000/(4450 x594) = 0.272N/mm2
Now allowable stress= Vc1 = = 4 N/mm2
V < Vc1, Hence Safe
V1 = 0.158 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.342 N/mm2
Vce = 0.684 N/mm2
So V < Vce , Hence Safe
Section 2 British Code (BS8110-1-1997)
2.7 General Isolated Foundation 7
Verification Manual — 67
Along Z Direction
Percentage of steel pt = = 0.158
Vumax =1/2 x (110.814+107.642)x1.481x4.45 = 719.87 KN
Developed shear stress V = = 0.272 N/mm2
Now allowable stress= Vc1 = = 4 N/mm2
V < Vc1, Hence Safe
V1 = 0.158 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.342 N/mm2
Vce = 0.684 N/mm2
So V < Vce , Hence Safe
Punching Shear
Punching shear is checked on a perimeter 1.5d from the column face.
68 — STAAD Foundation Advanced V8i
Chapter — 2
2.7 General Isolated Foundation 7
Area within Critical Perimeter Am = 2.082x2.082=4.335 m2
Vmax = 1640 KN
Critical perimeter Pm = 2 X ( b + h + 6 x d) = 8.328 m
Vm1 = Vmax/(Pm · d) = 0.3315 N/mm2
Now allowable stress= Vt1 = = 4 N/mm2
Vm1< Vt1 , Hence safe
V1 = 0.158 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.342 N/mm2
Vm1 < Vc, Hence safe
Figure 2-15: Section considered for punching shear
Section 2 British Code (BS8110-1-1997)
2.7 General Isolated Foundation 7
Verification Manual — 69
Bar Spacing
In the X Direction
No. of 12 mm bar = = 37
Spacing = = 120 mm
Spacing for 12 mm bar = 120 mm
In the Z Direction
No. of 12 mm bar = = 37
Spacing = = 120 mm
Spacing for 12 mm bar = 120 mm
70 — STAAD Foundation Advanced V8i
Chapter — 2
2.7 General Isolated Foundation 7
2.7.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth 594 mm 594 mm NoneCorner Pressure 92KN/m2
85.2 KN/m2
92 KN/m2
98.81KN/m2
92 KN/m2
85.91 KN/m2
92 KN/m2
98.81 KN/m2
None
Ku 0.027
0.027
0.0266
0.0266
Negligible
Governing Moment 1047.85KNm
1047.85KNm
1045 KNm
1045 KNm
Negligible
Shear Force(One-Way) 720 KN
720 KN
718.71 KN
718.71 KN
Negligible
Shear Force(Two-Way) 1640 KN 1638 KN NegligibleSteel required 12 @ 120 c/c 12 @ 118 c/c NegligibleResisting force for sliding 910.9 KN
910.9 KN
910.8 KN
910.8 KN
Negligible
Resisting Moment forOverturning
4053.5 KNm
4053.5 KNm
4053.4 KNm
4053.4 KNm
Same
Table 2-8: British verification example 7 comparison
2.8 General Combined Foundation 12.8.1 Reference
2.8.2 ProblemDesign a combined footing with the given data: Load Fy = 500 KN each column., fc = 25MPa, fy = 450 MPa, Column Dimension = 300 mm x 300 mm, Pedestal height-500 mm.and C/C column distance=3000 mm . Bearing Capacity of Soil = 150 KN/m2. Coefficient offriction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
Ht of soil =400 mm. Depth of GWT=200 mm
Section 2 British Code (BS8110-1-1997)
2.8 General Combined Foundation 1
Verification Manual — 71
2.8.3 SolutionFigure 2-16: Plan and Elevation
Approximate area of footing required = 2x500/150 m2 = 6.67 m2
Assuming 5 m x 1.5 m x 0.600 m footing dimension,
( left overhang=right overhang=1m)
Weight of footing = 5 m x 1.5 m x 0.600 x25 KN = 112.5 KN
Weight of pedestal=2x0.3x0.3x0.5x25=2.25 KN
Weight of soil above footing = (5 x 1.5-0.3x0.3x2 )x 0.400 x18 KN = 52.704 KN
Reduction of Weight due to buoyancy = 5 x 1.5 x (0.4+0.6-0.2) x9.81 KN = 58.86 KN
Therefore, total load on the footing = (2x500+112.5 +2.25+52.704 -58.86) KN = 1108.6 KN
Maximum pressure= 1108.6 /(5 x1.5) = 147.82 KN/ m2
147.82 KN/ m2 <150 KN/m2
Hence safe
Ultimate pressure = KN/m2 = 186.667 KN/m2
72 — STAAD Foundation Advanced V8i
Chapter — 2
2.8 General Combined Foundation 1
Critical load case and the governing factor of safety foroverturning
About Z Direction
Overturning Moment =0
max resisting Moment = 0.5 x 5x 1108.6 = 2771.5 KNm
Hence OK
About X Direction
Overturning Moment =0
max resisting Moment = 0.5 x 1.5 x 1108.6 = 831.45 KNm
Hence OK
Check For Trial Depth
Moment About Z Axis (sagging)
Bending moment at critical section, Mux = 140 KNm
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = Mu/fc.b.deff2 = 140x106/(25x1500x544x544) = 0.013 <0.156
Hence OK
Moment About Z Axis (hogging)
Bending moment at critical section, Mux = 174.9 KN-m
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = Mu/fc.b.deff2 = 0.016= <0.156
Hence OK
Moment About X Axis
Cantilever length=(1.5-0.3)/2 = 0.6 m
Bending moment at critical section, Mux = 186.667 x.5x0.62/2 =168 KNm
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = Mu/fc.b.deff2 = 168x106/(25x6500x544x544) = 0.005 <0.156
Section 2 British Code (BS8110-1-1997)
2.8 General Combined Foundation 1
Verification Manual — 73
Hence OK
Area of Steel Required
Along X Direction (Bottom)
Z = d = 0.998 d>0.95d
So, Z= 0.95d
Therefore, Astx = = 637 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 1170 mm2 ( as fy>250)
Provided area = 1170 m2m
Along X Direction (Top)
Z = d = 0.998 d>0.95d
So, Z= 0.95d
Therefore, Astx = = 792 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 1170 mm2 ( as fy>250)
Provided area = 1170 m2m
Along Z Direction (Bottom)
Z = d = 0.994 d>0.95d
So, Z= 0.95d
Therefore, Astx = = 761 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 3900 mm2
Provided area = 3900 m2m
Check for One-Way Shear
Percentage of steel pt = = 0.143
74 — STAAD Foundation Advanced V8i
Chapter — 2
2.8 General Combined Foundation 1
Vumax = 225.68 KN
Developed shear stress V = = 0.276 N/mm2
Now allowable stress= Vc1 = = 4 N/mm2
V < Vc1, Hence Safe
V1 = 0.143 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.331 N/mm2
Vce = 0.662 N/mm2
So V < Vce , Hence Safe
Punching Shear
For Column One
Punching shear is checked on a perimeter 1.5d = 816 mm from the column face.
2 way shear= 3.24 KN
Pm=300x2+300x2=544x12=7728 mm
τv = Vmax/(Pm · d) = 3.24x1000/(7728)x544 =0.00077 N/mm2
Now allowable stress= Vt1 = = 4 N/mm2
τv < Vt1 , Hence safe
For Column Two
Punching shear is checked on a perimeter 1.5d = 816 mm from the column face.
2 way shear= 3.24 KN
Pm=300x2+300x2=544x12=7728 mm
τv = Vmax/(Pm · d) = 3.24x1000/(7728)x544 =0.00077 N/mm2
Now allowable stress= Vt1 = = 4 N/mm2
τv < Vt1 , Hence safe
Section 2 British Code (BS8110-1-1997)
2.8 General Combined Foundation 1
Verification Manual — 75
Figure 2-17: Shear force and Bending Moment diagrams
76 — STAAD Foundation Advanced V8i
Chapter — 2
2.8 General Combined Foundation 1
2.8.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 147.82 KN/m2
147.82 KN/m2 None
Governing Moment 140 KN-m
174.9 KN-m
168 KN-m
135.77 KN-m
174.9 KN-m
168 KN-m
Negligible
Shear Force(One-Way) 225.68 KN 225.69 KN NegligibleShear Force(Two-Way) 3.24 KN
3.24 KN
3.24 KN
3.24 KN
None
Resisting Moment forOverturning (Z)
2771.5 KNm 2771.5 KNm Negligible
Resisting Moment forOverturning (X)
831.45 KNm 831.46 KNm Negligible
Table 2-9: British verification example 8 comparison
2.9 General Combined Foundation 22.9.1 Reference
2.9.2 ProblemDesign a combined footing with the given data: Load Fy = 600 KN, Mz=30 KNm, eachcolumn., fc = 25 MPa, fy = 450 MPa, Column Dimension = 300 mm x 300 mm, Pedestalheight-500 mm. and C/C column distance=3500 mm . Bearing Capacity of Soil = 140KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
No soil above footing and dry condition.
Section 2 British Code (BS8110-1-1997)
2.9 General Combined Foundation 2
Verification Manual — 77
2.9.3 SolutionFigure 2-18: Plan and Elevation
Approximate area of footing required = 2x600/140 m2 = 8.57 m2
Assuming 5.9 m x 1.7 m x 0.500 m footing dimension,
( left overhang=right overhang=1.2m)
Weight of footing = 5.9 m x 1.7 m x 0.500 x25 KN = 125.375 KN
Weight of pedestal=2x0.3x0.3x0.5x25=2.25 KN
Therefore, total load on the footing = (2x600+125.375 +2.25) KN = 1327.63 KN
Maximum pressure from axial load= 1327.63 /(5.9 x1.7) = 132.37 KN/ m2
Total Moment=30+30 = 60 KNm
CG of load= 2.9 m
CG of raft = 2.9 m
Eccentricity =2.95-2.9 =0.05 m
So Moment= P x Eccentricity = 1200x0.05 =60 KNm
Z= 1.7 x 5.92/6= 9.863 m3
So M/Z = 6.09 KN/m2
So stress at left end= P/A + M/Z= 138.46 KN/m2
78 — STAAD Foundation Advanced V8i
Chapter — 2
2.9 General Combined Foundation 2
So stress at left end= P/A - M/Z= 126.28 KN/m2
138.46 KN/ m2 <140 KN/m2
Hence safe
Critical load case and the governing factor of safety foroverturning
About Z Direction
Overturning Moment =60 KNm
max resisting Moment = 0.5 x 5.9x 1327.63 = 3916.5085 KNm
So FOS = 3916.5085/60 = 65.27 >1.5
Hence OK
About X Direction
Overturning Moment =0
max resisting Moment = 0.5 x 1.7 x 1327.63 = 1128.48 KNm
Hence OK
Check For Trial Depth against
Moment About Z Axis (sagging)
Bending moment at critical section, Mux = 214 KNm
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (500-50-0.5 x 12) mm = 444 mm
K = Mu/fc.b.deff2 = 214x106/(25x1700x444x444) = 0.0255 <0.156
Hence OK
Moment About Z Axis (hogging)
Bending moment at critical section, Mux = 231.62 KN-m
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (500-50-0.5 x 12) mm = 444 mm
K = Mu/fc.b.deff2 = 0.0276= <0.156
Hence OK
Moment About X Axis
Cantilever length=(1.7-0.3)/2 = 0.7 m
Bending moment at critical section, Mux = (158.98+176.02)/2 x5.9x0.72/2 =242.122 KNm
Section 2 British Code (BS8110-1-1997)
2.9 General Combined Foundation 2
Verification Manual — 79
Assuming 50 mm clear cover and 12 mm bar, effective depth
deff = (500-50-0.5 x 12) mm = 444 mm
K = Mu/fc.b.deff2 = 242x106/(25x6500x544x544) = 0.0083 <0.156
Hence OK
Area of Steel Required
Along X Direction (Bottom)
Z = d = 0.971 d>0.95d
So, Z= 0.95d
Therefore, Astx = = 1187 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 1105 mm2
Provided area = 1187 m2m
Along X Direction (Top)
Z = d = 0.968 d>0.95d
So, Z= 0.95d
Therefore, Astx = = 1284.5 m2m
Minimum area of steel Astmin = 0.0013 x B x D = 1105 mm2
Provided area = 1285 m2m
Along Z Direction (Bottom)
Z = d = 0.99 d>0.95d
So, Z= 0.95d
Therefore, Astx = = 1342.74 m2m
Minimum area of steel Astmin = 0.0013 x B x D =3835 mm2
Provided area = 3835 m2m
80 — STAAD Foundation Advanced V8i
Chapter — 2
2.9 General Combined Foundation 2
Check for One-Way Shear
Percentage of steel pt = = 0.17
Vumax = 347.24 KN
Developed shear stress V = 347.24x1000/(1700x444) = 0.46 N/mm2
Now allowable stress= Vc1 = = 4 N/mm2
V < Vc1, Hence Safe
V1 = 0.17 N/mm2
V2 = 1 N/mm2
V3 = 1 N/mm2
Vc = = 0.351 N/mm2
Vce = 0.702 N/mm2
So V < Vce , Hence Safe
Punching Shear
For Column One
Punching shear is checked on a perimeter 1.5d = 666 mm from the column face.
Two way shear = 380.43 KN
Pm=300x2+300x2=444x12=6528 mm
τv = Vmax/(Pm · d) = 380.43x1000/(6528)x544=0.131 N/mm2
Now allowable stress= Vt1 = = 4 N/mm2
τv < Vt1 , Hence safe
For Column Two
Punching shear is checked on a perimeter 1.5d = 666 mm from the column face.
Two way shear = 407.34 KN
Pm=300x2+300x2=444x12=6528 mm
τv = Vmax/(Pm · d) = 407.34x1000/(6528)x544 =0.14 N/mm2
Now allowable stress= Vt1 = = 4 N/mm2
τv < Vt1 , Hence safe
Section 2 British Code (BS8110-1-1997)
2.9 General Combined Foundation 2
Verification Manual — 81
Figure 2-19: Shear force and Bending Moment diagrams
82 — STAAD Foundation Advanced V8i
Chapter — 2
2.9 General Combined Foundation 2
2.9.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 138.46KN/m2
126.28KN/m2
138.45 KN/m2
126.28 KN/m2
None
Governing Moment 214 KN-m
231.62 KNm
242.122KNm
212 KN-m
231.78 KNm
249.42 KNm
Negligible
Shear Force(One-Way) 347.24 KN 347.24 KN NoneShear Force(Two-Way) 380.42 KN
407.34 KN
380.43 KN
407.34 KN
None
Resisting Moment for Over-turning (Z)
3916.5 KNm 3916.5 KNm None
Resisting Moment for Over-turning (X)
1128.48KNm
1128.48 KNm None
Table 2-10: British verification example 9 comparison
2.10 Mat Combined Foundation2.10.1 Reference‘Reinforced Concrete’ by T.J.Macgingley & B.S.Choo, Page 351 and Example: 11.4
2.10.2 ProblemDesign a rectangular base to support two columns carrying the following loads:
Column 1 Dead load 310 kN, imposed load 160 kN
Column 1 Dead load 310 kN, imposed load 160 kN
The columns are each 350 mm square and are spaced at 2.5 m centers. The width of thebase is not to exceed 2.0 m. the safe bearing pressure on the ground is 180 kN/m2. Thematerials are grade 35 concrete and grade 460 reinforcement.
Section 2 British Code (BS8110-1-1997)
2.10 Mat Combined Foundation
Verification Manual — 83
Figure 2-20: Plan and Elevation
2.10.3 SolutionLet us assume the self weight of the base is 130 kN.
Total vertical load = (310 + 160 + 430 + 220 + 130) = 1250 kN.
Area of base = 1250 / 160 = 7.81 m2 (considering safe base pressure as 160 kN/m2).
Length of base = 7.81/2 = 3.91 m
Let the dimension of the mat is as follows,
Width = 2 m,
Length = 4.5 m,
Depth = 0.6 m.
Hence self-weight of mat = 2 x 4.5 x 0.6 x 24 = 129.6 kN.
Hence, total vertical load = (310 + 160 + 430 + 220 + 129.6) = 1249.6 kN.
Actual base pressure = 1249.6 / (2 x 4.5) = 138.84 kN/m2.
Load Case I (DL & IL on both the column)
The ultimate loads are,
Column 1 load = 1.4 x 310 + 1.6 x 160 = 690 kN,
Column 2 load = 1.4 x 430 + 1.6 x 220 = 954 kN.
The distance of center of gravity from column 1 is checked for service load case 1:
x = (954 x 2.5)/(690 + 954) = 1.45 m.
84 — STAAD Foundation Advanced V8i
Chapter — 2
2.10 Mat Combined Foundation
The soil pressure is checked for service loads for case 1:
Base area = 4.5 x 2 =9.0 m2,
Base modulus = 2 x 4.52 / 6 = 6.75 m3.
Direct load = 310 + 160 + 430 + 220 + 129.6 = 1249.6 kN.
The moment about the centerline of the base is,
M = (430 + 220) 1.05 – (310 + 160) 1.45 = 1.0 kN-m.
Maximum pressure = 1249.6 / 9 + 1 / 6.75 = 138.9 kN / m2 < 180 kN / m2 (Hence safe)
Total uniformly distributed upward load = (690 + 954) / (4.5 x 2 / 2) = 365.33 kN / m.
Load Case II (DL & IL on column 1; DL on column 2)
The ultimate loads are,
Column 1 load = 1.4 x 310 + 1.6 x 160 = 690 kN,
Column 2 load = 1.0 x 430 = 430 kN.
Direct load = 310 + 160 + 430 + 129.6 = 1029.6 kN.
The moment about the centerline of the base is,
M = 430 X 1.54 – (310 + 160) 0.96 = 230 kN-m.
Maximum pressure = 1029.6 / 9 + 230 / 6.75 = 148.47 kN / m2 < 180 kN / m2 (Hencesafe)
Load Case III (DL on column 1; DL & IL on column 2)
The ultimate loads are,
Column 1 load = 1.0 x 310 = 310 kN,
Column 2 load = 1.4 x 430 + 1.6 x 220 = 954 kN.
Direct load = 310 + 430 + 220 + 129.6 = 1089.6 kN.
The moment about the centerline of the base is,
M = (430 + 220) 1.05 – 310 X 1.45 = 233 kN-m.
Maximum pressure = 1089.6 / 9 + 233 / 6.75 = 155.59 kN / m2 < 180 kN / m2 (Hence safe)
Section 2 British Code (BS8110-1-1997)
2.10 Mat Combined Foundation
Verification Manual — 85
Design of Longitudinal (Bottom) Steel
The maximum negative BM from Figure 6.18 is 221.7 kN-m
Assuming 40 mm clear cover and 20 mm bar diameter, effective depth = 600 – 40 – 20/2= 550 mm.
0.0104 < 0.156
Hence Safe
Therefore z = 0.95d,
86 — STAAD Foundation Advanced V8i
Chapter — 2
2.10 Mat Combined Foundation
= 970.95 mm2.
The minimum area of steel = 0.13 x 2000 x 600 / 100 = 1560 mm2 > calculated area ofsteel.
Provide minimum steel.
Provide 16 bars 12 mm in diameter at 125 mm centers to give area of 1808 mm2.
Design of Transverse (Top) Steel
The maximum positive BM from Figure 6.18 is 99.7 kN-m.
Assuming 40 mm clear cover and 20 mm bar diameter, effective depth = 600 – 40 – 20/2= 550 mm.
0.004 < 0.156
Hence Safe
Therefore z = 0.95d,
= 436.6 mm2.
The minimum area of steel = 0.13 x 2000 x 600 / 100 = 1560 mm2 > calculated area ofsteel.
Provide minimum steel as above.
Calculation of Vertical Shear
The maximum vertical shear from case 1 is V = 250.8 kN,
V = = 0.228 N/mm2.
= 0.39 N/mm2.
Hence no shear reinforcement is required.
Section 2 British Code (BS8110-1-1997)
2.10 Mat Combined Foundation
Verification Manual — 87
Punching Shear Check
The critical perimeter for punching shear check is at 1.5 d distance from the face of thecolumn. Here the perimeter crosses the boundary of the base on two sides. Hence punchingshear is less critical than the vertical shear in this case.
2.10.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Max BendingMoment (-)
221.7 kN-m 201.204 kN-m 9.2
Max BendingMoment (+)
99.7 kN-m 108.94 kN-m 9.2
Area of StealRequired
780 mm2/m 780 mm2/m None
Base Pressure 138.84kN/m2
136 kN/m2 2
Table 2-11: British verification example 10 comparison
2.11 General Isolated Foundation withEccentricity
2.11.1 Reference
2.11.2 ProblemDesign an isolated footing with the given data:
Loads:
Fx =-300 KN
Fy =-500 KN
Fz=-200 KN
Mz= 45.89 KNm
Mx=-98.32 KNm
Offset of column in X-direction (Oxd) =300 mm
Offset of column in Z-direction (Ozd) =300 mm
Density of soil =14 KN/m3
Depth of Soil = 0.5m
Density of Concrete = 25 KN/cum
Coefficient of Friction (μ) = 0.5
88 — STAAD Foundation Advanced V8i
Chapter — 2
2.11 General Isolated Foundation with Eccentricity
Safe Bearing Capacity of the Soil (σ) = 120 KN/m2
Factor of Safety against Overturning =1.5
Factor of Safety against Sliding = 1.5
Permissible soil pressure =
Column dimension = 0.3m x 0.3m,
Strength of concrete (fc’) = M-30 = 4349.39 Psi
Strength of steel (fy) = Fe-415
Figure 2-21: Plan and Elevation
Self-wt of footing, wt of soil and surcharge are not included for shear and momentcomputations
Section 2 British Code (BS8110-1-1997)
2.11 General Isolated Foundation with Eccentricity
Verification Manual — 89
2.11.3 SolutionDesign started with trial dimensions of 5.0m X 5.0m X 1.0m
Determination of base area of footing
The base area of footing is determined using service (unfactored) loads with the netpermissible soil pressure.
Net permissible soil pressure = 120 KN/ m2
Required base area of footing = (500 + 0.10 x 500)/ 120= 4.5833 m2
Use a 5 .0m x 5.0m square footing (Af =25 m2).
Using a depth of 1m;
Self-wt. of Footing =(5.0*5.0*1*25) = 625 KN
Wt. of soil = 14*0.5*[(5.0*5.0) –(0.3*0.3)] =174.37
Serviceability Check
The net moments are given by:-
Mz =+45.89 – (-300*1) +(-500*0.3) = 195.89 KNm
Mx= - 98.32 +(-200*1) –(-500*0.3) = -148.32 KNm
The pressure at the four corners are given by:-
σ 1 = ((500+625)/ 25) + (6*195.89/53) - (6*148.32/53) = 47.283 KN/m2
σ 2 = ((500+625)/ 25) - (6*195.89/53) - (6*148.32/53) = 28.478 KN/m2
σ 3 =((500+625)/ 25) - (6*195.89/53) + (6*148.32/53) = 42.717 KN/m2
σ 4 = ((500+625)/ 25) + (6*195.89/53) + (6*148.32/53) =61.522 KN/m2
which is < 120 KN/m2. Hence OK
Stability Check
Calculation for Overturning and Sliding:
For Sliding:
Along X- Direction
Disturbing force = -300 KN
Restoring Force = m*(Wt of Footing + Fy + Wt of Soil) = 649.685 KN
Hence, Factor of Safety against Sliding = (649.685/300) =2.166 > 1.5 Hence Safe
90 — STAAD Foundation Advanced V8i
Chapter — 2
2.11 General Isolated Foundation with Eccentricity
Along Z- Direction
Disturbing force = -200 KN
Restoring Force = mu*(Wt of Footing + Fy + Wt of Soil) = 649.685 KN
Hence, FacFor Overturning:tor of Safety against Sliding = (649.685/200) =3.2484 > 1.5Hence Safe
About X- Direction
Overturning Moment = Mx + Fz* (Ht of Pedestal + Depth of Footing) = -98.32– 200* (0 +1) = -298.32 KN-m
Restoring Moment = Fy * (Width of Footing *0.5 –Ozd)+ (Wt of Soil + Wt ofFooting) * Width of Footing*0.5 = 3098.425 KN-m
Hence, Factor of Safety against Overturning = (3098.425/298.32) =10.386 > 1.5 HenceSafe
About Z- Direction
Overturning Moment = Mx + Fz* (Ht of Pedestal + Depth of Footing) =45.89+ 300* (0 +1) = 345.89 KN-m
Restoring Moment = Fy * (Width of Footing *0.5 –Ozd)+ (Wt of Soil + Wt ofFooting) * Width of Footing*0.5 = 3398.425 KN-m
Hence, Factor of Safety against Overturning = (3398.425/345.89) =9.82516 > 1.5 HenceSafe
Base Pressure for Shear and Moment Calculation
The pressure at the four corners are given by:-
σ 1 = (500/ 25) + (6*195.89 /5.03) - (6*148.32 /5.03) = 22.2834KN/m2
σ 2 = (500/25) - (6*195.89 /5.03) - (6*148.32 /5.03) = 3.47792KN/m2
σ 3 =(500/ 25) - (6*195.89 /5.03) + (6*148.32 /5.03) = 17.7167 KN/m2
σ 4 = (500/ 25) + (6*195.89 /5.03) + (6*148.32 /5.03) = 36.52208 KN/m2
Check for Flexure and Calculation for Reinforcement
Factored loads and soil reaction:
To proportion the footing for strength (depth and required reinforcement) factored loads areused. For this problem, the factors used are all 1.0
Figure 2-22: Bending about major axes
Section 2 British Code (BS8110-1-1997)
2.11 General Isolated Foundation with Eccentricity
Verification Manual — 91
Bending About Z-axis Bending About X-axis
Critical section for moment is at the face of column
About X- axis
Average Base Pressure along one edge
=(22.2834+3.47792)/2 =12.8806 KN/m2
Average Base Pressure along other edge
=(17.7167+36.5221)/2 = 27.1194 KN/m2
Approximate Base Pressure at the critical section
=27.1194- {(27.1194 – 12.8806)/5.0*2.05} =21.2815 KN/ m2 [2.05 =5-(5/2+0.3+0.15)]
Hence, the moment at the critical section
Mu =5.0*{21.2815 *2.05*2.05*0.5+0.5*(27.1194-21.2815)* 2.05*2.05*2/3}=264.48 KNm
Effective depth (d) = 1000 – 50 – 20 = 930 mm
Hence safe
Therefore,
92 — STAAD Foundation Advanced V8i
Chapter — 2
2.11 General Isolated Foundation with Eccentricity
The minimum area of steel = 0.13 x 5000 x 1000 / 100 = 6500 mm2 > Calculated area ofsteel.
So, provide minimum steel = 6500 mm2
About Z- axis
Average Base Pressure along one edge
=(36.5221+22.2834)/2 =29.4027 KN/m2
Average Base Pressure along other edge
=(17.7167+3.47792)/2 = 10.5973 KN/m2
Approximate Base Pressure at the critical section
=29.4027- {(29.4027-10.5973)/5.0*2.65} =19.4358 KN/ m2 [2.65 =(5/2+0.3-0.15)]
Hence, the moment at the critical section
Mu =5.0*{19.4358 *2.65*2.65*0.5+0.5*(29.4027 –19.4358)*2.65*2.65*2/3}=457.874 KNm
Effective depth (d) = 1000 – 50 – 20 = 930 mm
Hence safe
Therefore,
The minimum area of steel = 0.13 x 5000 x 1000 / 100 = 6500 mm2 > Calculated area ofsteel.
So, provide minimum steel = 6500 mm2
Check for Shear
Assume overall footing thickness = 1.0m and average effective thickness d = 0.92m (36.22in)
Wide-beam action (One-Way Shear) :
Section 2 British Code (BS8110-1-1997)
2.11 General Isolated Foundation with Eccentricity
Verification Manual — 93
Along Z-Z axis
Vu = qs tributary area
Bw = 5.00m = 196.8504 in
qs is given by:-
Average Base Pressure along one edge
=(22.2834+3.47792)/2 =12.8806 KN/m2
Average Base Pressure along other edge
=(17.7167+36.5221)/2 = 27.1194 KN/m2
Approximate Base Pressure at the critical section
=27.1194- {(27.1194 – 12.8806)/5.0*1.13} =23.9014 KN/ m2 [1.13=5 -(5/2+0.3 +0.92 +0.15)]
Hence, the one- way shear at the critical section
Vux =5.0*{23.9014*1.13+0.5*(27.1194-23.9014)*1.13}= 144.134 KN
Design shear stress, v = 144.134/(5.0 x 0.93) =30.996 kN/ m2
Now, VC1 = min(0.8 √(fcu),5) N/ mm2= 4381.78 kN/ m2 > v (Hence Safe)
=348.5494 kN/ m2
Let us consider 1.5 times shear enhancement.
Vce = 1.5 x 348.5494 = 522.824 kN/m2 > v (Hence safe)
Hence no shear reinforcement is required.
Along X-X axis
Vu = qs tributary area
Bw = 5.00m = 196.8504 in
qs is given by:-
Average Base Pressure along one edge
=(36.5221+22.2834)/2 =29.4027 KN/m2
Average Base Pressure along other edge
94 — STAAD Foundation Advanced V8i
Chapter — 2
2.11 General Isolated Foundation with Eccentricity
=(17.7167+3.47792)/2 = 10.5973 KN/m2
Approximate Base Pressure at the critical section
=29.4027- {(29.4027-10.5973)/5.0*1.73} =22.89603 KN/ m2 [ 1.73=(5/2 +0.3–0.92 –0.15)]
Hence, the Design one-way shear at the critical section
Vuz =5.0*{22.89603*1.73+0.5*(29.4027-22.89603)*1.73}= 226.1924 KN
Design shear stress, v = 226.1924/(5.0 x 0.93) =48.64353 kN/ m2
Now, vC1 = min(0.8 √(fcu),5) N/ mm2= 4381.78 kN/ m2 > v (Hence Safe)
= 348.5494 kN/ m2
Let us consider 1.5 times shear enhancement.
Vce = 1.5 x 348.5494 = 522.824 kN/m2 > v (Hence safe)
Hence no shear reinforcement is required.
Section 2 British Code (BS8110-1-1997)
2.11 General Isolated Foundation with Eccentricity
Verification Manual — 95
Two-way action (Punching Shear)
Along X-X axis
[3090 mm = 300 + 2x(1.5 x 930)]
The punching shear will be calculated for an area outside the area enclosed by therectangle at a distance 1.5d from the column face as shown in figure.
Total pressure under the base = 5.0 x 5.0 x 10.5973 + 0.5 x 5.0 x 5.0 x (29.4027 –10.5973) = 500.00 kN.
Pressure at the critical sections:-
σa = 29.4027 – ((29.4027-10.5973)/5.0*0.955) = 25.810869 KN/m2
σb = 10.5973 + ((29.4027-10.5973)/5.0*0.955) = 14.189131 KN/m2
Pressure under enclosed rectangle = (3.09)2 x 14.189131 + 0.5 x (3.09)2 x (25.810869 –14.189131) = 190.962 kN
Punching shear force = 500.00-190.962 = 309.038 kN.
Critical perimeter = 3.09 x 4 =12.36 m.
96 — STAAD Foundation Advanced V8i
Chapter — 2
2.11 General Isolated Foundation with Eccentricity
Punching shear stress = 309.038/(12.36 x 0.93) = 26.885 kN / m2.
Hence, the punching shear stress is less than VC . Hence Safe
Along Z-Z axis
The punching shear will be calculated for an area outside the area enclosed by the rectangleat a distance 1.5d from the column face as shown in figure.
Total pressure under the base = 5.0 x 5.0 x 12.8806 + 0.5 x 5.0 x 5.0 x (27.1194 – 12.8806)= 500.00 kN.
Pressure at the critical sections:-
σa = 27.1194 – ((27.1194-12.8806)/5.0*0.955) = 24.3998 KN/m2
σb = 12.8806 + ((27.1194-12.8806)/5.0*0.955) = 15.60021 KN/m2
Punching shear force = 500.00-190.962 = 309.038 kN.
Critical perimeter = 3.09 x 4 =12.36 m.
Punching shear stress = 309.038/(12.36 x 0.93)= 26.885 kN / m2.
Section 2 British Code (BS8110-1-1997)
2.11 General Isolated Foundation with Eccentricity
Verification Manual — 97
Hence, the punching shear stress is less than VC . Hence Safe
Hence, the moment at the critical section
Mu =5.0*{19.4358 *2.65*2.65*0.5+0.5*(29.4027 –19.4358)*2.65*2.65*2/3}=457.874 KNm
Effective depth (d) = 1000 – 50 – 20 = 930 mm
2.11.4 Comparison
ReferenceResult
STAADFoundationResult*
Difference (Reasonsthere-of)
Moment about X 264.48KNm
259.98KNm
Error due to approx-imation in base pressureinterpolation
Moment about Z 457.874KNm
448.24KNm
Error due to approx-imation in base pressureinterpolation
Area of steel aboutX-X
6500.00mm2
6500.00mm2
Negligible
Area of steel aboutZ-Z
6500.00mm2
6500.00mm2
Negligible
Shear Stress
(One way) along X
48.64KN/ m2
46.66 KN/m2
Error due to approx-imation in base pressureinterpolation
Shear Stress
(One way) along Z
30.996KN/ m2
29.28 KN/m2
Error due to approx-imation in base pressureinterpolation
Shear Force
(Two way)
309.038KN
305.46 KN Error due to approx-imation in base pressureinterpolation
Factor of Safetyagainst Sliding (X)
2.1656 2.167 Negligible
Factor of Safetyagainst Sliding (Z)
3.2484 3.250 Negligible
Factor of Safetyagainst Over-turning (X)
10.386 10.392 Negligible
Factor of Safetyagainst Over-turning (Z)
9.82516 9.830 Negligible
Table 2-12: British verification example 13 comparisons
98 — STAAD Foundation Advanced V8i
Chapter — 2
2.11 General Isolated Foundation with Eccentricity
Section 3
Canadian Code (CSAA23.3-2004)3.1 CSA General Isolated Foundation 1
3.1.1 Reference
3.1.2 ProblemDesign of a square Isolated Footing
A tied column, 450 mm square, and reinforced with eight No. 35 bars carries an unfactoreddead load of 1300 kN and an unfactored live load of 1000 kN. Suitable soil with a factoredsoil bearing pressure of 300 kN/m2 is available at a depth of 1.5 m . Design a squarefooting.
The compressive strength f’c is 30 MPa for the column and 25 MPa for the footing. All steelhas fy=400 MPa. Unit weight of concrete and soil is 24 kN/m
2 and 16 kN/m2 respectively.
Verification Manual — 99
Figure 3-1: Plan and Elevation
3.1.3 Solution
Trial Footing Size
Calculate the initial footing size based on soil bearing capacity.
As per CSA A.23.3-04 cls. 8.3 and Annex C. the 2005 National Building Code of Canadaload combination factors must be used:
Factored Load = 1.25 DL + 1.5 LL = (1.25 X 1300 kN) + (1.5 x 1000 kN) =3,125 kN
Required area of footing: 3125/300 = 10.41 m2
Total Axial load = 3125+Self Weight of footing + weight of soil
Self Weight of footing = 3.6 x 3.6 x 0.75 x 24 = 233.28 KN
weight of soil=3.6 x 3.6 x 1.5 x 16 = 311.04 KN
For square footing, the axial force on the footing is:
3125+233.28+311.04 =3669.32 KN
So stress on soil=369.32/(3.6x3.6)=283.12 KN/m2
100 — STAAD Foundation Advanced V8i
Chapter — 3
3.1 CSA General Isolated Foundation 1
Calculate Factors of Safety
In this case, we do not have any sliding and overturning forces. The CSA A23.3-04recommends for a footing that experiences horizontal shear, the designer must make surethat this shear is transferred to the subgrade utilizing the passive soil resistance and thefriction between the subgrade and the footing surface. The passive soil resistance will beignored in STAAD Foundation to calculate the factor of safety against sliding check. Factorof safety against overturning must be checked as per the NBCC.
Anyway, max sliding force equals the axial load x coefficient of friction
for coeff. of friction =0.5,
Sliding force= 0.5x 3669.32 =1834.66 KN (same for X & Z dir)
Max resisting moment against overturning = axial force x Dimension/2= 0.5x3669.32x3.6 KNm = 6604.78 KNm (Same wrt both x and z axis).
Stress on soil from Factored load = 3125/(3.6x3.6)=241.126 KN/m2
Check for One-Way Shear
Along X Direction
Assuming 50 mm clear cover and 20 mm bar, effective depth
deff = (750-50-0.5 x 20) mm = 690 mm
Vumax =
= 768.22 KN
Ø = 0.65, λ = 1
dv = 0.9.deff = 0.9 x 690 = 621 mm
bw=3600 mm
Now allowable shear
Vc = =1030913 N =1031 KN
V < Vc, Hence Safe
Along Z Direction
Assuming 50 mm clear cover and 20 mm bar, effective depth
deff = (750-50-0.5 x 20) mm = 690 mm
Vumax = = 768.22 KN
Ø = 0.65, λ = 1
dv = 0.9.deff=0.9 x 690=621 mm
Section 3 Canadian Code (CSA A23.3-2004)
3.1 CSA General Isolated Foundation 1
Verification Manual — 101
bw = 3600 mm
Now allowable shear
Vc = = 1030913 N = 1031 KN
V < Vc, Hence Safe
Punching Shear
Punching shear is checked on a perimeter 0.5d = 345 mm from the column face.
Assuming 50 mm clear cover and 20 mm bar, effective depth
deff = (750-50-0.5 x 20) mm = 690 mm
Area within Critical Perimeter Am = (450+2x0.5x.69)2=1.2996 m2
Vmax = 241.126x(3.6x3.6-1.2996)=2811.63 KN
Critical perimeter Pm = 2 X ( b + h + 2x d) = 4.56 m
τv = Vmax/(Pm · d) = 0.8936 N/mm2
α=4
ß=L/B =4.5/4.5 =1
1.8525 N/mm2
2.5846 N/mm2
1.235 N/mm2
As effective depth>300 mm so the multiplier=1300/(1000+deff)=0.769
So,
Vr1= 1.424 N/mm2 =1424 KN/m2
Vr2= 1.987N/mm2 = 1987 KN/m2
Vr3= 0.9497 N/mm2 = 949.7 KN/m2
So min {Vr1, Vr2, Vr3} = 949.7 KN/m2
So allowable shear = Vc = 949.7 KN/m2
V < Vc , Hence safe
Development Length
Along Z Axis
ld = 0.45 k1 x k2 x k3 x k4 fy/√(f'c) dbk1 = 1 if clear cover is less than 300 mm or else use 0.45
102 — STAAD Foundation Advanced V8i
Chapter — 3
3.1 CSA General Isolated Foundation 1
k2 = 1 if coated reinforcement is used
k2 = 1.2 if epoxy coated reinforcement is used
k2 = 1.5 if epoxy coated reinforcement is used and clear cover is less than 3xdbk2 = 1.5 if bar spacing is less than 6x dbk3 = 1 Normal density concrete
k4 = 0.8 for 20M and smaller bar size
k4 = 1 for 20M and larger bar size
ld = 0.45 x 1 x 0.8 x 1 x 0.8 x (400 MPa)/√(25MPa) x 19.5 mm = 449.28 mm
Available Length = (3600-450)/2-50 = 1525 mm
Hence OK
Along X Axis
ld = 0.45 k1 x k2 x k3 x k4 fy/√(f'c) dbk1 = 1 if clear cover is less than 300 mm or else use 0.45
k2 = 1 if coated reinforcement is used
k2 = 1.2 if epoxy coated reinforcement is used
k2 = 1.5 if epoxy coated reinforcement is used and clear cover is less than 3xdbk2 = 1.5 if bar spacing is less than 6 xdbk3 = 1 Normal density concrete
k4 = 0.8 for 20M and smaller bar size
k4 = 1 for 20M and larger bar size
ld = 0.45 x 1 x 0.8 x 1 x 0.8 x (400 MPa)/√(25MPa) x 19.5 mm = 449.28 mm
Available Length = (3600-450)/2-50 = 1525 mm
Hence OK
Check For Trial Depth Against Moment
About X Axis
Bending moment at critical section:
Mux = = 1076.66 KN-m
α1 = 0.85-0.0015.f’c=0.8125
Øs=0.85
Section 3 Canadian Code (CSA A23.3-2004)
3.1 CSA General Isolated Foundation 1
Verification Manual — 103
= 0.62817
Assuming 50 mm clear cover and 20 mm bar, effective depth
deff = (750-50-0.5 x 20) mm = 690 mm
So, ρ =0.001892
Hence OK
About Z Axis
Bending moment at critical section,
Mux = = 1076.66 KN-m
α1 = 0.85-0.0015.f’c=0.8125
Øs=0.85
= 0.62817
Assuming 50 mm clear cover and 20 mm bar, effective depth
deff = (750-50-0.5 x 20) mm = 690 mm
So,ρ =0.001892
Hence OK
Area of Steel Required
Along X Direction (Bottom)
Astx =ρ.B.deff= 4700 m2m
Minimum area of steel Astmin = (0.2x√f’c /fy)xB.D= 6750 mm2
Provided area = 6750 m2m
Along Z Direction (Bottom)
Astz = ρ.L.deff= 4700 m2m
Minimum area of steel Astmin = (0.2x√f’c /fy)xB.D= 6750 mm2
Provided area = 6750 m2m
Along X Direction (Top)
Minimum area of steel Astmin = (0.2x√f’c /fy)xB.D= 6750 mm2
Provided area = 6750 m2m
104 — STAAD Foundation Advanced V8i
Chapter — 3
3.1 CSA General Isolated Foundation 1
(as no uplift is present so min steel is provided)
Along Z Direction (Top)
Minimum area of steel Astmin = (0.2x√f’c /fy)xB.D= 6750 mm2
Provided area = 6750 m2m
(as no uplift is present so min steel is provided)
3.1.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 286.45 KN/m2 283.5 KN/m2 NegligibleGoverning Moment 1076.66 KN-m
1076.66 KN-m
1076.64 KN-m
1076.66 KN-m
Negligible
Shear Force(One-Way) 768.22 KN
768.22 KN
768.01 KN
768.01 KN
Negligible
Shear Force(Two-Way) 2811.63 KN 2811.49 KN NegligibleResisting Shear Force(One-Way)
1031 KN
1031 KN
1031.14 KN
1031.14 KN
None
Resisting Shear Stress(Two-Way)
949.7 KN/m2 949.86KN/m2
Negligible
Resisting force forsliding
1834.66 KN
1834.66 KN
1837.09 KN
1837.09 KN
Negligible
Resisting Moment forOverturning
6604.78 KNm
6604.78 KNm
6613.4 KNm
6613.4 KNm
Negligible
Ast (B) 6750 mm
6750 mm
6750 mm
6750 mm
None
Ast (T) 6750 mm
6750 mm
6750 mm
6750 mm
None
Ld (rqrd) 449.28 mm
449.28 mm
449.28 mm
449.28 mm
None
Ld (available) 1525 mm
1525 mm
1525 mm
1525 mm
None
Table 3-1: CSA verification example 1 comparison
3.2 CSA General Isolated Foundation 23.2.1 Reference
Section 3 Canadian Code (CSA A23.3-2004)
3.2 CSA General Isolated Foundation 2
Verification Manual — 105
3.2.2 ProblemDesign of a square Isolated Footing
A tied column, 500 mm square, and reinforced with eight No. 35 bars carries an unfactoreddead load of 900 kN and an unfactored live load of 800 kN. Suitable soil with a factoredsoil bearing pressure of 300 kN/m2 is available at a depth of 1.5 m . Design a squarefooting.
The compressive strength f’c is 20 MPa for the column and 20 MPa for the footing. Allsteel has fy=350 MPa. Unit weight of concrete and soil is 24 kN/m
2 and 16 kN/m2
respectively.
Figure 3-2: Plan and Elevation
3.2.3 Solution
Trial Footing Size
Initial footing size is based on soil bearing capacity.
As per CSA A.23.3-04 cls. 8.3 and Annex C. the 2005 National Building Code of Canadaload combination factors must be used:
Factored Load = 1.25 DL + 1.5 LL = (1.25 X 900 kN) + (1.5 x 800 kN) =2,325 kN
Required area of footing: 2,325 /300 = 7.75 m2
106 — STAAD Foundation Advanced V8i
Chapter — 3
3.2 CSA General Isolated Foundation 2
Total Axial load = 2,325 +Self Weight of footing + weight of soil
Self Weight of footing = 3 x 3 x 0.6 x 24 = 129.6 KN
weight of soil=3 x 3 x 1.5 x 16 = 216 KN
For square footing, the axial force on the footing is:
2,325 +129.6 + 216 =2670.6 KN
So stress on soil=2670.6 /(3x3)=296.73 KN/m2
Calculate Factors of Safety
In this case, we do not have any sliding and overturning forces. The CSA A23.3-04recommends for a footing that experiences horizontal shear, the designer must make surethat this shear is transferred to the subgrade utilizing the passive soil resistance and thefriction between the subgrade and the footing surface. The passive soil resistance will beignored in STAAD Foundation to calculate the factor of safety against sliding check. Factorof safety against overturning must be checked as per the NBCC.
Anyway, max sliding force =axial load x coeff of friction
for coeff of friction =0.5,
Sliding force= 0.5x 2670.6 =1335.3 KN (same for X & Z dir)
Max resisting moment against overturning = axial force x Dimension/2 = 0.5x2670.6x3 KNm = 4005.45 KNm (Same WRT both x and z axis).
Stress on soil from Factored load=2325/(3x3)=258.33 KN/m2
Check for One-Way Shear
Along X Direction
Assuming 50 mm clear cover and 20 mm bar, effective depth
deff = (600-50-0.5 x 20) mm = 540 mm
Vumax = = 550.24 KN
Ø = 0.65, λ = 1
dv = 0.9.deff = 0.9 x 490 = 441 mm
bw = 3000 mm
Now allowable shear
Vc = =655986 N =655.99 KN
V < Vc, Hence Safe
Section 3 Canadian Code (CSA A23.3-2004)
3.2 CSA General Isolated Foundation 2
Verification Manual — 107
Along Z Direction
Assuming 50 mm clear cover and 20 mm bar, effective depth
deff = (600-50-0.5 x 20) mm = 540 mm
Vumax = = 550.24 KN
Ø = 0.65, λ = 1
dv = 0.9.deff = 0.9 x 490 = 441 mm
bw = 3000 mm
Now allowable shear
Vc = = 655986 N = 655.99 KN
V < Vc, Hence Safe
Punching Shear
Punching shear is checked on a perimeter 0.5d = 270 mm from the column face.
Assuming 50 mm clear cover and 20 mm bar, effective depth
deff = (600-50-0.5 x 20) mm = 540 mm
Area within Critical Perimeter Am = (500+2x0.5x.54)2 = 1.0816 m2
Vmax = 258.33 x (3x3-1.0816) = 2045.56 KN
Critical perimeter Pm = 2 x ( b + h + 2x d) = 4.16 m
τv = Vmax/(Pm · d) = 0.91 N/mm2
α=4
ß=L/B =5/5 =1
1.657 N/mm2
2.645 N/mm2
1.1046 N/mm2
As effective depth > 300 mm so the multiplier = 1300/(1000+deff) = 0.844
So,
108 — STAAD Foundation Advanced V8i
Chapter — 3
3.2 CSA General Isolated Foundation 2
Vr1= 1.398 N/mm2 =1398KN/m2
Vr2= 2.232N/mm2 ==2232 KN/m2
Vr3= 0.932 N/mm2 =932 KN/m2
So min{ Vr1,Vr2,Vr3} = 932 KN/m2
So allowable shear = Vc = 932 KN/m2
V < Vc , Hence safe
Development Length
Along Z Axis
ld = 0.45 k1 x k2 x k3 x k4 fy/√(f'c) dbk1 = 1 if clear cover is less than 300 mm or else use 0.45
k2 = 1 if coated reinforcement is used
k2 = 1.2 if epoxy coated reinforcement is used
k2 = 1.5 if epoxy coated reinforcement is used and clear cover is less than 3xdbk2 = 1.5 if bar spacing is less than 6 xdbk3 = 1 Normal density concrete
k4 = 0.8 for 20M and smaller bar size
k4 = 1 for 20M and larger bar size
ld = 0.45 x 1 x 0.8 x 1 x 0.8 x (350 MPa)/√(20MPa) x 19.5 mm = 439.52 mm
Available Length = (3000-500)/2-50 = 1200 mm
Hence OK
Along X Axis
ld = 0.45 k1 x k2 x k3 x k4 fy/√(f'c) dbk1 = 1 if clear cover is less than 300 mm or else use 0.45
k2 = 1 if coated reinforcement is used
k2 = 1.2 if epoxy coated reinforcement is used
k2 = 1.5 if epoxy coated reinforcement is used and clear cover is less than 3xdbk2 = 1.5 if bar spacing is less than 6 xdbk3 = 1 Normal density concrete
k4 = 0.8 for 20M and smaller bar size
k4 = 1 for 20M and larger bar size
ld = 0.45 x 1 x 0.8 x 1 x 0.8 x (350 MPa)/√(20MPa) x 19.5 mm = 439.52 mm
Available Length = (3000-500)/2-50 = 1200 mm
Hence OK
Section 3 Canadian Code (CSA A23.3-2004)
3.2 CSA General Isolated Foundation 2
Verification Manual — 109
Check For Trial Depth Against Moment
About X Axis
Bending moment at critical section
Mux = = 605.46 KN-m
α1 = 0.85-0.0015.f’c=0.82
Øs=0.85
= 0.0346
Assuming 50 mm clear cover and 20 mm bar, effective depth
deff = (600-50-0.5 x 20) mm = 540 mm
So,ρ =0.002405
Hence OK
About Z Axis
Bending moment at critical section
Mux = = 605.46 KN-m
α1 = 0.85-0.0015.f’c=0.82
Øs=0.85
= 0.0346
Assuming 50 mm clear cover and 20 mm bar, effective depth
deff = (600-50-0.5 x 20) mm = 540 mm
So,ρ =0.002405
Hence OK
Area of Steel Required
Along X Direction (Bottom)
Astx =ρ.B.deff= 3896 m2m
110 — STAAD Foundation Advanced V8i
Chapter — 3
3.2 CSA General Isolated Foundation 2
Minimum area of steel Astmin = (0.2x√f’c /fy)xB.D= 4599.9 mm2
Provided area = 4600 m2m
Along Z Direction (Bottom)
Astz = ρ.L.deff= 3896 m2m
Minimum area of steel Astmin = (0.2x√f’c /fy)xB.D= 4599.9 mm2
Provided area = 4600 m2m
Use #20 @ 190 c/c
Along X Direction (Top)
Minimum area of steel Astmin = (0.2x√f’c /fy)xB.D= 4599.9 mm2
Provided area = 4600 m2m
(as no uplift force is present only min steel is provided)
Use #20 @ 190 c/c
Along Z Direction (Top)
Minimum area of steel Astmin = (0.2x√f’c /fy)xB.D= 4599.9 mm2
Provided area = 4600 m2m
(as no uplift force is present only min steel is provided)
Use #20 @ 190 c/c
Section 3 Canadian Code (CSA A23.3-2004)
3.2 CSA General Isolated Foundation 2
Verification Manual — 111
3.2.4 Comparison
Value of Reference ResultSTAAD
FoundationResult
PercentDifference
Bearing Pressure 296.73 KN/m2 296.07KN/m2
Negligible
Governing Moment 605.46 KN-m
605.46 KN-m
605.46 KN-m
605.46 KN-m
None
Shear Force(One-Way)
550.24 KN
550.24 KN
550.06 KN
550.06 KN
Negligible
Shear Force(Two-Way)
2045.56 KN 2045.45 KN Negligible
Resisting force forsliding
1335.3KN 1335.3KN 1332.3 KN
1332.3 KN
Negligible
Resisting Momentfor Overturning
4005.45 KNm 4005.45 KNm
3996.827KNm
3996.827KNm
Negligible
Ast (B) #20@190 c/c
#20@190 c/c
#20@190c/c
#20@190c/c
None
Ast (T) #20@190 c/c
#20@190 c/c
#20@190c/c
#20@190c/c
None
Ld (rqrd) 439.52 mm
439.52 mm
439.52 mm
439.52 mm
None
Ld (available) 1200 mm
1200 mm
1200 mm
1200 mm
None
Table 3-2: CSA verification example 2 comparison
3.3 CSA General Isolated Foundation 3 3.3.1 Reference
3.3.2 ProblemDesign an isolated footing with the given data: Load Fy = 1200 KN, fc = 30 MPa, fy = 400MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity of Soil = 90KN/m2.
112 — STAAD Foundation Advanced V8i
Chapter — 3
3.3 CSA General Isolated Foundation 3
Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5. Heightof soil above footing=450 mm, GWT is 300 mm from GL.
Surcharge= 10 KN/m2
Figure 3-3: Plan and Elevation
3.3.3 SolutionApproximate area of footing required = 1200/90 m2 = 13.33 m2
Assuming 4.3 m x 4.3 m x 0.500 m footing dimension,
Weight of footing = 4.3 x 4.3 x 0.500 x 25 KN = 231.125 KN
Weight of above soil = 4.3 x 4.3 x 0.450 x 18 KN = 149.77 KN
Reduction of Weight due to buoyancy = 4.3x4.3 x (0.500+0.450-0.300) x 9.81KN = 117.9 KN
Load due to surcharge = 4.3x4.3 x 10 KN =184.9 KN
Therefore, total load on the footing = (1200+231.125 +149.77 +184.9 -117.9)KN = 1647.895 KN
Maximum pressure = 1647.895 /(4.3x4.3) = 89.12 KN/m2
89.12 KN/ m2 <90 KN/m2
Hence safe
Section 3 Canadian Code (CSA A23.3-2004)
3.3 CSA General Isolated Foundation 3
Verification Manual — 113
Stress for Factor design = 1.25x1200/(4.3x4.3) = 81.12 KN/m2
Critical load case and the governing factor of safety forsliding
Along X Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation
Total Service load on foundation = 1647.895 KN
Max resisting force against sliding = 0.5 x 1647.895 KN = 823.95 KN
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation
Total Service load on foundation = 1647.895 KN
Max resisting force against sliding = 0.5 x 1647.895 KN = 823.95 KN
Hence OK
Critical load case and the governing factor of safety foroverturning
WRT X Direction
Overturning Moment = 0
max resisting Moment = 0.5 x 4.3 x 1647.895 = 3542.97 KNm
Hence OK
WRT Z Direction
Overturning Moment = 0
max resisting Moment = 0.5 x 4.3 x 1647.895 = 3542.97 KNm
Hence OK
114 — STAAD Foundation Advanced V8i
Chapter — 3
3.3 CSA General Isolated Foundation 3
3.3.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 89.12 KN/m2
89.03 KN/ m2 Negligible
Resisting force for sliding(x)
823.95 KN 823.12 KN Negligible
Resisting Moment forOverturning (z)
3542.97KNm
3539.366KNm
Negligible
Resisting force for sliding(z)
823.95 KN 823.12 KN Negligible
Resisting Moment forOverturning (x)
3542.97KNm
682.862 KNm Negligible
Table 3-3: CSA verification example 3 comparison
3.5 CSA Pilecap Foundation 13.3.5 Reference
3.3.6 ProblemDesign pilecap foundation with the given data: Load Fy = 800 KN, fc = 25 MPa, fy = 450MPa, Column Dimension = 250 mm x 250 mm. Pedestal ht= 500 mm
Pile Data
Dia of pile= 400 mm.
Vertical capacity = 250 KN,
Horizontal capacity = 100 KN
Uplift capacity = 80 KN
Section 3 Canadian Code (CSA A23.3-2004)
3.5 CSA Pilecap Foundation 1
Verification Manual — 115
Figure 3-4: Elevation and Plan, with dimension and loads
3.3.7 Solutiondepth of pilecap= 1.5 x piledia, D=600 mm
Take D=600 mm
c/c pile distance = 3xpile dia =1200 mm. Edge diatance =350 mm
Assuming 4 pile combination,
Coordinates of piles considering pedestal at 0,0,0)
Pile No X Coordinate (mm) Z Coordinate (mm)1 -600 -6002 -600 6003 600 6004 600 -600
pilecap dimension is 1900 mm x1900 mm x 600 mm
Weight of footing = 1.9 x1.9 x 0.60 x 25 KN = 54.15 KN
Weight of pedestal = 0.25 x 0.25 x 0.5 x 25 KN = 0.78 KN
Therefore, total load on the pilecap = (800+54.15 +0.78) KN = 854.93 KN
116 — STAAD Foundation Advanced V8i
Chapter — 3
3.5 CSA Pilecap Foundation 1
So Pile reaction = 854.93 /4= 213.73 KN < 250 KN, Hence OK
As there is no lateral load, moment or uplift force, so each pile is safe in lateral & upliftcapacity.
Factored Design
Load factor for self wt is taken =1
Load factor for axial load is taken 1.25
SO, Load on pilecap = 1.25x800+54.15 x1+0.78x1= 1054.93 KN
Load on each pile =1054.93 /4=263.73 KN
Figure 3-5: Bending sections considered
Calculation of Moment wrt Z Axis
For moment wrt X1X1
Contribution from pile 1=from pile2=263.73 x 0.475=125.27 KNm
So Total Mz X1X1 = 250.54 KNm
For moment wrt X2X2
Contribution from pile3=from pile4=263.73 x 0.475=125.27 KNm
So Total Mz X2X2 = 250.54 KNm
So Max value of Mz = 250.54 KNm
Check For Trial Depth against moment wrt Z Axis
Bending moment at critical section, Muz = 250.54 KN-m
Section 3 Canadian Code (CSA A23.3-2004)
3.5 CSA Pilecap Foundation 1
Verification Manual — 117
Assuming 50 mm clear cover, 75 mm pile in pilecap & and 11.3 mm bar ( Bar No 10),effective depth
deff = 463.7 mm
B =1900 mm ,
Øc = Resistance Factor of concrete = 0.6 (Clause No 8.4.2)
α1 = 0.8125 (Clause No 10.1.7.c)
ß1 = 0.8475 (Clause No 10.1.7.c)
c = (700.d)/(700+fy) = 282.25 mm (Clause No 10.5.2)
a = 239.208 mm (Clause No 10.1.7.a)
C = 5539 x 103 KN(Clause No 10.1.7.a)
Resisting Moment=C.(d-a/2)=1906 KNm
Muz < Resisting Moment, Hence OK
Calculation of Moment wrt X Axis
For moment wrt Z1Z1
Contribution from pile 1=from pile4=263.73 x 0.475=125.27 KNm
So Total Mx Z1Z1 = 250.54KNm
For moment wrt Z2Z2
Contribution from pile 2=from pile3=263.73 x 0.475=125.27 KNm
So Total Mx Z2Z2 = 250.54KNm
So Max value of MX = 250.54 KNm
Check For Trial Depth against moment wrt X Axis
Bending moment at critical section, Mux = 250.54 KN-m
deff = 463.7 mm
B =1900 mm ,
C=5539 x 103 KN
Resisting Moment=C.(d-a/2)=1906 KNm
Mux < Resisting Moment, Hence OK
118 — STAAD Foundation Advanced V8i
Chapter — 3
3.5 CSA Pilecap Foundation 1
Calculation of Shear parallel to X Axis
Figure 3-6: Shear sections considered
For shear wrt X1X1
Contribution from pile 1 =pile2=263.73 x528=139.25 KN
So Total V X1X1 = 274.5 KN
For shear wrt X2X2
Contribution from pile 3=pile4=263.73 x528=139.25 KN
So Total V X2X2 = 274.5 KN
So Max V parallel to X direction = 274.5 KN
Check for One-Way Shear (along X dir)
Shear Strength Vr = 260/(1000+d).Øc.λ.√(f'c ).bw.d=>0.1.λ.Øc.√(f^' c).bw.d
= max(469.497, 264.309) KN = 469.5 KN (Clause no 11.3.5.2)
Where
Øc = Resistance Factor of concrete=0.6 (Clause No 8.4.2)
λ = factor to account Concrete density=1(Clause No 8.6.5)
bw = Section Width=1900 mm
d = effective Depth= 463.7 mm (Clause 11.0)
VX < VResistanceX, Hence Safe
Calculation of Shear parallel to Z Axis
For shear wrt Z1Z1
Section 3 Canadian Code (CSA A23.3-2004)
3.5 CSA Pilecap Foundation 1
Verification Manual — 119
Contribution from pile 1 =pile 4 =263.73 x528=139.25 KN
So Total V Z1Z1 = 274.5 KN
For shear wrt Z2Z2
Contribution from pile 2=pile 3 =263.73 x528=139.25 KN
So Total V Z2Z2 = 274.5 KN
So Max V parallel to Z direction = 274.5 KN
Check for One-Way Shear (along Z dir)
Shear Strength Vr=260/(1000+d).Øc.λ.√(f'c ).bw.d=>0.1.λ.Øc.√(f^' c).bw.d
= max(469.497, 264.309) KN = 469.5 KN
VZ < VResistanceZ, Hence Safe
Punching ShearFigure 3-7: Two-way shear sections considered
Punching shear is checked on a perimeter 0.5d =231.85 mm from the column face.
Contribution from pile 1=from pile2=from pile3=from pile 4= 263.73 KN
So total punching shear Vmax= 1054.92 KN
b0=Perimeter of failure line at d/2 distance from column face=2.(Column Length+ColumnWidth+2d)x 2= 4x(250+463.7/2+463.7/2)=2854.88
Therefore Shear stress τc= =Vmax/(b0 x d)= 797 KN/m2
Calculation of punching shear stress capacity
λ = 1 (Clause 8.6.5)
Øc = 0.6 (Clause 8.4.2)
f'c = Strength of concrete (in MPa)
ßc = (Column Length)/(Column Width)=1900/1900=1
αs = 4 (Clause No 13.0 & 13.4.4.a)
120 — STAAD Foundation Advanced V8i
Chapter — 3
3.5 CSA Pilecap Foundation 1
mod factor=1
Vr1=(1+2/ßc).0.2.λ.Øc.√(f'c).mod factor=1800 KN/m2 (Eqn no 13.5 Clause no 13.4.4a)
Vr2=(0.2+(αs. dv)/bo).λ.Øc.√(f'c).mod factor=2549 KN/m2 (Eqn no 13.6 Clause no13.4.4b)
Vr3=0.4.λ.Øc.√(f'c).mod factor= 1200 KN/m2 (Eqn no 13.7 Clause no 13.4.4c)
Vr=Min (Vr1,Vr2,Vr3)=1200 KN/m2
V < VResistance , Hence safe
Area of Steel Required
Along X Direction
Calculate Kr (neutral axis/depth ratio) for Actual Bending Moment
Where
α1= 0.85- 0.0015.f’c>=0.67 (Clause No 10.1.7)
Øc = 0.6 (clause 8.4.2)
Øs = 0.85 (clause 8.4.3)
Solving the equation ρ (steel area ratio = 0.165 %
Therefore, Astx = ρ.b,d= 1450 m2m
Minimum area of steel Astmin = 0.2/100 x B x D = 2280 mm2
Provided area = 2280 mm2
Along Z Direction
Calculate Kr (neutral axis/depth ratio) for Actual Bending Moment
Solving the previously stated equation ρ (steel area ratio = 0.165 %
Therefore, Astx = ρ.b,d= 1450 m2m
Minimum area of steel Astmin = 0.2/100 x B x D = 2280 mm2
Provided area = 2280 mm2
Section 3 Canadian Code (CSA A23.3-2004)
3.5 CSA Pilecap Foundation 1
Verification Manual — 121
Check for Development Length
Ld (required)=1.15.k1.k2.k3.k4.fy/((dcs+Kr) ).Ab/√(f'c )= 380.7 mm
(CSA A23-3-04 Clause No 12.2.2 & 12.2.3)
Ld (available)Along X=(Length-pedestal length) 1/2 –Cover=775 mm
Ld (required)<Ld (available)Along X
Hence OK
Ld (available)Along Z=(Length-pedestal length) 1/2 -Cover=775 mm
Ld (required)<Ld (available)Along Z
Hence OK
3.3.8 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Depth 600 mm 598 mm NegligibleGoverning Moment (wrtX axis)
250.54 KN-m
250.54 KN-m None
Resisting Moment (wrt Zaxis)
1906 KN-m 1933 KN-m Negligible
Governing Moment (wrtX axis)
250.54 KN-m
250.54 KN-m None
Resisting Moment (wrt Zaxis)
1906 KN-m 1933 KN-m Negligible
Shear Force(One-Way) X 274.5 KN 274.3 KN NoneShear Resistance(One-Way) X
469.5 KN 471.8 KN Negligible
Shear Force(One-Way) Z 274.5 KN 274.3 KN NoneShear Resistance(One-Way) Z
469.5 KN 471.8 KN Negligible
Shear stress(Two-Way) 797 KN/m2 787.6 KN/m2 NoneResistance Shear Stress(Two-Way)
1200 KN/m2 1200 KN/m2 None
Ld required 381 mm 381 mm NoneLd Available ( Along X) 775 mm 775 mm NoneLd Available ( Along Z) 775 mm 775 mm NoneAst ( Along X) 2280 mm2 2240 mm2 Negligible
Table 3-4: CSA verification example 5 comparison
3.4 CSA General Combined Foundation s1 3.4.1 Reference
122 — STAAD Foundation Advanced V8i
Chapter — 3
3.4 CSA General Combined Foundation s1
3.4.2 ProblemDesign a combined footing with the given data: Load Fy = 900 KN each column., fc = 30MPa, fy = 400 MPa, Column Dimension = 250 mm x 250 mm, Pedestal height-400 mm.and C/C column distance=3500 mm . Bearing Capacity of Soil = 120 KN/m2. Coefficient offriction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
Ht of soil =500 mm. Depth of GWT=200 mm. Surcharge= 5 KN/m2
Figure 3-8: Plan and Elevation
3.4.3 SolutionApproximate area of footing required = 2x900/120 m2 = 15 m2
Assuming 5.7 m x 3.15 m x 0.500 m footing dimension,
left overhang = right overhang = 1.1 m, C/C col dist=3500 mm
Weight of footing = 5.7 x 3.15 x0.500 x25 KN = 224.44 KN
Weight of pedestal=2x0.25x0.25x0.4x25=1.25 KN
Weight of soil above footing = (5.7 x 3.15-2x0.25x0.25) x 0.500 x18 KN =160.47 KN
Reduction of Weight due to buoyancy = 5.7 x 3.15 x (0.500+0.500-0.200)x9.81 KN = 140.91 KN
Surcharge load = ( 5.7x3.15-2x0.25x0.25)x5= 89.15 KN
Therefore, total load on the footing is
Section 3 Canadian Code (CSA A23.3-2004)
3.4 CSA General Combined Foundation s1
Verification Manual — 123
(2x900+224.44 +1.25+160.47 +89.15 -140.91) KN = 2134.4 KN
Maximum pressure= 2134.4 /(5.7 x3.15) = 118.87 KN/m2
118.87 KN/ m2 <120 KN/m2 (Hence safe)
Critical load case and the governing factor of safety foroverturning
About Z Direction
Overturning Moment =0
Total Service load on foundation = 2134.4 KN
max resisting Moment = 0.5 x 5.7x 2134.4 = 6083 KNm
Hence OK
About X Direction
Overturning Moment =0
Total Service load on foundation = 2134.4 KN
max resisting Moment = 0.5 x 3.15x 2134.4 = 3361.7 KNm
Hence OK
3.4.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 118.87KN/m2
118.87 KN/m2 None
Resisting Moment forOverturning (Z)
6083 KNm 6083 KNm None
Resisting Moment forOverturning (X)
3361.7 KNm 3361.7 KNm None
Table 3-5: CSA verification example 5 comparison
124 — STAAD Foundation Advanced V8i
Chapter — 3
3.4 CSA General Combined Foundation s1
Section 4
Indian Code (IS 456 -2000)4.1 IS General Isolated Foundation 1
4.1.1 Reference‘Reinforced Concrete’ by A.K. Jain, Page 539, Example 18.2.
4.1.2 ProblemDesign an isolated footing with the given data: Load Fy = 1000 KN, fc = 15 MPa, fy = 415MPa, Column Dimension = 400 mm X 400 mm, Bearing Capacity of Soil = 100 KN/m2,and Load Factor = 1.5.
Verification Manual — 125
Figure 4-1: Plan and Elevation
4.1.3 SolutionApproximate area of footing required = 1000/10 m2 = 10 m2
Assuming 3.5 m x 3.5 m x 0.6 m footing dimension (I = 12.5 m4)
Weight of footing = 3.5 x 3.5 x 0.6 x 25 KN = 183.75 KN
Therefore, total load on the footing = (1000 +183.75) KN = 1183.75 KN
Maximum pressure = 1183.75/(3.5 x 3.5) KN/ m2 = 96.633 KN/m2 <100KN/m2
Hence safe
Ultimate pressure = 1000 x 1.5/ (3.5 x 3.5) KN/m2 = 122.45 KN/m2
Bending moment at critical section,
Mu = 122.45 x 3.5 x 1.55 x 1.55/2 = 514.826 KN-m
Assuming 35 mm clear cover and 10 mm bar, effective depth
de = (600-35-0.5 x 10) mm = 560 mm
Ku,max = = 0.479
126 — STAAD Foundation Advanced V8i
Chapter — 4
4.1 IS General Isolated Foundation 1
Ru,max = 0.36 x fc x Ku,max x (1-0.42 Ku,max) = 2.066
Mulim = Ru,max x B x de2 = 2267.642 x 106 N-mm = 2267.642 KN-m> Mu
Hence safe
Area of Steel Required
Area of steel required along length,
Ast = 0.5 x x B x de = 2646.4 mm2
Minimum area of steel Astmin = 0.0012 x B x D = 2520 mm2
Check for One-Way Shear
Percentage of steel pt = = 0.135
Corresponding allowable c = 0.28 N/mm2
Developed shear stress c =
Vumax = 122.45 x 3.5 x = 424.289 KN
Developed shear stress c = = 0.2165 N/mm2 < c,all (Hencesafe)
Check for Two-Way Shear
Vumax = 1500 KN
Developed shear stress c = = 0.698 N/mm2
Ks = min (0.5+1,1) = 1
Allowable shear stress = Ks x c = 1 x 0.25 = 0.968 N/mm2
Note: There is no deduction for the upward force underneath the area enclosed by thecritical perimeter. This approach is conservative.
Section 4 Indian Code (IS 456 -2000)
4.1 IS General Isolated Foundation 1
Verification Manual — 127
Spacing
No. of 10 mm bar = = 33.69 (34)
Spacing = = 102.73 mm
Spacing for 10 mm bar = 102.73 mm
Figure 4-2: Plan of Reinforcement
128 — STAAD Foundation Advanced V8i
Chapter — 4
4.1 IS General Isolated Foundation 1
Figure 4-3: Cross Section showing Reinforcement
4.1.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth 560 mm 560 mm NoneGoverning Moment 514.826 KN-m 514.821 KN-m NegligibleArea of Steal 2646.40 mm2 2645.01 mm2 0.05Shear Stress (One-Way)
0.216 N/mm2 0.216 N/mm2 None
Shear Stress (Two-Way)
0.698 N/mm2 0.700 N/mm2 0.286
Table 4-1: IS verification example 1 comparison
4.2 IS General Isolated Foundation 24.2.1 Reference‘Reinforced Concrete Structure’ by Punmia-Jain-Jain, Example 25.1.
4.2.2 ProblemDesign an isolated footing with the given data: Load Fy = 600 KN, fc = 15 MPa, fy = 250MPa, Column Dimension = 500 mm x 500 mm, and Bearing Capacity of Soil = 120 KN/m2.
Section 4 Indian Code (IS 456 -2000)
4.2 IS General Isolated Foundation 2
Verification Manual — 129
Figure 4-4: Plan and Elevation
4.2.3 SolutionApproximate area of footing required = 600/ 120 m2 = 5 m2
Assuming 2.4 m x 2.4 m x 0.35 m footing dimension,
Weight of footing = 2.4 x 2.4 x 0.35 x 25 KN = 50.4 KN
Therefore, total load on the footing = (600+50.4) KN = 650.4 KN
Maximum pressure = 650.4 / (2.4 x 2.4) KN/ m2 = 112.92 KN/m2 <120KN/m2
Hence safe
Ultimate pressure = 600 x 1.5 /(2.4 x 2.4) KN/m2 = 156.25 KN/m2
Bending moment at critical section, Mu = 56.25 x 2.4 x 0.95 x 0.95 /2=169.21875 KN-m
Assuming 50 mm clear cover and 12 mm bar, effective depth
de = (350-50-0.5 x 12) mm = 294 mm
130 — STAAD Foundation Advanced V8i
Chapter — 4
4.2 IS General Isolated Foundation 2
Ku,max = = 0.53
Ru,max = 0.36 x fc x Ku,max x (1- 0.42 Ku,max) = 2.225
Mulim = Ru,max x B x de2 = 461.568 x 106 N-mm = 461.568 KN-m > Mu
Hence safe
Area of Steel Required
Area of steel required along length,
Ast = 0.5 x x B x de = 2837.87 mm2
Minimum area of steel Astmin = 0.0015 x B x D = 1260 mm2
Check for One-Way Shear
Percentage of steel pt = 100·Ast/(B·de) = 0.4022
Corresponding allowable c = 0.42 N/mm2
Developed shear stress c =
Vumax = 156.25 x 2.4 x = 246 KN
Developed shear stress c = = 0.3486N/mm2 < c,all
Hence safe
Check for Two-Way Shear
Vumax = 900 KN
Developed shear stress c = = 0.96 N/mm2
Ks = min (0.5+1, 1) = 1
Allowable shear stress = Ks x c = 1 x 0.25 = 0.968 N/mm2
Hence safe
Note: There is no deduction for the upward force underneath the area enclosed by thecritical perimeter. This approach is conservative.
Section 4 Indian Code (IS 456 -2000)
4.2 IS General Isolated Foundation 2
Verification Manual — 131
Spacing
No. of 12 mm bar = = 25.09 (26)
Spacing = = 91.52 mm
Spacing for 12 mm bar = 91.52 mm
Figure 4-5: Elevation and Plan showing reinforcement design
132 — STAAD Foundation Advanced V8i
Chapter — 4
4.2 IS General Isolated Foundation 2
4.2.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth 294 mm 294 mm NoneGoverning Moment 169.2187 KN-
m169.2187 KN-m None
Area of Steel 2837.87 mm2 2836.34 mm2 0.05Shear Stress (One-Way)
0.3486N/mm2
0.3486 N/mm2 None
Shear Stress (Two-Way)
0.96 N/mm2 0.96 N/mm2 None
Table 4-2: IS verification example 2 comparison
4.3 IS General Isolated Foundation 34.3.1 Reference
4.3.2 ProblemDesign an isolated footing with the given data: Load Fy = 2000 KN, fc = 25 MPa, fy = 415MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity of Soil = 100KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
Section 4 Indian Code (IS 456 -2000)
4.3 IS General Isolated Foundation 3
Verification Manual — 133
Figure 4-6: Plan and Elevation
4.3.3 SolutionApproximate area of footing required = 2000/100 m2 = 20 m2
Assuming 4.95 m x 4.95 m x 0.700 m footing dimension,
Weight of footing = 4.95x4.95x0.7 x 25 KN = 428.79 KN
Therefore, total load on the footing = (2000+428.79) KN = 2428.79 KN
Maximum pressure = 2428.79/(4.95x4.95) = 99.124 KN/ m2 <100 KN/m2
Hence safe
Ultimate pressure = KN/m2 = 122.436 KN/m2
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force =0
134 — STAAD Foundation Advanced V8i
Chapter — 4
4.3 IS General Isolated Foundation 3
max Resisting force = µ x Total Service load on foundation =0.5 x 2428.79 =1214.395 KN
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 4.95 x 2428.79 = 6011.25 KNm
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation =0.5 x 2428.79 =1214.395 KN
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 4.95 x 2428.79 = 6011.25 KNm
Hence OK
Check For Trial Depth Against Moment
About X Axis
Bending moment at critical section
Mux = 122.436 x 4.95 x 2.325 x 2.325 / 2 = 1638.06 KN-m
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (700-50-0.5 x 16) mm = 642 mm
K=700/(1100+0.87x fy )= 0.479107
Ru= 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 7026 KNm
Hence OK
About Z Axis
Bending moment at critical section
Mux = 122.436 x 4.95 x 2.325 x 2.325 / 2 = 1638.06 KN-m
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (700-50-0.5 x 16) mm = 642 mm
K=700/(1100+0.87x fy )= 0.479107
Ru= 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Section 4 Indian Code (IS 456 -2000)
4.3 IS General Isolated Foundation 3
Verification Manual — 135
Resisting Moment =Ru. B deff2 = 7026 KNm
Hence OK
Area of Steel Required
Along X Direction
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 7358 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 4158 mm2 ( as fy>250)
Provided area = 7358 m2m
Along Z Direction
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 7358 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 4158 mm2 ( as fy>250)
Provided area = 7358 m2m
Check for One-Way Shear
Along X Direction
Percentage of steel pt = = 0.2315
Vumax = 122.436 x 4.95 x = 1020 KN
Developed shear stress V = = 0.321 N/mm2
Now allowable stress= 0.348 N/mm2
V < τc
Hence Safe
136 — STAAD Foundation Advanced V8i
Chapter — 4
4.3 IS General Isolated Foundation 3
Along Z Direction
Percentage of steel pt = = 0.2315
Vumax = 122.436 x 4.95 x = 1020 KN
Developed shear stress V = = 0.321 N/mm2
Now allowable stress= 0.348 N/mm2
V < τc
Hence Safe
Punching Shear
Punching shear is checked on a perimeter 0.5d = 321 mm from the column face.
Area within Critical Perimeter Am = 0.887 m2
Vmax = 2892 KN
Critical perimeter Pm = 2 X ( b + h + 6 x d) = 3.768 m
τv = Vmax/(Pm · d) = 1.19 N/mm2
ß=L/B =4.95/4.95 =1
k=0.5 +ß=1.5 , k<=1
Hence, k=1
Now allowable stress
τc =k.0.25.√fck = 1.25 N/mm2
τv < τc , Hence safe
Section 4 Indian Code (IS 456 -2000)
4.3 IS General Isolated Foundation 3
Verification Manual — 137
4.3.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 99.124KN/m2
99.124 KN/m2 None
Governing Moment 1638.06KN-m
1638.038 KN-m
None
Shear Force(One-Way) 1020 KN 1019 KN NegligibleShear Force(Two-Way) 2892 KN 2891 KN NegligibleResisting force for sliding(X)
1214.395KN
1214.397 KN None
Resisting Moment forOverturning (Z)
6011.25KNm
6011.155 KNm None
Resisting force for sliding(Z)
1214.395KN
1214.397 KN None
Resisting Moment forOverturning (X)
6011.25KNm
6011.155 KNm None
Table 4-3: IS verification example 3 comparison
4.4 IS General Isolated Foundation 44.4.1 Reference
4.4.2 ProblemDesign an isolated footing with the given data: Load Fy = 1000 KN, fc = 25 MPa, fy = 415MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity of Soil = 110KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning=1.5 Surcharge=20 KN/m2
138 — STAAD Foundation Advanced V8i
Chapter — 4
4.4 IS General Isolated Foundation 4
Figure 4-7: Plan and Elevation
4.4.3 SolutionApproximate area of footing required = 1000/110 m2 = 8.33 m2
Assuming 3.65 m x 3.65 m x 0.600 m footing dimension,
Weight of footing = 3.65x3.65x0.6 x 25 KN = 199.8 KN
Surcharge= 20 KN/m2
Surcharge force=20x3.65x3.65= 266.4 KN
Therefore, total load on the footing = (1000+266.4+199.8)= 1466.2 KN
Maximum pressure = 1466.2/(3.65x3.65)=
110 KN/m2 (Hence OK)
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force =0
Max Resisting force = µ x Total Service load on foundation
Total Service load on foundation =1466.2 KN
Section 4 Indian Code (IS 456 -2000)
4.4 IS General Isolated Foundation 4
Verification Manual — 139
Max Resisting force =0.5 x 1466.2 = 733.1 KN
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 3.65 x 1466.2 = 2675.815 KNm
Hence OK
Along Z Direction
Sliding force =0
Max Resisting force = µ x Total Service load on foundation
Total Service load on foundation =1466.2 KN
Max Resisting force =0.5 x 1466.2 = 733.1 KN
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 3.65 x 1466.2 = 2675.815 KNm
Hence OK
4.4.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 110 KN/m2 109.9 KN/m2 NegligibleResisting Moment forOverturning (x)
2675.815KNm
2672.535 KNm Negligible
Resisting force for sliding(z)
733.1 KN 732.2 KN Negligible
Resisting Moment forOverturning (z)
2675.815KNm
2672.535 KNm Negligible
Resisting force for sliding(x)
733.1 KN 732.2 KN Negligible
Table 4-4: IS verification example 4 comparison
4.5 IS General Isolated Foundation 54.5.1 Reference
4.5.2 ProblemDesign an isolated footing with the given data: Load Fy = 1200 KN, fc = 25 MPa, fy = 415MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity of Soil = 110
140 — STAAD Foundation Advanced V8i
Chapter — 4
4.5 IS General Isolated Foundation 5
KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5.Height of soil above footing=450 mm, dry condition.
Figure 4-8: Plan and Elevation
4.5.3 SolutionApproximate area of footing required = 1200/110 m2 = 10.91 m2
Assuming 3.7 m x 3.7 m x 0.55 m footing dimension,
Weight of footing = 3.7x3.7x0.55 x 25 KN = 188.237 KN
Weight of above soil = 3.7x3.7x0.45 x 18 KN = 110.889 KN
Therefore, total load on the footing = (1200+188.237+110.889) KN = 1499.126KN
Maximum pressure = 1499.126/(3.7x3.7) = 109.5 KN/m2 <110 KN/m2
Hence safe
Ultimate pressure = KN/m2 = 131.4828 KN/m2
Section 4 Indian Code (IS 456 -2000)
4.5 IS General Isolated Foundation 5
Verification Manual — 141
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation = 0.5 x 1499.126= 749.6 KN
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 3.7 x 1499.126 = 2773.383 KNm
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation = 0.5 x 1499.126= 749.6 KN
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 3.7 x 1499.126 = 2773.383 KNm
Hence OK
Check For Trial Depth against moment about X Axis
Bending moment at critical section,
Mux = 131.4828 x 3.7 x 1.7 x 1.7/2 = 702.97 KN-m
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (550-50-0.5 x 16) mm = 492 mm
K=700/(1100+0.87x fy )= 0.479107
Ru= 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4443 N/mm2
Resisting Moment =Ru. B deff2 = 3084.8 KNm
Hence OK
Check For Trial Depth against moment about Z Axis
Bending moment at critical section,
Mux = 131.4828 x 3.7 x 1.7 x 1.7/2 = 702.97 KN-m
Assuming 50 mm clear cover and 16 mm bar, effective depth
142 — STAAD Foundation Advanced V8i
Chapter — 4
4.5 IS General Isolated Foundation 5
deff = (550-50-0.5 x 16) mm = 492 mm
K=700/(1100+0.87x fy )= 0.479107
Ru= 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4443 N/mm2
Resisting Moment =Ru. B deff2 = 3084.8 KNm
Hence OK
Area of Steel Required
Along X Direction
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 4120 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 2442 mm2 ( as fy>250)
Provided area = 4120 m2m
Along Z Direction
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 4120 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 2442 mm2 ( as fy>250)
Provided area = 4120 m2m
Check for One-Way Shear ( along X dir)
Percentage of steel pt = = 0.226
Vumax = 131.4828 x 3.7 x = 587.7 KN
Developed shear stress τv = 587.7x1000/(3700x492)
= 0.322 N/mm2
Now allowable stress= 0.344 N/mm2
τv < τc
Hence Safe
Section 4 Indian Code (IS 456 -2000)
4.5 IS General Isolated Foundation 5
Verification Manual — 143
Check for One-Way Shear ( along Z dir)
Percentage of steel pt = = 0.226
Vumax = 131.4828 x 3.7 x = 587.7 KN
Developed shear stress τv = 587.7x1000/(3700x492) = 0.322 N/mm2
Now allowable stress= 0.344 N/mm2
τv < τc
Hence Safe
Punching Shear
Punching shear is checked on a perimeter 0.5d = 246 mm from the column face.
Area within Critical Perimeter Am = 0.627 m2
Vmax = 1718 KN
Critical perimeter Pm = 2 X ( b + h + 6 x d) = 3.168 m
τv = Vmax/(Pm · d) = 1.1 N/mm2
ß=L/B =3.7/3.7 =1
k=0.5 +ß=1.5 , k<=1
Hence, k=1
Now allowable stress= τc =k.0.25.√fck = 1.25 N/mm2
τv < τc , Hence safe
144 — STAAD Foundation Advanced V8i
Chapter — 4
4.5 IS General Isolated Foundation 5
4.5.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 109.5KN/m2
109.45 KN/m2 Negligible
Governing Moment (x&Z) 702.97 KN-m
700.1 KN-m Negligible
Shear Force(One-Way) (x&Z)
587.7 KN 586 KN Negligible
Shear Force(Two-Way) 1718 KN 1716.5 KN NegligibleResisting force for sliding(X)
749.6 KN 749.187 KN Negligible
Resisting Moment forOverturning (Z)
2773.4 KNm 2771.9 KNm Negligible
Resisting force for sliding(Z)
749.6 KN 749.187 KN Negligible
Resisting Moment forOverturning (X)
2773.4 KNm 2771.9 KNm Negligible
Table 4-5: IS verification example 5 comparison
4.6 IS General Isolated Foundations 64.6.1 Reference
4.6.2 ProblemDesign an isolated footing with the given data: Load Fy = 2000 KN, fc = 25 MPa, fy = 415MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity of Soil = 100KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5.Height of soil above footing=500 mm, depth of GWT =200 mm
Section 4 Indian Code (IS 456 -2000)
4.6 IS General Isolated Foundations 6
Verification Manual — 145
Figure 4-9: Plan and Elevation
4.6.3 SolutionApproximate area of footing required = 2000/100 m2 = 20 m2
Assuming 4.95 m x 4.95 m x 0.700 m footing dimension,
Weight of footing = 4.95x4.95x0.7 x 25 KN = 428.79 KN
Weight of above soil = 4.95x4.95x0.5 x18 KN = 220.522 KN
Reduction of Weight due to buoyancy = 4.95x4.95x0.5 x18 KN = 240.369 KN
Therefore, total load on the footing = (2000+428.79+220.522-240.369) KN =2408.943 KN
Maximum pressure = 2408.943/(4.95x4.95) = 99.12 KN/m2 <100 KN/m2
Hence safe
Ultimate pressure = KN/m2 = 122.436 KN/m2
146 — STAAD Foundation Advanced V8i
Chapter — 4
4.6 IS General Isolated Foundations 6
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation = 0.5 x 2408.943= 1204.5 KN
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 4.95 x 2408.943 = 5962 KNm
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation=0.5 x 2408.943 =1204.5 KN
Hence OK
Overturning Moment =0
max resisting Moment = 0.5 x 4.95 x 2408.943 = 5962 KNm
Hence OK
Check For Trial Depth against moment
About X Axis
Bending moment at critical section
Mux = 122.436 x 4.95 x 2.325 x 2.325 / 2 = 1638.06 KN-m
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (700-50-0.5 x 16) mm = 642 mm
K=700/(1100+0.87x fy )= 0.479107
Ru= 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 7026 KNm
Hence OK
About Z Axis
Bending moment at critical section
Section 4 Indian Code (IS 456 -2000)
4.6 IS General Isolated Foundations 6
Verification Manual — 147
Mux = 122.436 x 4.95 x 2.325 x 2.325 / 2 = 1638.06 KN-m
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (700-50-0.5 x 16) mm = 642 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 7026 KNm
Hence OK
Area of Steel Required
Along X Direction
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 7358 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 4158 mm2 ( as fy>250)
Provided area = 7358 m2m
Along Z Direction
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 7358 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 4158 mm2 ( as fy>250)
Provided area = 7358 m2m
148 — STAAD Foundation Advanced V8i
Chapter — 4
4.6 IS General Isolated Foundations 6
Check for One-Way Shear
Along X Direction
Percentage of steel pt = = 0.2315
Vumax = 122.436 x 4.95 x = 1020 KN
Developed shear stress V = = 0.321 N/mm2
Now allowable stress= 0.348 N/mm2
V < τc
Hence Safe
Along Z Direction
Percentage of steel pt = = 0.2315
Vumax = 122.436 x 4.95 x = 1020 KN
Developed shear stress V = = 0.321 N/mm2
Now allowable stress= 0.348 N/mm2
V < τc
Hence Safe
Punching Shear
Punching shear is checked on a perimeter 0.5d = 321 mm from the column face.
Area within Critical Perimeter Am = 0.887 m2
Vmax = 2892 KN
Critical perimeter Pm = 2 X ( b + h + 6 x d) = 3.768 m
τv = Vmax/(Pm · d) = 1.19 N/mm2
ß=L/B =4.95/4.95 =1
k=0.5 +ß=1.5 , k<=1
Hence, k=1
Now allowable stress= τc =k.0.25.√fck = 1.25 N/mm2
Section 4 Indian Code (IS 456 -2000)
4.6 IS General Isolated Foundations 6
Verification Manual — 149
τv < τc , Hence safe
4.6.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 98.314KN/m2
98.2832KN/m2
None
Governing Moment (x&Z) 1638.06KN-m
1634 KN-m Negligible
Shear Force(One-Way) (x&Z)
1020 KN 1017 KN Negligible
Shear Force(Two-Way) 2892 KN 2889.7 KN NegligibleResisting force for sliding(x)
1204 KN 1204 KN None
Resisting Moment forOverturning (z)
5962 KNm 5960 KNm Negligible
Resisting force for sliding(z)
1204 KN 1204 KN None
Resisting Moment forOverturning (x)
5962 KNm 5960 KNm Negligible
Table 4-6: IS verification example 6 comparison
4.7 IS General Isolated Foundation 74.7.1 Reference
4.7.2 ProblemDesign an isolated footing with the given data: Load Fy = 1500 KN, Fz=120 KN fc = 25MPa, fy = 415 MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity ofSoil = 120 KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS againstoverturning =1.5
150 — STAAD Foundation Advanced V8i
Chapter — 4
4.7 IS General Isolated Foundation 7
Figure 4-10: Plan and Elevation
4.7.3 SolutionApproximate area of footing required = 1500/120 m2 = 12.50 m2
Assuming 3.95 m x 3.95 m x 0.600 m footing dimension,
Weight of footing = 3.95x3.95x0.6 x 25 KN = 234.04 KN
Therefore, total axial load on the footing = (1500+234.04) KN = 1734.04 KN
Maximum axial pressure =P/A= 1734.04 /(3.95x3.95) = 111.138 KN/ m2
Moment due to lateral load= 120x0.6 72 KNm
Total moment (Mx=72 KNm
Zx=3.95x3.952/6 = 10.27 mm3
M/Z=7.01 KN/m2
So,
σ 1=P/A –M/Z=104.129 KN/m2
σ 2=P/A –M/Z=104.129 KN/m2
σ 3=P/A +M/Z=118.148 KN/m2
σ 4=P/A +M/Z=118.148 KN/m2
118.148 KN/m2 <120 KN/m2 (Hence safe)
Section 4 Indian Code (IS 456 -2000)
4.7 IS General Isolated Foundation 7
Verification Manual — 151
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation = 0.5 x 1734.04 =867.02 KN
Hence OK
Overturning Moment =72 KNm
max resisting Moment = 0.5 x 3.95 x 1734.04 = 3429.729 KNm
FOS = 47.6 > 1.5
Hence OK
Along Z Direction
Sliding force =120
max Resisting force = µ x Total Service load on foundation = 0.5 x 1734.04 =867.02 KN
FOS = 7.22 > 1.5
Hence OK
Overturning Moment =0 KNm
max resisting Moment = 0.5 x 3.95 x 1734.04 = 3429.729 KNm
Hence OK
Check For Trial Depth Against Moment
About X Axis
Critical section for moment is at the face of column; wrt z axis:
Average Base Pressure along one edge = (113.69 + 154.73)x0.5 = 144.21KN/m2 (left end)
Average Base Pressure along other edge = (113.69 + 154.73)x0.5 = 144.21KN/m2 (right end)
Approximate Base Pressure at the left critical section = 144.21 + (144.21-144.21) x 2125/3950 = 144.21 KN/m2
Approximate Base Pressure at the right critical section = 144.21 + (144.21-144.21) x 1825/3950 = 144.21 KN/m2
Hence, the moment at the critical section, Mu = F x LA
Where:
152 — STAAD Foundation Advanced V8i
Chapter — 4
4.7 IS General Isolated Foundation 7
F = (144.21 + 144.21) x 0.5 x 1.825 x 3.95 = 1039.57 KN
LA = (144.21 + 2x 144.21) x 1.825/ [3x (144.21 + 144.21)] = 0.913 m
Mu (right) = 949.13 kNm
So, max moment wrt Z axis Mu (z) = 950 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 16) mm = 542 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 3997 KNm
Hence OK
About Z Axis
Critical section for moment is at the face of column; wrt x axis:
Average Base Pressure along one edge = (133.69 + 133.69)x0.5 = 133.69KN/m2 (left end)
Average Base Pressure along other edge = (154.73 + 154.73)x0.5 = 154.73KN/m2 (right end)
Approximate Base Pressure at the left critical section = 154.73 + (133.69-154.731) x 2125/3950 = 143.42 KN/m2
Section 4 Indian Code (IS 456 -2000)
4.7 IS General Isolated Foundation 7
Verification Manual — 153
Approximate Base Pressure at the right critical section = 154.73 + (133.69-154.73) x 1825/3950 = 145.01 KN/m2
Hence, the moment at the critical section, Mu = F x LA
Where:
F = (133.69 + 143.42) x 0.5 x 1.825 x 3.95 = 1080.38 KN
LA = (143.42 + 2x 133.69) x 1.825/ [3x (144.21 + 144.21)] = 0.923 m
Mu (right) = 997.19 kNm
So, max moment wrt Z axis Mu (z) = 998 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 16) mm = 542 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 3997 KNm
Hence OK
Area of Steel Required
Along X Direction
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
154 — STAAD Foundation Advanced V8i
Chapter — 4
4.7 IS General Isolated Foundation 7
Astx = 5056 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 2844 mm2 ( as fy>250)
Provided area = 5056 m2m
Along Z Direction
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 5323 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 2844 mm2 ( as fy>250)
Provided area = 5323 m2m
Check for One-Way Shear
Along X Direction
Percentage of steel pt = = 0.236
Average Base Pressure along one edge = (133.69 + 154.73)x0.5 = 144.21KN/m2
Average Base Pressure along other edge = (133.69 + 154.73)x0.5 = 144.21KN/m2
Approximate Base Pressure at the left critical section = 144.21 + (144.21 -144.21) x 2667/3950 = 144.21 KN/m2
Approximate Base Pressure at the right critical section = 144.21 + (144.21 -144.21) x 2667/3950 = 144.21 KN/m2
Hence, the SF at critical section
F = (144.21 + 144.21) x0.5 x 1.283 x 3.95 = 730.84 KN
So max SF along X axis Fux = 731 KN
Developed shear stress τv = 731 x 1000 / (3950 x 542) = 0.341 N/mm2
Section 4 Indian Code (IS 456 -2000)
4.7 IS General Isolated Foundation 7
Verification Manual — 155
Now allowable stress= 0.348 N/mm2
τv < τc, Hence Safe
Along Z Direction
Percentage of steel pt = = 0.2486
Average Base Pressure along one edge = (133.69 + 133.69)x0.5 = 133.69KN/m2
Average Base Pressure along other edge = (154.73 + 154.73)x0.5 = 154.73KN/m2
Approximate Base Pressure at the left critical section = 154.73 + (133.69 -154.73) x 2667/3950 = 144.21 KN/m2
Approximate Base Pressure at the right critical section = 154.73 + (133.69 -154.73) x 1283/3950 = 144.21 KN/m2
Hence, the SF at critical section (left)
F = (133.69 + 140.53) x0.5 x 1.283 x 3.95 = 694.84 KN
Hence, the SF at critical section (right)
F = (15473 + 147.90) x0.5 x 1.283 x 3.95 = 766.83 KN
So max SF along X axis Fux = 731 KN
156 — STAAD Foundation Advanced V8i
Chapter — 4
4.7 IS General Isolated Foundation 7
So max SF=767 KN
Developed shear stress τv = 767 x 1000 / (3950 x 542) = 0.358 N/mm2
Now allowable stress= 0.359 N/mm2
τv < τc
Hence Safe
Punching Shear
Punching shear is checked on a perimeter 0.5d = 271 mm from the column face.
Area within Critical Perimeter Am = 0.709 m2
Vmax = 2148 KN
Critical perimeter Pm = 2 X ( b + h + 6 x d) = 3368 mm
τv = Vmax/(Pm · d) = 1.177 N/mm2
ß=L/B =3.95/3.95 =1
k=0.5 +ß=1.5 , k<=1
Hence, k=1
Now allowable stress= τc =k.0.25.√fck = 1.25 N/mm2
τv < τc
Hence safe
Section 4 Indian Code (IS 456 -2000)
4.7 IS General Isolated Foundation 7
Verification Manual — 157
Figure 4-11: Final Plan Dimensions
4.7.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Max BearingPressure
104.129KN/m2
104.129 KN/m2 None
MinBearingPressure
118.148 KN 118.148 KN None
GoverningMoment
999 KN-m
950 KN-m
994 KN-m
946 KN-m
Negligible
Shear Force(One-Way)
767 KN
731 KN
764 KN
728 KN
Negligible
Shear Force(Two-Way)
2148 KN 2146 KN Negligible
Table 4-7: IS verification example 7 comparison
4.8 IS Toolkit Combined 14.8.1 Reference
158 — STAAD Foundation Advanced V8i
Chapter — 4
4.8 IS Toolkit Combined 1
4.8.2 ProblemDesign a combined footing with the given data: Load Fy = 400 KN each column., fc = 25MPa, fy = 415 MPa, Column Dimension = 300 mm x 300 mm, Pedestal height-500 mm.and C/C column distance=3000 mm . Bearing Capacity of Soil = 120 KN/m2. Coefficient offriction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
Figure 4-12: Plan and Elevation
4.8.3 SolutionApproximate area of footing required = 2x400/120 m2 = 6.67 m2
Assuming 5.75 m x 1.35 m x 0.600 m footing dimension,
(left overhang = right overhang = 1.375 m)
Weight of footing = 5.75 m x 1.35 m x 0.600 x 25 KN = 116.375 KN
Weight of pedestal=2x 0.3 x 0.3 x 0.5 x 25 = 2.25 KN
Therefore, total load on the footing = (2x400+116.375+2.25) KN = 918.625 KN
Maximum pressure = 918.625 /(5.75x1.35) = 118.34 KN/ m2 < 120 KN/m2
Hence safe
Ultimate pressure = 800 x 1.5/ (5.75 x 1.35) KN/m2 = 154.589 KN/m2
Section 4 Indian Code (IS 456 -2000)
4.8 IS Toolkit Combined 1
Verification Manual — 159
Critical load case and the governing factor of safety foroverturning
With Respect to Z Direction
Overturning Moment =0
max resisting Moment = 0.5 x 5.75 x 918.625 = 2641 KNm
Hence OK
With Respect to X Direction
Overturning Moment =0
max resisting Moment = 0.5 x 1.35 x 918.625 = 620 KNm
Hence OK
Check For Trial Depth Against Moment
About Z Axis (Sagging)
Bending moment at critical section, Mux = 197.2 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 1376 KNm
Hence OK
About Z Axis (Hogging)
Bending moment at critical section, Mux = 37.49 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 1376 KNm
Hence OK
160 — STAAD Foundation Advanced V8i
Chapter — 4
4.8 IS Toolkit Combined 1
With Respect to X Axis
Cantilever length = (1.35-0.3)/2 = 0.525 m
Bending moment at critical section, Mux = 154.589 x5.75 x0.5252/2 =122.5KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 =5860 KNm
Hence OK
Area of Steel Required
Along X Direction (Bottom)
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 1029 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 972 mm2 ( as fy>250)
Provided area = 1029 m2m
Along X Direction (Top)
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 192 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 972 mm2 ( as fy>250)
Provided area = 972 m2m
Along Z Direction (Bottom)
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Section 4 Indian Code (IS 456 -2000)
4.8 IS Toolkit Combined 1
Verification Manual — 161
Astz = 627 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 4140 mm2 ( as fy>250)
Provided area = 4140 m2m
Figure 4-13: Dimension, Moment, and Shear and diagrams
Check for One-Way Shear
Percentage of steel pt = = 0.133
Vumax = 168.2 KN
162 — STAAD Foundation Advanced V8i
Chapter — 4
4.8 IS Toolkit Combined 1
Developed shear stress V = 168.2 x 1000 / (1350 x 544)= 0.229 N/mm2
Now allowable stress= 0.29 N/mm2
V < τc, Hence Safe
Punching Shear
For Column 1
Punching shear is checked on a perimeter 0.5d = 272 mm from the column face.
2 way shear= 489.89 KN
τv = Vmax/(Pm · d) = 489.89 x 1000/(300 x 2 + 300 x 2 + 544 x 4) x 544 =0.2668 N/mm2
ß=L/B = 5.75/1.35 = 4.26
k=0.5 +ß=5.26 , k<=1
Hence, k=1
Now allowable stress= τc =k.0.25.√fck = 1.25 N/mm2
τv < τc , Hence safe
For Column 2
Punching shear is checked on a perimeter 0.5d = 272 mm from the column face.
2 way shear= 489.89 KN
τv = Vmax/(Pm · d) = 489.89 x 1000 / (300 x 2 + 300 x 2 +544 x 4) x 544= 0.2668 N/mm2
ß=L/B =5.75/1.35 =4.26
k=0.5 +ß=5.26 , k<=1
Hence, k=1
Now allowable stress= τc =k.0.25.√fck = 1.25 N/mm2
τv < τc , Hence safe
Section 4 Indian Code (IS 456 -2000)
4.8 IS Toolkit Combined 1
Verification Manual — 163
4.8.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 118.35KN/m2
118.35 KN/m2 None
Governing Moment 197 KN-m
37.49 KN-m
122.5 KN-m
191.4 KN-m
37.4 KN-m
122.5 KN-m
Negligible
Shear Force(One-Way) 168.2 KN 168.2 KN NoneShear Force(Two-Way) 489.89 KN
489.89 KN
489.88 KN
489.88 KN
Negligible
Resisting Moment forOverturning (Z)
2641 KNm 2641 KNm None
Resisting Moment forOverturning (X)
620 KNm 620 KNm None
Table 4-8: IS verification example 8 comparison
4.9 IS Toolkit Combined Foundation 24.9.1 Reference
4.9.2 ProblemDesign a combined footing with the given data: Load Fy = 350 KN each column., fc = 25MPa, fy = 415 MPa, Column Dimension = 300 mm x 300 mm, Pedestal height-500 mm.and C/C column distance=3000 mm . Bearing Capacity of Soil = 110 KN/m2. Coefficient offriction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
Ht of soil =500 mm. Dry condition
164 — STAAD Foundation Advanced V8i
Chapter — 4
4.9 IS Toolkit Combined Foundation 2
Figure 4-14: Plan and Elevation
4.9.3 SolutionApproximate area of footing required = 2x350/110 m2 = 6.36 m2
Assuming 5 m x 1.65 m x 0.600 m footing dimension,
( left overhang=right overhang=1m)
Weight of footing = 5 m x 1.65 m x 0.600 x25 KN = 123.75 KN
Weight of pedestal=2x0.3x0.3x0.5x25=2.25 KN
Weight of soil above footing = 5 m x 1.65 m x 0.500 x18 KN = 74.25 KN
Therefore, total load on the footing = (2x350+123.75+2.25+74.25) KN =900.25 KN
Maximum pressure = 900.25 /(5 x1.65) = 109.12 KN/ m2
109.12 KN/ m2 <110 KN/m2
Hence safe
Ultimate pressure = 700 x 1.5 / (5.0 x 1.65) = 127.273 KN/m2
Section 4 Indian Code (IS 456 -2000)
4.9 IS Toolkit Combined Foundation 2
Verification Manual — 165
Critical load case and the governing factor of safety foroverturning
About Z Direction
Overturning Moment =0
max resisting Moment = 0.5 x 5x 900.25 = 2250 KNm
Hence OK
About X Direction
Overturning Moment =0
max resisting Moment = 0.5 x 1.65 x 900.25 = 742.7 KNm
Hence OK
Check For Trial Depth
Moment About Z Axis (Sagging)
Bending moment at critical section, Mux = 105 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 1681.78 KNm
Hence OK
Moment About Z Axis (Hogging)
Bending moment at critical section, Mux = 131.2 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 1681.78 KNm
Hence OK
Moment About X Axis
Cantilever length=(1.65-0.3)/2 = 0.675 m
166 — STAAD Foundation Advanced V8i
Chapter — 4
4.9 IS Toolkit Combined Foundation 2
Bending moment at critical section
Mux = 127.273 x5x0.6752/2 = 144.97 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 =5096.3 KNm
Hence OK
Area of Steel Required
Along X Direction (Bottom)
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 541 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 1188 mm2 ( as fy>250)
Provided area = 1188 mm2
Along X Direction (Top)
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 677 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 1188 mm2 ( as fy>250)
Provided area = 1188 mm2
Along Z Direction (Bottom)
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astz = 742 m2m
Minimum area of steel Astmin = 0.0012 x B x D = 3600 mm2 ( as fy>250)
Provided area = 3600 mm2
Section 4 Indian Code (IS 456 -2000)
4.9 IS Toolkit Combined Foundation 2
Verification Manual — 167
Check for One-Way Shear
Percentage of steel pt = = 0.133
Vumax = 169.3 KN
Developed shear stress τv = 169.3 x 1000 / (1650 x 544) = 0.1886 N/mm2
Now allowable stress= 0.29 N/mm2
τv < τc, Hence Safe
Punching Shear
For Column One
Punching shear is checked on a perimeter 0.5d = 272 mm from the column face.
2 way shear= 434.3 KN
τv = Vmax/(Pm · d) = 434.3 x 1000 / (300 x 2 + 300 x 2 + 544 x 4) x 544= 0.2356 N/mm2
ß=L/B =5.75/1.35 =4.26
k=0.5 +ß=5.26 , k<=1
Hence, k=1
Now allowable stress= τc =k.0.25.√fck = 1.25 N/mm2
τv < τc , Hence safe
For Column Two
Punching shear is checked on a perimeter 0.5d = 272 mm from the column face.
2 way shear= 434.3 KN
τv = Vmax/(Pm · d) = 434.3 x 1000 / (300 x 2 + 300 x 2 + 544 x 4) x 544= 0.2356 N/mm2
ß=L/B =5.75/1.35 =4.26
k=0.5 +ß=5.26 , k<=1
Hence, k=1
Now allowable stress= τc =k.0.25.√fck = 1.25 N/mm2
τv < τc , Hence safe
168 — STAAD Foundation Advanced V8i
Chapter — 4
4.9 IS Toolkit Combined Foundation 2
Figure 4-15: Shear Force and Bending Moment diagrams
Section 4 Indian Code (IS 456 -2000)
4.9 IS Toolkit Combined Foundation 2
Verification Manual — 169
4.9.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 109.12KN/m2
108.92KN/m2
Negligible
Governing Moment 105 KN-m
131.2 KN-m
144.97 KN-m
101.8 KN-m
131.2 KN-m
144.97 KN-m
Negligible
Shear Force(One-Way) 169.3 KN 169.26 KN NoneShear Force(Two-Way) 434.3 KN
434.3 KN
434.3 KN
434.3 KN
None
Resisting Moment forOverturning (Z)
2250 KNm 2246 KNm Negligible
Resisting Moment forOverturning (X)
742.7 KNm 741.37KNm None
Table 4-9: IS verification example 9 comparison
4.10 IS Toolkit Combined Foundation 34.10.1 Reference
4.10.2 ProblemDesign a combined footing with the given data: Load Fy = 350 KN each column., fc = 25MPa, fy = 415 MPa, Column Dimension = 300 mm x 300 mm, Pedestal height-500 mm.and C/C column distance=3000 mm . Bearing Capacity of Soil = 130 KN/m2. Coefficientof friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
Ht of soil =500 mm. Depth of GWT=200 mm
170 — STAAD Foundation Advanced V8i
Chapter — 4
4.10 IS Toolkit Combined Foundation 3
Figure 4-16: Plan and Elevation
4.10.3 SolutionApproximate area of footing required = 2 x 500/130 m2 = 7.69 m2
Assuming 5.4 m x 1.65 m x 0.600 m footing dimension,
(left overhang = right overhang = 1.2m)
Weight of footing = 5.4 m x 1.65 m x 0.600 x25 KN = 133.65 KN
Weight of pedestal=2x0.3x0.3x0.5x25=2.25 KN
Weight of soil above footing = 5.4 m x 1.65 m x 0.500 x18 KN = 80.19 KN
Reduction of Weight due to buoyancy = 5.4 m x 1.65 m x (0.5+0.6-0.2) x9.81KN = 78.67 KN
Therefore, total load on the footing = (2x500+133.65+2.25+80.19-78.67) KN =1137.42 KN
Maximum pressure= 1137.42 /(5.4 x1.65) = 127.66 KN/ m2
127.66 KN/ m2 <130 KN/m2
Hence safe
Ultimate pressure = 1000 x 1.5 / (5.4 x 1.65) = 168.35 KN/m2
Section 4 Indian Code (IS 456 -2000)
4.10 IS Toolkit Combined Foundation 3
Verification Manual — 171
Critical load case and the governing factor of safety foroverturning
wrt Z Direction
Overturning Moment =0
max resisting Moment = 0.5 x 5x 1137.42 = 3071 KNm
Hence OK
Wrt X Direction
Overturning Moment =0
max resisting Moment = 0.5 x 1.65 x 1137.42 = 938.37 KNm
Hence OK
Check For Trial Depth Against Moment
About Z Axis (Sagging)
Bending moment at critical section
Mux = 200 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 1681.78 KNm
Hence OK
About Z Axis (Hogging)
Bending moment at critical section
Mux = 112.4 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 1681.78 KNm
Hence OK
172 — STAAD Foundation Advanced V8i
Chapter — 4
4.10 IS Toolkit Combined Foundation 3
About X Axis
Cantilever length = (1.65-0.3)/2 = 0.675 m
Bending moment at critical section, Mux = 168.35 x5.4x0.6752/2 = 207 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 =5504 KNm
Hence OK
Area of Steel Required
Along X Direction (Bottom)
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 1040 mm2
Minimum area of steel Astmin = 0.0012 x B x D = 1188 mm2 ( as fy>250)
Provided area = 1188 mm2
Along X Direction (Top)
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 579 mm2
Minimum area of steel Astmin = 0.0012 x B x D = 1188 mm2 ( as fy>250)
Provided area = 1188 mm2
Along Z Direction (Bottom)
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astz = 1062 mm2
Section 4 Indian Code (IS 456 -2000)
4.10 IS Toolkit Combined Foundation 3
Verification Manual — 173
Minimum area of steel Astmin = 0.0012 x B x D = 3888 mm2 ( as fy>250)
Provided area = 3888 mm2
Figure 4-17: Shear Force and Bending Moment diagrams
Check for One-Way Shear
Percentage of steel pt = = 0.133
Vumax = 223.95 KN
Developed shear stress V = 223.95 x 1000 / (1650 x 544) = 0.249 N/mm2
Now allowable stress= 0.29 N/mm2
V < τc, Hence Safe
174 — STAAD Foundation Advanced V8i
Chapter — 4
4.10 IS Toolkit Combined Foundation 3
Punching Shear
For Column 1
Punching shear is checked on a perimeter 0.5d = 272 mm from the column face.
2 way shear= 630.07 KN
τv = Vmax/(Pm · d) = 630.07 x 1000 / (300 x 2 + 300 x 2 + 544 x 4) x 544= 0.343 N/mm2
ß=L/B =5.4/1.65 =3.27
k=0.5 +ß=4.27 , k<=1
Hence, k=1
Now allowable stress= τc =k.0.25.√fck = 1.25 N/mm2
τv < τc , Hence safe
For Column 2
Punching shear is checked on a perimeter 0.5d = 272 mm from the column face.
2 way shear= 630.07 KN
τv = Vmax/(Pm · d) = 630.07 x 1000 / (300 x 2 + 300 x 2 + 544 x 4) x 544= 0.343 N/mm2
ß=L/B =5.4/1.65 =3.27
k=0.5 +ß=4.27 , k<=1
Hence, k=1
Now allowable stress= τc =k.0.25.√fck = 1.25 N/mm2
τv < τc , Hence safe
Section 4 Indian Code (IS 456 -2000)
4.10 IS Toolkit Combined Foundation 3
Verification Manual — 175
4.10.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 127.48KN/m2
127.66KN/m2
Negligible
Governing Moment 200 KN-m
112.4 KN-m
207 KN-m
199.9 KN-m
112.4 KN-m
207 KN-m
Negligible
Shear Force(One-Way) 223.95 KN 223.89 KN NegligibleShear Force(Two-Way) 630.07 KN
630.07 KN
630.08 KN
630.08 KN
None
Resisting Moment forOverturning (Z)
3071 KNm 3067 KNm Negligible
Resisting Moment forOverturning (X)
938.4 KNm 937 KNm Negligible
Table 4-10: IS verification example 10 comparison
4.11 IS Toolkit Combined Foundation 44.11.1 Reference
4.11.2 ProblemDesign a combined footing with the given data: Load Fy = 350 KN & Fx=-30 KN eachcolumn., fc = 25 MPa, fy = 415 MPa, Column Dimension = 300 mm x 300 mm, Pedestalheight-500 mm. and C/C column distance=4000 mm . Bearing Capacity of Soil = 90KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning=1.5. No soil above footing. Dry condition
176 — STAAD Foundation Advanced V8i
Chapter — 4
4.11 IS Toolkit Combined Foundation 4
Figure 4-18: Plan and Elevation
4.11.3 SolutionApproximate area of footing required = 2x350/00 m2 = 7.78 m2
Assuming 6 m x 1.75 m x 0.600 m footing dimension,
(left overhang = right overhang = 1 m)
Weight of footing = 6 m x 1.75 m x 0.600 x25 KN = 157.5 KN
Weight of pedestal = 2 x 0.3 x 0.3 x 0.5 x 25 = 2.25 KN
Therefore, total load on the footing = (2x350+157.5 +2.25) KN = 859.75 KN
Maximum pressure for axial load=P/A = 859.75 /(6x1.75) = 81.88 KN/ m2
Moment on each col = 30 x (0.5 x 0.6) = 33 KNm
So total moment = 33 + 33 = 66 KNm
Z=1.75x62/6 = 10.5 m3
M/Z = 66/10.5 = 6.28 KN/m2
Streaa at left end = 81.88+6.28= 88.16 KN/m2
Streaa at right end = 81.88-6.28= 75.6 KN/m2
88.16 KN/ m2 <90 KN/m2
Hence safe
Section 4 Indian Code (IS 456 -2000)
4.11 IS Toolkit Combined Foundation 4
Verification Manual — 177
Critical load case and the governing factor of safety foroverturning
wrt Z Direction
Overturning Moment =0
max resisting Moment = 0.5 x 6 x 859.75 = 2579.25 KNm
Hence OK
Wrt X Direction
Overturning Moment =0
max resisting Moment = 0.5 x 1.75 x 859.75 = 752.28 KNm
Hence OK
Check For Trial Depth against moment
About Z Axis (Sagging)
Bending moment at critical section
Mux = 95 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 1783.71 KNm
Hence OK
About Z Axis (Hogging)
Bending moment at critical section
Mux = 264.25 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 = 1783.71 KNm
Hence OK
178 — STAAD Foundation Advanced V8i
Chapter — 4
4.11 IS Toolkit Combined Foundation 4
About X Axis
Cantilever length=(1.75-0.3)/2 = 0.725 m
Bending moment at critical section, Mux = (109.43+90.57) x6x0.7252/2 = 157KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth
deff = (600-50-0.5 x 12) mm = 544 mm
K = 700/(1100+0.87x fy )= 0.479107
Ru = 0.36 .fck. Kumax .(1-0.42Kumax) = 3.4442 N/mm2
Resisting Moment =Ru. B deff2 =5860 KNm
Hence OK
Area of Steel Required
Along X Direction (Bottom)
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 490 mm2
Minimum area of steel Astmin = 0.0012 x B x D = 1260mm2 ( as fy>250)
Provided area = 1260 mm2
Along X Direction (Top)
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Astx = 1380 mm2
Minimum area of steel Astmin = 0.0012 x B x D = 1260 mm2 ( as fy>250)
Provided area = 1380 mm2
Along Z Direction (Bottom)
From IS -456-2000 Annex G, G-1, b:
Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck)
So solving equation for Ast,
Section 4 Indian Code (IS 456 -2000)
4.11 IS Toolkit Combined Foundation 4
Verification Manual — 179
Astz = 807 mm2
Minimum area of steel Astmin = 0.0012 x B x D = 4321 mm2 ( as fy>250)
Provided area = 4320 mm2
Check for One-Way Shear
Percentage of steel pt = 0.133
Vumax = 248.613 KN
Developed shear stress V = 0.261 N/mm2
Now allowable stress= 0.29 N/mm2
V < τc, Hence Safe
Punching Shear
For Column One
Punching shear is checked on a perimeter 0.5d = 272 mm from the column face.
2 way shear= 449.289 KN
τv = Vmax/(Pm · d) = 449.289 x 1000 / (300 x 2 + 300 x 2 + 544 x 4) x544 = 0.245 N/mm2
ß=L/B =6/1.75 =3.43
k=0.5 +ß=4.43 , k<=1
Hence, k=1
Now allowable stress= τc =k.0.25.√fck = 1.25 N/mm2
τv < τc , Hence safe
For Column Two
Punching shear is checked on a perimeter 0.5d = 272 mm from the column face.
2 way shear= 458.245 KN
τv = Vmax/(Pm · d) = 458.245 x 1000 / (300 x 2 + 300 x 2 + 544 x 4) x544 = 0.2496 N/mm2
ß=L/B =6/1.75 =3.43
k=0.5 +ß=4.43 , k<=1
Hence, k=1
Now allowable stress= τc =k.0.25.√fck = 1.25 N/mm2
τv < τc , Hence safe
180 — STAAD Foundation Advanced V8i
Chapter — 4
4.11 IS Toolkit Combined Foundation 4
Figure 4-19: Shear Force and Bending Moment diagrams
Section 4 Indian Code (IS 456 -2000)
4.11 IS Toolkit Combined Foundation 4
Verification Manual — 181
4.11.4 Comparison
Value of ReferenceResult
STAADFoundation
Result
Percent Dif-ference
Bearing Pressure 88.17 KN/m2
75.59 KN/m2
88.16 KN/m2
75.6 KN/m2
Negligible
Governing Moment 129.7 KN-m
264.25 KN-m
157 KN-m
95 KN-m
264.25 KN-m
167 KN-m
8.5%
None
6%Shear Force(One-Way) 248.61 KN 248.61 KN NoneShear Force(Two-Way) 449.289 KN
458.245 KN449.29 KN
458.24 KN
None
Resisting Moment forOverturning (Z)
2579.25 KNm 2579.25 KNm None
Resisting Moment forOverturning (X)
752.28 KNm 752.28 KNm None
Table 4-11: IS verification example 11 comparison
4.12 IS Pilecap 14.12.1 Reference
4.12.2 ProblemDesign pilecap foundation with the given data: Load Fy = 800 KN, fc = 25 MPa, fy = 415MPa, Column Dimension = 250 mm x 250 mm. Pedestal ht= 500 mm
Pile Data- Dia of pile= 400 mm
Vertical capacity = 250 KN
Horizontal capacity = 100 KN
Uplift capacity = 80 KN
182 — STAAD Foundation Advanced V8i
Chapter — 4
4.12 IS Pilecap 1
Figure 4-20: Plan and Elevation
4.12.3 Solutiondepth of pilecap is equal to 1.5x the pile diameter, D = 600 mm
Take D= 920 mm
c/c pile distance is equal to 3x the pile diameter =1200 mm. Edge distance = 350 mm
Assuming four pile combination, Coordinates of piles (considering pedestal at 0,0,0)
Pile NoX Coor-dinate(mm
Z Coor-dinate(mm)
1 -600 -6002 -600 6003 600 6004 600 -600
Table 4-12: Pile Locations in Plan
pilecap dimension is 1900 mm x1900 mm x 650 mm
Weight of footing = 1.9 x1.9 x 0.92 x 25 KN = 83.03 KN
Section 4 Indian Code (IS 456 -2000)
4.12 IS Pilecap 1
Verification Manual — 183
Weight of pedestal = 0.25 x 0.25 x 0.5 x 25 KN = 0.78 KN
Therefore, total load on the pilecap = (800 + 83.03 + 0.78) KN = 883.81 KN
So Pile reaction = 883.81 /4 = 220.95 KN < 250 KN
Hence OK
As there is no lateral load , moment or uplift force, so each pile is safe in lateral & upliftcapacity.
Factored Design
Load factor for self wt is taken =1
Load factor for axial load is taken 1.5
So, Load on pilecap = 1.5(800) + 1(883.81) + 1(0.78) = 1,283.81 KN
Load on each pile = 1,283.81/4 = 320.95 KN
Calculation of Moment about Z Axis
For moment wrt X1X1
Contribution from pile 1 = from pile 2 = 320.95 x 0.475 = 152.45 KNm
So Total Mz X1X1 = 304.9 KNm
For moment wrt X2X2
Contribution from pile 3 = from pile 4 = 320.95 x 0.475 = 152.45 KNm
So Total Mz X2X2 = 304.9 KNm
So Max value of Mz = 304.9 KNm
Calculation of Moment about X Axis
For moment wrt Z1Z1
184 — STAAD Foundation Advanced V8i
Chapter — 4
4.12 IS Pilecap 1
Contribution from pile 1 = from pile 4 = 320.95 6 x 0.475=152.45 KNm
So Total Mx Z1Z1 = 304.9 KNm
For moment wrt Z2Z2
Contribution from pile 2 = from pile 3 = 320.95 6 x 0.475=152.45 KNm
So Total Mx Z2Z2 = 304.9 KNm
So Max value of MX = 304.9 KNm
Check For Trial Depth against moment
About Z Axis
Bending moment at critical section
Muz = 304.9 KNm
Assuming 50 mm clear cover, 50 mm pile in pilecap & and 12 mm bar, effective depth
deff = 814 mm
K = 700/(1,100 + 0.87· fy ) = 0.479107
Ru = 0.36·fck·Kumax ·(1-0.42·Kumax) = 3.4442 N/mm2
B = 1,900 mm, deff = 814 mm
Resisting Moment =Ru·B·deff2 = 4,336 KNm
Hence OK
About X Axis
Bending moment at critical section
Mux = 304.9 KN-m
Assuming 50 mm clear cover, 50 mm pile in pilecap & and 12 mm bar, effective depth
deff = 814 mm
K=700/(1,100 + 0.87· fy )= 0.479107
Ru = 0.36·fck·Kumax ·(1-0.42·Kumax) = 3.4442 N/mm2
B =1,900 mm, deff = 814 mm
Resisting Moment =Ru·B·deff2 = 4,336 KNm
Hence OK
Area of Steel Required
Along X Direction
From IS -456-2000 Annex G, G-1, b:
Section 4 Indian Code (IS 456 -2000)
4.12 IS Pilecap 1
Verification Manual — 185
M f A d= 0.87u y st
A f
bd f
1 − st y
ck
So solving equation for Ast,
Astx = 1,050 mm2
Minimum area of steel Astmin = 0.0012 x B x D = 2,098 mm2 ( as fy > 250)
Provided area = 2,098 mm2
Along Z Direction
From IS -456-2000 Annex G, G-1, b:
M f A d= 0.87u y st
A f
bd f
1 − st y
ck
So solving equation for Ast,
AstZ = 1,050 mm2
Minimum area of steel Astmin = 0.0012 x B x D = 2,098 mm2 ( as fy > 250)
Provided area = 2,098 mm2
Calculation of Shear
Parallel to X Axis
For shear wrt X1X1
Contribution from pile 1 = pile 2 = 320.95 x 0.67 = 215.03 KN
So Total V X1X1 = 430 KN
For shear wrt X2X2
186 — STAAD Foundation Advanced V8i
Chapter — 4
4.12 IS Pilecap 1
Contribution from pile 3 = pile 4 = 320.95 x 0.67 = 215.03 KN
So Total V X2X2 = 430 KN
So Maximum V parallel to X direction = 430 KN
Parallel to Z Axis
For shear wrt Z1Z1
Contribution from pile 1 = pile 4 = 320.95 x 0.67 = 215.03 KN
So Total V Z1Z1 = 430 KN
For shear wrt Z2Z2
Contribution from pile 2 = pile 3 = 320.95 x 0.67 = 215.03 KN
So Total V Z2Z2 = 430 KN
So Max V parallel to Z direction = 430 KN
Check for One-Way Shear
Along X Direction
Percentage of steel pt = 100·Ast/(B·de) = 0.136
Vumax = 430 KN
Developed shear stress V = 430 x 1,000 / 1,900 x 814 = 0.278 N/mm2
Now allowable stress= 0.29 N/mm2
V < τc, Hence Safe
Along Z Direction
Percentage of steel pt = 100·Ast/(B·de) = 0.136
Vumax = 430 KN
Developed shear stress V = 430 x 1,000 / 1,900 x 814 = 0.278 N/mm2
Now allowable stress= 0.29 N/mm2
V < τc, Hence Safe
Section 4 Indian Code (IS 456 -2000)
4.12 IS Pilecap 1
Verification Manual — 187
Punching Shear
Punching shear is checked on a perimeter 0.5d = 407 mm from the column face.
Contribution from pile 1 = from pile 2 = from pile 3 = from pile 4 = 276.4 KN
So total punching shear Vmax= 1,105.7 KN
Pm = 4 x (250 + 814/2 + 814/2) = 4,256 mm
τv = Vmax/(Pm · d) = 0.319 N/mm2
ß = L/B =1,900/1,900 = 1
k = 0.5 + ß = 1.5 , k ≤ 1
Hence, k = 1
Now allowable stress= τc = k(0.25)√fck = 1.25 N/mm2
τv < τc , Hence safe
188 — STAAD Foundation Advanced V8i
Chapter — 4
4.12 IS Pilecap 1
4.12.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Pile Reaction, Service(KN)
220.95 220.5 None
Pile Reaction, Ultimate(KN)
320.95 320.5 None
Governing Moment, Mx(KNm)
304.9 304.5 None
Governing Moment, Mz(KNm)
304.9 304.5 None
Shear Force, One-Way,X (KN)
430 429.5 None
Shear Force, One-Way,Z (KN)
430 429.5 None
Shear Force, Two-Way(KN)
1,105.7 1,104.3 None
Table 4-13: IS verification example 12 comparison
4.13 IS Pilecap 24.13.1 Reference
4.13.2 ProblemDesign pilecap foundation with the given data: Load Fy = 1,100 KN, Mx= 50 KNm, Fz= 50KN,fc = 25 MPa, fy = 415 MPa, Column Dimension = 250 mm x 250 mm. Pedestal ht= 500mm
Diameter of pile= 400 mm.
Vertical capacity =300 KN,
Horizontal capacity = 100 KN
Uplift capacity = 80 KN
Pedestal dimensions: 250 mm x 250 mm
Section 4 Indian Code (IS 456 -2000)
4.13 IS Pilecap 2
Verification Manual — 189
Figure 4-21: Plan, Elevation, and Pedestal dimensions
4.13.3 Solutiondepth of pilecap is equal to 1.5x the pile diameter, D = 600 mm
Take D = 1,255 mm
c/c pile distance = 3x pile diameter =1,200 mm. Edge distance =350 mm
Assuming five pile combination,
Coordinates of piles considering pedestal at 0, 0, 0
190 — STAAD Foundation Advanced V8i
Chapter — 4
4.13 IS Pilecap 2
PileNo
X Coordinate(mm)
Z Coordinate(mm)
1 -849 -8492 -849 8493 0 04 849 -8495 849 -849
Table 4-14: Pile Coordinates in Plan
pilecap dimension is 2,400 mm x 2,400 mm x 1,255 mm
Weight of footing = 2.4 x 2.4 x 1.255 x 25 KN = 180.72 KN
Weight of pedestal = 0.25 x 0.25 x 0.5 x 25 KN = 0.78 KN
Therefore, total load on the pilecap = (1,100 + 180.72 + 0.78) KN = 1,281.5 KN
So Pile reaction from axial load= 1,281.5 /5= 256.3 KN
Moment from lateral load = (1.255 + 0.5) x 50= 87.75 KNm
Moment Mx ( from input) = 50 KNm
So Total moment = 137.75 KNm
Using Rivet theory:
Reaction from moment= ±137.75(0.849)/[4(0.8492)] = ±40.56 KNm
So
Reaction at Pile 2= reaction at pile 5 = 256.3 + 40.56 = 296.86 KN
Reaction at Pile 1= reaction at pile 4 = 256.3 - 40.56 = 215.74 KN
Reaction at Pile 3= 256.3 KN
So Critical vertical reaction= 297 KN< 300 KN
Lateral reaction = 50/5 = 10 KN < 50 KN, Hence OK
As there is no net uplift load, so each pile is safe in uplift capacity.
Factored Design
Load factor for self wt is taken =1
Load factor for axial load is taken 1.5
So, Axial Load on pilecap = 1.5(1,100) + 1(180.72) + 1(0.78) = 1,831.5 KN
Moment on pilecap = 1.5(137.75) = 206.62 KNm
Load on each pile from axial reaction = 1,831.5/5 = 366.3 KN
Reaction from moment= ±206.62(0.849)/[4(0.8492)] = ±60.84 KNm
So
Reaction at Pile 2= reaction at pile 5 = 366.3 + 60.84 = 427.14 KN
Reaction at Pile 1= reaction at pile 4 = 366.3 - 60.84 = 305.46 KN
Section 4 Indian Code (IS 456 -2000)
4.13 IS Pilecap 2
Verification Manual — 191
Reaction at Pile 3= 366.3 KN
Calculation of Moment
Moment is calculated at face of column
About Z Axis
For moment wrt X1X1
Contribution from pile 1 = 305.46 x 0.724 = 221.15 KNm
Contribution from pile 2 = 427.14 x 0.724 = 309.25KNm
Contribution from pile 3 = 1.7 KNm
So Total Mz X1X1 = 532.1 KNm
For moment wrt X2X2
Contribution from pile 4 = 305.46 x 0.724 = 221.15 KNm
Contribution from pile 5 = 427.14 x 0.724 = 309.25KNm
Contribution from pile 3 = 1.7 KNm
So Total Mz X2X2 = 532.1 KNm
So Max value ofMz = 532.1 KNm
About X Axis
For moment wrt Z1Z1
192 — STAAD Foundation Advanced V8i
Chapter — 4
4.13 IS Pilecap 2
Contribution from pile 1 = 305.46 x 0.724 = 221.15 KNm
Contribution from pile 4 = 305.46 x 0.724 = 221.15 KNm
Contribution from pile 3 = 1.7 KNm
So Total Mx Z1Z1 = 444 KNm
For moment wrt Z2Z2
Contribution from pile 2 = 427.14 x 0.724 = 309.25 KNm
Contribution from pile 5 = 427.14 x 0.724 = 309.25 KNm
Contribution from pile 3 = 1.7 KNm
So Total Mx Z2Z2 = 620.2 KNm
So Max value ofMX = 620.2 KNm
Check For Trial Depth
Moment About Z Axis
Bending moment at critical section
Muz = 532.1 KN-m
Assuming 50 mm clear cover, 50 mm pile in pilecap & and 12 mm bar, effective depth
deff = 1,149 mm
K = 700/(1,100 + 0.87x fy ) = 0.479107
Ru = 0.36 (fck) Kumax (1-0.42Kumax) = 3.4442 N/mm2
B =2,400 mm, deff = 1,149 mm
Resisting Moment =Ru. B deff2 = 10,913 KNm
Hence OK
Moment About X Axis
Bending moment at critical section
Mux = 620.2 KN-m
Assuming 50 mm clear cover, 50 mm pile in pilecap & and 12 mm bar, effective depth
deff = 1,149 mm
K = 700/(1,100 + 0.87x fy ) = 0.479107
Ru = 0.36 (fck) Kumax (1-0.42Kumax) = 3.4442 N/mm2
B = 2,400 mm, deff = 1,149 mm
Resisting Moment =Ru. B deff2 = 10,913 KNm
Hence OK
Section 4 Indian Code (IS 456 -2000)
4.13 IS Pilecap 2
Verification Manual — 193
Area of Steel Required
Along X Direction
From IS -456-2000 Annex G, G-1, b:
M f A d= 0.87u y st
A f
bd f
1 − st y
ck
So solving equation for Ast,
Astx = 1,510 mm2
Minimum area of steel Astmin = 0.0012 x B x D = 3,614 mm2 ( as fy > 250)
Provided area = 3,614 mm2
Along Z Direction
From IS -456-2000 Annex G, G-1, b:
M f A d= 0.87u y st
A f
bd f
1 − st y
ck
So solving equation for Ast,
AstZ = 1,293 mm2
Minimum area of steel Astmin = 0.0012 x B x D = 3,614 mm2 ( as fy > 250)
Provided area = 3,614 mm2
Calculation of Shear
According to Amendment 1shear is checked on a perimeter 0.5d =574.5 mm from thecolumn face.
194 — STAAD Foundation Advanced V8i
Chapter — 4
4.13 IS Pilecap 2
Parallel to X Axis
For shear wrt X1X1
Contribution from pile 1 = 305.46 x 0.873 = 266.67 KN
Contribution from pile 2 = 427.14 x 0.873 = 372.89 KN
So Total V X1X1 = 639.56 KN
For shear wrt X2X2
Contribution from pile 4 = 305.46 x 0.873 = 266.67 KN
Contribution from pile 5 = 427.14 x 0.873 = 372.89 KN
So Total V X2X2 = 639.56 KN
So Max V parallel to X direction = 639.56 KN
Parallel to Z Axis
For shear wrt Z1Z1
Contribution from pile 1 = 305.46 x 0.873 = 266.67 KN
Contribution from pile 4 = 305.46 x 0.873 = 266.67 KN
Contribution from pile 3 = 0 KN
So Total V Z1Z1 = 533.34 KN
For shear wrt Z2Z2
Contribution from pile 2 = 427.14 x 0.873 = 372.89 KN
Contribution from pile 5 = 427.14 x 0.873 = 372.89 KN
Contribution from pile 3 = 0 KN
Section 4 Indian Code (IS 456 -2000)
4.13 IS Pilecap 2
Verification Manual — 195
So Total V Z2Z2 = 745.7 KN
So Max V parallel to Z direction = 745.7 KN
Check for One-Way Shear
Along X Direction
Percentage of steel pt = 100·Ast/(B·de) = 0.131
Vumax = 639.56 KN
Developed shear stress V = 639.56 x 103 / (2,400 x 1,149) = 0.232 N/mm2
Now allowable stress= 0.29 N/mm2
V < τc, Hence Safe
Along Z Direction
Percentage of steel pt = 100·Ast/(B·de) = 0.131
Vumax = 745.75 KN
Developed shear stress V = 745.75 x 103 / (2,400 x 1,149) = 0.27 N/mm2
Now allowable stress= 0.29 N/mm2
V < τc, Hence Safe
Punching Shear
Punching shear is checked on a perimeter 0.5d = 574.5 mm from the column face.
Contribution from pile 1 = from pile 4 = 300.6 KN
Contribution from pile 2 = from pile 5 = 420.3 KN
Contribution from pile 3 = 0 KN
So total punching shear Vmax= 1,441.8 KN
Pm = 4x(250 + 574.5 + 574.5) = 5,596 mm
196 — STAAD Foundation Advanced V8i
Chapter — 4
4.13 IS Pilecap 2
τv = Vmax/(Pm · d) = 0.224 N/mm2
ß = L/B = 2,400/2,400 = s1
k = 0.5 +ß = 1.5 , k ≤ 1
Hence, k = 1
Now allowable stress= τc =k(0.25)√fck = 1.25 N/mm2
τv < τc , Hence safe
4.13.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Pile Reaction, Service(KN)
215.74
296.86
256.3
215.74
296.86
215.62
296.788
256.203
215.617
296.788
Negligible
Pile Reaction, Ulti-mate (KN)
305.46
427.14
366.3
305.46
427.14
305.32
427.081
366.203
305.324
427.081
Negligible
Governing Moment(KNm)
532
620
531
619.5
Negligible
Shear Force, One-Way(KN)
640
746
641
747
Negligible
Shear Force, Two-Way(KN)
1441.8 1435.7 Negligible
Table 4-15: IS verification example 13 comparison
4.14 IS Mat Combined Foundation 14.14.1 Reference‘Reinforced Concrete Design’ by Pillai & Menon, Page 652, Example 14.7.
4.14.2 ProblemDesign a combined footing for two columns with the given data: C1 (400 mm x 400 mm)with 4-25 Ø bars and C2 (500 mm x 500mm) with 4-28 Ø bars supporting axial loads P1 =900 KN and P2 = 1600 KN respectively (under service dead and live loads). The column C1is an exterior column whose exterior face is flush with the property line. The center-to-centre distance between C1 and C2 is 4.5 meters. The allowable soil pressure at the base of
Section 4 Indian Code (IS 456 -2000)
4.14 IS Mat Combined Foundation 1
Verification Manual — 197
the footing, 1.5 m below ground level, is 240 KN/m2. Assume a steel of grade Fe 415 inthe columns as well as the footing, and a concrete grade of M 20 in the footing.
Figure 4-22: Footing Plan
Figure 4-23: >Loads on Footing
4.14.3 SolutionDimension of Mat (Based on the bearing Capacity given):
Length = 6.16 m
Width = 2 m
Depth = 0.95 m
Calculation for base-pressure
Self-weight of mat = 6.16 x 2 x 0.95 x 25 KN = 292.6 KN
Total load on the mat = (1600+900+200.2) KN = 2792.6 KN
Base pressure = 279.6 / (6.16 x 2) KN/m2 = 226.67 KN/m2 < 240 KN/m2
(Hence Safe)
Ultimate load for C1 = Pu1 = 1.5 x 900 = 1350 KN
Ultimate load for C2 = Pu2 = 1.5 x 1600 = 2400 KN
198 — STAAD Foundation Advanced V8i
Chapter — 4
4.14 IS Mat Combined Foundation 1
Then uniformly distributed upward load = (Pu1+Pu2)/6.16 KN/m = 608.8KN/m
Developed shear stress,
v = = 0.533 N/mm2 < c,allowable
Hence safe
Maximum shear for C2 = 2400 KN
Developed shear stress,
v = = 0.508 N/mm2 < c,allowable
Hence safe
Note: There is no deduction for the upward force underneath the area enclosed by thecritical perimeter. This approach is conservative.
Calculation of reinforcement
Maximum negative moment Mu(-) = 1227 KN-m
Maximum negative moment/width = 1227/2 KN-m/m = 613.5 KN-m/m
Area of steel required on top face along length,
Ast = 0.5 x x B x deB = 1000 mm
de = 865 mm
Mu= 613.5 x 106 N-mm
Ast = 2067.97 mm2/m
Ast,min = 0.0012 x B x D = 1140mm2/m
Section 4 Indian Code (IS 456 -2000)
4.14 IS Mat Combined Foundation 1
Verification Manual — 199
Figure 4-24: Shear Force (kN, top) and Bending Moment (kNm, bottom) diagrams
4.14.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Max BendingMoment(-)
603.201 KN-m/m
613.5 KN-m/m 1.68
Max BendingMoment(+)
219.687 KN-m/m
223 KN-m/m 1.48
Area of StealRequired
2014.835mm2/m
2067.97 mm2/m 2.56
Base Pressure 227 KN/m2 226.67 KN/m2 Negligible
Table 4-16: IS verification example 14 comparison
200 — STAAD Foundation Advanced V8i
Chapter — 4
4.14 IS Mat Combined Foundation 1
Section 5
United States Code (ACI318 -2005)5.1 US General Isolated Foundation 1
5.1.1 Reference‘Notes on ACI318-02 Building Code Requirements for Structural Concrete with DesignApplications’ by B.A. Fanella and B. G. Robert, Page 22-7, Example 22.1-22.3.
5.1.2 ProblemDesign an isolated footing with the given data: Service dead load = 350 kips, Service liveload = 275 kips, Service surcharge = 100 psf, Average weight of soil above footing = 130 pcf,Permissible soil pressure = 4.5 ksf, Column dimension = 30 x 12 in, Strength of concrete(fc’) = 3,000 psi, and Strength of steel (fy) = 60,000 psi.
Verification Manual — 201
Figure 5-1: Elevation and loads
5.1.3 SolutionDetermination of base area of footing:
The base area of footing is determined using service (unfactored) loads with the netpermissible soil pressure.
Total weight of surcharge = (0.130 x 5 + 0.1) = 0.75 ksf
Net permissible soil pressure = 4.5 – 0.75 = 3.75 ksf
Required base area of footing = (320 + 275) / 3.75 = 166.667 ft2
[Clause 15.2.2]
Use a 13 x 13 ft square footing (Af = 169 ft2).
Factored loads and soil reaction:
To proportion the footing for strength (depth and required reinforcement) factored loadsare used. [Clause 15.2.1]
Pu = 1.2 x 350 + 1.6 x 275 = 860 kips [Eq. 9-2]
qu = (Pu/A) = (860/169) = 5.089 ksf
202 — STAAD Foundation Advanced V8i
Chapter — 5
5.1 US General Isolated Foundation 1
Figure 5-2: Considered sections for two-way (bo) and beam (bw) action
Depth requirement for shear usually controls the footing thickness.
Both wide action and two-way action for strength computation need to be investigated todetermine the controlling shear criteria for depth. [Clause 11.2]
Assume overall footing thickness = 33 in. and average effective thickness d = 28 in. = 2.33ft.
Wide-beam action
Vu = qs x tributary area
Bw = 13 ft = 156 in.
Tributary area = 13(6.0 – 2.33) = 47.71 ft2
Vu = 5.089 x 47.71 = 242.796 kips
φV = φ(2√(f'c)bwd) [Eq 11 - 3]
= 0.75(2√(3000) x 156 x 28)/1000 [Clause 9.3.2.3]
= 359 kips > Vu O.K.
Two-way action
Vu = qs x tributary area
Tributary area = = 152.889 ft2
Vu = 5.089 x 152.889 = 778.052 kips
Section 5 United States Code (ACI 318 -2005)
5.1 US General Isolated Foundation 1
Verification Manual — 203
= Minimum of
[Eq 11-33,11-34 & 11-35 respectively]
bo = 2(30 + 28) + 2(12 + 28) = 196 in.
bo/d = 196/28 = 7
= 40 for interior columns
=
φVc = 0.75 x 3.6 √(3000) x 196 x 28/1000 = 812 kips > Vu = 780 kips
O.K.
Calculation of ReinforcementFigure 5-3: Critical section for moment (long projection)
Critical section for moment is at face of column [Clause 15.4.2]
Mu = 5.089 x 13 x 62/2 = 1190.862 ft-kips
Compute required As assuming tension-controlled section ( φ = 0.9)
[Clause 10.3.4, 9.3.2.1]
204 — STAAD Foundation Advanced V8i
Chapter — 5
5.1 US General Isolated Foundation 1
Required Rn = psi
p(gross area) = (d/h) x 0.0022 = (28/33) x 0.0022 = 0.00186
Check minimum As required for footings of uniform thickness; for grade 60 reinforcement:[Clause 10.5.4]
ρmin = 0.00180 < 0.00186 O.K. [Clause 7.12.2]
Required As = ρbd = 0.0022 x 156 x 28 = 9.61 in.2
Try 13-No. 8bars (As = 10.27 in.2) each way
Check for Development Length
Critical section for development length is same as that for moment (at face of column).[Clause 15.6.3]
Ld = [Eq. 12-1]
Clear cover (bottom and side) = 3.0 in.
Center-to-center bar spacing = in.
[Clause 12.2.4]
C = minimum of
Ktr = 0 (no transverse reinforcement)
= 3.5 > 2.5, use 2.5 [Clause 12.2.3]
α = 1.0 (less than 12 in. of concrete below bars) [Clause 12.2.4]
β = 1.0 (uncoated reinforcement)
αβ= 1.0 < 1.7
γ = 1.0 (larger than No.7 bars)
Section 5 United States Code (ACI 318 -2005)
5.1 US General Isolated Foundation 1
Verification Manual — 205
λ = 1.0 (Normal weight concrete)
Ld = = 32.9 in. >12.0 in. O.K. [Clause12.2.1]
Since Ld = 32.9 in. is less than the available embedment length in the short direction(156/2 - 30/2 - 3 = 60 in.), the No.8 bars can be fully developed.
Use 13 – No.8 each way.
5.1.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth 28 in 28 in NoneGoverning Moment 1190.86 ft-
kips1190.77 ft-kips Negligible
Area of Steal 9.61 in2 9.70 in2 0.94Shear Stress (One-Way)
242.79 kips 242.56 kips Negligible
Shear Stress (Two-Way)
778.05 kips 778.01 kips Negligible
Table 5-1: US verification example 1 comparison
5.2 US General Isolated Foundation 25.2.1 Reference
5.2.2 ProblemDesign an isolated footing with the given data: Load Fy = 200 Kip, fc = 4 Ksi, fy = 60 Ksi,Column Dimension = 12 inch x 12 inch, and Bearing Capacity of Soil = 2.2 Kip/sqft.Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
206 — STAAD Foundation Advanced V8i
Chapter — 5
5.2 US General Isolated Foundation 2
Figure 5-4: Elevation and Plan
5.2.3 SolutionApproximate area of footing required = 200/2.2 = 90.9 sqft
Assuming 122 inch x122 inch x18 inch footing dimension,
Weight of footing = 122 x122 x18 x 0.159/(123)= 24.66 Kip
Therefore, total load on the footing = (200+24.66) KN = 224.66 Kip
Maximum pressure = 224.66 /(122 x 122) = 0.0151 Ksi=2.17 Kip/sqft <2.2Kip/sqft (Hence safe)
Ultimate pressure =200x1.5/(122x122)= KN/m2 = 0.020156 Ksi
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force = 0
max Resisting force = µ x Total Service load on foundation = 0.5 x 224.66 =112.33 Kip
Hence OK
Section 5 United States Code (ACI 318 -2005)
5.2 US General Isolated Foundation 2
Verification Manual — 207
Overturning Moment = 0
max resisting Moment = 0.5x 122 x 224.66 = 13704.26 in·kip
Hence OK
Along Z Direction
Sliding force = 0
max Resisting force = µ x Total Service load on foundation = 0.5 x 224.66 =112.33 Kip
Hence OK
Overturning Moment = 0
max resisting Moment = 0.5x 122 x 224.66 = 13704.26 in·kip
Hence OK
Punching Shear
Punching shear is checked on a perimeter 0.5d = 7.5 inch from the column face.
Effective Depth=D-clear cover-1=18-2-1=15 inch
Punching Shear Vm = 0.018813 x 122 x 122 - 0.0189 x 27 x 27 = 266.24 Kip
Critical perimeter Pm = 2 X ( b + h + 2 x d) = 108 inch
Vm1 = Vmax / (Pm*d)= 164.81 Ksi
ßc=Width of col/depth of col=12/12=1
bc=2.(b+d+2.deff)=108 inch
V1 √fc.bc.d = (2+4/1).√(4000) x 108 x 15 = 614746.78 lb
V2 √fc.bc.d = (40x15/108+2). √(4000) x 108 x 15 =774125.57 lb
V2 = 4.√fc.bc.de=4.√(4000) x 108 x 15 = 409831.18 lb
Vc = min {V1, V2, V3} =409831.185 lb
So, 0.75Vc = 307.374 Kip
Vm< 0.75.Vc , Hence safe
Check for One-Way Shear
Along Z Direction
Vumax = 0.0189 x 122 x = 92.24 Kip
208 — STAAD Foundation Advanced V8i
Chapter — 5
5.2 US General Isolated Foundation 2
Now allowable shear = Vc1 = = 2x√(4000) x 122 x 15 lb =231.48 Kip
0.75.Vc1=173.61 Kip
V < Vc1, Hence Safe
So Vumax < Vc1 , Hence Safe
Along Z Direction
Vumax = 0.0189 x 122 x = 92.24 Kip
Now allowable shear = Vc1 = = 2x√(4000) x 122 x 15 lb =231.48 Kip
0.75.Vc1=173.61 Kip
V < Vc1, Hence Safe
So Vumax < Vc1 , Hence Safe
Check For Trial Depth Against Moment
About X Axis
m = fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 ( as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.02138
ρmin = 0.0018 ( as fy=60)
Bending moment at critical section
Mux = 0.0189 x 122 x 55 x 55 / 2 = 3487.55 in·kip
So Resisting Moment =Mnz= Muz/Ø =3875.56 in·kip
Rn = Mnz/b.d2 =0.1412 Ksi
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002405
Ρmin < ρ < ρmax Hence OK
About Z Axis
m = fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 ( as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
Section 5 United States Code (ACI 318 -2005)
5.2 US General Isolated Foundation 2
Verification Manual — 209
ρmax = 0.75. ρbal = 0.02138
ρmin = 0.0018 ( as fy=60)
Bending moment at critical section
Mux = 0.0189 x 122 x 55 x 55 /2 = 3487.55 in·kip
So Resisting Moment = Mnz = Muz/Ø =3875.56 in·kip
Rn = Mnz/b.d2 =0.1412 Ksi
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002405
Ρmin < ρ < ρmax Hence OK
Area of Steel Required
Along X Direction
ρx = 0.002405
Therefore, Astx = ρx*b*d = 4.4 in2
Along Z Direction
ρz = 0.002405
Therefore, Astz = ρz*b*d = 4.4 in2
5.2.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth 15 inch 15 inch NoneBearing Pressure 0.0151 Ksi 0.0151 Ksi NoneGoverning Moment 3487 in·kip
3487 in·kip
3471 in·kip
3471 in·kip
Negligible
Shear Force(One-Way) 92.24 Kip
92.24 Kip
91.8 Kip
91.8 Kip
Negligible
Shear Force(Two-Way) 266.24 Kip 266.29 Kip NegligibleResisting force for sliding 112.33 Kip 112.33 Kip NoneResisting Moment forOverturning
13704.26in·kip
13703.75 in·kip Negligible
Table 5-2: US verification example 2 comparison
210 — STAAD Foundation Advanced V8i
Chapter — 5
5.2 US General Isolated Foundation 2
5.3 US General Isolated Foundation 35.3.1 Reference
5.3.2 ProblemDesign an isolated footing with the given data: Load Fy = 250 Kip, fc = 4 Ksi, fy = 60 Ksi,Column Dimension = 12 inch x 12 inch, and Bearing Capacity of Soil = 2Kip/sqft.Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
Figure 5-5: Elevation and Plan
5.3.3 SolutionApproximate area of footing required = 250/2 = 125 sqft
Assuming 160 inch x160 inch x21 inch footing dimension,
Weight of footing 160 x160 x21 x 0.159/(123)= 49.47 Kip
Weight of soil above footing 160 x160 x32 x 0.159/(123)= 53.57 Kip
Therefore, total load on the footing = (250+49.47 +53.57) KN = 353.04 Kip
Section 5 United States Code (ACI 318 -2005)
5.3 US General Isolated Foundation 3
Verification Manual — 211
Maximum pressure = 353.04/(160x160) = 0.0138 Ksi=1.9872 Kip/sqft <2Kip/sqft
Hence safe
Ultimate pressure = 200 x 1.5/(122 x 122)= KN/m2 = 0.020156 Ksi
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation = 0.5 x 353.04 =176.52 Kip
Hence OK
Overturning Moment =0
max resisting Moment = 0.5x 160 x 353.04 = 28243.2 in·kip
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation =0.5 x 353.04 =176.52 Kip
Hence OK
Overturning Moment =0
max resisting Moment = 0.5x 160 x 353.04 = 28243.2 in·kip
Hence OK
Punching Shear
Punching shear is checked on a perimeter 0.5d = 9 inch from the column face.
Effective Depth=D-clear cover-1=21-2-1=18 inch
Punching Shear Vm= 0.013673x160x160-0.0137x30x30=337.68 Kip
Critical perimeter Pm = 2 X ( b + h + 2 x d) = 120 inch
ßc=Width of col/depth of col=12/12=1
bc=2.(b+d+2.deff)=120 inch
V1 √fc.bc.d = (2+4/1).√(4000) x120x18 =819662.37 lb
212 — STAAD Foundation Advanced V8i
Chapter — 5
5.3 US General Isolated Foundation 3
V2 √fc.bc.d = (40x18/120+2).√(4000) x120x18=1092883.16 lb
V2= 4 .√fc.bc.de=4.√(4000) x120x18=546441.58 lb
Vc =
=546441.58 lb
So, 0.75Vc=409.832 Kip
Vm< 0.75xVc , Hence safe
Check for One-Way Shear
Along X Direction
Vumax = 0.0137 x 160 x = 122.76 Kip
Now allowable shear = Vc1 = = 2x√(4000) x160x18 lb =364.3 Kip
0.75.Vc1 = 273.2 Kip
So Vumax < 0.75x Vc1, Hence Safe
Along Z Direction
Vumax = 0.0137 x 160 x = 122.76 Kip
Now allowable shear = Vc1 = = 2x√(4000) x160x18 lb =364.3 Kip
0.75.Vc1 = 273.2 Kip
So Vumax <0.75x Vc1 , Hence Safe
Check For Trial Depth against moment
About X Axis
m = fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 ( as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.02138
ρmin = 0.0018 ( as fy=60)
Bending moment at critical section
Mux = = 0.0137 x 160 x 74 x 74 /2 = 6002 in·kip
So Resisting Moment =Mnz= Muz/Ø =6668.89 in·kip
Section 5 United States Code (ACI 318 -2005)
5.3 US General Isolated Foundation 3
Verification Manual — 213
Rn = Mnz/b.d2 =0.1287 Ksi
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002188
Ρmin < ρ < ρmax Hence OK
About Z Axis
m=fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 ( as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.02138
ρmin = 0.0018 ( as fy=60)
Bending moment at critical section
Mux = = 0.0137 x 160 x 74 x 74 / 2 = 6002 in·kip
So Resisting Moment =Mnz= Muz/Ø =6668.89 in·kip
Rn = Mnz/b.d2 =0.1287 Ksi
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002188
Ρmin < ρ < ρmax Hence OK
Area of Steel Required
Along X Direction
ρx = 0.002188
Therefore, Astx = ρx*b*d = 6.3 in2
Along Z Direction
ρz = 0.002188
Therefore, Astz = ρz*b*d = 6.3 in2
214 — STAAD Foundation Advanced V8i
Chapter — 5
5.3 US General Isolated Foundation 3
5.3.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth 18 inch 18 inch NoneBearing Pressure 0.0138 Ksi 0.0138 Ksi NoneGoverning Moment 6002 in·kip
6002 in·kip5989 in·kip
5989 in·kip
Negligible
Shear Force(One-Way) 92.24 Kip
92.24 Kip
91.8 Kip
91.8 Kip
Negligible
Shear Force(Two-Way) 337.68 Kip 337.7 Kip NoneResisting force forsliding
176.52 Kip 176.37 Kip Negligible
Resisting Moment forOverturning
28243.2 in·kip 28218.85in·kip
Negligible
Table 5-3: US verification example 3 comparison
5.4 US General Isolated Foundation 45.4.1 Reference
5.4.2 ProblemDesign an isolated footing with the given data: Load Fy = 300 Kip, fc = 4 Ksi, fy = 60 Ksi,Column Dimension = 12 inch x 12 inch, and Bearing Capacity of Soil = 2.1Kip/sqft.Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
Section 5 United States Code (ACI 318 -2005)
5.4 US General Isolated Foundation 4
Verification Manual — 215
Figure 5-6: Elevation and Plan
5.4.3 SolutionApproximate area of footing required =300/2.1 = 142.86 sqft
Assuming 158 inch x158 inch x21 inch footing dimension,
Weight of footing 158 x158 x21 x 0.159/(123)= 48.24 Kip
Weight of soil above footing 158 x158 x25 x 0.159/(123)= 40.82 Kip
Reduction of Weight due to buoyancy = 158 x158 x(25+21-10) x 3.61398x10-5= 32.479 Kip
Therefore, total load on the footing = (300+48.24 +40.82 -32.479) = 356.581Kip
Maximum pressure = 356.581 /(158x158) = 0.0143 Ksi=2.059 Kip/sqft <2.1Kip/sqft
Hence safe
Ultimate pressure =200x1.5/(122x122)= KN/m2 = 0.020156 Ksi
216 — STAAD Foundation Advanced V8i
Chapter — 5
5.4 US General Isolated Foundation 4
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation=0.5 x 356.581 =178.29 Kip
Hence OK
Overturning Moment =0
max resisting Moment = 0.5x 158 x 356.581 = 28169.899 in·kip
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation=0.5 x 356.581 =178.29 Kip
Hence OK
Overturning Moment =0
max resisting Moment = 0.5x 158 x 356.581 = 28169.899 in·kip
Hence OK
Punching Shear
Punching shear is checked on a perimeter 0.5d = 9 inch from the column face.
Effective Depth=D-clear cover-1=21-2-1=18 inch
Punching Shear Vm= 0.016825 x 158 x 158 - 0.0169 x 30 x 30 = 404.81 Kip
Critical perimeter Pm = 2 X ( b + h + 2 x d) = 120 inch
ßc = Width of col/depth of col = 12/12=1
bc = 2.(b+d+2.deff) = 120 inch
Section 5 United States Code (ACI 318 -2005)
5.4 US General Isolated Foundation 4
Verification Manual — 217
Figure 5-7: Section considered for two-way shear
V1 √fc.bc.d = (2+4/1).√(4000) x120x18 =819662.37 lb
V2 √fc.bc.d = (40x18/120+2).√(4000) x120x18=1092883.16lb
V3= 4.√fc.bc.de=4.√(4000) x120x18=546441.58 lb
Vc = min{V1, V2, V3} = 546441.58 lb
So, 0.75Vc=409.832 Kip
Vm< 0.75.Vc , Hence safe
Check for One-Way Shear
Along X Direction
Vumax = 0.0169 x 158 x = 146.87 Kip
Now allowable shear = Vc1 = = 2x√(4000) x158x18 lb = 359.74 Kip
0.75.Vc1=269.81 Kip
So Vumax <0.75x Vc1 , Hence Safe
218 — STAAD Foundation Advanced V8i
Chapter — 5
5.4 US General Isolated Foundation 4
Along Z Direction
Vumax = 0.0169 x 158 x = 146.87 Kip
Now allowable shear = Vc1 = = 2x√(4000) x158x18 lb = 359.74 Kip
0.75.Vc1=269.81 Kip
So Vumax < 0.75xVc1 , Hence Safe
Check for Trial Depth
Moment About X Axis
m=fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 ( as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.021381
ρmin = 0.0018 ( as fy=60)
Bending moment at critical section
Mux = 0.0169 x 158 x 73 x 73 / 2 = 7114.95 in·kip
So Resisting Moment =Mnz= Muz/Ø =7905.56 in·kip
Rn = Mnx/b.d2 =0.1545 Ksi
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002637
Ρmin < ρ < ρmax Hence OK
Moment About Z Axis
m=fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 ( as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.021381
ρmin = 0.0018 ( as fy=60)
Bending moment at critical section
Mux = 0.0169 x 158 x 73 x 73 / 2 = 7114.95 in·kip
So Resisting Moment =Mnz= Muz/Ø =7905.56 in·kip
Rn = Mnz/b.d2 =0.1545 Ksi
Section 5 United States Code (ACI 318 -2005)
5.4 US General Isolated Foundation 4
Verification Manual — 219
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002637
Ρmin < ρ < ρmax Hence OK
Area of Steel Required
Along X Direction
ρx = 0.002637
Therefore, Astx = ρx*b*d = 7.45 in2
Along Z Direction
ρz = 0.002637
Therefore, Astz = ρz*b*d = 7.45 in2
5.4.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth 18 inch 18 inch NoneBearing Pressure 0.0143 Ksi 0.0143 Ksi NoneGoverning Moment 7114.95
in·kip
7114.95in·kip
7082.85 in·kip
7082.85 in·kip
Negligible
Shear Force(One-Way) 146.87 Kip
146.87 Kip
146.2 Kip
146.2 Kip
Negligible
Shear Force(Two-Way) 404.81 Kip 404.86 Kip NoneResisting force for sliding 178.29 Kip 178.18 Kip NegligibleResisting Moment forOverturning
28169.899in·kip
28152.53 in·kip Negligible
Table 5-4: US verification example 4 comparison
5.5 US General Isolated Foundation 55.5.1 Reference
5.5.2 ProblemDesign an isolated footing with the given data: Load Fy = 200 Kip,Mx=Mz=240 in·kip. fc= 4 Ksi, fy = 60 Ksi, Column Dimension = 12 inch x 12 inch, and Bearing Capacity of Soil
220 — STAAD Foundation Advanced V8i
Chapter — 5
5.5 US General Isolated Foundation 5
= 2.2 Kip/sqft. Coefficient of friction =0.5, FOS against sliding =1.5, FOS againstoverturning =1.5
Figure 5-8: Elevation and Plan
5.5.3 SolutionApproximate area of footing required = 200/2.2 = 90.9 sqft
Assuming 130 inch x130 inch x19 inch footing dimension,
Weight of footing 130 x130 x19 x 0.159/(123)= 29.55 Kip
Therefore, total load on the footing = (200+29.55) KN = 229.55 Kip
Zx = 130x1302 = 366166.667 in3
Zz = 130x1302 = 366166.667 in3
Maximum pressure from axial load = 229.55/(130x130) = 0.0136 Ksi
Mx/Zx=240/366166.667 =0.0007 Ksi
Mz/Zz=240/366166.667 =0.0007 Ksi
So stress at four corners –
Section 5 United States Code (ACI 318 -2005)
5.5 US General Isolated Foundation 5
Verification Manual — 221
σ1=P/A-Mx/Zx+Mz/Zz= 0.0136 Ksi
σ2=P/A-Mx/Zx-Mz/Zz= 0.0122 Ksi
σ3=P/A+Mx/Zx-Mz/Zz= 0.0136 Ksi
σ4=P/A+Mx/Zx+Mz/Zz= 0.015 Ksi
Max stress = 0.0136 Ksi = 2.16 Ki/sqft <2.2 Kip/sqft (Hence safe)
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
For Sliding
Sliding force =0
max Resisting force = µ x Total Service load on foundation = 0.5 x 229.55 =114.775 Kip
Hence OK
Along Z Direction
Sliding force =0
max Resisting force = µ x Total Service load on foundation =0.5 x 229.55 =114.775 Kip
Hence OK
For overturning
About X Direction
Overturning Moment =240 in·kip
max resisting Moment = 0.5x 130 x 229.55 = 14920.75 in·kip
FOS= 14920.75/240 = 62.17>1.5
Hence OK
About Z Direction
Overturning Moment =240 in·kip
max resisting Moment = 0.5x 130 x 229.55 = 14920.75 in·kip
FOS= 14920.75/240 = 62.17>1.5
Hence OK
222 — STAAD Foundation Advanced V8i
Chapter — 5
5.5 US General Isolated Foundation 5
Punching Shear
Punching shear is checked on a perimeter 0.5d = 8 inch from the column face.
Effective Depth=D-clear cover-1=19-2-1=16 inch
Punching Shear Vm= 0.018813x122x122-0.0189x27x27=266.24 Kip
Critical perimeter Pm = 2 X ( b + h + 2 x d) = 108 inch
Vm1 = Vmax/(Pm · d) = 164.81 Ksi
ßc=Width of col/depth of col=12/12=1
bc=2.(b+d+2.deff)=108 inch
V1 √fc.bc.d = (2+4/1).√(4000) x108x15 =614746.78 lb
V2 √fc.bc.d = (40x15/108+2).√(4000) x108x15=774125.57 lb
V2= 4.√fc.bc.de=4.√(4000) x108x15=409831.18 lb
Vc = min{V1, V2, V3} = 409831.185 lb
So, 0.75Vc=307.374 Kip
Vm< 0.75xVc , Hence safe
Section 5 United States Code (ACI 318 -2005)
5.5 US General Isolated Foundation 5
Verification Manual — 223
Check for One-Way Shear
Along X Direction
Critical section for moment is at distance d from the face of the column.
Shear at Longitudinal Direction (X Axis)
Average Base Pressure along one edge = (0.014733 + 0.016569) x0.5 = 0.157Ksi
Average Base Pressure along other edge = (0.016569 + 0.018405) x 0.5 =0.0175 Ksi
Approximate Base Pressure at the left critical section = 0.0175 + (0.0157 -0.0175) x87/130 = 0.0163 Ksi
Approximate Base Pressure at the right critical section = 0.0175 + (0.0157 -0.0175) x 43/130 = 0.0170 Ksi
Hence, the shear force at the critical section:
F = (0.0175 + 0.0170) x0.5 x 43 x 130 = 96.43 kip
So, max shear force along X axis, Fux = 97 kip
Now allowable shear = Vc1 = = 2x√(4000) x130x16 lb =263.101 Kip
0.75.Vc1 = 197.327 Kip
So Vumax < 0.75x Vc1 , Hence Safe
224 — STAAD Foundation Advanced V8i
Chapter — 5
5.5 US General Isolated Foundation 5
Along Z Direction
Average Base Pressure along one edge = (0.014733 + 0.016569) x0.5 = 0.157Ksi
Average Base Pressure along other edge = (0.016569 + 0.018405) x 0.5 =0.0175 Ksi
Approximate Base Pressure at the left critical section = 0.0175 + (0.0157 -0.0175) x87/130 = 0.0163 Ksi
Approximate Base Pressure at the right critical section = 0.0175 + (0.0157 -0.0175) x 43/130 = 0.0170 Ksi
Hence, the shear force at the critical section:
F = (0.0175 + 0.0170) x0.5 x 43 x 130 = 96.43 kip
So, max shear force along Z axis, Fuz = 97 kip
Now allowable shear = Vc1 = = 2x√(4000) x122x15 lb =263.101 Kip
0.75.Vc1 = 197.327 Kip
So Vumax <0.75x Vc1 , Hence Safe
About Z Axis
Critical section for moment is at the face of the column.
Section 5 United States Code (ACI 318 -2005)
5.5 US General Isolated Foundation 5
Verification Manual — 225
Average Base Pressure along one edge = (0.014733 + 0.016569) x 0.5 =0.0157 Ksi (left end)
Average Base Pressure along other edge = (0.016569 + 0.018405) x 0.5 =0.0175 Ksi (right end)
Approximate Base Pressure at the left critical section = 0.0175 + (0.0157 -0.0175) x 71/130 = 0.0166 Ksi
Approximate Base Pressure at the right critical section = 0.0175 + (0.0157 -0.0175) x 59/130 = 0.0167 Ksi
Hence, the moment at the critical section (right):
Mu = F x LA
F = (0.0175 + 0.0167) x 0.5 x 59 x 130 = 131.16 Kip
LA = (0.0167 + 2 x 0.0175) x 59/(3x (0.0167 + 0.0175)) = 29.731 inches
Mu (right) = 3899.52 in-kips
So, max moment wrt Z axis, Mu(x) = 3900 in-kips
m=fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 ( as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.021381
ρmin = 0.0018 ( as fy=60)
So Resisting Moment =Mnz= Muz/Ø =4333.3334 in·kip
Rn = Mnz/b.d2 =0.1303 Ksi
2m.Rn/fy <1 , Hence OK
226 — STAAD Foundation Advanced V8i
Chapter — 5
5.5 US General Isolated Foundation 5
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002215
Ρmin < ρ < ρmax Hence OK
Check for Trial Depth Against Moment
About X Axis
Critical section for moment is at the face of the column.
Average Base Pressure along one edge = (0.014733 + 0.016569) x 0.5 = 0.0157Ksi (left end)
Average Base Pressure along other edge = (0.016569 + 0.018405) x 0.5 =0.0175 Ksi (right end)
Approximate Base Pressure at the left critical section = 0.0175 + (0.0157 -0.0175) x 71/130 = 0.0166 Ksi
Approximate Base Pressure at the right critical section = 0.0175 + (0.0157 -0.0175) x 59/130 = 0.0167 Ksi
Hence, the moment at the critical section (right):
Mu = F x LA
F = (0.0175 + 0.0167) x 0.5 x 59 x 130 = 131.16 Kip
LA = (0.0167 + 2 x 0.0175) x 59/(3x (0.0167 + 0.0175)) = 29.731 inches
Mu (right) = 3899.52 in-kips
So, max moment wrt Z axis, Mu(z) = 3900 in-kips
m=fy/0.85.fc=60/(0.85x4) = 17.6471
Section 5 United States Code (ACI 318 -2005)
5.5 US General Isolated Foundation 5
Verification Manual — 227
ß1 = 0.85 ( as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.021381
ρmin = 0.0018 ( as fy=60)
So Resisting Moment =Mnz= Muz/Ø =4333.3334 in·kip
Rn = Mnz/b.d2 =0.1303 Ksi
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002215
Ρmin < ρ < ρmax Hence OK
Area of Steel Required
Along X Direction
ρx = 0.002215
Therefore, Astx = ρx*b*d = 4.61 in2
Along Z Direction
ρz = 0.002215
Therefore, Astz = ρz*b*d = 4.61 in2
228 — STAAD Foundation Advanced V8i
Chapter — 5
5.5 US General Isolated Foundation 5
5.5.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth 16 inch 16 inch NoneBearing Pressure 0.0136 Ksi
0.0122 Ksi
0.0136 Ksi
0.015 Ksi
0.0136 Ksi
0.0123 Ksi
0.0136 Ksi
0.0149 Ksi
None
Governing Moment 3899.52in·kip
3899.52in·kip
3893.52 in·kip
3893.52 in·kip
Negligible
Shear Force(One-Way) 96.43 Kip
96.43 Kip
96.05 Kip
96.05 Kip
Negligible
Shear Force(Two-Way) 266.96 Kip 267.01 Kip NegligibleResisting force for sliding 114.775 Kip
114.775 Kip
114.773 Kip
114.773 Kip
None
Resisting Moment forOverturning
14920.75in·kip
14920.75in·kip
14920.466in·kip
14920.466in·kip
Negligible
Table 5-5: US verification example 5 comparison
5.6 US General Isolated Foundation 65.6.1 Reference
5.6.2 ProblemDesign an isolated footing with the given data: Load Fy = 1000 KN, Concrete grade M25,Steel Grade Fe 415, Pedestal Dimension = 250 mm x 250 mm x 500 mm.
Bearing Capacity of Soil = 120 KN/m2. Coefficient of friction =0.4, FOS against sliding=1.4, FOS against overturning =1.4
Soil Depth is 500 mm , depth of GWT from GL is 200 mm and surcharge on foundation
is 5 KN/m2. (consider unt wight of soil 18 KN/m2)
Section 5 United States Code (ACI 318 -2005)
5.6 US General Isolated Foundation 6
Verification Manual — 229
Figure 5-9: Elevation and Plan
5.6.3 SolutionApproximate area of footing required = 1000/120 = 8.33 m2
Assuming 3140 mm x 3140 mm footing dimension, with 490 mm depth
Punching Shear
Weight of footing = 3.14 x 3.14 x 0.49 x 25 = 120.78 KN
Punching Shear Vm = 1400/(3.14 x 3.14) x (3.14 x 3.14-0.665 x 0.665) =1337.2 KN
Critical perimeter Pm = 2 x (b + d + 2 x d) = 2660 mm
Vm1 = Vmax/(Pm .d) = 1211.34 KN/m2
ßc = Width of col/depth of col = 250/250 = 1
bc = 2.(b+d+2.deff) = 2660 mm
V1 = (2+4/ßc)√fc.bc.d = 0.083x(2+4/1)x√25 x 2660 x 415x 1/1000 = 2748.7KN
V2 = (40.d/b+2)√fc.bc.d = 0.083x(40x 415/2660+2)x√25 x 2660 x 415x1/1000 = 3775.17 KN
V3 = 4.√fc.bc.de =0.083 x 4 x √25 x 2660 x 415x 1/1000 =1832.47 KN
Vc =min(V1,V2,V3) =1832.47
230 — STAAD Foundation Advanced V8i
Chapter — 5
5.6 US General Isolated Foundation 6
So, 0.75Vc = 1374.35 KN
Vm < 0.75.Vc , Hence safe
Check for One-Way Shear
Along X Direction
Vumax = 141.993 x 3.14 x ((3.14-0.25)/2-0.415) = 459.23 KN
Now allowable shear = Vc1 =2√fc.b.d = 0.083x2x√25 x 3140 x 415x 1/1000 =1081.57 KN
0.75.Vc1=811.18 KN
V < Vc1, Hence Safe
So Vumax < Vc1 , Hence Safe
Along Z Direction
Vumax = 141.993 x 3.14 x ((3.14-0.25)/2-0.415) = 459.23 KN
Now allowable shear = Vc1 =2√fc.b.d =0.083x2x√25 x 3140 x 415x 1/1000 =1081.57 KN
0.75.Vc1=811.18 KN
V < Vc1, Hence Safe
So Vumax < Vc1 , Hence Safe
Check For Trial Depth Against Moment
About X Axis
m = fy/0.85.fc = 415/(0.85x25) = 19.529
ß1 = 0.85 ( as fc < 27.6 N/mm2)
ρbal = 0.85.ß1.fc.87/fy.(87 + fy) = 0.025759
ρmax = 0.75. ρbal = 0.0193
ρmin = 0.0018 ( as fy = 415 N/mm2)
Bending moment at critical section, Mux = 1/2 x 141.993 x 3.14 x [(3.14-0.25)/2)]2 = 465.48 KNm
So Resisting Moment = Mnz = Muz/Ø = 517.2 KNm
Rn = Mnz/b.d2 = 0.956 N/mm2
2m.Rn/fy < 1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002359
Ρmin < ρ < ρmax Hence OK
Section 5 United States Code (ACI 318 -2005)
5.6 US General Isolated Foundation 6
Verification Manual — 231
About Z Axis
m = fy/0.85.fc = 415/(0.85x25) = 19.529
ß1 = 0.85 ( as fc < 27.6 N/mm2)
ρbal = 0.85.ß1.fc.87/fy.(87 + fy) = 0.025759
ρmax = 0.75. ρbal = 0.0193
ρmin = 0.0018 ( as fy = 415 N/mm2)
Bending moment at critical section, Muz = 1/2 x 141.993 x 3.14 x [(3.14-0.25)/2)]2 = 465.48 KNm
So Resisting Moment = Mnz = Muz/Ø = 517.2 KNm
Rn = Mnz/b.d2 = 0.956 N/mm2
2m.Rn/fy < 1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002359
Ρmin < ρ < ρmax Hence OK
Area of Steel Required
Along X Direction
ρz = 0.002359
Therefore, Astx = ρz.b.d = 3074 m2m
Along Z Direction
ρx = 0.002359
Therefore, Astz = ρx.b.d = 3074 m2m
232 — STAAD Foundation Advanced V8i
Chapter — 5
5.6 US General Isolated Foundation 6
5.6.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Effective Depth 415 mm 415 mm NoneBearing Pressure 119.92 KN/m2 119.96 KN/m2 NoneResisting force for sliding 472.936 KN
472.936 KN
472.945 KN
472.945 KN
None
Resisting Moment for Over-turning
1856.23 KNm
1856.23 KNm
1856.276 KNm
1856.276 KNm
Negligible
Governing Moment 465.48 KNm
465.48 KNm
465.48 KNm
465.48 KNm
None
Shear Force(One-Way) 459.23 KN
459.23 KN
459.4 KN
459.4 KN
Negligible
Shear Resistance (One-Way) 811.18 KN
811.18 KN
810.737 KN
810.737 KN
Negligible
Shear Force(Two-Way) 1337.2 KN 1337.28 KN NoneShear Resistance (Two-Way) 1374.35 KN 1372.8 KN NegligibleReinf X 3074 m2m 3076.9 m2m NegligibleReinf Z 3074 m2m 3076.9 m2m Negligible
Table 5-6: US verification example 6 comparison
5.7 US General Isolated Foundation 75.7.1 Reference
5.7.2 ProblemDesign an isolated footing with the given data: Load Fy = -1200 KN, Fx=Fz=5 KN,Mx=Mz=10 KNm. fc = 25 N/m2m, fy = 415 N/m2m, Column Dimension = 250 mm x 250mm, and Bearing Capacity of Soil = 120 KN/m2. Assume 500 mm soil depth above footingand depth of GWT 200 mm. Assume unit weight of concrete & soil are 25 & 18 KN/cumrespectively. Coefficient of friction =0.4, FOS against sliding =1.4, FOS against overturning=1.4
Section 5 United States Code (ACI 318 -2005)
5.7 US General Isolated Foundation 7
Verification Manual — 233
Figure 5-10: Elevation and Plan
5.7.3 SolutionApproximate area of footing required = 1200/120 = 10 m2
Assuming 3500 mm x 3500 mm x 540 mm footing dimension,
Weight of footing = 3.5 x 3.5 x 0.54 x 25 = 165.38 KN
Weight of soil = (3.5 x 3.5- 0.25 x 0.25) x 0.5 x 18 = 109.69 KN
Weight reduction for Buoyancy = 3.5 x 3.5 x (0.54 + 0.5 – 0.2) x 9.81 =100.95 KN
Surcharge Load = (3.5 x 3.5 – 0.25 x 0.25) x 5 = 60.94 KN
Therefore, total Axial load on the footing = 1435.063 KN
Total Moment on the footing-
Mx = 10 + 5x 0.54 = 12.7 KNm
Mz = 10 - 5x 0.54 = 7.3 KNm
Zx = 3.5x3.52 /6 = 7.1458 cum
Zz = 3.5x3.52 /6 = 7.1458 cum
Maximum pressure from axial load = 1435.063 /(3.5 x 3.5) = 117.15 KN/m2
Mx/Zx = 12.7 /7.1458 = 1.78 KN/m2
Mz/Zz = 7.3 /7.1458 = 1.03 KN/m2
234 — STAAD Foundation Advanced V8i
Chapter — 5
5.7 US General Isolated Foundation 7
So stress at four corners –
σ1 = P/A-Mx/Zx+Mz/Zz= 116.39 KN/m2
σ2 = P/A-Mx/Zx-Mz/Zz= 114.35 KN/m2
σ3 = P/A+Mx/Zx-Mz/Zz = 117.09 KN/m2
σ4 = P/A+Mx/Zx+Mz/Zz= 119.94 KN/m2
Max stress = 119.94 KN/m2 < 120 KN/m2 (Hence safe)
Critical load case and the governing factor of safety foroverturning and sliding
Along X Direction
For Sliding
Sliding force = 5 KN
max Resisting force = µ x Total Service load on foundation = 0.4 x 1435.063 =574 KN
Hence OK
Along Z Direction
Sliding force = 5 KN
max Resisting force = µ x Total Service load on foundation = 0.4 x 1435.063 =574 KN
Hence OK
For Overturning
About X Direction
Overturning Moment = 12.7 KNm
max resisting Moment = 0.5x 3.5 x 1435.063 = 2511.36 KNm
FOS= 2511.36/12.7 = 197.75 > 1.4
Hence OK
About Z Direction
Overturning Moment = 7.3 KNm
max resisting Moment = 0.5x 3.5 x 1435.063 = 2511.36 KNm
FOS= 2511.36/7.3 = 344 > 1.4
Hence OK
Section 5 United States Code (ACI 318 -2005)
5.7 US General Isolated Foundation 7
Verification Manual — 235
Section Design
Fy = -1.4 x 1200 KN = -1680 KN
Fx = 1.4 x 5 KN = 7 KN
Fz = 1.4 x 5 KN = 7 KN
Mx = 1.4 x 10 KNm = 14 KNm
Mz = 1.4 x 10 KNm = 14 KNm
Modifying Moments due to lateral forces:
Mx= 17.78 KNm & Mz= 10.22 KNm
D= 540 mm, So deff = 650- 50-25 = 465 mm
Punching Shear
Punching shear is checked on a perimeter 0.5d = 232.5 from the column face.
Effective Depth= 465 mm
Punching Shear bc = 1609.9 KN = 1610 KN
Figure 5-11: Corner pressure values on plan for punching shear
Critical perimeter Pm = 2 X ( b + h + 2 x d) = 2860 mm
Vm1 = Vmax/(bc .d) = 1.21 N/m2m
ßc = Width of col/depth of col=250/250=1
V1 = (2+4/ßc)√fc.bc.d = 3311.45 KN
V2 = (40.d/b+2)√fc.bc.d = 4693.15 KN
V3 = 4.√fc.bc.de=2207.63 KN
236 — STAAD Foundation Advanced V8i
Chapter — 5
5.7 US General Isolated Foundation 7
Vc =min(V1,V2,V3) = 2207.63 KN
So, 0.75Vc = 1655.73 KN
Vm< 0.75xVc , Hence safe
Check for One-Way Shear
Along X Direction
Critical Section for shear is at d distance from face of column
Average Base pressure at left edge = 134.66 KN/m2
Average Base pressure at right edge = 139.64 KN/m2
Approximate Base pressure at left critical section = 136.311 KN/m2
Approximate Base pressure at right critical section = 137.99 KN/m2
Figure 5-12: One-way shear pressure values along x-direction
Hence Maximum Shear Force at critical section = 563.589 KN
Now allowable shear = Vc1 = 2√fc.b.d= 1350.825 KN
0.75.Vc1 = 1013.12 KN
So Vumax < 0.75x Vc1 , Hence Safe
Along Z Direction
Critical Section for shear is at d distance from face of column
Average Base pressure at left edge = 138.59 KN/m2
Average Base pressure at right edge = 135.71 KN/m2
Approximate Base pressure at left critical section = 137.636 KN/m2
Approximate Base pressure at right critical section = 136.665 KN/m2
Section 5 United States Code (ACI 318 -2005)
5.7 US General Isolated Foundation 7
Verification Manual — 237
Figure 5-13: One-way shear pressure values along z-direction
Hence Maximum Shear Force at critical section = 561 KN
Now allowable shear = Vc1 = 2√fc.b.d = 1350.825 KN
0.75.Vc1 = 1013.12 KN
So Vumax < 0.75x Vc1 , Hence Safe
Check For Flexure
Critical Section for Moment is at the face of column
m = fy/0.85.fc = 19.5295
ß1 = 0.85 (as fc=M 25)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.025729
ρmax = 0.75. ρbal = 0.019297
ρmin = 0.0018
Check For Trial Depth Against Moment
About Z Axis
Average Base pressure at left edge = 138.59 KN/m2
Average Base pressure at right edge = 135.71 KN/m2
Approximate Base pressure at left critical section = 137.26 KN/m2
Approximate Base pressure at right critical section = 137.05 KN/m2
238 — STAAD Foundation Advanced V8i
Chapter — 5
5.7 US General Isolated Foundation 7
Figure 5-14: Bending pressure about Z axis
So Maximum Bending Moment at Critical Section = 638.54 KNm
So Resisting Moment = Mnz = Muz/Ø = 710 KNm
Rn = Mnz/b.d2 = 0.93822 N/m2m
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002313
Ρmin < ρ < ρmax Hence OK
About X Axis
Average Base pressure at left edge = 134.66 KN/m2
Average Base pressure at right edge = 139.64 KN/m2
Approximate Base pressure at left critical section = 136.98 KN/m2
Approximate Base pressure at right critical section = 137.33 KN/m2
Figure 5-15: Bending pressure about X axis
So Maximum Bending Moment at Critical Section = 641.93 KNm
So Resisting Moment =Mnz= Muz/Ø = 642 KNm
Section 5 United States Code (ACI 318 -2005)
5.7 US General Isolated Foundation 7
Verification Manual — 239
Rn = Mnz/b.d2 = 0.9426 N/m2m
2m.Rn/fy < 1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002325
Ρmin < ρ < ρmax Hence OK
Area of Steel Required
Along X Direction
ρz = 0.002313
Therefore, Astx = ρz.b.d = 3765 m2m
Along Z Direction
ρx = 0.002325
Therefore, Astz = ρx.b.d = 3784 m2m
5.7.4 Comparison
Value of Reference ResultSTAAD Foun-
dationResult
Percent Dif-ference
Effective Depth 540 mm 540 mm NoneBearing Pressure 116.39 KN/m2
114.35 KN/m2
117.9 KN/m2
119.95 KN/m2
116.397 KN/m2
114.35 KN/m2
117.91 KN/m2
119.95 KN/m2
None
Resisting force for sliding 574.05 KN (Xdir)
574.05 KN (Zdir
574.05 KN (Xdir)
574.05 KN (Zdir)
None
Resisting Moment for Over-turning
2511 KNm (WRTZ)
2511 KNm (WRTX)
2511 KNm (WRTZ)
2511 KNm (WRTX)
None
Governing Moment 639 KNm
642 KNm
638 KNm
642 KNm
Negligible
Shear Force(One-Way) 564 KN
561 KN
564 KN
561 KN
Negligible
Shear Force(Two-Way) 1610 KN 1610 KN None
Table 5-7: US Verification problem 9 comparison
240 — STAAD Foundation Advanced V8i
Chapter — 5
5.7 US General Isolated Foundation 7
5.8 US General Combined Foundation 15.8.1 Reference
5.8.2 ProblemDesign a combined footing with the given data: Load Fy = 60 Kip each column., fc = 4 Ksi,fy = 60 Ksi, Column Dimension = 12 inch x 12 inch, Pedestal height-20 inch. and C/Ccolumn distance=195 inch . Bearing Capacity of Soil = 2 Kip/sqft. Coefficient of friction=0.5, FOS against sliding =1.5, FOS against overturning =1.5
Ht of soil =24 inch. Depth of GWT=10 inch
5.8.3 SolutionFigure 5-16: Elevation and Plan
Approximate area of footing required = 2x60/2 sqft = 60 sqft
Assuming 275 inch x40 inch x 24 inch footing dimension,
( left overhang=right overhang = 40 inch)
Weight of footing = 275 x 40 x 24 x 0.159/123 = 24.3Kip
Section 5 United States Code (ACI 318 -2005)
5.8 US General Combined Foundation 1
Verification Manual — 241
Weight of pedestal=2 x 12 x 12 x 20 x 0.159 /123 = 0.530 kip
Weight of soil above footing = (275 x 40-2x12x12) x 24 x 0.127/123 = 18.9 Kip
Reduction of Weight due to buoyancy = 275 x 40 x (24 +24-10) x3.61398x10-5 = 15.1Kip
Therefore, total load on the footing = (2x60+24.3+18.9- 15.1) = 148.624 Kip
Maximum pressure= 148.624 /(275x40) = 0.0136 Ksi = 1.9584 Kip/sqft < 2Kip/sqft
Hence safe
Ultimate pressure = 1.4x2x60/(275x40) = 0.015273 Ksi
Critical load case and the governing factor of safety foroverturning
With Respect to Z Direction
Overturning Moment =0
max resisting Moment = 0.5 x 275x 148.624 = 20435.8 in·kip
Hence OK
With Respect to X Direction
Overturning Moment =0
max resisting Moment = 0.5 x 40x 148.624 = 2972.48 in·kip
Hence OK
242 — STAAD Foundation Advanced V8i
Chapter — 5
5.8 US General Combined Foundation 1
Figure 5-17: Shear Force and Bending Moment diagrams
Punching Shear
For Column 1
Punching shear is checked on a perimeter 0.5d = 10.5 inch from the column face.
deff = (24-2-1) inch = 21 inch
2 way shear Vm = 67.37 Kip
ßc=Width of col/depth of col=12/12=1
Section 5 United States Code (ACI 318 -2005)
5.8 US General Combined Foundation 1
Verification Manual — 243
bc=2.(b+d+2.deff)=132 inch
V1 √fc.bc.d = (2+4/1).√(4000) x132x21 = 1051900 lb
V2 √fc.bc.d = (40x21/132+2).√(4000) x132x21 = 1466284.9lb
V3= 4.√fc.bc.de = 4.√(4000) x132x21 = 701266.694 lb
Vc = min{V1, V2, V3} = 701266.694 lb
So, 0.75Vc=525.95 Kip
Vm< 0.75xVc , Hence safe
For Column 2
Punching shear is checked on a perimeter 0.5d = 10.5 inch from the column face.
deff = (24-2-1) inch = 21 inch
2 way shear Vm = 67.37 Kip
ßc=Width of col/depth of col=12/12=1
bc=2.(b+d+2.deff)=132 inch
V1 √fc.bc.d = (2+4/1).√(4000) x132x21 = 1051900 lb
V2 √fc.bc.d = (40x21/132+2).√(4000) x132x21 = 1466284.9lb
V3 = 4.√fc.bc.de = 4.√(4000) x132x21 = 701266.694 lb
Vc = min{V1, V2, V3} = 701266.694 lb
So, 0.75Vc=525.95 Kip
Vm< 0.75xVc , Hence safe
Check for One-Way Shear
Vumax = 43.072 Kip
Now allowable shear = Vc1 = = 2x√(4000) x40x21 lb =106.252 Kip
0.75.Vc1=79.69 Kip
So Vumax < 0.75xVc1 , Hence Safe
Check For Trial Depth against moment
About Z Axis (Sagging)
m=fy/0.85.fc=60/(0.85x4) = 17.6471
244 — STAAD Foundation Advanced V8i
Chapter — 5
5.8 US General Combined Foundation 1
ß1 = 0.85 (as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.021381
ρmin = 0.0018 ( as fy=60)
Bending moment at critical section
Mux = 488.74 in·kip
deff = (24-2-1) inch = 21 inch
So Resisting Moment =Mnz= Muz/Ø =543.04 in·kip
Rn = Mnx/b.d2 = 0.0308 Ksi
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.000516
Hence OK
About Z Axis (Hogging)
m=fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 (as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.021381
ρmin = 0.0018 ( as fy=60
Bending moment at critical section
Mux = 2414.897 in·kip
deff = (24-2-1) inch = 21 inch
So Resisting Moment =Mnz= Muz/Ø =2683.219 in·kip
Rn = Mnx/b.d2 = 0.1522 Ksi
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.002597
ρmax Hence OK
With Respect to the X Axis
m=fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 (as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.021381
ρmin = 0.0018 ( as fy=60
Section 5 United States Code (ACI 318 -2005)
5.8 US General Combined Foundation 1
Verification Manual — 245
Cantilever length=(40-12)/2 = 14 inch
Bending moment at critical section
Mux = 411.608 in·kip
deff = (24-2-1) inch = 21 inch
So Resisting Moment =Mnz= Muz/Ø =457.34 in·kip
Rn = Mnx/b.d2 = 0.0038 Ksi
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.000064
Hence OK
Reinforcement Calculation
ρz (top) = 0.002597
ρz (bot) = 0.0018
ρx = 0.0018
Therefore, Ast =ρ*b*d
Area of Steel Required along X dir ( bot) = 1.512 in2
Area of Steel Required along X dir (top) = 2.18 in2
Area of Steel Required along Z dir ( bot) = 10.395 in2
5.8.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 0.0136 Ksi 0.0135 Ksi NegligibleGoverning Moment 488.736
in·kip
2414.897in·kip
411.608in·kip
461.95 in·kip
2414.41 in·kip
411 in·kip
Negligible
Shear Force(One-Way) 42.73 Kip 43.07 Kip NegligibleShear Force(Two-Way) 66.8 Kip
66.8 Kip
67.37 Kip
67.37 Kip
Negligible
Resisting Moment forOverturning
2972.44in·kip
20435.52in·kip
2972.48 in·kip
20435.8 in·kip
Negligible
Table 5-8: US verification example 7 comparison
246 — STAAD Foundation Advanced V8i
Chapter — 5
5.8 US General Combined Foundation 1
5.9 US General Combined Foundation 25.9.1 Reference
5.9.2 ProblemDesign a combined footing with the given data: Load Fy = 60 Kip, Mz=360 in·kip for eachcolumn., fc = 4 Ksi, fy = 60 Ksi, Column Dimension = 12 inch x 12 inch, Pedestal height-20 inch. and C/C column distance=195 inch . Bearing Capacity of Soil = 2 Kip/sqft.Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
Figure 5-18: Elevation and Plan
5.9.3 SolutionApproximate area of footing required = 2x60/2 sqft = 60 sqft
Assuming 275 inch x44 inch x 24 inch footing dimension,
( left overhang=right overhang = 40 inch)
Weight of footing = 275 x 44 x 24 x 0.159/123 = 26.73 Kip
Weight of pedestal=2x12x12x20x0.159/123 = 0.530 kip
Therefore, total load on the footing = (2x60+26.73 +0.530) Kip = 147.26 Kip
Maximum pressure from axial load= P/A = 147.26 /(275x44) = 0.0122 Ksi
Mz=360+360=720 Kip
Mz=0
Section 5 United States Code (ACI 318 -2005)
5.9 US General Combined Foundation 2
Verification Manual — 247
Zz= 44x2752/6 = 554583.334 inch3
Mz/Zz = 720/554583.334 =0.0013 Ksi
So, stress at left end
σ1 = P/A + Mz/Zz = 0.0135 Ksi
stress at right end
σ1 = P/A - Mz/Zz = 0.0109 Ksi
So maximum stress= 0.0135 Ksi= 1.944 Kip/sqft < 2 Kip/sqft
Hence safe
Critical load case and the governing factor of safety foroverturning
wrt Z Direction
Overturning Moment =0
max resisting Moment = 0.5 x 275x 147.26 = 20248.25 in·kip
Hence OK
Wrt X Direction
Overturning Moment =0
max resisting Moment = 0.5 x 44x 147.26 = 3239.72 in·kip
Hence OK
Punching Shear
For Column One
Punching shear is checked on a perimeter 0.5d = 10.5 inch from the column face.
deff = (24-2-1) inch = 21 inch
2 way shear Vm = 67.48 Kip
ßc=Width of col/depth of col=12/12=1
bc=2.(b+d+2.deff)=132 inch
V1 √fc.bc.d = (2+4/1).√(4000) x132x21 = 1051900 lb
V2 √fc.bc.d = (40x21/132+2).√(4000) x132x21 = 1466284.9lb
V3= 4.√fc.bc.de = 4.√(4000) x132x21 = 701266.694 lb
248 — STAAD Foundation Advanced V8i
Chapter — 5
5.9 US General Combined Foundation 2
Vc = min{V1, V2, V3} = 701266.694 lb
So, 0.75Vc=525.95 Kip
Vm< 0.75xVc , Hence safe
For Column Two
Punching shear is checked on a perimeter 0.5d = 10.5 inch from the column face.
deff = (24-2-1) inch = 21 inch
2 way shear Vm = 70.28 Kip
ßc=Width of col/depth of col=12/12=1
bc=2.(b+d+2.deff)=132 inch
V1 √fc.bc.d = (2+4/1).√(4000) x132x21 = 1051900 lb
V2 √fc.bc.d = (40x21/132+2).√(4000) x132x21 = 1466284.9 lb
V3 = 4.√fc.bc.de = 4.√(4000) x132x21 = 701266.694 lb
Vc= min{V1, V2, V3} = 701266.694 lb
So, 0.75Vc=525.95 Kip
Vm< 0.75xVc , Hence safe
Check for One-Way Shear
Vumax = 47.126 Kip
Now allowable shear = Vc1 = = 2x√(4000) x44x21 lb =116.877 Kip
0.75.Vc1=87.66 Kip
So Vumax < 0.75xVc1 , Hence Safe
Check For Trial Depth against moment
About Z Axis (sagging)
m=fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 (as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.0214
ρmin = 0.0018 ( as fy=60)
Bending moment at critical section, Mux = 791 in·kip
deff = (24-2-1) inch = 21 inch
So Resisting Moment =Mnz= Muz/Ø =879 in·kip
Section 5 United States Code (ACI 318 -2005)
5.9 US General Combined Foundation 2
Verification Manual — 249
Rn = Mnx/b.d2 = 0.0453 Ksi
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.000761
Hence OK
About Z Axis (hogging)
m=fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 (as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.0214
ρmin = 0.0018 ( as fy=60
Bending moment at critical section, Mux = 2440 in·kip
deff = (24-2-1) inch = 21 inch
Ø = 0.9
So Resisting Moment =Mnz= Muz/Ø =2711.1967 in·kip
Rn = Mnx/b.d2 = 0.1398 Ksi
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.00238
ρmax Hence OK
About X Axis
m=fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 (as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.0214
ρmin = 0.0018 ( as fy=60
Cantilever length=(40-12)/2 = 14 inch
Bending moment at critical section, Mux = 0.013885x275x162/2 =552.82in·kip
deff = (24-2-1) inch = 21 inch
So Resisting Moment =Mnz= Muz/Ø =614.24 in·kip
Rn = Mnx/b.d2 = 0.0051 Ksi
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.000086
Hence OK
250 — STAAD Foundation Advanced V8i
Chapter — 5
5.9 US General Combined Foundation 2
Reinforcement Calculation
ρz (bot) = 0.0018
ρz (top) = 0.00238
ρx(bot) = 0.0018
Therefore, Ast = ρ*b*d
Area of Steel Required along X dir ( bot) = 1.7 in2
Area of Steel Required along X dir (top) = 2.2 in2
Area of Steel Required along Z dir ( bot) = 10.4 in2
Section 5 United States Code (ACI 318 -2005)
5.9 US General Combined Foundation 2
Verification Manual — 251
Figure 5-19: Shear Force and Bending Moment diagrams
252 — STAAD Foundation Advanced V8i
Chapter — 5
5.9 US General Combined Foundation 2
5.9.4 Comparison
Value of Reference ResultSTAAD
FoundationResult
Percent Dif-ference
Bearing Pressure 0.0135 Ksi
0.0109 Ksi
0.0135 Ksi
0.0109 Ksi
None
Governing Moment 791 in·kip
2440 in·kip
552.82 in·kip
830 in·kip
2439.66in·kip
534 in·kip
Negligible
Shear Force(One-Way) 47.126 Kip 46.8 Kip NegligibleShear Force(Two-Way) 67.48 Kip
70.28 Kip
66.91 Kip
69.81 Kip
Negligible
Resisting Moment forOverturning
3239.72 in·kip20248.25 in·kip
3239.518in·kip
20246.985in·kip
Negligible
Table 5-9: US verification example 8 comparison
5.10 US General Combined Foundation 35.10.1 Reference
5.10.2 ProblemDesign a combined footing with the given data: Load Fy = 1500 KN on each column.,Concrete Grade = M 25, Steel Grade Fe 415, Column Dimension = 250 mm x250 mm,Pedestal height-500 mm each. and C/C column distance=5000 mm . Bearing Capacity ofSoil = 120 KN/m2., FOS against overturning =1.4
Ht of soil =500 mm. Depth of GWT=200 mm
Section 5 United States Code (ACI 318 -2005)
5.10 US General Combined Foundation 3
Verification Manual — 253
5.10.3 SolutionFigure 5-20: Elevation and Plan
Approximate area of footing required = 2x1500/120 = 25 m2
Assuming 7000 mm 4500 mm x 840 mm footing dimension,
( left overhang=right overhang = 1000 mm)
Weight of footing = 7 x 4.5 x 0.84 x 25 = 661.5 KN
Weight of pedestal=2 x 0.25 x 0.25 x 0.5 x 25 = 1.5625 KN
Weight of soil above footing = (7 x 4.5- 0.25 x0.25 x 2) x 0.5 x 18 = 282.375 KN
Reduction of Weight due to buoyancy = 7 x 4.5 x (0.84+0.5-0.2) x 9.81 = 352.277 KN
Surcharge = (7 x 4.5 -0.25 x0.25 x2) x 5 = 156.875 KN
Therefore, total load on the footing = (2x1500+661.5 +1.5625 - 352.277 +156.875) = 3750.04KN
Maximum pressure= 3750.04 /(7 x 4.5) = 119.05 KN/m2 =119.05 KN/m2 120 KN/m2
Hence safe
254 — STAAD Foundation Advanced V8i
Chapter — 5
5.10 US General Combined Foundation 3
Critical load case and the governing factor of safety foroverturning
With Respect to Z Direction
Overturning Moment =0
max resisting Moment = 0.5 x 7x 3750 = 13125 KNm
Hence OK
With Respect to X Direction
Overturning Moment =0
max resisting Moment = 0.5 x 4.5 x 3750 = 8437.5 KNm
Hence OK
Ultimate design
Ultimate pressure = 1.4 x 2 x1500/(7 x 4.5) = 133.33 KN/m2
Deff = 784 mm
Figure 5-21: Shear Force and Bending Moment diagrams
Punching Shear
For Column 1
Punching shear is checked on a perimeter 0.5d = 392 mm from the column face.
Section 5 United States Code (ACI 318 -2005)
5.10 US General Combined Foundation 3
Verification Manual — 255
2 way shear Vm = 1957.5 KN
ßc = Width of col/depth of col=250/250 = 1
bc = 2·(b + d + 2·deff) = 4136 mm
V1= (2 + 4/βc)√(fc·bc·d) = 8074 KN
V2 = (40·d/b + 2)√fc.bc.d = 12894.7 KN
V3= 4.√fc·bc·de = 5382.76 KN
Vc = min(V1, V2, V3) = 5382.76 KN
So, 0.75·Vc = 4037 KN
Vm < 0.75·Vc , Hence safe
For Column 2
Punching shear is checked on a perimeter 0.5d = 392 mm from the column face.
2 way shear Vm = 1957.5 KN
ßc = Width of col/depth of col=250/250 = 1
bc = 2·(b + d + 2·deff) = 4136 mm
V1= (2 + 4/βc)√(fc·bc·d) = 8074 KN
V2 = (40·d/b + 2)√fc·bc·d = 12894.7 KN
V3= 4·√fc·bc·de = 5382.76 KN
Vc = min(V1, V2, V3) = 5382.76 KN
So, 0.75·Vc = 4037 KN
Vm< 0.75xVc , Hence safe
Check for One-Way Shear
Vumax = 954 KN
Now allowable shear = Vc1 = 2 √fc·b·d = 2928 KN
0.75·Vc1 = 2196 KN
So Vumax < 0.75·Vc1 , Hence Safe
Check For Trial Depth against moment
m=fy/0.85.fc=415/(0.85x25) = 19.5295
ß1 = 0.85 (as fc=25 N/m2m)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.025729
ρmax = 0.75. ρbal = 0.019297
ρmin = 0.0018 ( as fy=415 N/m2m)
256 — STAAD Foundation Advanced V8i
Chapter — 5
5.10 US General Combined Foundation 3
About Z Axis (Sagging)
Bending moment at critical section
Muz = 300.54 KNm
So Resisting Moment =Mnz= Muz/Ø =333.93 KNm
Rn = Mnz/b.d2 = 0.1208 N/m2m
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.000292 <ρmax Hence OK
Take ρ = ρmin = 0.0018
Hence OK
About Z Axis (Hogging)
Bending moment at critical section
Muz = 1574.8 KNm
So Resisting Moment =Mnz= Muz/Ø =1749.8 KNm
Rn = Mnz/b.d2 = 0.6327 N/m2m
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.001548 <ρmax Hence OK
Take ρ = ρmin = 0.0018
Hence OK
With Respect to the X Axis
Cantilever length = (4500 - 250)/2 = 2125 mm
Bending moment at critical section
Mux = 2107.4 KNm
So Resisting Moment =Mnx= Mux/Ø =2341.55 KNm
Rn = Mnx/b.d2 = 0.762 N/m2m
2m.Rn/fy <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.001871 < ρmax
Hence OK
Reinforcement Calculation
ρz (top) = 0.0018
ρz (bot) = 0.0018
ρx = 0.001871
Section 5 United States Code (ACI 318 -2005)
5.10 US General Combined Foundation 3
Verification Manual — 257
Therefore, Ast =ρ·b·d
Area of Steel Required along X dir ( bot) = 6350 mm2
Area of Steel Required along X dir (top) = 6350 mm2
Area of Steel Required along Z dir ( bot) = 10268 mm2
5.10.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure(KN/m2)
119.05 119.05 None
Governing Moment(KNm)
300.54
1574.82
2107.4
293.97
1574.60
2107.4
Negligible
Shear Force, One-Way (KN)
954.8 43.07 Kip Negligible
Shear Force, Two-Way (KN)
1957.4
1957.4
1957.4
1957.4
None
Table 5-10: US verification example 7 comparison
5.11 US General Combined Foundation 45.11.1 Reference
5.11.2 ProblemDesign a combined footing with the given data: Load Fy = -1200 KN & Fx= 10 KN on eachcolumn., Concrete Grade = M 25, Steel Grade Fe 415, Column Dimension = 250 mm x250mm, Pedestal height-500 mm each. and C/C column distance=5000 mm . BearingCapacity of Soil = 120 KN/m2., FOS against overturning =1.4
258 — STAAD Foundation Advanced V8i
Chapter — 5
5.11 US General Combined Foundation 4
5.11.3 SolutionFigure 5-22: Elevation and Plan
Approximate area of footing required = 2x1200/120 = 20 m2
Assuming 7000 mm 3250 mm x 530 mm footing dimension,
( left overhang=right overhang = 1000 mm)
Weight of footing = 7 x 3.25 x 0.53 x 25 = 301.44 KN
Weight of pedestal=2 x 0.25 x 0.25 x 0.5 x 25 = 1.5625 KN
Therefore, total load on the footing = (2x1200+301.44 +1.5625) = 2703 KN
Mz1 = -10 x (0.5+0.53) = -10.3 KNm
Mz2 = -10 x (0.5+0.53) = -10.3 KNm
Maximum pressure from axial load= 2703/(7 x3.25) = 118.813 KN/ m2
Total Moment = -10.3 + -10.3 = -20.6 KNm
CG of load= 3.5085 m
CG of raft = 3.5 m
Eccentricity =-8.5833 mm
Section 5 United States Code (ACI 318 -2005)
5.11 US General Combined Foundation 4
Verification Manual — 259
So Moment= P x Eccentricity = -20.6 KNm
Hence OK
Zz= 3.25 x 72/6 = 26.542 m3
So M/Z = -0.78 KN/m2
So stress at left end= P/A - M/Z= 118.04 KN/m2
So stress at right end= P/A + M/Z= 119.6 KN/m2
Maximum pressure =119.6 KN/m2 120 KN/m2
Hence safe
Critical load case and the governing factor of safety foroverturning
With Respect to Z Direction
Overturning Moment =20.6 KNm
max resisting Moment = 0.5 x 7x 2703 = 9460 KNm
So FOS= 9460/20.6 = 459.25 >1.4
Hence OK
With Respect to X Direction
Overturning Moment =0
max resisting Moment = 0.5 x 3.25x 2703 = 4392.4 KNm
Hence OK
Ultimate design
Ultimate pressure from axial load = 1.4 x 2 x1200/(7 x 3.25) = 147.692 KN/m2
Mz1 = 1.4x-10 x90.5+0.53) = -14.42 KNm
Mz2 = 1.4x-10 x90.5+0.53) = -14.42 KNm
Total Moment = -14.42 + -14.42 = -28.84 KNm
CG of load= 3.5085 m
CG of raft = 3.5 m
Eccentricity =-8.5833 mm
So Moment= P x Eccentricity = -28.84 KNm (Hence OK)
Zz= 3.25 x 72/6 = 26.542 m3
So M/Z = -1.09 KN/m2
So stress at left end= P/A - M/Z= 146.61 KN/m2
260 — STAAD Foundation Advanced V8i
Chapter — 5
5.11 US General Combined Foundation 4
So stress at right end= P/A + M/Z= 148.79 KN/m2
Deff = 474 mm
Figure 5-23: Shear Force and Bending Moment diagrams
Punching Shear
For Column 1
Punching shear is checked on a perimeter 0.5d = 392 mm from the column face.
Two way shear, Vm = 1602.987 KN
Section 5 United States Code (ACI 318 -2005)
5.11 US General Combined Foundation 4
Verification Manual — 261
ßc = Width of col/depth of col=250/250 = 1
bc = 2·(b + d + 2·deff) = 2896 mm
V1= (2 + 4/βc)√(fc)·bc·d = 3418 KN
V2 = (40·d/b + 2)√(fc)·bc·d = 4868.97 KN
V3= 4.√(fc)·bc·de = 2278.69 KN
Vc = min(V1, V2, V3) = 2278.69 KN
So, 0.75·Vc = 1709 KN
Vm < 0.75·Vc , Hence safe
For Column 2
Punching shear is checked on a perimeter 0.5d = 392 mm from the column face.
Two way shear, Vm = 1602.17 KN
ßc = Width of col/depth of col=250/250 = 1
bc = 2·(b + d + 2·deff) = 2896 mm
V1= (2 + 4/βc)√(fc)·bc·d = 3418 KN
V2 = (40·d/b + 2)√(fc)·bc·d = 4868.97 KN
V3= 4.√(fc)·bc·de = 2278.69 KN
Vc = min(V1, V2, V3) = 2278.69 KN
So, 0.75·Vc = 1709 KN
Vm< 0.75·Vc , Hence safe
Check for One-Way Shear
Vumax = 916.99 KN
Now allowable shear = Vc1 = 2 √(fc)·b·d = 1278 KN
0.75·Vc1 = 958.96 KN
So Vumax < 0.75·Vc1 , Hence Safe
Check For Trial Depth against moment
m = fy/0.85·fc=415/(0.85x25) = 19.53
ß1 = 0.85 (as fc = 25 N/mm2)
ρbal = 0.85·ß1·fc·87/fy·(87 + fy) = 0.025729
ρmax = 0.75·ρbal = 0.0193
ρmin = 0.0018 ( as fy=415 N/mm2)
About Z Axis (Sagging)
Bending moment at critical section
262 — STAAD Foundation Advanced V8i
Chapter — 5
5.11 US General Combined Foundation 4
Muz = 238.94 KNm
So Resisting Moment = Mnz= Muz/φ = 265.5 KNm
Rn = Mnz/b·d2 =0.3636 N/mm2
2·m·Rn/fy <1 , Hence OK
ρ = 1/m· (1-√1-2m·Rn/fy) = 0.000884 <ρmaxHence OK
Take ρ = ρmin = 0.0018
Hence OK
About Z Axis (Hogging)
Bending moment at critical section
Muz = 1259.84KNm
So Resisting Moment = Mnz= Muz/φ = 1400 KNm
Rn = Mnz/b·d2 = 1.9171 N/mm2
2·m·Rn/fy < 1 , Hence OK
ρ = 1/m· (1-√1-2m·Rn/fy) = 0.00485 < ρmaxHence OK
Take ρ = ρmin = 0.0018
Hence OK
With Respect to the X Axis
Cantilever length = (3250-250)/2 = 1500 mm
Bending moment at critical section
Mux = 1163 KNm
So Resisting Moment =Mnx= Mux/φ = 1292 KNm
Rn = Mnz/b·d2 =1.593 N/mm2
2·m·Rn/fy < 1 , Hence OK
ρ = 1/m· (1-√1-2m·Rn/fy) = 0.003995 < ρmaxHence OK
Reinforcement Calculation
ρz (top) = 0.0018
ρz (bot) = 0.0018
ρx = 0.004
Therefore, Ast =ρ·b·d
Section 5 United States Code (ACI 318 -2005)
5.11 US General Combined Foundation 4
Verification Manual — 263
Area of Steel Required along X dir ( bot) = 2773 mm2
Area of Steel Required along X dir (top) = 7472 mm2
Area of Steel Required along Z dir ( bot) = 13256 mm2
5.11.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure(KN/m2)
119.6
118.04
119.6
118.04
None
Governing Moment(KNm)
239
1260
1163
237
1260
1169
Negligible
Shear Force, One-Way (KN)
917 917 None
Shear Force, Two-Way (KN)
1602.99
1602.17
1602.99
1602.18
None
Table 5-11: US verification example 7 comparison
5.12 US Pilecap Foundation 15.12.1 Reference
5.12.2 ProblemDesign pilecap foundation with the given data: Load Fy = 330 kip, fc = 4 ksi, fy = 60 ksi,Column Dimension = 12 in x 12 in. Pedestal ht= 20 in.
Dia of pile= 18 in
Vertical capacity = 65 kip
Horizontal capacity = 20 kip
Uplift capacity = 15 kip
264 — STAAD Foundation Advanced V8i
Chapter — 5
5.12 US Pilecap Foundation 1
Figure 5-24: Elevation and Plan
5.12.3 SolutionDepth of pilecap= 1.5 x pile diameter, D = 27 in.
Take D = 31 in.
c/c pile distance = 3 x pile diameter =54 mm
Edge distance =18 inch
Assuming 6 pile combination, coordinates of piles (considering pedestal at 0,0,0):
Section 5 United States Code (ACI 318 -2005)
5.12 US Pilecap Foundation 1
Verification Manual — 265
PileNo
X Coor-dinate (in)
Z Coor-dinate (in)
1 -54 -272 -54 273 0 -274 0 275 54 -276 54 27
Table 5-12: Pile Coordinates in Plan
Pilecap Length = 2(54)+2(18) = 144 inch
Pilecap Width = 54+2(18) = 90 inch
pilecap dimension is 144 inch x90 inch x 31 inch
Weight of footing = 144 x 90 x 31 x 0.16/123 = 37.2 kip
Weight of pedestal = 12 x 12 x 20 x 0.16 /123 = 0.267 kip
Therefore, total load on the pilecap = (330+37.2 +0.267) =367.467 kip
So Pile reaction = 367.467 /6= 61.244 kip < 65 kip
Hence OK
As there is no lateral load , moment or uplift force, so each pile is safe in lateral & upliftcapacity.
Factored Design
Load factor for self wt is taken = 1
Load factor for axial load is taken = 1.4
So, Load on pilecap = 1.4(330) + 1(37.2)+0 1(.267) = 499.467
Load on each pile =499.467/6=83.245 kip
266 — STAAD Foundation Advanced V8i
Chapter — 5
5.12 US Pilecap Foundation 1
Punching ShearFigure 5-25: Section considered for punching shear
Punching shear is checked on a perimeter 0.5d =13inch from the column face.
Contribution from pile 1 = from pile2 = from pile5 = from pile 6 = 83.245 kip
Contribution from pile 3 = from pile4 = 0.944 x 83.245 = 78.58 kip
So total punching shear Vm= 490.14 kip
Pm = 4·(12+13+13) =152 inch
ß = L/B =12/12 =1
V1= (2 + 4/βc)√(fc)·bc·d = (2+4/1)·√(4000)·152·26 =1499.6·(10)3 lb
V2 = (40·d/b + 2)√(fc)·bc·d = (40·26/152 + 2)·√(4000)·152·26 = 2210·(10)3 lb
V3= 4.√(fc)·bc·de = 4·√(4000)·152·26= 999.78·(10)3 lb
Vc = min(V1, V2, V3) = 999.78 kip
So, 0.75·Vc = 749.8 kip
Vm< 0.75·Vc , Hence safe
Punching Shear Check for Corner Piles
Corner piles are 1,2,5,6
Section 5 United States Code (ACI 318 -2005)
5.12 US Pilecap Foundation 1
Verification Manual — 267
Each pile is taking reaction 83.245 kip
d critical = 5.486 inch
Effective depth = 26 inch
d critical< Effective depth, Hence Safe
Calculation of Shear
Parallel to X Axis
For shear wrt X1X1
Contribution from pile 1 =pile2=83.245 Kip
Contribution from pile 3,4,5,6 =0 Kip
So Total V X1X1 = 166.49 Kip
For shear wrt X2X2
Contribution from pile 5 =pile6=83.245 Kip
Contribution from pile 1,2,3,4 =0 Kip
So Total V X2X2 = 166.49 Kip
So V parallel to X direction = 166.49 Kip
Now allowable shear = Vc1 =2√(fc)·bc·d =2·√(4000)·90·26 lb =295.99·(10)3 lb
0.75·Vc1=222 Kip
V < Vc1, Hence Safe
Parallel to Z Axis
For shear wrt Z1Z1
Contribution from pile 1 =pile 6 =pile 7 =83.245 x0.222=18.498 Kip
Contribution from pile 2 =pile 4 =pile 6 =0 Kip
So Total V Z1Z1 = 55.5 Kip
For shear wrt Z2Z2
Contribution from pile 2 =pile 4 =pile 6 =83.245 x0.167=18.498 Kip
Contribution from pile 1 =pile 3 =pile 5 =0 Kip
So Total V Z2Z2 = 55.5 Kip
So V parallel to Z direction = 55.5 Kip
Now allowable shear = Vc1 =2√(fc)·bc·d =2·√(4000)·90·26 lb =295.99·(10)3 lb
0.75·Vc1 = 222 Kip
V < Vc1, Hence Safe
268 — STAAD Foundation Advanced V8i
Chapter — 5
5.12 US Pilecap Foundation 1
Calculation of Moment
For either direction:
m = fy/0.85·fc= 60/(0.85·4) = 17.65
ß1 = 0.85 (as fc = 4)
ρbal = 0.85·ß1·fc·87/fy·(87 + fy) = 0.028507
ρmax = 0.75·ρbal = 0.02138
ρmin = 0.0018 ( as fy= 60 Ksi)
Calculation of Moment about Z Axis
Calculation of Mz-
For moment wrt X1X1
Contribution from pile 1=from pile2=83.245 x 48=3995.76 in·kip
Contribution from pile 3=from pile 4=12 in·kip
Contribution from pile 5,6=0 in·kip
So Total Mz X1X1 = 8014 in·kip = 670 ft·kip
For moment wrt X2X2
Contribution from pile 5=from pile6=83.245 x 48=3995.76 in·kip
Contribution from pile 3=from pile 4=12 in·kip
Section 5 United States Code (ACI 318 -2005)
5.12 US Pilecap Foundation 1
Verification Manual — 269
Contribution from pile 5,6=0 in·kip
So Total Mz X2X2 = 8014 in·kip = 670 ft·kip
So Resisting Moment = Mnz= Muz/φ = 744.44 ft·kip
Rn = Mnz/b·d2 = 0.147 Ksi
2·m·Rn/fy = 0.0864 <1 , Hence OK
ρ = 1/m· (1-√1-2m·Rn/fy) = 0.0025
ρmin< ρ < ρmax, Hence OK
Calculation of Moment about X Axis
Calculation of Mx-
For moment wrt Z1Z1
Contribution from pile 1=from pile 3=from pile 5= 83.245 x 21=1748.145in·kip
So Total Mx Z1Z1 = 437 ft·kip
For moment wrt Z2Z2
Contribution from pile 2=from pile 4=from pile 6= 83.245 x 21=1748.145in·kip
So Total Mx Z2Z2 = 437 ft·kip
So Max value of MX = 437 ft·kip
So Resisting Moment = Mnx= Mxux/φ = 485.55 ft·kip
Rn = Mnz/b·d2 = 0.06 Ksi
2·m·Rn/fy = 0.035 <1 , Hence OK
ρ = 1/m· (1-√1-2m·Rn/fy) = 0.001
So ρ= ρmin=0.0018
ρ < ρmax, Hence OK
Area of Steel Required
Along X Direction
ρ = 0.0025
b = 90 in, d=26 in
Therefore, Astx = 5.85 in2
Along Z Direction
ρ = 0.0018
270 — STAAD Foundation Advanced V8i
Chapter — 5
5.12 US Pilecap Foundation 1
b = 144 in , d=26 in
Therefore, Astxz = 6.74 in2
5.12.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Pile Reaction (kip) 83.245 83.244 NoneGoverning Moment(ft·kip)
670
437
718
502.6
15%
Shear Force, One-Way(kip)
166.49
55.5
166.49
55.5
None
Shear Force, Two-Way(kip)
490.14 490.217 Negligible
Table 5-13: US verification example 10 comparison
5.13 US Pilecap Foundation 25.13.1 Reference
5.13.2 ProblemDesign pilecap foundation with the given data: Load Fy = 150 kip, Mx= 50 ft·kip. fc = 4ksi, fy = 60 ksi, Column Dimension = 12 inchx12 inch. Pedestal ht= 20 inch
Pile Data- Dia of pile= 18 inch
Vertical capacity = 65 kip,
Horizontal capacity = 20 kip
Uplift capacity = 15 kip
Section 5 United States Code (ACI 318 -2005)
5.13 US Pilecap Foundation 2
Verification Manual — 271
Figure 5-26: Elevation and Plan
272 — STAAD Foundation Advanced V8i
Chapter — 5
5.13 US Pilecap Foundation 2
5.13.3 Solutiondepth of pilecap= 1.5xpiledia, D=27 inch
Take D=27 inch
c/c pile diatance = 3xpile dia =54 mm. Edge diatance =18 inch
Assume a 4 pile combination.
Coordinates of piles; considering pedestal at 0,0,0
PileNo
X Coor-dinate (in)
Z Coordinate(in)
1 -27 -272 -27 273 27 274 27 -27
Table 5-14: Pile Coordinates in Plan
Pilecap Length = 54+2x18 = 90 inch
Pilecap Width = 54+2x18 = 90 inch
pilecap dimension is 90 inch x90 inch x 27 inch
Weight of footing = 90 x 90 x 27 x 0.16/123 = 20.25 kip
Weight of pedestal = 12 x 12 x 20 x 0.16 /123 = 0.267 kip
Therefore, total load on the pilecap = (150+20.25 +0.267) =170.517 kip
So Pile reaction from axial load = 170.517 /4= 42.629 kip
Moment Mx ( from input) = 50 ft·kip =600 in·kip
Using Rivet theory-
Reaction from moment= +/- 600x0.27/(4x272) = +/-5.55 Kip
So,
Reaction at Pile 2= reaction at pile 3 = 42.629 +5.55 = 48.185 Kip
Reaction at Pile 1= reaction at pile 4 = 42.629 -5.55 = 37.085Kip
So Critical vertical reaction= 48.185 Kip < 65 kip
As there is no net uplift/lateral load, so each pile is safe in uplift & lateral capacity.
Factored Design
Load factor for self wt is taken =1
Load factor for axial load is taken 1.4
So, Axial Load on pilecap = 1.4x150+20.25 x1+0.267x1= 230.517 Kip
Moment on pilecap = 1.4x50 ft·kip = 840 in·kip
Load on each pile from axial reaction =230.517 /4=57.629 Kip
Reaction from moment= +/- 840x27/(4x272) = +/-7.78 Kip
Section 5 United States Code (ACI 318 -2005)
5.13 US Pilecap Foundation 2
Verification Manual — 273
So,
Reaction at Pile 2= reaction at pile 3 = 57.629 +7.78 = 65.409 Kip
Reaction at Pile 1= reaction at pile 4 = 57.629 -7.78 = 49.849 Kip
Punching ShearFigure 5-27: Section considered for two-way shear
Punching shear is checked on a perimeter 0.5d =11.5 inch from the column face.
Contribution from pile 1=from pile 4= 49.849 Kip
Contribution from pile 2=from pile 3= 65.409 Kip
So total punching shear Vm= 230.516 kip
Pm = 4x(12+11+11) =136 inch
ß=L/B =12/12 =1
274 — STAAD Foundation Advanced V8i
Chapter — 5
5.13 US Pilecap Foundation 2
V1 √fc.bc.d = (2+4/1).√(4000) x136 x 22 =1135.4 x1000 lb
V2 √fc.bc.d = (40x22/136+2).√(4000) x136x22= 1602.9 x 1000 lb
V3 = 4.√fc.bc.de = 4.√(4000) x 136 x 22= 756.9 x 1000 lb
Vc = min{V1, V2, V3} = 756.9 kip
So, 0.75Vc = 567.7 Kip
Vm< 0.75.Vc , Hence safe
Punching Shear Check for Corner Piles
Corner piles are 1,2,3,4
Pile 1/4 are taking reaction 49.849 Kip & Pile 2/3 are taking reaction 65.409 Kip
d critical = 4.46 inch
Effective depth = 22 inch
d critical< Effective depth, Hence Safe
Section 5 United States Code (ACI 318 -2005)
5.13 US Pilecap Foundation 2
Verification Manual — 275
Calculation of ShearFigure 5-28: Section considered for one-way shear
Parallel to X Axis
For shear wrt X1X1
Contribution from pile 1 =49.849 x 0.444=22.155 Kip
Contribution from pile 2 =65.409 x 0.444=29.04 Kip
Contribution from pile 3,4 =0 KN
So Total V X1X1 = 51.195 Kip
For shear wrt X2X2
Contribution from pile 4 =49.849 x 0.444=22.155 Kip
Contribution from pile 3 =65.409 x 0.444=29.04 Kip
Contribution from pile 1,2 =0 KN
So Total V X2X2 = 51.195 Kip
276 — STAAD Foundation Advanced V8i
Chapter — 5
5.13 US Pilecap Foundation 2
So V parallel to X direction = 51.195 Kip
Now allowable shear = Vc1 = = 2x√(4000) x 90 x 22 lb = 250.4 x1000 lb
0.75.Vc1=187.84 Kip
V < Vc1, Hence Safe
Parallel to Z Axis
For shear wrt Z1Z1
Contribution from pile 1 =49.849 x 0.444=22.155 Kip
Contribution from pile 4 =49.849 x 0.444=22.155 Kip
Contribution from pile 2,3 =0 KN
So Total V Z1Z1 = 44.31 Kip
For shear wrt Z2Z2
Contribution from pile 2 =65.409 x 0.444=29.04 Kip
Contribution from pile 3 =65.409 x 0.444=29.04 Kip
Contribution from pile 1,4 =0 KN
So Total V Z2Z2 = 58.08 Kip
So V parallel to Z direction = 58.08 kip
Now allowable shear = Vc1 = = 2x√(4000) x 90 x 22 lb = 250.4 x1000 lb
0.75.Vc1 = 187.8 Kip
V < Vc1, Hence Safe
Section 5 United States Code (ACI 318 -2005)
5.13 US Pilecap Foundation 2
Verification Manual — 277
Calculation of MomentFigure 5-29: Section considered for bending
About Z Axis
Calculation of Mz-
For moment wrt X1X1
Contribution from pile 1=49.849 x21/12=87.24 ft·kip
Contribution from pile 4=65.409 x21/12=114.46 ft·kip
Contribution from pile 3,4=0 in·kip
So Total Mz X1X1 = 207.1 ft·kip
For moment wrt X2X2
Contribution from pile 4=49.849 x21/12=87.24 ft·kip
278 — STAAD Foundation Advanced V8i
Chapter — 5
5.13 US Pilecap Foundation 2
Contribution from pile 3=65.409 x21/12=114.46 ft·kip
Contribution from pile 1,2=0 in·kip
So Total Mz X2X2 = 207.1 ft·kip
So max Mz = 207.1 ft·kip
So Resisting Moment =Mnz= Muz/Ø =224.11 ft·kip
m=fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 ( as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.02138
ρmin = 0.0018 ( as fy=60)
Rn = Mnz/b.d2 =0.0617 Ksi
2m.Rn/fy = 0.0363 <1 , Hence OK
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.001
So, ρ =ρmin = 0.0018
ρ < ρmax Hence OK
About X Axis
Calculation of Mx-
For moment wrt Z1Z1
Contribution from pile 1=from pile 4=49.849 x 21/12=87.24 ft·kip
Contribution from pile 2=from pile 3=0 ft·kip
So Total Mx Z1Z1 = 174.47 ft·kip
For moment wrt Z2Z2
Contribution from pile 2=from pile 3=65.409 x 21/12=114.465 ft·kip
Contribution from pile 1=from pile 4=0 ft·kip
So Total Mx Z2Z2 = 228.93 ft·kip
So Max value of MX = 228.93 ft·kip
So Resisting Moment =Mnz= Muz/Ø =254.37 ft·kip
m=fy/0.85.fc=60/(0.85x4) = 17.6471
ß1 = 0.85 ( as fc=4)
ρbal = 0.85.ß1.fc.87/fy.(87+fy) = 0.028507
ρmax = 0.75. ρbal = 0.02138
ρmin = 0.0018 ( as fy=60
Rn = Mnz/b.d2 =0.07 Ksi
2m.Rn/fy = 0.0412 <1 , Hence OK
Section 5 United States Code (ACI 318 -2005)
5.13 US Pilecap Foundation 2
Verification Manual — 279
ρ = 1/m. (1-√1-2m.Rn/fy) = 0.0012
So ρ= ρmin=0.0018
ρ < ρmax Hence OK
Area of Steel Required
Along X Direction
ρ = 0.0018
b= 90 inch , d=22 inch
Therefore, Astx = 3.6 in2
Along Z Direction
ρ = 0.0018
b= 90 inch , d=22 inch
Therefore, AstZ = 3.6 in2
5.13.4 Comparison
Value of Reference ResultSTAAD Foun-
dationResult
Percent Dif-ference
Pile Reaction 49.849 Kip
65.409 Kip
49.851 Kip
65.407 Kip
None
GoverningMoment
207.1 ft·kip 228.93ft·kip
219.654 ft·kip
294.254 ft·kip
Negligible
Shear Force(One-Way)
51.195 Kip 58.08Kip
51.226 Kip
58.14 Kip
None
Shear Force(Two-Way)
230.516 kip 230.517 kip None
Table 5-15: US verification example 11 comparison
5.14 US Pilecap Foundation 35.14.1 Reference
5.14.2 ProblemDesign pilecap foundation with the given data: Load Fy = 1000 KN, fc = M 25, fy = Fe 415
Column Dimension = 250 mm x 250 mm, Pedestal ht= 500 mm
280 — STAAD Foundation Advanced V8i
Chapter — 5
5.14 US Pilecap Foundation 3
Dia of pile= 300 mm
Vertical capacity = 250 KN
Horizontal capacity = 50 KN
Uplift capacity = 100 KN
Figure 5-30: Elevation and Plan
5.14.3 SolutionDepth of pilecap= 1.5 x pile diameter, D = 450 mm
Take D = 655 mm
c/c pile distance = 3 x pile diameter =1200 mm
Edge distance =350 mm
Assuming five pile combination, coordinates of piles (considering pedestal at 0,0,0):
PileNo
X Coordinate(mm)
Z Coordinate(mm)
1 -848.528 -848.5282 -848.528 848.5283 0 04 848.528 -848.5285 848.528 848.528
Table 5-16: Pile Coordinates in Plan
Section 5 United States Code (ACI 318 -2005)
5.14 US Pilecap Foundation 3
Verification Manual — 281
Pilecap Length = 2(850)+2(350) = 2400 mm
Pilecap Width = 2(850)+2(350) = 2400 mm
pilecap dimension is 2400 mm x 2400 mm x 740 mm
Weight of footing = 2.4 x 2.4 x 0.74 x 25 = 106.56 KN
Weight of pedestal = 0.25 x 0.25 x 0.5 x 25 = 0.78 KN
Therefore, total load on the pilecap= (1000+106.56 +0.78) =1107.34 KN
So Pile reaction = 1107.34 /5 = 221.47 KN < 250 KN
Hence OK
As there is no lateral load , moment or uplift force, so each pile is safe in lateral & upliftcapacity.
Factored Design
Load factor for self wt is taken = 1
Load factor for axial load is taken = 1.4
So, Load on pilecap = 1.4(1000) + 1(106.56)+0 1(0.78) = 1507.34 KN
Load on each pile = 1507.34/5 = 301.468 KN
deff = 740 - 50 - 50 - 25 = 615 mm
Punching ShearFigure 5-31: Section considered for punching shear
Punching shear is checked on a perimeter 0.5d =307.5 mm from the column face.
Contribution from pile 1 = from pile2 = from pile4 = from pile 5 = 301.468KN
Contribution from pile 3 = 0 KN
So total punching shear Vm= 1205.9 KN
Pm = 4·(250 + 307.5 + 307.5) =3460 mm
ß = L/B = 250/250 = 1
282 — STAAD Foundation Advanced V8i
Chapter — 5
5.14 US Pilecap Foundation 3
V1= (2 + 4/βc)√(fc)·bc·d = 5298.5 KN
V2 = (40·d/b + 2)√(fc)·bc·d = 5530.9 KN
V3= 4.√(fc)·bc·de = 3532 KN
Vc = min(V1, V2, V3) = 3532 KN
So, 0.75·Vc =2649 KN
Vm< 0.75·Vc , Hence safe
Punching Shear Check for Corner Piles
Corner piles are 1, 2, 4, & 5
Each pile is taking reaction 301.47 KN
B1 = 1418.27 mm & B2 =2025 mm
d1 = 151 mm
d2 = 211 mm
d critical =212 mm
Effective depth = 615 mm
d critical < Effective depth, Hence Safe
Calculation of ShearFigure 5-32: Section considered for one-way shear
Parallel to X Axis
Shear Plane is at a distance d (615 mm from face of column)
For shear wrt X1X1
Contribution from pile 1 = pile 2 = 0.8667 x 301.47 = 261.27 KN
Contribution from pile 3,4,5 =0 KN
So Total V X1X1 = 522.548 KN
Section 5 United States Code (ACI 318 -2005)
5.14 US Pilecap Foundation 3
Verification Manual — 283
For shear wrt X2X2
Contribution from pile 4 = pile 5 = 0.8667 x 301.47=261.27 KN
Contribution from pile 3,2,1 =0 KN
So, Total V X2X2 = 522.548 KN
Shear, V, parallel to X direction = 522.548 KN
Now allowable shear = Vc1 =2√(fc)·bc·d = 1225 KN
0.75·Vc1= 918.8 KN
V < Vc1, Hence Safe
Parallel to Z Axis
For shear wrt Z1Z1
Contribution from pile 1 =pile 4 = 0.8667 x 301.47 = 261.27 KN
Contribution from pile 2 = pile 3 = pile 5 = 0 KN
So Total V Z1Z1 = 522.548 KN
For shear wrt Z2Z2
Contribution from pile 2 = pile 5 = 0.8667 x 301.47 = 261.27 KN
Contribution from pile 1 = pile 3 = pile 4 =0 KN
So Total V Z2Z2 = 522.548 KN
Shear, V, parallel to Z direction = 522.548 KN
Now allowable shear = Vc1 =2√(fc)·bc·d = 1225 KN
0.75·Vc1= 918.8 KN
V < Vc1, Hence Safe
Calculation of Moment
For either direction:
m = fy/0.85·fc= 415/(0.85·25) = 19.529
ß1 = 0.85 (as fc = M 25)
ρbal = 0.85·ß1·fc·87/fy·(87 + fy) = 0.025729
ρmax = 0.75·ρbal = 0.019297
ρmin = 0.0018 (as fy= 415 N/mm2)
284 — STAAD Foundation Advanced V8i
Chapter — 5
5.14 US Pilecap Foundation 3
Figure 5-33: Section considered for moment
Calculation of Moment about Z Axis
Calculation of Mz-
For moment wrt X1X1
Contribution from pile 1 = pile 2 = 301.47 x 0.725 = 218.56 KNm
Contribution from pile 3 = 0.083 x 301.47 x 0.0083 = 0.21 KNm
Contribution from pile 4= pile 5 = 0 KNm
So Total Mz X1X1 = 437.34 KNm = 440 KNm
For moment wrt X2X2
Contribution from pile 4 = pile 5 = 301.47 x 0.725 = 218.56 KNm
Contribution from pile 3 = 0.083 x 301.47 x 0.0083 = 0.21 KNm
Contribution from pile 4 = pile 5 =0 KNm
So Total Mz X2X2 = 437.34 KNm = 440 KNm
So Resisting Moment = Mnz= Muz/φ = 488.89 KNm = 490 KNm
Rn = Mnz/b·d2 = 0.5398 N/mm2
2·m·Rn/fy = 0.0508 <1 , Hence OK
ρ = 1/m· (1-√1-2m·Rn/fy) =0.00132
ρ= ρmin=0.0018
ρ < ρmax, Hence OK
Calculation of Moment about X Axis
Calculation of Mx-
For moment wrt Z1Z1
Contribution from pile 1= pile 4 = 301.47 x 0.725 = 218.56 KNm
Contribution from pile 3=0.083 x 301.47 x 0.0083 = 0.21 KNm
Section 5 United States Code (ACI 318 -2005)
5.14 US Pilecap Foundation 3
Verification Manual — 285
Contribution from pile 2 = pile 5 = 0 KNm
So Total Mx Z1Z1 = 437.34 KNm = 440 KNm
For moment wrt Z2Z2
Contribution from pile 2= pile 5 = 301.47 x 0.725 = 218.56 KNm
Contribution from pile 3 = 0.083 x 301.47 x 0.0083 = 0.21 KNm
Contribution from pile 1 = pile 4 = 0 KNm
So Total Mx Z2Z2 = 437.34 KNm = 440 KNm
So Max value of MX = 440 KNm
So Resisting Moment = Mnx= Mxux/φ = 488.89 KNm =490 KNm
Rn = Mnz/b·d2 = 0.5398 N/mm2
2·m·Rn/fy = 0.0508 <1 , Hence OK
ρ = 1/m· (1-√1-2m·Rn/fy) = 0.00132
So ρ= ρmin=0.0018
ρ < ρmax, Hence OK
Area of Steel Required
Along X Direction
ρ = 0.0018
b = 2400 mm, d = 615 mm
Therefore, Astx = 2657 mm2
Along Z Direction
ρ = 0.0018
b = 2400 mm, d = 615 mm
Therefore, Astz = 2657 mm2
286 — STAAD Foundation Advanced V8i
Chapter — 5
5.14 US Pilecap Foundation 3
5.14.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Pile Reaction, Service(KN)
221.5 221.4 Negligible
Pile Reaction, Ulti-mate (KN)
301.5 301.4 Negligible
Governing Moment(KNm)
489
489
485
485
Negligible
Shear Force, One-Way(KN)
523
523
520
520
Negligible
Shear Force, Two-Way(KN)
1206 1206 None
Table 5-17: US verification example 11 comparison
5.15 US Pilecap Foundation 45.15.1 Reference
5.15.2 ProblemDesign pilecap foundation with the given data: Load Fy = -1200 KN & Mz = 100 KNm, fc =M 25, fy = Fe 415
Column Dimension = 250 mm x 250 mm, Pedestal ht= 500 mm
Dia of pile= 300 mm
Vertical capacity = 250 KN
Horizontal capacity = 50 KN
Uplift capacity = 50 KN
Section 5 United States Code (ACI 318 -2005)
5.15 US Pilecap Foundation 4
Verification Manual — 287
Figure 5-34: Elevation and Plan
5.15.3 SolutionDepth of pilecap= 1.5 x pile diameter, D = 450 mm
Take D = 780 mm
c/c pile distance = 3 x pile diameter = 900 mm
Edge distance =350 mm
Assuming six pile combination, coordinates of piles (considering pedestal at 0,0,0):
288 — STAAD Foundation Advanced V8i
Chapter — 5
5.15 US Pilecap Foundation 4
PileNo
X Coordinate(mm)
Z Coordinate(mm)
1 -900 -4502 -900 4503 0 -4504 0 4505 900 -4506 900 450
Table 5-18: Pile Coordinates in Plan
Pilecap Length =2(900) + 2(350) = 2500 mm
Pilecap Width = 900 + 2(350) = 1600 mm
pilecap dimension is 2500 mm x 1600 mm x 780 mm
Weight of footing = 2.5 x 1.6 x 0.78 x 25 = 78 KN
Weight of pedestal = 0.25 x 0.25 x 0.5 x 25 = 0.78 KN
Therefore, total load on the pilecap = 1200 + 78 + 0.78 = 1278.78 KN
So Pile reaction from axial load = 1278.78/6= 213.13 KN
So Pile reaction at Pile1 /Pile 2 = 213.13 +100·0.9/(4·0.9·0.9) = 240.91 KN
So Pile reaction at Pile3 /Pile 4 = 213.13 KN
So Pile reaction at Pile5 /Pile 6 = 213.13 - 100·0.9/(4·0.9·0.9) = 185.35 KN
So Critical Pile reaction = 240.91 KN < 250 KN
Hence OK
As there is no lateral load , moment or uplift force, so each pile is safe in lateral & upliftcapacity. Similarly, as there is no tension pile case so each pile is safe again uplift.
Factored Design
Load factor for self wt is taken = 1
Load factor for axial load is taken = 1.4
So, Load on pilecap = 1.4(1200) + 1(78) + 1(0.78) = 1758.78 KN
So Pile reaction from axial load = 1758.78/6 = 293.13 KN
Moment (Mz) = 1.4(100) = 140 KNm
So Pile reaction at Pile 1 /Pile 2 = 293.13 + 140·0.9/(4·0.9·0.9) = 332.02 KN
So Pile reaction at Pile 3 /Pile 4 = 293.13 KN
So Pile reaction at Pile 5 /Pile 6 = 293.13 -140·0.9/(4·0.9·0.9) = 254.24 KN
deff = 780 - 50 - 50 - 25 = 655 mm
Punching Shear
Punching shear is checked on a perimeter 0.5d =327.5 mm from the column face.
Section 5 United States Code (ACI 318 -2005)
5.15 US Pilecap Foundation 4
Verification Manual — 289
Figure 5-35: Section considered for punching shear
Contribution from pile 1 = pile 2 = 1(332.02) =332.02 KN
Contribution from pile 3 = pile 4= 0.492(293.13) = 144.22 KN
Contribution from pile 5 = pile 6 = 1(254.24) = 254.24 KN
So total punching shear Vm= 2(333.02 + 144.22 + 254.24) = 1462.96 KN
Pm = 4·(250 + 327.5 + 327.5) = 3620 mm
ß = L/B = 250/250 = 1
V1= (2 + 4/βc)√(fc)·bc·d = 5904 KN
V2 = (40·d/b + 2)√(fc)·bc·d = 9090 KN
V3= 4.√(fc)·bc·de = 3936 KN
Vc = min(V1, V2, V3) = 3936 KN
So, 0.75·Vc = 2952 KN
Vm< 0.75·Vc , Hence safe
Punching Shear Check for Corner Piles
Corner piles are 1, 2, 5, & 6
Critical Pile 1 & 2 with axial Reaction 333.02 KN
B1 = 1450 mm & B2 =2105 mm
d1 = 163 mm
d2 = 225 mm
d critical =225 mm
290 — STAAD Foundation Advanced V8i
Chapter — 5
5.15 US Pilecap Foundation 4
Effective depth = 655 mm
d critical < Effective depth, Hence Safe
Calculation of ShearFigure 5-36: Section considered for one-way shear
Parallel to X Axis
Shear Plane is at a distance d (655 mm from face of column)
For shear wrt X1X1
Contribution from pile 1 = pile 2 =0.9x 333.03 = 299.72 KN
Contribution from piles 3, 4, 5, & 6 =0 KN
So Total V X1X1 = = 2(299.72) KN= 599.4 KN
For shear wrt X2X2
Contribution from pile 5 = pile 6 = 0.9(254.24) = 228.82 KN
Contribution from piles 1, 2, 3, & 4 = 0 KN
So, Total V X2X2 = 2(228.82) = 457.63 KN
Shear, V, parallel to X direction = 599.4 KN
Section 5 United States Code (ACI 318 -2005)
5.15 US Pilecap Foundation 4
Verification Manual — 291
Now allowable shear = Vc1 =2√(fc)·bc·d = 869.8 KN
0.75·Vc1= 652 KN
V < Vc1, Hence Safe
Parallel to Z Axis
For shear wrt Z1Z1
Contribution from all piles = 0 KN
So Total V Z1Z1 = 0 KN
For shear wrt Z2Z2
Contribution from all piles =0 KN
So Total V Z2Z2 = 0 KN
Shear, V, parallel to Z direction = 0 KN
No shear parallel to the Z axis, Hence Safe
Calculation of Moment
For either direction:
m = fy/0.85·fc= 415/(0.85·25) = 19.529
ß1 = 0.85 (as fc = M 25)
ρbal = 0.85·ß1·fc·87/fy·(87 + fy) = 0.025729
ρmax = 0.75·ρbal = 0.019297
ρmin = 0.0018 (as fy= 415 N/mm2)
292 — STAAD Foundation Advanced V8i
Chapter — 5
5.15 US Pilecap Foundation 4
Figure 5-37: Section considered for moment
Calculation of Moment about Z Axis
Calculation of Mz
For moment wrt X1X1
Contribution from pile 1 = pile 2 = 333.02(0.775) = 258.1 KNm
Contribution from pile 3 = pile 4 = 0.083(293.13·0.0083) = 0.2 KNm
Contribution from pile 5 = pile 6 = 0 KNm
So Total Mz X1X1 = 516.6 KNm = 520 KNm
For moment wrt X2X2
Contribution from pile 5 = pile 6 = 254.24(0.775) = 197 KNm
Contribution from pile 3 = pile 4 = 0.083(293.13·0.0083) = 0.2 KNm
Contribution from pile 1 = pile 2 =0 KNm
So Total Mz X2X2 = 394.4 KNm = 395 KNm
So Critical value of Mz =520 KNm
So Resisting Moment = Mnz= Muz/φ = 577.78 KNm = 580 KNm
Rn = Mnz/b·d2 = 0.845 N/mm2
2·m·Rn/fy = 0.0795 <1 , Hence OK
ρ = 1/m· (1-√1-2m·Rn/fy) = 0.002
ρ = ρmin=0.0018
ρmin < ρ < ρmax, Hence OK
Section 5 United States Code (ACI 318 -2005)
5.15 US Pilecap Foundation 4
Verification Manual — 293
Calculation of Moment about X Axis
Calculation of Mx
For moment wrt Z1Z1
Contribution from pile 1 = 332.02(0.325) = 107.9 KNm
Contribution from pile 3 = 293.13(0.325) = 95.27 KNm
Contribution from pile 5 = 254.24(0.325) = 82.63 KNm
Contribution from piles 2, 4, & 6 = 0 KNm
So Total Mx Z1Z1 =285.8 KNm = 286 KNm
For moment wrt Z2Z2
Contribution from pile 2 = 332.02(0.325) = 107.9 KNm
Contribution from pile 4 = 293.13(0.325) = 95.27 KNm
Contribution from pile 6 = 254.24(0.325) = 82.63 KNm
Contribution from piles 1, 3, & 5 = 0 KNm
So Total Mx Z2Z2 = 285.8 KNm = 286 KNm
So Max value of Mx = 286 KNm
So Resisting Moment = Mnx= Mxux/φ = 317.78 KNm =318 KNm
Rn = Mnz/b·d2 = 0.2964 N/mm2
2·m·Rn/fy = 0.0279 <1 , Hence OK
ρ = 1/m· (1-√1-2m·Rn/fy) = 0.00072
So ρ= ρmin=0.0018
ρ < ρmax, Hence OK
Area of Steel Required
Along X Direction
ρ = 0.0020
b = 1600 mm, d = 655 mm
Therefore, Astx = 2096 mm2
Along Z Direction
ρ = 0.0018
b = 2500 mm, d = 655 mm
Therefore, Astz = 2948 mm2
294 — STAAD Foundation Advanced V8i
Chapter — 5
5.15 US Pilecap Foundation 4
5.15.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Pile Reaction, Service(KN)
241
241
213
213
185
185
241
241
213
213
185
185
Negligible
Pile Reaction, Ulti-mate (KN)
332
332
293
293
254
254
332
332
293
293
254
254
None
Governing Moment(KNm)
578
318
572
318
Negligible
Shear Force, One-Way(KN)
600
0
599
0
Negligible
Shear Force, Two-Way(KN)
1463 1462 Negligible
Table 5-19: US verification example 13 comparison
5.16 US Mat Combined Foundation 15.16.1 Reference‘Foundation Analysis and Design – Fifth Edition’ by J.E. Bowles, Page 475-481, Example9-1.
5.16.2 ProblemDesign a rectangular combined footing using the conventional method given. fc’ = 3000psi(column and footing), fy = 60000 psi, qa = 2 ksf.
Section 5 United States Code (ACI 318 -2005)
5.16 US Mat Combined Foundation 1
Verification Manual — 295
Figure 5-38: Elevation and dimensions
Column 1 Column 212 in. x 12 in. 15 in. x 15 in.4 No. 7 bars 4 No. 8 barsDL = 60 kips DL = 110 kipsLL = 60 kips LL = 90 kips
5.16.3 Solution
Step 1- Find out ultimate soil pressure
Pu 1 = 1.2 x 60 + 1.6 x 60 = 168 kips
Pu 2 = 1.2 x 110 + 1.6 x 90 = 276 kips
ΣPw = P1 + P2 = 60 + 60 + 110 + 90 = 320 kips
Ultimate ratio UR= (168 + 276) / 320 = 1.3875
qult = qa x UR= 2 x 1.3875 = 2.775 ksf
This is necessary so that eccentricity is not introduced in finding L using working loadsand then switching to “ultimate” values.
Step 2 - Find footing dimensions L and B; first locate loadresultant from center of column 1
ΣMcol1 = R where R = Pu = 168 + 276 = 444 KN
444 = 15 x 276
= 9.324 ft
To make the resultant 444 kips (factored loads) fall at L/2:
L = (9.324 + 0.5) x 2 = 19.648 ft
We will use 19.75 ft.
296 — STAAD Foundation Advanced V8i
Chapter — 5
5.16 US Mat Combined Foundation 1
Step 3 - Find B
BLq = 444
B = = 8.143 ft
Use B = 8.17 ft.
Step 4 - Find out bending moment and shear force
Uniformly distributed upward load = (Pu 1 + Pu 2) / 19.75 = 22.48 kip / ft
Shear between column 1 and 2 using integration (set integration constant by inspection):
dV =
V = 22.48 x – 168
V = 0 at x = = 7.47 ft (locates point of Mmax)
Moment between column 1 and 2 (again set integration constant by inspection):
dM =
M = – 168 (x – 0.5)
At x = 1(right face of column 1),
M = -72.76 ft-kips
Maximum negative M at V = 0 is
M = - 168 (7.47 – 0.5) = -543.76 ft-kips
These values are Mu values and can be directly used to compute steel quantities.
Section 5 United States Code (ACI 318 -2005)
5.16 US Mat Combined Foundation 1
Verification Manual — 297
Figure 5-39: Forces on foundation
Maximum positive bending moment is at the face of column 2
= 22.48 x (3.625)2 / 2 = 147.7 ft-kips
Maximum shear force at the face of column 2
= 22.48 x 14.875 – 168 = 166.39 kips
Figure 5-40: Shear and Bending diagrams
Step 5 - Select depth based on analysis for both wide-beam and diagonal tension
a. Critical location for wide-beam is readily obtained.
b. Diagonal tension may have to be investigated for three conditions:i. three-side zone, column 1
ii. four-side zone, column 2
iii. three-side zone, column 2
Check wide beam first (slope of shear diagram = constant) using V diagram:
B vc d = 166.39 – 22.48 d
vc = 11.825 ksf (allowable = )
8.17 x 11.825 d = 166.39 – 22.48 d
298 — STAAD Foundation Advanced V8i
Chapter — 5
5.16 US Mat Combined Foundation 1
d = = 1.397 ft (16.765 in)
Checking diagonal tension at column 1 using “d” just obtained for a three-side zone and
vc = = 164.317 psi = 23.66 ksf
Perim. = (12 + 8.38) x 2 + 12 + 16.765 = 69.525 in = 5.794 ft
The net shear is column load – upward soil force in diagonal tension zone:
A = = 4.07 ft2
V = Pcol -Psoil = 168 – 4.07 x = 156.8 kips
Actual v = = 19.37 ksf < 23.66 ksf (O.K.)
At column 2 a four side zone gives
A = = 7.01 ft2
And
V = 276 – 7.01 x = 256.74 kips
Perim. = (15 + 16.765) x = 10.59 ft
v = = 17.354 ksf < 23.66 ksf (O.K.)
By inspection a three-side diagonal tension is not critical at column 2.
Step 6 - Design negative steel (between columns 1 and 2)
For fy = 60 and fc’ = 3 ksi and b = 12 in, obtain a = 1.96As:
As (d - a/2) =
As (16.765 – 0.98 As) = = 14.79
As = 0.94 in2 / ft
Section 5 United States Code (ACI 318 -2005)
5.16 US Mat Combined Foundation 1
Verification Manual — 299
p = = 0.00467 > (O.K.) < maximum allowable percent ofsteel
Use 12 No. 8 bars at 8.2 –in spacing across top of footing:
As = 12(0.79) = 9.48 > 7.68 in2
Run 1/3 of bars full length of footing (less 3 in end cover):
Ld is O.K.
Step 7 - Find steel in short direction in column 1
B’ = 12 + 16.765 x 0.75 = 24.574 in = 2.05 ft
L’ = = 3.585 ft
q = = 10.03 ksf (conservative)
M = x 12 = 773.45 in-kips
Take d = (16.765 – 1) in to allow for longitudinal rebars:
As (15.765 – 0.98 As) = = 14.323
As = 0.98 in2 / ft
p is O.K. from previous calculation. Use 4 No. 7 bars at 6 in:
Ld = 0.04 x 0.60 x 60000 x = 26.3 in
or
Ld = 0.004 x 0.875 x 60000 = 21 in
Ld furnished = 3.585 x 12 – 3 = 40 in
Compute short direction steel at column 2; use d= 15 in:
B’ = 15 + 16 x 1.5 = 39 in = 3.25 ft
L’ = = 3.46 ft
q = = 10.394 ksf (conservative)
300 — STAAD Foundation Advanced V8i
Chapter — 5
5.16 US Mat Combined Foundation 1
M = x 12 = 746.6 in-kips
As (15.765 – 0.98 As) = = 14.379
As = 0.98 in2 / ft
Use 6 No. 7 bars at 6.5 in
Step 8 - Check dowel requirements of column to footing
At column 1 the supporting area is not on all sides; therefore the bearing stress is limitedto:
fc = 0.75 x 0.7 x fc’ = 1.575 ksi
p = 12 x12 x 1.575 = 226.8 > 168 kips (dowels not required for load transfer)
Use 4 dowels to provide at least 0.05Ag:
As = 0.005 x 144 = 0.72 in2
Use 4 No. 6 for 4 x (0.44) = 1.76 in2 at column 2 with concrete all around
> 2
Use 2
fc = 0.75 x 0.7 fc x 2 = 3.15 ksi
P = 15 x 15 x 3.15 = 708.75 >> 276
Use four dowels same size as column 1.
Step 9 - Conclusion
Steel in cantilever portion is found to be 0.28 for moment and 0.67 in2 / ft for minimumrequirement of 200 / fy (could use 0.28 x 1.33 >= T and S alternatively but would requireincreasing other steel by 1 / 3 also)
Use 10 No. 7 bars
Run five bars full length to use as chairs for short direction steel.
Section 5 United States Code (ACI 318 -2005)
5.16 US Mat Combined Foundation 1
Verification Manual — 301
5.16.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Average Base Pressure 0.01911kip/in2
0.02 kip/in2 4.657
Maximum NegativeBending Moment
543.76 ft-kips
529.064 ft-kips
2.70
Maximum PositiveBending Moment
147.7 ft-kips 149.12 ft-kips 0.96
Required Area ofReinforcement
0.94 in2/ft 0.909 in2/ft 3.3
Table 5-20: US verification example 12 comparison
5.17 US General Isolated Foundation withSliding & Overturning
5.17.1 Reference
5.17.2 ProblemDesign an isolated footing with the given data:
Density of soil =14 KN/cum
Depth of Soil = 0.5m
Density of Concrete = 25 KN/cum
Coefficient of Friction (m) = 0.5
Safe Bearing Capacity of the Soil (s) = 120 KN/m2
Factor of Safety against Overturning =1.5
Factor of Safety against Sliding = 1.5
Permissible soil pressure =
Column dimension = 0.3m x 0.3m,
Strength of concrete (fc’) = M-30 = 4349.39 Psi
Strength of steel (fy) = Fe-415
Loads:
Fx =-300 KN
Fy =-500 KN
Fz=-200 KN
Mz= -10.32KNm
302 — STAAD Foundation Advanced V8i
Chapter — 5
5.17 US General Isolated Foundation with Sliding & Overturning
Mx=45.89 KNm
Note: Self weight of footing, wt of soil and surcharge are not included for shear andmoment computations.
Figure 5-41: Plan and Elevation
5.17.3 SolutionDesign started with trial dimensions of 3.75m X 3.75m X 1.0m
Determination of base area of footing
The base area of footing is determined using service (unfactored) loads with the netpermissible soil pressure.
Section 5 United States Code (ACI 318 -2005)
5.17 US General Isolated Foundation with Sliding & Overturning
Verification Manual — 303
Net permissible soil pressure = 120 KN/ m2
Required base area of footing = [500 + 0.10(500)]/120 = 4.5833 m2
Use a 3.75m 3.75m square footing (Af =14.0625 m2).
Using a depth of 1m;
Self-wt. of Footing =(3.75*3.75*1*25) = 351.562 KN
Wt. of soil = 14*0.5*{(3.75*3.75) –(0.3*0.3)} =97.8075 KN
Serviceability Check
The net moments are given by:-
Mz = -10.32 – (-300*1) = 289.68 KNm
Mx= +45.89 +(-200*1) = -154.11 KNm
The pressure at the four corners are given by:-
s 1 = ((500+351.562)/ 14.0625) + (6*154.11/3.753) - (6*289.68/3.753) = 75.980 KN/m2
s 2 = ((500+351.562)/ 14.0625) - (6*154.11/3.753) - (6*289.68/3.753) = 10.0621 KN/m2
s 3 =((500+351.562)/ 14.0625) - (6*154.11/3.753) + (6*289.68/3.753) = 45.131 KN/m2
s 4 = ((500+351.562)/ 14.0625) + (6*154.11/3.753) + (6*289.68/3.753) = 111.049 KN/m2
which is < 120 KN/m2. Hence OK
Stability Check
Calculation for Overturning and Sliding
For Sliding
Along X- Direction:
Disturbing force = -300 KN
Restoring Force = μ*(Wt of Footing + Fy + Wt of Soil) = 474.6848 KN
Hence, Factor of Safety against Sliding = (474.6848/300) =1.5823 > 1.5 Hence Safe
Along Z- Direction:
Disturbing force = -200 KN
Restoring Force = μ*(Wt of Footing + Fy + Wt of Soil) = 474.6848 KN
Hence, Factor of Safety against Sliding = (474.6848/200) =2.373 > 1.5 Hence Safe
304 — STAAD Foundation Advanced V8i
Chapter — 5
5.17 US General Isolated Foundation with Sliding & Overturning
For Overturning
About X- Direction:
Overturning Moment = Mx + Fz* (Ht of Pedestal + Depth of Footing) = 45.89– 200* (0 +1) = -154.11 KN-m
Restoring Moment = (Fy + Wt of Soil + Wt of Footing) *Width of Footing*0.5= 1780.068 KN-m
Hence, Factor of Safety against Overturning = (1780.068/154.11) =11.5506 > 1.5 Hence Safe
About Z- Direction:
Overturning Moment = Mx + Fz* (Ht of Pedestal + Depth of Footing) =-10.32+ 300* (0 +1) = 289.68 KN-m
Restoring Moment = (Fy + Wt of Soil + Wt of Footing) *Width of Footing*0.5= 1780.068 KN-m
Hence, Factor of Safety against Overturning = (1780.068/289.68) =6.1449 > 1.5 Hence Safe
Check For Shear
Factored loads and soil reaction:
To proportion the footing for strength (depth and required reinforcement) factored loads areused. For this problem, the factors used are all 1.0
The pressure at the four corners are given by:-
s 1 = (500/ 14.0625) + (6*154.11/3.753) - (6*289.68/3.753) = 50.9804 KN/m2
s 2 = (500/ 14.0625) - (6*154.11/3.753) - (6*289.68/3.753) = -14.9378 KN/m2
s 3 =(500/ 14.0625) - (6*154.11/3.753) + (6*289.68/3.753) = 20.1307 KN/m2
s 4 = (500/ 14.0625) + (6*154.11/3.753) + (6*289.68/3.753) = 86.049 KN/m2
Average pressure:-
qu = (s 1 +s 2 +s 3+s 4) / 4 = 35.555 KN/ m2
Figure 5-42: Critical section for punching shear is at d/2
Section 5 United States Code (ACI 318 -2005)
5.17 US General Isolated Foundation with Sliding & Overturning
Verification Manual — 305
Depth requirement for shear usually controls the footing thickness. Both wide action andtwo-way action (punching shear) for strength computation need to be investigated todetermine the controlling shear criteria for depth.
Assume overall footing thickness = 1.0m and average effective thickness d = 0.92m (36.22in)
Wide-beam action (One-Way Shear) :
Along Z-Z axis: -
Vu = qs tributary area
Bw = 3.75m = 147.6378 in
qs is given by:-
Average Base Pressure along one edge = (50.98041-14.9379)/2 =18.02126KN/m2
Average Base Pressure along other edge = (20.1307+86.049)/2 = 53.0899KN/m2
Approximate Base Pressure at the critical section = 53.0899- {(53.0899 -18.02126)/3.75*0.805} =45.56183 KN/ m2 [0.805=3.75-(3.75/2+0.92+0.15)]
Hence, the one- way shear at the critical section
Vux =3.75*{45.56183*0.805+0.5*(53.0899-45.56183)*0.805}= 148.9025 KN
Along X-X axis:-
Vu = qs tributary area
Bw = 3.75m = 147.6378 in
qs is given by:-
Average Base Pressure along one edge = (86.049+50.98041)/2 =68.5147KN/m2
Average Base Pressure along other edge = (20.1307-14.9379)/2 = 2.5964KN/m2
Approximate Base Pressure at the critical section = 68.5147- {(68.5147-2.5964)/3.75*0.805} =54.36424 KN/ m2[0.805=(3.75/2–0.92–0.15)]
Hence, the one-way shear at the critical section
Vuz =3.75*{54.36424*0.805+0.5*(68.5147-54.36424)*0.805}= 185.47 KN
φVu = φ(2√(f'c)bwd) = 0.75(2√(4349.39) 147.6378 36.22)/1000 =529.0018 kips = 2354.06 KN > Vux and Vuz
Hence O.K.
Two-way action (Punching Shear):
Vu = qs tributary area
306 — STAAD Foundation Advanced V8i
Chapter — 5
5.17 US General Isolated Foundation with Sliding & Overturning
Tributary area = 14.0625 - (0.3+ 0.92)·(0.3 + 0.92) = 12.5741 m2
Vu = 35.555 12.5741 = 447.0791 KN = 100.467 Kip.
= Minimum of
bo = 2(0.3+0.3+2*0.92) = 4.88m =192.126 in
= = 5.304348
= 40 for interior columns
=
Vc = 0.75 4 x 192.126 36.2205/1000 = 1376.82 kips > Vu= 100.467 kips
O.K.
Calculation for reinforcementFigure 5-43: Critical section for moment is at the face of column
Section 5 United States Code (ACI 318 -2005)
5.17 US General Isolated Foundation with Sliding & Overturning
Verification Manual — 307
Bending about X Axis Bending About Z Axis
About X Axis
Average Base Pressure along one edge = (50.98041-14.9379)/2 =18.02126KN/m2
Average Base Pressure along other edge = (20.1307+86.049)/2 = 53.0899KN/m2
Approximate Base Pressure at the critical section = 53.0899- {(53.0899 -18.02126)/3.75*1.725} =36.958 KN/ m2 [1.725= 3.75-(3.75/2+0.15)]
Hence, the moment at the critical section
Mu =3.75*{36.958*1.725*1.725*0.5+0.5*(53.0899-36.958)*1.725*1.725*2/3}=266.2033 KNm
Required Rn = KN/m2 =13.5105psi
(gross area) = (d/h) 0.00022 = (0.92/1.0) 0.00027 = 0.000207
Check minimum As required for footings of uniform thickness; for grade 415 reinforcement:
min = 0.00180
Since is < min, so = min =0.00180
308 — STAAD Foundation Advanced V8i
Chapter — 5
5.17 US General Isolated Foundation with Sliding & Overturning
Required As = bd = 0.00180 3.75 0.92 = 0.00621 m2 = 6210 m2m
About Z Axis
Average Base Pressure along one edge = (86.049+50.98041)/2 =68.5147KN/m2
Average Base Pressure along other edge = (20.1307-14.9379)/2 = 2.5964KN/m2
Approximate Base Pressure at the critical section = 68.5147- {(68.5147-2.5964)/3.75*1.725} =38.1923 KN/ m2 [1.725=(3.75/2-0.15)]
Hence, the moment at the critical section
Mu =3.75*{38.1923*1.725*1.725*0.5+0.5*(68.5147-38.1923)*1.725*1.725*2/3}=325.87126 KNm
Compute required As assuming tension-controlled section ( = 0.9)
Required Rn = KN/m2 =8.44355psi
p(gross area) = (d/h) 0.00014 = (0.92/1.0) 0.00014 = 0.000129
Check minimum As required for footings of uniform thickness; for grade 415 reinforcement:
min = 0.00180
Since is < min, so = min =0.00180
Required As = bd = 0.00180 3.75 0.92 = 0.00621 m2 = 6210 m2m
Try with 16mm bars (Af =201.06 m2m)
So, no. of bars reqd = 6210/ 201.06 =31 bars
Check for development length
Critical section for development length is same as that for moment (at face of column).
As per ACI- 12.2.2 and T-1.12.2 of Reinforced Concrete Design by Salmon-Wang; For # 35Mbars and smaller:
Section 5 United States Code (ACI 318 -2005)
5.17 US General Isolated Foundation with Sliding & Overturning
Verification Manual — 309
Ld = 0.02 Ab = 0.02* 201.06*(415/300.5) = 304.68 mm
Available development length of the bars = 0.5*(L-Dcol) –C cover = 1675 mm> 304.68 mm.
Hence OK
Clear cover (bottom and side) = 50 mm
Center-to-center bar spacing = {3750-2*(50+8)}/30 = 121.13 mm
This is to be checked with the minimum and maximum spacing permissible.
310 — STAAD Foundation Advanced V8i
Chapter — 5
5.17 US General Isolated Foundation with Sliding & Overturning
5.17.4 Comparison
Value of ReferenceResult
STAADFoundationResult*
Difference (Reasonsthere-of)
Moment about X(KNm)
266.2033 269.53 Error due toapproximation in basepressure interpolation
Moment about Z(KNm)
325.87126 328.41 m Error due toapproximation in basepressure interpolation
Area of steel aboutX-X (mm2)
6210 6106.05 Error due toapproximation in basepressure interpolation
Area of steel aboutZ-Z (mm2)
6210 6241.05 Error due toapproximation in basepressure interpolation
Shear force
(One way) along X(KN)
185.47 186.09 Error due toapproximation in basepressure interpolation
Shear force
(One way) along Z(KN)
148.9025 144.21 Error due toapproximation in basepressure interpolation
Shear force
(Two way) (KN)
447.079 447.38 Negligible
Factor of Safetyagainst Sliding (X)
1.582 1.582 Negligible
Factor of Safetyagainst Sliding (Z)
2.373 2.373 Negligible
Factor of SafetyagainstOverturning (X)
11.5506 11.550 Negligible
Factor of SafetyagainstOverturning (Z)
6.1449 6.145 Negligible
Table 5-21: US verification example 14 comparison
5.18 US General Isolated Foundation withEccentric Loading
5.18.1 Reference
5.18.2 ProblemDesign an isolated footing with the given data:
Section 5 United States Code (ACI 318 -2005)
5.18 US General Isolated Foundation with Eccentric Loading
Verification Manual — 311
Offset of column in X-direction (Oxd) =300 mm
Offset of column in Z-direction (Ozd) =300 mm
Density of soil =14 KN/m3
Depth of Soil = 0.5m
Density of Concrete = 25 KN/m3
Coefficient of Friction (m) = 0.5
Safe Bearing Capacity of the Soil (s) = 120 KN/m2
Factor of Safety against Overturning =1.5
Factor of Safety against Sliding = 1.5
Permissible soil pressure =
Column dimension = 0.3m x 0.3m,
Strength of concrete (fc’) = M-30 = 4349.39 Psi
Strength of steel (fy) = Fe-415
Loads:
Fx =-300 KN
Fy =-500 KN
Fz=-200 KN
Mz= 45.89 KNm
Mx=-98.32 KNm
Note: Self weight of footing, wt of soil and surcharge are not included for shear andmoment computations.
312 — STAAD Foundation Advanced V8i
Chapter — 5
5.18 US General Isolated Foundation with Eccentric Loading
Figure 5-44: Plan and Elevation
5.18.3 SolutionDesign started with trial dimensions of 5.0m X 5.0m X 1.0m
Determination of base area of footing:
The base area of footing is determined using service (unfactored) loads with the netpermissible soil pressure.
Net permissible soil pressure = 120 KN/ m2
Required base area of footing = [500 + 0.10(500)]/120 = 4.5833 m2
Use a 5 .0m 5.0m square footing (Af =25 m2).
Using a depth of 1m;
Section 5 United States Code (ACI 318 -2005)
5.18 US General Isolated Foundation with Eccentric Loading
Verification Manual — 313
Self-wt. of Footing =(5.0*5.0*1*25) = 625 KN
Wt. of soil = 14*0.5*{(5.0*5.0) –(0.3*0.3)} =174.37 KN
Serviceability Check
The net moments are given by:
Mz =+45.89 – (-300*1) +(-500*0.3) = 195.89 KNm
Mx= - 98.32 +(-200*1) –(-500*0.3) = -148.32 KNm
The pressure at the four corners are given by:
σ1 = ((500+625)/ 25) + (6*195.89 /5.03) - (6*148.32/5.03) = 47.28336KN/m2
σ2 = ((500+625)/25) - (6*195.89 /5.03) - (6*148.32 /5.03) = 28.478 KN/m2
σ3 =((500+625)/ 25) - (6*195.89 /5.03) + (6*148.32 /5.03) = 42.7167 KN/m2
σ4 = ((500+625)/ 25) + (6*195.89 /5.03) + (6*148.32/5.03) = 61.522 KN/m2
which is < 120 KN/m2. Hence OK
Stability Check
Calculation for Overturning and Sliding
For Sliding
Along X- Direction:
Disturbing force = -300 KN
Restoring Force = m*(Wt of Footing + Fy + Wt of Soil) = 649.685 KN
Hence, Factor of Safety against Sliding = (649.685/300) =2.1656 > 1.5
Hence Safe
Along Z- Direction:
Disturbing force = -200 KN
Restoring Force = m*(Wt of Footing + Fy + Wt of Soil) = 649.685 KN
Hence, Factor of Safety against Sliding = (649.685/200) =3.2484 > 1.5
Hence Safe
For Overturning
About X- Direction:
Overturning Moment = Mx + Fz* (Ht of Pedestal + Depth of Footing) = -98.32– 200* (0 +1) = -298.32 KN-m
314 — STAAD Foundation Advanced V8i
Chapter — 5
5.18 US General Isolated Foundation with Eccentric Loading
Restoring Moment = Fy * (Width of Footing *0.5 –Ozd)+ (Wt of Soil + Wt ofFooting) * Width of Footing*0.5 = 3098.425 KN-m
Factor of Safety against Overturning = (3098.425/298.32) =10.386 > 1.5
Hence Safe
About Z- Direction:
Overturning Moment = Mx + Fz* (Ht of Pedestal + Depth of Footing) =45.89+ 300* (0 +1) = 345.89 KN-m
Restoring Moment = Fy * (Width of Footing *0.5 –Ozd)+ (Wt of Soil + Wt ofFooting) * Width of Footing*0.5 = 3398.425 KN-m
Factor of Safety against Overturning = (3398.425/345.89) =9.82516 > 1.5
Hence Safe
Check for Shear
Factored Loads and Soil Reaction
To proportion the footing for strength (depth and required reinforcement) factored loads areused. For this problem, the factors used are all 1.0
The pressure at the four corners are given by:
σ1 = (500/ 25) + (6*195.89 /5.03) - (6*148.32 /5.03) = 22.2834KN/m2
σ2 = (500/25) - (6*195.89 /5.03) - (6*148.32 /5.03) = 3.47792KN/m2
σ3 =(500/ 25) - (6*195.89 /5.03) + (6*148.32 /5.03) = 17.7167 KN/m2
σ4 = (500/ 25) + (6*195.89 /5.03) + (6*148.32 /5.03) = 36.52208 KN/m2
Average pressure:
qu = (σ1 +σ2 +σ3+σ4) / 4 = 20.000 KN/ m2
Figure 5-45: Critical section for punching shear at d/2
Depth requirement for shear usually controls the footing thickness. Both wide action andtwo-way action (punching shear) for strength computation need to be investigated todetermine the controlling shear criteria for depth.
Assume overall footing thickness = 1.0m and average effective thickness d = 0.92m (36.22in)
Section 5 United States Code (ACI 318 -2005)
5.18 US General Isolated Foundation with Eccentric Loading
Verification Manual — 315
Wide-beam action (One-Way Shear)
Along Z-Z axis: -
Vu = qs tributary area
Bw = 5.00m = 196.8504 in
qs is given by:
Average Base Pressure along one edge =(22.2834+3.47792)/2 =12.8806 KN/m2
Average Base Pressure along other edge =(17.7167+36.5221)/2 = 27.1194 KN/m2
Approximate Base Pressure at the critical section = 27.1194- {(27.1194 –12.8806)/5.0*1.13} =23.9014 KN/ m2 [1.13=5 -(5/2 +0.3 +0.92 +0.15)]
Hence, the one- way shear at the critical section
Vux =5.0*{23.9014*1.13+0.5*(27.1194-23.9014)*1.13}= 144.134 KN
Along X-X axis:
Vu = qs tributary area
Bw = 5.00m = 196.8504 in
qs is given by:
Average Base Pressure along one edge =(36.5221+22.2834)/2 =29.4027 KN/m2
Average Base Pressure along other edge =(17.7167+3.47792)/2 = 10.5973 KN/m2
Approximate Base Pressure at the critical section = 29.4027- {(29.4027-10.5973)/5.0*1.73}=22.89603 KN/ m2 [ 1.73=(5/2 +0.3 –0.92 –0.15)]
Hence, the one-way shear at the critical section
Vuz =5.0*{22.89603*1.73+0.5*(29.4027-22.89603)*1.73}= 226.1924 KN
φVu = φ (2√(f'c)bwd) = 0.75(2√(4349.39) 196.8504 36.22)/1000 =705.3265 kips = 3138.703 KN > Vux and Vuz
Hence O.K.
Two-way action (Punching Shear)
Vu = qs tributary area
Tributary area = [25.000 - (0.3 + 0.92)x(0.3 + 0.92)] = 23.5116 m2
Vu = 20.000 x 23.5116 = 470.232 KN = 105.6701 Kip.
316 — STAAD Foundation Advanced V8i
Chapter — 5
5.18 US General Isolated Foundation with Eccentric Loading
= Minimum of
bo = 2(0.3+0.3+2*0.92) = 4.88m =192.126 in
= = 5.304348
= 40 for interior columns
=
Vc = 0.75 4 x 192.126 36.2205/1000 = 1376.82 kips > Vu= 100.467 kips O.K.
Calculation for reinforcement
Critical section for moment is at the face of column
Bending about X Axis Bending About Z Axis
Section 5 United States Code (ACI 318 -2005)
5.18 US General Isolated Foundation with Eccentric Loading
Verification Manual — 317
About X-Axis
Average Base Pressure along one edge = (22.2834+3.47792)/2 =12.8806KN/m2
Average Base Pressure along other edge = (17.7167+36.5221)/2 = 27.1194KN/m2
Approximate Base Pressure at the critical section = 27.1194- {(27.1194 –12.8806)/5.0*2.05} =21.2815 KN/ m2 [2.05 =5-(5/2+0.3+0.15)]
Hence, the moment at the critical section
Mu = 5.0*{21.2815 *2.05*2.05*0.5+0.5*(27.1194-21.2815)* 2.05*2.05*2/3}=264.48 KNm
Required Rn = KN/m2 =10.067 psi
ρ(gross area) = (d/h) 0.0001675 = (0.92/1.0) 0.0001675 = 0.0001541
Check minimum As required for footings of uniform thickness; for grade 415 reinforcement:
ρmin = 0.00180
Since ρ is < ρmin, ρ = ρmin =0.00180
Required As = ρbd = 0.00180 5.0 0.92 = 0.00828 m2 = 8280 mm2
About Z- axis:
Average Base Pressure along one edge = (36.5221+22.2834)/2 =29.4027KN/m2
Average Base Pressure along other edge = (17.7167+3.47792)/2 = 10.5973KN/m2
Approximate Base Pressure at the critical section = 29.4027- {(29.4027-10.5973)/5.0*2.65} =19.4358 KN/ m2 [2.65 =(5/2+0.3-0.15)]
Hence, the moment at the critical section
Mu =5.0*{19.4358 *2.65*2.65*0.5+0.5*(29.4027 –19.4358)*2.65*2.65*2/3}=457.874 KNm
Compute required As assuming tension-controlled section ( = 0.9)
318 — STAAD Foundation Advanced V8i
Chapter — 5
5.18 US General Isolated Foundation with Eccentric Loading
Required Rn = KN/m2 =17.429 psi
ρ(gross area) = (d/h) 0.00029 = (0.92/1.0) 0.00029 = 0.000267
Check minimum As required for footings of uniform thickness; for grade 415 reinforcement:
ρmin = 0.00180
Since ρ is < ρmin , ρ = ρmin =0.00180
Required As = ρbd = 0.00180 5.0 0.92 = 0.00828 m2 = 8280 mm2
Try with 20 mm bars (Af =314.16 mm2)
So, no. of bars required = 8280/ 314.16 =27 bars
Check for development length
Critical section for development length is same as that for moment (at face of column).
As per ACI- 12.2.2 and T-1.12.2 of Reinforced Concrete Design by Salmon-Wang:
Ld = 0.02 Ab (For # 35M bars and smaller)
= 0.02* 314.16*(415/300.5) = 476.0625m
Available development length of the bars= 0.5*(L-Dcol) –C cover = 2375 mm> 476.0625 mm. Hence OK
Clear cover (bottom and side) = 50mm
Center-to-center bar spacing = {5000-2*(50+10)}/26 = 187.6923 mm
This is to be checked with the minimum and maximum spacing permissible.
Section 5 United States Code (ACI 318 -2005)
5.18 US General Isolated Foundation with Eccentric Loading
Verification Manual — 319
5.18.4 Comparison
Value of ReferenceResult
STAADFoundationResult*
Difference (Reasonsthere-of)
Moment about X 264.48KNm
264.53KNm
Negligible
Moment about Z 457.874KNm
457.83KNm
Negligible
Area of steel aboutX-X
8280mm2
8906.40mm2
Error due toapproximation in basepressure interpolation
Area of steel aboutZ-Z
8280mm2
8321.40mm2
Error due toapproximation in basepressure interpolation
Shear force
(One way) along X
226.1924KN
225.67 KN Error due toapproximation in basepressure interpolation
Shear force
(One way) along Z
144.134KN
143.58 KN Negligible
Shear force
(Two way)
470.232KN
470.01 KN Negligible
Factor of Safetyagainst Sliding (X)
2.1656 2.166 Negligible
Factor of Safetyagainst Sliding (Z)
3.2484 3.248 Negligible
Factor of SafetyagainstOverturning (X)
10.386 10.386 Negligible
Factor of SafetyagainstOverturning (Z)
9.82516 9.825 Negligible
Table 5-22: US verification example 15 comparison
320 — STAAD Foundation Advanced V8i
Chapter — 5
5.18 US General Isolated Foundation with Eccentric Loading
Section 6
Deadman Anchors (ACI318 -2005)6.1 Deadman Guy Anchor US 1
6.1.1 Reference380 ft Brenham (Wesley), TX guyed tower Design Project
6.1.2 ProblemDesign an anchor block for a guy rod supporting the following load condition
Axial Tension = 83.815 Kip
Slope with Horizontal = 54.231 degree
Min area required for guy rod =1.677 sq.inch, i.e if single guy rod is used,mindia of rod required = 1.5 inch
Necessary Factors of Safety are as follows
FOS against Uplift = 1.5
FOS against sliding = 2
Ultimate Load Factor = 1.3
Material Specification-
Assume Strength of Concrete = 4 Ksi
Strength of Steel = 60 Ksi
Verification Manual — 321
Strength of Gye Rod steel = 50 Ksi
unit weight of Concrete = 150 lb/cu.ft
unit weight of Soil = 62.4 lb/cu.ft
Soil & GWT condition-
LayerIndex No
LayerType
Depth ofLayer
Cohesion(psf)
Angle ofFriction
Dry Density(pcf)
1 Sand (0-2) 0 20 1152 Sand (2-15) 0 30 1153 Sand (15-below) 0 30 115
Table 6-1: Soil Test Report Summary
Assume depth of Ground Water Table from GL = 8 ft
Assume soil cone angle of uplift = 30 degree
6.1.3 SolutionFirst let us calculate the Horizontal & Vertical components of Axial Tension at guy rod
Horizontal component of load (H) = P.cos θ = 83.815 x Cos 54.231 = 48.9656 Kip
Vertical component of load (V)= P.sin θ = 83.815 x Sin 54.231 = 68.0245Kip
Properties of soil (divided into relevant small strips each max 1/2 ft thick)
322 — STAAD Foundation Advanced V8i
Chapter — 6
6.1 Deadman Guy Anchor US 1
Kp=tan2 (450+ Ø/2)
Kp=tan2 (450- Ø/2)
Note: Ø is in degrees
Pa= γ.h.KpSo Pa or a particular layer = Pa of previous layer + γ.h.KaWhere:
Ka= Active EP coeff of the present layer
γ = Soil density of Soil at present layer
h= Thickness of present layer)
Section 6 Deadman Anchors (ACI 318 -2005)
6.1 Deadman Guy Anchor US 1
Verification Manual — 323
Thus
Pp= γ.h.Kp + 2C.√KpSo Pp or a particular layer = Pp of previous layer + γ.h.KpWhere:
Kp= Passive EP coeff of the present layer
γ = Soil density of Soil at present layer
h= Thickness of present layer
C= Cohesion of Present layer)
Note: Here, γ= Density of soil which is used when soil layer is above GWT
If Soil layer is below GWT then submerged density of soil (γ-γsoil) is used
Adhesion factor α = 0.31 + 0.34/C
Figure 6-1: Deadman Anchor Guy Tension Block section
α <=1
C= Cohesion in Kip/ft2 unit
324 — STAAD Foundation Advanced V8i
Chapter — 6
6.1 Deadman Guy Anchor US 1
Figure 6-2: Dispersion of soil against vertical uplift diagram
Soil Depth upper lvl oflayer(ft)
Soil Depth lower lvl oflayer(ft)
avg Pp effective onblock surface (psf)
weightedavg Pp(lb/ft)
0 0.5 0 00.5 1 0 01 1.5 0 01.5 2 0 02 2.5 0 02.5 3 0 03 3.5 0 03.5 4 0 04 4.5 0 04.5 5 0 05 5.5 0 05.5 6 0 06 6.5 0 06.5 7 2167.1918 1083.5967 7.5 2340.028 1170.0147.5 8 2512.8643 1256.4328 8.5 2638.8093 1319.4058.5 9 2717.8631 1358.9329 9.5 2796.9169 1398.4589.5 10 2875.9707 1437.98510 10.5 0 010.5 11 0 011 11.5 0 011.5 12 0 012 12.5 0 0
Section 6 Deadman Anchors (ACI 318 -2005)
6.1 Deadman Guy Anchor US 1
Verification Manual — 325
Soil Depth upper lvl oflayer(ft)
Soil Depth lower lvl oflayer(ft)
avg Pp effective onblock surface (psf)
weightedavg Pp(lb/ft)
12.5 13 0 013 13.5 0 013.5 14 0 014 14.5 0 014.5 15 0 0
Figure 6-3: Dispersion line diagram
Check for Safety against Sliding
Tot Passive resistance per unit length = 9024.823 lb/ft
Length = 11.5 ft
Tot Passive resistance = 9024.823 x 11.5 /1000 = 103.786 kip
Allowable Horizontal Load on Anchor = 48.9656 Kip
Safety Factor against Horizontal Load = 103.786 / 48.9656 = 2.12
FOS is greater than min required FOS, Hence OK
Check for Safety against Uplift
given value of dispersion angle = 30 degree
Let us consider wedge at all sides with dimension of 0.5 ft
As wedge is present so dispersion is to be started from bottom of block
326 — STAAD Foundation Advanced V8i
Chapter — 6
6.1 Deadman Guy Anchor US 1
Height of soil above top level of block = 6.5 ft
Height of water effecting the weight of concrete = 10 - 8 = 2 ft
Weight of Concre Block = LxBxHx unit wt of concrete = 11.5 x 4 x 3.5 x 0.15= 24.15 kip
reduction of concrete weight due to buoyancy = 2 x 4 x 11.5 x 62.4/1000 =5.7408 kip
So, total buoyant weight of concrete = 24.15-5.7408 = 18.4092Kip
Weight of soil over top of anchor in a truncated pyramid = 215.93 Kip
Uplift Resistance due to Soil/Concrete Adhesion = 0 Kip
Therefore, Total resistance against uplift = 18.4092 + 215.93 + 0 = 234.34 Kip
Allowable anchor uplift resistance = V = 68.0245 Kip
Net Safety factor = 234.34 / 68.0245 = 3.445
Safety Factor against Horizontal Load = 1.5
FOS is greater than min required FOS, Hence OK
Section 6 Deadman Anchors (ACI 318 -2005)
6.1 Deadman Guy Anchor US 1
Verification Manual — 327
Design checks for the top & front face rebar
Top Rebar Design Check
Figure 6-4: Top rebar force diagram
Vertical Force (V)= 68.0245 Kip
Length (L)= 11.5 Kip
Force/Length = w=V/L = 5.91517391304348 Kip
Bending Moment = w.L2/8 = 97.786 ft·kip
Factored Moment M = 97.786 x 1.3 = 127.1218 ft·kip
Strength of concrete = 4 Ksi
Strength of Steel = 60 Ksi
Figure 6-5: Bending moment diagram - top
φ = 0.9
ß = 0.85 - 0.05x (fc-4)
0.85>=ß >=0.65
ß = 0.85
width (B) = 4 ft
Effective Depth = Deff = D-clear cover-Tie bar dia -0.5xtop rebar dia
Hence, deff = 38.19 inch
Area of each top rebar = 0.601015625 sq.inch
Total area of Top Rebar = As = 2.4040625 Ksi
a = As.fy/(ß.fck.B) = 0.883847 inch
328 — STAAD Foundation Advanced V8i
Chapter — 6
6.1 Deadman Guy Anchor US 1
Resisting Moment = M1 = φ.As.fy.(deff-a/2) =408.37 ft·kip
ratio = 408.37 / 127.1218 = 3.213 >1,
Hence OK
Resisting Moment is greater than Factored Moment, Hence Safe
Front face Rebar Design Check
Vertical Force (V)= 48.9656 Kip
Length (L) = 11.5 ft
Force/Length = w=V/L = 4.25787826086957 Kip/ft
Bending Moment = w.L2/8 = 70.389 ft·kip
Factored Moment M = 91.5057 ft·kip
Strength of concrete = 4 Ksi
Figure 6-6: Bending moment diagram - front face
Strength of Steel = 60 Ksi
φ = 0.9
ß = 0.85 - 0.05x (fc-4)
0.85>=ß >=0.65
ß = 0.85
width (B) = 3.5 ft
Effective Depth = Deff = D-clear cover-Tie bar dia -0.5xtop rebar dia
Hence, deff = 44.19 inch
Area of each front rebar = 0.601015625 sq.inch
Total area of Front Rebar = As = 1.803046875 sq.inch
a = As.fy/(ß.fck.B) = 0.757583 inch
Resisting Moment = M1 = φ.As.fy.(deff-a/2) = 355.47 ft·kip
ratio = 355.472 / 91.5057 = 3.885 >1, Hence OK
Resisting Moment is greater than Factored Moment, Hence Safe
Section 6 Deadman Anchors (ACI 318 -2005)
6.1 Deadman Guy Anchor US 1
Verification Manual — 329
6.1.4 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Sliding Resistance (kips) 103.786 103.71 NegligibleUplift Resistance (kips) 234.34 234.495 NegligibleHorizontal FOS 2.12 2.117 NegligibleVertical FOS 3.445 3.448 NegligibleFactored moment resisted by top rebar(ft-kip)
127.122 127.086 Negligible
Max. moment capacity (vertically hog-ging) (ft-kip)
408.37 407.66 Negligible
Factored moment resisted by front rebar(ft-kip)
91.506 91.553 Negligible
Max. moment capacity (horizontallyhogging) (ft-kip)
355.472 354.856 Negligible
Table 6-2: Deadman Anchor (US) verification example 1 comparison
6.2 Deadman Guy Anchor US 26.2.1 Reference380 ft Brenham (Wesley), TX guyed tower Design Project
6.2.2 ProblemDesign an anchor block for a guy rod supporting the following load condition-
Axial Tension = 75.926 Kip
Slope with Horizontal = 49.816 degree
Min area required for guy rod =1.519 sq.inch, i.e if single rod is used,min dia of rodrequired = 1.4 inch
330 — STAAD Foundation Advanced V8i
Chapter — 6
6.2 Deadman Guy Anchor US 2
Figure 6-7: Deadman Anchor Guy Tension Block section
Necessary FOS are as follows-
FOS against Uplift = 1.5
FOS against sliding = 2
Ultimate Load Factor = 1.3
Material Specification-
Assume Strength of Concrete = 4 Ksi
Strength of Steel = 60 Ksi
Strength of Gye Rod steel = 50 Ksi
unit weight of Concrete = 150 lb/cu.ft
unit weight of Soil = 62.4 lb/cu.ft
Soil & GWT condition
LayerIndex No
LayerType
Depth ofLayer
Cohesion(psf)
Angle ofFriction
Dry Density(pcf)
1 clay (0-2) 0 0 1062 clay (2-15) 800 0 1063 clay (15-below) 800 0 106
Table 6-3: Soil test report summary
Assume depth of Ground Water Table from GL = 8 ft
Assume soil cone angle of uplift = 0 degree
6.2.3 SolutionFirst let us calculate the Horizontal & Vertical components of Axial Tension at gyerod
Section 6 Deadman Anchors (ACI 318 -2005)
6.2 Deadman Guy Anchor US 2
Verification Manual — 331
Horizontal component of load (H) = P.cos θ = 75.926 x Cos 49.816 = 48.9706 Kip
Vertical component of load (V)= P.sin θ = 75.926 x Sin 49.816 = 58.0229Kip
Properties of soil (divided into relevant small strips each max 1/2 ft thick)
Kp=tan2 (450 + Ø/2)
Kp=tan2 (450 - Ø/2)
Note: Ø is in degree
Pa= γ.h.Kp
332 — STAAD Foundation Advanced V8i
Chapter — 6
6.2 Deadman Guy Anchor US 2
So Pa or a particular layer = Pa of previous layer + γ.h.KaWhere:
Ka= Active EP coeff of the present layer
γ = Soil density of Soil at present layer
h= Thickness of present layer
Thus
Pp= γ.h.Kp + 2C.√KpSo Pp or a particular layer = Pp of previous layer + γ.h.KpWhere:
Kp= Passive EP coeff of the present layer
γ = Soil density of Soil at present layer
h= Thickness of present layer
C= Cohesion of Present layer
Note: Here γ= Density of soil which is used when soil layer is above GWT
If Soil layer is below GWT then submerged density of soil (γ-γsoil) is used
Adhesion factor α = 0.31 + 0.34/C
α <=1
C= Cohesion in Kip/ft2 unit
Figure 6-8: Dispersion of soil against vertical uplift
Section 6 Deadman Anchors (ACI 318 -2005)
6.2 Deadman Guy Anchor US 2
Verification Manual — 333
Soil Depth upper lvl oflayer(ft)
Soil Depth lower lvl oflayer(ft)
avg Pp effective onblock surface (psf)
weightedavg Pp(lb/ft)
0 0.5 0 00.5 1 0 01 1.5 0 01.5 2 0 02 2.5 0 02.5 3 0 03 3.5 0 03.5 4 0 04 4.5 0 04.5 5 0 05 5.5 0 05.5 6 0 06 6.5 0 06.5 7 2317.4172 1158.7097 7.5 2370.4843 1185.2427.5 8 2423.5513 1211.7768 8.5 2460.9987 1230.4998.5 9 2482.8262 1241.4139 9.5 2504.6538 1252.3279.5 10 2526.4814 1263.24110 10.5 0 010.5 11 0 011 11.5 0 011.5 12 0 012 12.5 0 012.5 13 0 013 13.5 0 013.5 14 0 014 14.5 0 014.5 15 0 0
Table 6-4: Soil layers
Check for Safety against Sliding
Tot Passive resistance per unit length = 8543.207 lb/ft
Length = 14 ft
Tot Passive resistance = 8543.207 x 14 /1000 = 119.605 kip
Allowable Horizontal Load on Anchor = 48.9706 Kip
Safety Factor against Horizontal Load = 119.605 / 48.9706 = 2.443
FOS is greater than min required FOS, Hence OK
334 — STAAD Foundation Advanced V8i
Chapter — 6
6.2 Deadman Guy Anchor US 2
Check for Safety against Uplift
given value of dispersion angle = 0 degree
Let us consider no wedge to support uplift load
As wedge is not present so dispersion is to be started from top of block
Height of soil above top level of block = 6.5 ft
Height of water effecting the weight of concrete = 10 - 8 = 2 ft
Weight of Concrete Block = LxBxHx unit wt of concrete = 14 x 4 x 3.5 x 0.15= 29.4 kip
reduction of concrete weight due to buoyancy = 2 x 4 x 14 x 62.4/1000 =6.9888 kip
So, total buoyant weight of concrete = 29.4-6.9888 = 22.4112Kip
Weight of soil over top of anchor in a truncated pyramid = 38.58 Kip
Uplift Resistance due to Soil/Concrete Adhesion = 74.08 Kip
Therefore, Total resistance against uplift = 22.4112 + 38.58 + 74.08 = 135.072Kip
Allowable anchor uplift resistance = V = 58.0229 Kip
Net Safety factor = 135.072 / 58.0229 = 2.328
Safety Factor against Horizontal Load = 1.5
FOS is greater than min required FOS, Hence OK
Section 6 Deadman Anchors (ACI 318 -2005)
6.2 Deadman Guy Anchor US 2
Verification Manual — 335
Design checks for the top & front face rebar
Top Rebar Design Check
Vertical Force (V)= 58.0229 Kip
Length (L)= 14 Kip
Figure 6-9: Top rebar force diagram
Force/Length = w=V/L = 4.14449285714286 Kip
Bending Moment = w.L2/8 = 101.541 ft·kip
Factored Moment M = 101.541 x 1.3 = 132.0033 ft·kip
Strength of concrete = 4 Ksi
Strength of Steel = 60 Ksi
φ = 0.9
ß = 0.85 - 0.05x (fc-4)
0.85>=ß >=0.65
ß = 0.85
width (B) = 4 ft
Effective Depth = Deff = D-clear cover-Tie bar dia -0.5xtop rebar dia
Figure 6-10: Bending moment diagram - top
Hence, deff =38.19 inch
Area of each top rebar = 0.601015625 sq.inch
Total area of Top Rebars = As = 2.4040625 Ksi
a = As.fy/(ß.fck.B) = 0.883847 inch
336 — STAAD Foundation Advanced V8i
Chapter — 6
6.2 Deadman Guy Anchor US 2
Resisting Moment = M1 = φ.As.fy.(deff-a/2) = 408.37
ft·kip
ratio = 408.37 / 132.0033 = 3.094 >1, Hence OK
Resisting Moment is greater than Factored Moment, Hence Safe
Front face Rebar Design Check
Vertical Force (V)= 48.9706 Kip
Length (L) = 14 ft
Force/Length = w=V/L = 3.4979 Kip/ft
Bending Moment = w.L2/8 = 85.699 ft·kip
Factored Moment M = 111.4087 ft·kip
Figure 6-11: Bending moment diagram - front face
Strength of concrete = 4 Ksi
Strength of Steel = 60 Ksi
φ = 0.9
ß = 0.85 - 0.05x (fc-4)
0.85>=ß >=0.65
ß = 0.85
width (B) = 3.5 ft
Effective Depth = Deff = D-clear cover-Tie bar dia -0.5xtop rebar dia
Hence, deff = 44.19 inch
Area of each front rebar = 0.601015625 sq.inch
Total area of Front Rebar = As = 1.803046875 sq.inch
a = As.fy/(ß.fck.B) = 0.757583 inch
Resisting Moment = M1 = φ.As.fy.(deff-a/2) = 355.47 ft·kip
ratio = 355.472 / 111.4087 = 3.191 >1, Hence OK
Resisting Moment is greater than Factored Moment, Hence Safe
Section 6 Deadman Anchors (ACI 318 -2005)
6.2 Deadman Guy Anchor US 2
Verification Manual — 337
6.2.4 Comparison
Value of ReferenceResult
STAADFoundation
Result
Percent Dif-ference
Sliding Resistance (Kip) 119.605 119.542 negligibleUplift Resistance (Kip) 135.072 135.123 negligibleHorizontal FOS 2.443 2.44 negligibleVertical FOS 2.328 2.329 negligiblefactored moment resisted by toprebar ( ft·kip)
132.0033 131.963 negligible
Max moment capacity(vertically hogging) (ft·kip)
408.37 407.66 negligible
factored moment resisted byfront rebar (ft·kip)
111.4087 111.454 negligible
Max moment capacity(horizontally hogging) (ft·kip)
355.472 354.865 negligible
Table 6-5: Deadman Anchor (US) verification example 2 comparison
6.3 Deadman Guy Anchor US 36.3.1 Reference380 ft Brenham (Wesley), TX guyed tower Design Project
6.3.2 ProblemDesign an anchor block for a guy rod supporting the following load condition
Axial Tension = 92.435 Kip
Slope with Horizontal = 31.289 degree
Min area required for guy rod =1.849 sq.inch, i.e if single rod is used,min diaof rod required = 1.6 inch
Necessary FOS are as follows
FOS against Uplift = 1.5
FOS against sliding = 2
Ultimate Load Factor = 1.3
Material Specification
Assume Strength of Concrete = 4 Ksi
Strength of Steel = 60 Ksi
Strength of Gye Rod steel = 50 Ksi
unit weight of Concrete = 150 lb/cu.ft
unit weight of Soil = 62.4 lb/cu.ft
338 — STAAD Foundation Advanced V8i
Chapter — 6
6.3 Deadman Guy Anchor US 3
Soil & GWT condition
LayerIndex No
LayerType
Depth ofLayer
Cohesion(psf)
Angle ofFriction
Dry Density(pcf)
1 silt (0-2) 500 20 1052 silt (2-15) 500 20 1053 silt (15-
below)500 20 105
Table 6-6: Soil test report summary
Assume depth of Ground Water Table from GL = 8 ft
Assume soil cone angle of uplift = 20 degree
6.3.3 SolutionFirst let us calculate the Horizontal & Vertical components of Axial Tension at gyerod
Horizontal component of load (H) = P.cos θ = 92.435 x Cos 31.289 = 78.9806 Kip
Vertical component of load (V)= P.sin θ = 92.435 x Sin 31.289 = 48.024 Kip
Properties of soil (divided into relevant small strips each max 1/2 ft thick)
Section 6 Deadman Anchors (ACI 318 -2005)
6.3 Deadman Guy Anchor US 3
Verification Manual — 339
Kp=tan2 (450+Ø/2)
Kp=tan2 (450-Ø/2)
Note: Ø is in degree
Pa= γ.h.Kp
340 — STAAD Foundation Advanced V8i
Chapter — 6
6.3 Deadman Guy Anchor US 3
Figure 6-12: Deadman Anchor Guy Tension Block section
So Pa or a particular layer = Pa of previous layer + γ.h.KaWhere:
Ka= Active EP coeff of the present layer
γ = Soil density of Soil at present layer
h= Thickness of present layer
Pp= γ.h.Kp + 2C.√KpSo Pp or a particular layer = Pp of previous layer + γ.h.KpWhere:
Kp= Passive EP coeff of the present layer
γ = Soil density of Soil at present layer
h= Thickness of present layer
C= Cohesion of Present layer
Note: Here γ= Density of soil which is used when soil layer is above GWT
If Soil layer is below GWT then submerged density of soil (γ-γsoil) is used
Adhesion factor α = 0.31 + 0.34/C
α <=1
C= Cohesion in Kip/ft2 unit
Section 6 Deadman Anchors (ACI 318 -2005)
6.3 Deadman Guy Anchor US 3
Verification Manual — 341
Figure 6-13: Dispersion of soil against vertical uplift diagram
Soil Depth upper lvl oflayer(ft)
Soil Depth lower lvl oflayer(ft)
avg Pp effective onblock surface (psf)
weightedavg Pp(lb/ft)
0 0.5 0 00.5 1 0 01 1.5 0 01.5 2 0 02 2.5 0 02.5 3 0 03 3.5 0 03.5 4 0 04 4.5 0 04.5 5 0 05 5.5 0 05.5 6 0 06 6.5 0 06.5 7 0 07 7.5 2984.5298 1492.2657.5 8 3091.7854 1545.8938 8.5 3167.1708 1583.5858.5 9 3210.6859 1605.3439 9.5 3254.2011 1627.1019.5 10 3297.7162 1648.85810 10.5 3341.2313 1670.61610.5 11 3384.7465 1692.37311 11.5 3428.2616 1714.13111.5 12 3471.7768 1735.888
Table 6-7: Soil layers
342 — STAAD Foundation Advanced V8i
Chapter — 6
6.3 Deadman Guy Anchor US 3
Soil Depth upper lvl oflayer(ft)
Soil Depth lower lvl oflayer(ft)
avg Pp effective onblock surface (psf)
weightedavg Pp(lb/ft)
12 12.5 0 012.5 13 0 013 13.5 0 013.5 14 0 014 14.5 0 014.5 15 0 0
Check for Safety against Sliding
Tot Passive resistance per unit length = 16316.053 lb/ft
Length = 10 ft
Tot Passive resistance = 16316.053 x 10 /1000 = 163.161 kip
Allowable Horizontal Load on Anchor = 78.9806 Kip
Safety Factor against Horizontal Load = 163.161 / 78.9806 = 2.066
FOS is greater than min required FOS, Hence OK
Check for Safety against Uplift
given value of dispersion angle = 20 degree
Let us consider no wedge to support uplift load
As wedge is not present so dispersion is to be started from top of block
Section 6 Deadman Anchors (ACI 318 -2005)
6.3 Deadman Guy Anchor US 3
Verification Manual — 343
Figure 6-14: Dispersion line diagram
Height of soil above top level of block = 7 ft
Height of water effecting the weight of concrete = 12 - 8 = 4 ft
Weight of Concre Block = LxBxHx unit wt of concrete = 10 x 4 x 5 x 0.15 =30 kip
reduction of concrete weight due to buoyancy = 4 x 4 x 10 x 62.4/1000 =9.984 kip
So, total buoyant weight of concrete = 30-9.984 = 20.016Kip
Weight of soil over top of anchor in a truncated pyramid = 61.98 Kip
Uplift Resistance due to Soil/Concrete Adhesion = 69.3 Kip
344 — STAAD Foundation Advanced V8i
Chapter — 6
6.3 Deadman Guy Anchor US 3
Therefore, Total resistance against uplift = 20.016 + 61.98 + 69.3 = 151.296Kip
Allowable anchor uplift resistance = V = 48.024 Kip
Net Safety factor = 151.296 / 48.024 = 3.151
Safety Factor against Horizontal Load = 1.5
FOS is greater than min required FOS, Hence OK
Now Design check for the top & front face rebar are to bedone
Top Rebar Design Check
Vertical Force (V)= 48.024 Kip
Figure 6-15: Top rebar force diagram
Length (L)= 10 Kip
Force/Length = w=V/L = 4.8024 Kip
Bending Moment = w.L2/8 = 60.03 ft·kip
Factored Moment M = 60.03 x 1.3 = 78.039 ft·kip
Strength of concrete = 4 Ksi
Strength of Steel = 60 Ksi
φ = 0.9
ß = 0.85 - 0.05x (fc-4)
0.85>=ß >=0.65
ß = 0.85
width (B) = 4 ft
Effective Depth = Deff = D-clear cover-Tie bar dia -0.5xtop rebar dia
Section 6 Deadman Anchors (ACI 318 -2005)
6.3 Deadman Guy Anchor US 3
Verification Manual — 345
Figure 6-16: Bending moment diagram - top
Hence, deff = 56.19 inch
Area of each top rebar = 0.601015625 sq.inch
Total area of Top Rebars = As = 2.4040625 Ksi
a = As.fy/(ß.fck.B) = 0.883847 inch
Resisting Moment = M1 = φ.As.fy.(deff-a/2) = 603.1 ft·kip
ratio = 603.099 / 78.039 = 7.729 >1, Hence OK
Resisting Moment is greater than Factored Moment, Hence Safe
Front face Rebar Design Check
Vertical Force (V)= 78.9806 Kip
Length (L) = 10 ft
Force/Length = w=V/L = 7.89806 Kip/ft
Bending Moment = w.L2/8 = 98.726 ft·kip
Factored Moment M = 128.3438 ft·kip
Figure 6-17: Bending moment diagram - front face
Strength of concrete = 4 Ksi
Strength of Steel = 60 Ksi
φ = 0.9
ß = 0.85 - 0.05x (fc-4)
0.85>=ß >=0.65
ß = 0.85
width (B) = 5 ft
Effective Depth = Deff = D-clear cover-Tie bar dia -0.5xtop rebar dia
346 — STAAD Foundation Advanced V8i
Chapter — 6
6.3 Deadman Guy Anchor US 3
Hence, deff = 44.19 inch
Area of each front rebar = 0.601015625 sq.inch
Total area of Front Rebar = As = 1.803046875 sq.inch
a = As.fy/(ß.fck.B) = 0.530308 inch
Resisting Moment = M1 = φ.As.fy.(deff-a/2) = 356.39 ft·kip
ratio = 356.394 / 128.3438 = 2.777 >1, Hence OK
Resisting Moment is greater than Factored Moment, Hence Safe
6.3.4 Comparison
Value of ReferenceResult
STAADFoundation
Result
Percent Dif-ference
Sliding Resistance (Kip) 163.161 163.306 NegligibleUplift Resistance (Kip) 151.296 151.355 NegligibleHorizontal FOS 2.066 2.064 NegligibleVertical FOS 3.151 3.153 Negligiblefactored moment resisted by toprebar ( ft·kip)
78.039 78.011 Negligible
Max moment capacity (verticallyhogging) (ft·kip)
603.099 602.06 Negligible
factored moment resisted byfront rebar (ft·kip)
128.3438 128.361 Negligible
Max moment capacity(horizontally hogging) (ft·kip)
356.394 355.775 Negligible
Table 6-8: Deadman Anchor (US) verification example 3 comparison
6.4 Deadman Guy Anchor US 46.4.1 Reference
6.4.2 ProblemDesign an anchor block for a guy rod supporting the following load condition-
Axial Tension = 250 Kip
Slope with Horizontal = 50 degree
Min area required for guy rod =4.167 sq.inch, (i.e if single rod is used, thenmin dia of rod required = 2.4 inch).
Section 6 Deadman Anchors (ACI 318 -2005)
6.4 Deadman Guy Anchor US 4
Verification Manual — 347
Figure 6-18: Deadman Anchor Guy Tension Block section
Necessary FOS are as follows-
FOS against Uplift = 1.5
FOS against sliding = 2
Ultimate Load Factor = 1.3
Material Specification-
Assume Strength of Concrete = 4 Ksi
Strength of Steel = 60 Ksi
Strength of Gye Rod steel = 60 Ksi
unit weight of Concrete = 150 lb/cu.ft
unit weight of Soil = 62.4 lb/cu.ft
Soil & GWT condition
LayerIndex No
LayerType
Depth ofLayer
Cohesion(psf)
Angle ofFriction
Dry Density(pcf)
1 sand (0-3) 0 20 1042 silt (3-5) 500 22 1053 silt (5-8) 800 15 1054 silt (8-10) 800 20 1065 silt (10-12) 850 15 1066 silt (12-20) 850 15 1068 silt (20-below) 850 15 106
Table 6-9: Soil layers
Assume depth of Ground Water Table from GL = 9 ft
Assume soil cone angle of uplift = 28 degree
348 — STAAD Foundation Advanced V8i
Chapter — 6
6.4 Deadman Guy Anchor US 4
6.4.3 SolutionFirst let us calculate the Horizontal & Vertical components of Axial Tension at guy rod
Horizontal component of load (H) = P.cos θ = 250 x Cos 50 = 160.6297 Kip
Vertical component of load (V)= P.sin θ = 250 x Sin 50 = 191.5676 Kip
Properties of soil (divided into relevant small strips each max 1/2 ft thick)
Kp=tan2 (450+Ø/2)
Kp=tan2 (450-Ø/2)
Note: Ø is in degree
Pa= γ.h.KpSo Pa or a particular layer = Pa of previous layer + γ.h.KaWhere:
Ka= Active EP coeff of the present layer
γ = Soil density of Soil at present layer
h= Thickness of present layer)
Pp= γ.h.Kp + 2C.√KpSo Pp or a particular layer = Pp of previous layer + γ.h.KpWhere
Kp= Passive EP coeff of the present layer
γ = Soil density of Soil at present layer
h= Thickness of present layer
C= Cohesion of Present layer
Note: Here γ= Density of soil which is used when soil layer is above GWT
If Soil layer is below GWT then submerged density of soil (γ-γsoil) is used
Adhesion factor α = 0.31 + 0.34/C
α <=1
C= Cohesion in Kip/ft2 unit
Section 6 Deadman Anchors (ACI 318 -2005)
6.4 Deadman Guy Anchor US 4
Verification Manual — 349
Figure 6-19: Dispersion of soil against vertical uplift diagram
350 — STAAD Foundation Advanced V8i
Chapter — 6
6.4 Deadman Guy Anchor US 4
Check for Safety against Sliding
Tot Passive resistance per unit length = 34451.907 lb/ft
Length = 12 ft
Section 6 Deadman Anchors (ACI 318 -2005)
6.4 Deadman Guy Anchor US 4
Verification Manual — 351
Tot Passive resistance = 34451.907 x 12 /1000 = 413.423 kip
Allowable Horizontal Load on Anchor = 160.6297 Kip
Safety Factor against Horizontal Load = 413.423 / 160.6297 = 2.574
FOS is greater than min required FOS, Hence OK
Check for Safety against Uplift
given value of dispersion angle = 28 degree
Let us consider wedge at all sides with dimension of 0.5 ft
As wedge is present so dispersion is to be started from bottom of block
Height of soil above top level of block = 8 ft
Height of water effecting the weight of concrete = 16 - 9 = 7 ft
Weight of Concrete Block = LxBxHx unit wt of concrete = 12 x 6 x 8 x 0.15 =86.4 kip
352 — STAAD Foundation Advanced V8i
Chapter — 6
6.4 Deadman Guy Anchor US 4
reduction of concrete weight due to buoyancy = 7 x 6 x 12 x 62.4/1000 =31.4496 kip
So, total buoyant weight of concrete = 86.4-31.4496 = 54.9504Kip
Weight of soil over top of anchor in a truncated pyramid = 491.29 Kip
Uplift Resistance due to Soil/Concrete Adhesion = 172.97 Kip
Therefore, Total resistance against uplift = 54.9504 + 491.29 + 172.97 =719.211 Kip
Allowable anchor uplift resistance = V = 191.5676 Kip
Net Safety factor = 719.211 / 191.5676 = 3.755
Safety Factor against Horizontal Load = 1.5
FOS is greater than min required FOS, Hence OK
Design checks for the top & front face rebar
Top Rebar Design Check
Figure 6-20: Top rebar force diagram
Vertical Force (V)= 191.5676 Kip
Length (L)= 12 Kip
Force/Length = w=V/L = 15.9639666666667 Kip
Bending Moment = w.L2/8 = 287.352 ft·kip
Factored Moment M = 287.352 x 1.3 = 373.55 ft·kip
Strength of concrete = 4 Ksi
Strength of Steel = 60 Ksi
Figure 6-21: Bending moment diagram - top
Section 6 Deadman Anchors (ACI 318 -2005)
6.4 Deadman Guy Anchor US 4
Verification Manual — 353
φ = 0.9
ß = 0.85 - 0.05x (fc-4)
0.85>=ß >=0.65
ß = 0.85
width (B) = 6 ft
Effective Depth = Deff = D-clear cover-Tie bar dia -0.5xtop rebar dia
Hence, deff = 92.19 inch
Area of each top rebar = 0.601015625 sq.inch
Total area of Top Rebar = As = 3.60609375 Ksi
a = As.fy/(ß.fck.B) = 0.883847 inch
Resisting Moment = M1 = φ.As.fy.(deff-a/2) = 1488.8 ft·kip
ratio = 1488.835 / 373.5576 = 3.986 >1, Hence OK
Resisting Moment is greater than Factored Moment, Hence Safe
Front face Rebar Design Check
Vertical Force (V)= 160.6297 Kip
Length (L) = 12 ft
Force/Length = w=V/L = 13.3858083333333 Kip/ft
Bending Moment = w.L2/8 = 240.945 ft·kip
Factored Moment M = 313.2285 ft·kip
Strength of concrete = 4 Ksi
Strength of Steel = 60 Ksi
Figure 6-22: Bending moment diagram - front face
φ = 0.9
ß = 0.85 - 0.05x (fc-4)
0.85>=ß >=0.65
ß = 0.85
width (B) = 8 ft
354 — STAAD Foundation Advanced V8i
Chapter — 6
6.4 Deadman Guy Anchor US 4
Effective Depth = Deff = D-clear cover-Tie bar dia -0.5xtop rebar dia
Hence, deff = 68.19 inch
Area of each front rebar = 0.601015625 sq.inch
Total area of Front Rebar = As = 3.60609375 sq.inch
a = As.fy/(ß.fck.B) = 0.662885 inch
Resisting Moment = M1 = φ.As.fy.(deff-a/2) = 1101.2 ft·kip
ratio = 1101.17 / 313.2285 = 3.516 >1, Hence OK
Resisting Moment is greater than Factored Moment, Hence Safe
6.4.4 Comparison
Value of ReferenceResult
STAADFoundation
Result
Percent Dif-ference
Sliding Resistance (Kip) 413.423 413.174 negligibleUplift Resistance (Kip) 719.211 719.281 negligibleHorizontal FOS 2.574 2.571 negligibleVertical FOS 3.755 3.756 negligiblefactored moment resisted by toprebar ( ft·kip)
373.5576 373.447 negligible
Max moment capacity (verticallyhogging) (ft·kip)
1488.835 1486.29 negligible
factored moment resisted byfront rebar (ft·kip)
313.2285 313.359 negligible
Max moment capacity (hor-izontally hogging) (ft·kip)
1101.17 1099.277 negligible
Table 6-10: Deadman Anchor (US) verification example 4 comparison
Section 6 Deadman Anchors (ACI 318 -2005)
6.4 Deadman Guy Anchor US 4
Verification Manual — 355
356 — (Undefined variable: Primary.ProductName)
Chapter 6
6.4 Deadman Guy Anchor US 4
Section 7
Drilled Pier Foundations7.1 Drilled Pier Foundation 1 API
7.1.1 ReferenceAPI RP 2A-WSD
7.1.2 ProblemDesign axial capacity for drilled pier with the given data: Design Method: API
Load Fy= 100 kip, fc= 4 ksi, fy= 60 ksi, Straight pier, pier diameter= 2 ft, pier height= 30ft, water level at 40 ft.
Soil Profile by Layer
1. Sand, 8 ft deep, angle of friction 30 deg, Avg Density 108 lb/ft3,
Density- Loose
2. Sand, 13 ft deep, angle of friction 34 deg, Avg Density 110 lb/ft3,
Density- Medium
3. Clay - , 9 ft deep, cohesion 2 kip/ft2, Avg Density 110 lb/ft3,
Density- Dense
Elasticity of Soil 0.3 ksi
Verification Manual — 357
Figure 7-1: Pier Elevation
Factor of safety
End bearing - 3
Skin Friction - 3
% of Capacity Used
End bearing - 100%
Skin Friction - 100%
Neglected zone for skin friction
Top - 5ft
Bottom - Pier Dia = 2ft
Concrete Properties
fc= 4ksi
Ec= 3605ksi
358 — STAAD Foundation Advanced V8i
Chapter — 7
7.1 Drilled Pier Foundation 1 API
Density= 150lb/ft3
Rebar Properties
fy= 60ksi
Es= 29000ksi
7.1.3 Solution
Critical Depth
Critical depth is set to be calculated by program
Effective Overburden Pressure
Po= (Soil Density of respective layer x Depth to the center of the layer)
Effects of water and critical depth are also considered calculating Po
Layer Effective Overburden Pres-sure (lb/ft2)
Layer1 432Layer2 1579Layer3 2789
Skin Friction
Ψ Factor from API RP 2A-WSD 6.4.2
Ψ = Cohesion / Effective Overburden Pressure
Layer ΨLayer1 0Layer2 0Layer3 0.7171
α Factor from API RP 2A-WSD 6.4.2
α = 0.5 x Ψ -0.5 Ψ <=1.0
α = 0.5 x Ψ -0.25 Ψ >1.0
Layer αLayer1 0Layer2 0Layer3 0.59045
Section 7 Drilled Pier Foundations
7.1 Drilled Pier Foundation 1 API
Verification Manual — 359
K Coefficient of lateral earth pressure from API RP 2A-WSD 6.4.3
K=0.8 (for straight pier)
δ Friction angle between soil and pier
Calculated based on API RP 2A-WSD Table 6.4.3-1
Shaft friction (f), from API RP 2A-WSD 6.4.2 & 6.4.3
For cohesive soil layerf = α x c
For cohesionless soil layerf = K xPo x tanδ
Layer Shaft Friction (psf)Layer1 125.788Layer2 589.040Layer3 1180.889
Skin Friction Resistance (Qf), from API RP 2A-WSD 6.4.1
Qf = f x As
Layer Qf (kip)Layer1 6.3228Layer2 48.1136Layer3 66.7777Total Skin Friction 121.214
Modified Skin Friction Based on Neglected Zones for Skin Friction
Qf (modified) is calculated by considering top and bottom neglect layer
Layer Qf_modified(kip)
Layer1 2.3711Layer2 48.1136Layer3 51.9382Total Modified SkinFriction
102.423
Base Resistance
Unit end bearing (q), from API RP 2A-WSD 6.4.2 & 6.4.3
For cohesive soil layer q = 9 x c
For cohesionless soil layer q =po x Nq
Layer q (kip)Layer1 5.184Layer2 31.58Layer3 18.0
End Bearing for each layer (Qp), from API RP 2A-WSD 6.4.1
Qp = q x Ap
360 — STAAD Foundation Advanced V8i
Chapter — 7
7.1 Drilled Pier Foundation 1 API
Layer Qp (kip)Layer1 16.286Layer2 99.211Layer3 56.549
End Bearing for bottom Layer, Qp_bott = 56.549 kips
Unfactored Capacity
Factored Capacity
7.1.4 Comparison
Value ofSTAAD Foun-
dationResult
ReferenceResult Difference
UnfactoredTip Resistance 56.571 kip 56.549 kip NegligibleUnfactored SkinResistance
102.487 kip 102.423 kip Negligible
Unfactored Total AxialCapacity
144.916 kip 144.834 kip Negligible
FactoredTip Resistance 18.857 kip 18.849 kip NegligibleFactored Skin Resistance 34.162 kip 34.141 kip NegligibleFactored Total AxialCapacity
48.305 kip 48.278 kip Negligible
Table 7-1: Drilled Pier (API) verification example 1 comparison
7.2 Drilled Pier Foundation 2 API7.2.1 ReferenceAPI RP 2A-WSD
7.2.2 ProblemDesign axial capacity for drilled pier with the given data: Design Method:API
Load Fy= 100kip, fc= 4ksi, fy= 60ksi, Straight pier, pier diameter= 4ft, pier height= 39ft,water level at 50ft.
Section 7 Drilled Pier Foundations
7.2 Drilled Pier Foundation 2 API
Verification Manual — 361
Soil Profile by Layer
1. Clay - , 6ft deep, cohesion 1kip/ft2, Avg Density 105lb/ft3, Density- Very Loose
2. Clay - , 13ft deep, cohesion 1.1kip/ft2, Avg Density 110lb/ft3, Density- Medium
3. Clay - , 8ft deep, cohesion 2kip/ft2, Avg Density 111lb/ft3, Density- Dense
4. Clay - , 12ft deep, cohesion 3kip/ft2, Avg Density 113lb/ft3, Density- Very Dense
Elasticity of Soil 0.3ksi
K = 0.8
Factor of safety
End bearing - 3
Skin Friction - 3
% of Capacity Used
End bearing - 100%
Skin Friction - 100%
Neglected zone for skin friction
Top - 5ft
Bottom - Pier Dia = 4ft
Concrete Properties
fc= 4ksi
Ec= 3605ksi
Density= 150lb/ft3
Rebar Properties
fy= 60ksi
Es= 29000ksi
362 — STAAD Foundation Advanced V8i
Chapter — 7
7.2 Drilled Pier Foundation 2 API
Figure 7-2: Pier Elevation
7.2.3 Solution
Critical Depth
Critical depth is set to be calculated by program
Effective Overburden Pressure
Po= (Soil Density of respective layer x Depth to the center of the layer)
Effects of water and critical depth are also considered calculating Po
Section 7 Drilled Pier Foundations
7.2 Drilled Pier Foundation 2 API
Verification Manual — 363
Layer Effective Overburden Pres-sure (lb/ft2)
Layer1 315Layer2 1345Layer3 1874Layer4 1566
Skin Friction
Ψ Factor from API RP 2A-WSD 6.4.2
Ψ = Cohesion / Effective Overburden Pressure
Layer ΨLayer1 3.1746Layer2 0.8178Layer3 1.0672Layer4 1.9157
α Factor
Layer αLayer1 0.55Layer2 0.55Layer3 0.55Layer4 0.55
K Coefficient of lateral earth pressure from API RP 2A-WSD 6.4.3
K=0.8 (for straight pier)
δ Friction angle between soil and pier
Calculated based on API RP 2A-WSD Table 6.4.3-1
Shaft friction (f), from API RP 2A-WSD 6.4.2 & 6.4.3
For cohesive soil layerf = α x c
For cohesionless soil layerf = K xPo x tanδ
Layer Shaft Friction (psf)Layer1 550Layer2 605Layer3 1100Layer4 1650
Skin Friction Resistance (Qf), from API RP 2A-WSD 6.4.1
Qf = f x As
Layer Qf (psf)Layer1 41.469Layer2 98.835
364 — STAAD Foundation Advanced V8i
Chapter — 7
7.2 Drilled Pier Foundation 2 API
Layer Qf (psf)Layer3 110.584Layer4 248.814Total Skin Friction 499.702
Modified Skin Friction Based on Neglected Zones for Skin Friction
Qf (modified) is calculated by considering top and bottom neglect layer
Layer Qf_modified(psf)
Layer1 6.9115Layer2 98.835Layer3 110.584Layer4 165.876Total Skin Fric-tion
382.206
Base Resistance
Unit end bearing (q), from API RP 2A-WSD 6.4.2 & 6.4.3
For cohesive soil layerq = 9 x c
For cohesionless soil layerq =po x Nq
Layer q (psf)Layer1 9000Layer2 9900Layer3 18000Layer4 27000
End Bearing for each layer (Qp), from API RP 2A-WSD 6.4.1
Qp = q x Ap
Layer Qp (psf)Layer1 113.097Layer2 124.407Layer3 226.195Layer4 339.292
End Bearing for bottom Layer
Qp_bott = 339.292 kip
Unfactored Capacity
Section 7 Drilled Pier Foundations
7.2 Drilled Pier Foundation 2 API
Verification Manual — 365
Factored Capacity
7.2.4 Comparison
Value ofSTAAD Foun-
dationResult
ReferenceResult Difference
UnfactoredTip Resistance 339.429 kip 339.292 kip NegligibleUnfactored SkinResistance
382.486 kip 382.206 kip Negligible
Unfactored Total AxialCapacity
648.371 kip 647.985 kip Negligible
FactoredTip Resistance 113.143 kip 113.097 kip NegligibleFactored Skin Resistance 127.495 kip 127.402 kip NegligibleFactored Total AxialCapacity
216.124 kip 215.995 kip Negligible
Table 7-2: Drilled Pier (API) verification example 2 comparison
7.3 Drilled Pier Foundation 3 FHWA7.3.1 ReferenceFHWA-IF-99-025
7.3.2 ProblemDesign axial capacity for drilled pier with the given data: Design Method:FHWA
Load Fy= 100kip, fc= 4ksi, fy= 60ksi, Straight pier, pier diameter= 2ft,
pier height= 30ft, water level at 40ft.
Soil Profile
1. Sand, 8ft deep, angle of friction 30deg, Avg Density 108lb/ft3, N60- 11
2. Sand, 13ft deep, angle of friction 34deg, Avg Density 110lb/ft3, N60- 14
3. Clay - , 9ft deep, cohesion 2kip/ft2, Avg Density 110lb/ft3, N60- 16
Elasticity of Soil 0.3ksi
Factor of safety
366 — STAAD Foundation Advanced V8i
Chapter — 7
7.3 Drilled Pier Foundation 3 FHWA
End bearing - 3
Skin Friction - 3
% of Capacity Used
End bearing - 100%
Skin Friction - 100%
Neglected zone for skin friction
Top - 5ft
Bottom - Pier Dia = 2ft
Concrete Properties
fc= 4ksi
Ec= 3605ksi
Density= 150lb/ft3
Rebar Properties
fy= 60ksi
Es= 29000ksi
Section 7 Drilled Pier Foundations
7.3 Drilled Pier Foundation 3 FHWA
Verification Manual — 367
Figure 7-3: Pier Elevation
7.3.3 Solution
Critical Depth
Critical depth is set to be calculated by program
Effective Overburden Pressure
Po= (Soil Density of respective layer x Depth to the center of the layer)
Effects of water and critical depth are also considered calculating Po
368 — STAAD Foundation Advanced V8i
Chapter — 7
7.3 Drilled Pier Foundation 3 FHWA
Layer Effective Overburden Pres-sure (lb/ft2)
Layer1 432Layer2 1579Layer3 1925
Skin Friction
α Factor from FHWA-IF-99-025 Eqn 11.6
α = 0.55
Layer αLayer1 0Layer2 0Layer3 0.55
β Dimensionless correlation factor from FHWA-IF-99-025 Eqn 11.18
Layer βLayer1 0.9017Layer2 0.8536Layer3 0
δ Friction angle between soil and pier
Assumed to be same as soil friction angle
Shaft friction (f), from FHWA-IF-99-025 Eqn 11.16 & 11.17
For cohesive soil layerf = α x su
For cohesionless soil layerf = β x σ vi
Layer Shaft Friction (psf)Layer1 389.50Layer2 1347.86Layer3 1100.0
Skin Friction Resistance (Qf), from FHWA-IF-99-025 Eqn 10.2
Rs = f x As
Layer Rs (kip)Layer1 19.578Layer2 110.095Layer3 62.204Total Skin Friction 191.877
Modified Skin Friction Based on Neglected Zones for Skin Friction
Qf (modified) is calculated by considering top and bottom neglect layer
Section 7 Drilled Pier Foundations
7.3 Drilled Pier Foundation 3 FHWA
Verification Manual — 369
Layer Rs_modified(kip)
Layer1 7.342Layer2 110.095Layer3 48.381Total Modified SkinFriction
165.817
Base Resistance
Unit end bearing (q), from FHWA-IF-99-025 Eqn 11.1, 11.2 & 11.4a
For cohesive soil layerq = 9 x c
For cohesionless soil layerq =po x Nq
Layer q (kip)Layer1 13.2Layer2 15.6Layer3 5.611
End Bearing for each layer (Qp), from FHWA-IF-99-025 Eqn 10.2
RB = q x Ap
Layer RB (kip)Layer1 41.469Layer2 49.009Layer3 17.628
End Bearing for bottom Layer, RB-bott = 17.628 kips
Un-factored Capacity
Factored Capacity
370 — STAAD Foundation Advanced V8i
Chapter — 7
7.3 Drilled Pier Foundation 3 FHWA
7.3.4 Comparison
Value ofSTAAD Foun-
dationResult
ReferenceResult Difference
UnfactoredTip Resistance 17.635 kip 17.628 kip NegligibleUnfactored SkinResistance
165.884 kip 165.817 kip Negligible
Unfactored Total AxialCapacity
169.376 kip 169.308 kip Negligible
FactoredTip Resistance 5.878 kip 5.876 kip NegligibleFactored Skin Resistance 55.295 kip 55.272 kip NegligibleFactored Total AxialCapacity
56.459 kip 56.436 kip Negligible
Table 7-3: Drilled Pier (FHWA) verification example 3 comparison
7.4 Drilled Pier Foundation 4 FHWA7.4.1 ReferenceFHWA-IF-99-025
7.4.2 ProblemDesign axial capacity for drilled pier with the given data: Design Method:FHWA
Load Fy= 100kip, fc= 4ksi, fy= 60ksi, Straight pier, pier diameter= 4ft, pier height= 39ft,water level at 50ft.
Soil Profile
1. Clay - , 6ft deep, cohesion 1kip/ft2, Avg Density 105lb/ft3, N60 10
2. Clay - , 13ft deep, cohesion 1.1kip/ft2, Avg Density 110lb/ft3, N60 12
3. Clay - , 8ft deep, cohesion 2kip/ft2, Avg Density 111lb/ft3, N60 14
4. Clay - , 12ft deep, cohesion 3kip/ft2, Avg Density 113lb/ft3, N60 15
Elasticity of Soil 0.3ksi
Factor of safety
End bearing - 3
Skin Friction - 3
% of Capacity Used
End bearing - 100%
Skin Friction - 100%
Neglected zone
for skin frictionTop - 5ft
Bottom - Pier Dia = 4ft
Section 7 Drilled Pier Foundations
7.4 Drilled Pier Foundation 4 FHWA
Verification Manual — 371
Concrete Properties
fc= 4ksi
Ec= 3605ksi
Density= 150lb/ft3
Rebar Properties
fy= 60ksi
Es= 29000ksi
Figure 7-4: Pier Elevation
7.4.3 Solution
Critical Depth
Critical depth is set to be calculated by program
372 — STAAD Foundation Advanced V8i
Chapter — 7
7.4 Drilled Pier Foundation 4 FHWA
Effective Overburden Pressure
Po= (Soil Density of respective layer x Depth to the center of the layer)
Effects of water and critical depth are also considered calculating Po
Layer Effective Overburden Pres-sure (lb/ft2)
1 3152 13453 18744 1380
Skin Friction
α Factor from FHWA-IF-99-025 Eqn 11.6
α = 0.55 (for all layers)
Layer α1 0.552 0.553 0.554 0.55
β Dimensionless correlation factor from FHWA-IF-99-025 Eqn 11.18
β = 0 (for all layers)
δ Friction angle between soil and pier
Assumed to be same as soil friction angle
Shaft friction (f), from FHWA-IF-99-025 Eqn 11.16 & 11.17
For cohesive soil layerf = α x su
For cohesionless soil layerf = β x σ vi
Layer Shaft Friction (psf)1 5502 6053 11004 1650
Skin Friction Resistance (Qf), from FHWA-IF-99-025 Eqn 10.2
Rs = f x As
Section 7 Drilled Pier Foundations
7.4 Drilled Pier Foundation 4 FHWA
Verification Manual — 373
Layer Rs (kip)1 41.4692 98.8353 110.5844 248.814Σ (Total Skin Friction) 499.702
Modified Skin Friction Based on Neglected Zones for Skin Friction
Qf (modified) is calculated by considering top and bottom neglect layer
Layer Rs_modified(kip)
1 6.9122 98.8353 110.5844 165.876Σ (Total ModifiedSkin Friction)
382.206
Base Resistance
Unit end bearing (q), from FHWA-IF-99-025 Eqn 11.1, 11.2 & 11.4a
For cohesive soil layerq = 9 x c
For cohesionless soil layerq =po x Nq
Layer q (kip)1 3.6462 3.8803 5.6114 27
End Bearing for each layer (Qp), from FHWA-IF-99-025 Eqn 10.2
RB = q x Ap
Layer RB (kip)1 45.8152 48.7593 70.5104 339.292
End Bearing for bottom Layer, RB-bott = 339.292 kips
Un-factored Capacity
374 — STAAD Foundation Advanced V8i
Chapter — 7
7.4 Drilled Pier Foundation 4 FHWA
Factored Capacity
7.4.4 Comparison
Value ofSTAAD Foun-
dationResult
ReferenceResult Difference
Unfactored Tip Resistance 339.429 kip 339.292 kip NegligibleUnfactored SkinResistance
382.360 kip 382.206 kip Negligible
Unfactored Total AxialCapacity
648.246 kip 647.985 kip Negligible
FactoredTip Resistance 113.143 kip 113.097 kip NegligibleFactored Skin Resistance 127.453 kip 127.453 kip NegligibleFactored Total AxialCapacity
216.082 kip 213.658 kip Negligible
Table 7-4: Drilled Pier (FHWA) verification example 4 comparison
7.5 Drilled Pier Foundation 5 VESIC
7.5.1 ReferenceAlternate Vesic Method
7.5.2 ProblemDesign axial capacity for drilled pier with the given data: Design Method: Alternate VesicMethod
Load Fy= 100kip, fc= 4ksi, fy= 60ksi, Straight pier, pier diameter= 2ft,
pier height= 30ft, water level at 40ft.
Soil Profile
1. Sand, 8ft deep, angle of friction 30deg, Avg Density 108lb/ft3,
2. Sand, 13ft deep, angle of friction 34deg, Avg Density 110lb/ft3,
3. Clay, 9ft deep, cohesion 2kip/ft2, Avg Density 110lb/ft3,
Section 7 Drilled Pier Foundations
7.5 Drilled Pier Foundation 5 VESIC
Verification Manual — 375
Elasticity of Soil 0.3ksi
Factor of safety
End bearing - 3
Skin Friction - 3
% of Capacity Used
End bearing - 100%
Skin Friction - 100%
Neglected zone for skin friction
Top - 5ft
Bottom - Pier Dia = 2ft
Concrete Properties
fc= 4ksi
Ec= 3605ksi
Density= 150lb/ft3
Rebar Properties
fy= 60ksi
Es= 29000ksi
376 — STAAD Foundation Advanced V8i
Chapter — 7
7.5 Drilled Pier Foundation 5 VESIC
Figure 7-5: Pier Elevation
7.5.3 Solution
Critical Depth
Critical depth is set to be calculated by program
Effective Overburden Pressure
Po= (Soil Density of respective layer x Depth to the center of the layer)
Effects of water and critical depth are also considered calculating Po
Section 7 Drilled Pier Foundations
7.5 Drilled Pier Foundation 5 VESIC
Verification Manual — 377
Layer Effective Overburden Pres-sure (psf)
1 4322 15793 1925
Skin Friction
α Adhesion Factor for Drilled Pier in Cohesive Soil
α = 0.55
Layer α1 02 03 0.55
K Coefficient of lateral earth pressure
K=0.8 (for straight pier)
β Lateral Earth Pressure and Friction Angle Factor
Layer β1 0.4622 0.5403 0
δ Friction angle between soil and pier
Assumed to be same as soil friction angle
Shaft friction (f), from Alpha or Beta Method
For cohesive soil layerf = α x c
For cohesionless soil layerf = K xPo x tanδ
Layer Shaft Friction (psf)1 199.5322 852.0393 1100
tan(δ1) = 0.675
Skin Friction Resistance (Qf), from FHWA-IF-99-025 Eqn 10.2
Rs = f x As
Layer Rs (kip)1 10.0302 69.5963 62.204Σ (Total Skin Friction) 141.829
Modified Skin Friction Based on Neglected Zones for Skin Friction
378 — STAAD Foundation Advanced V8i
Chapter — 7
7.5 Drilled Pier Foundation 5 VESIC
Qf (modified) is calculated by considering top and bottom neglect layer
Layer Rs_modified(kip)
1 3.7612 69.5963 48.381Σ (Total Modified SkinFriction)
121.737
Base Resistance
Cohesive Soil (Bottom Layer)
Factor Fr = 1
Factor Ncp = 9
Cohesionless Soil (Bottom Layer)
Factor Nqp = 0
Unit end bearing (q), from FHWA-IF-99-025 Eqn 11.1, 11.2 & 11.4a
For cohesive soil layer q = Fr x Nqp x c
For cohesionless soil layer q =po x Nqp
Layer q (psf)1 02 03 18000
End Bearing for each layer (Qp), from FHWA-IF-99-025 Eqn 10.2
RB = q x Ap
Layer RB (kip)1 02 03 56.549
End Bearing for bottom Layer, RB_bott = 56.549 kip
Un-factored Capacity
Section 7 Drilled Pier Foundations
7.5 Drilled Pier Foundation 5 VESIC
Verification Manual — 379
Factored Capacity
7.5.4 Comparison
Value ofSTAAD Foun-
dationResult
ReferenceResult Difference
UnfactoredTip Resistance 56.571 kip 16.549 kip NegligibleUnfactored SkinResistance
121.824 kip 121.737 kip Negligible
Unfactored Total AxialCapacity
164.253 kip 164.149 kip Negligible
FactoredTip Resistance 18.857 kip 5.516 kip NegligibleFactored Skin Resistance 40.608kip 40.579 kip NegligibleFactored Total AxialCapacity
54.751 kip 54.716 kip Negligible
Table 7-5: Drilled Pier (Vesic) verification example 5 comparison
7.6 Drilled Pier Foundation 6 Vesic7.6.1 ReferenceAlternate Vesic Method
7.6.2 ProblemDesign axial capacity for drilled pier with the given data: Design Method: Alternate VesicMethod
Load Fy= 100kip, fc= 4ksi, fy= 60ksi, Straight pier, pier diameter= 4ft, pier height= 39ft,water level at 50ft.
Soil Profile
1. Clay - , 6ft deep, cohesion 1kip/ft2, Avg Density 105lb/ft3, Density- Very Loose
2. Clay - , 13ft deep, cohesion 1.1kip/ft2, Avg Density 110lb/ft3, Density- Medium
3. Clay - , 8ft deep, cohesion 2kip/ft2, Avg Density 111lb/ft3, Density- Dense
4. Clay - , 12ft deep, cohesion 3kip/ft2, Avg Density 113lb/ft3, Density- Very Dense
Elasticity of Soil 0.3ksi
Factor of safety
End bearing - 3
Skin Friction - 3
% of Capacity Used
380 — STAAD Foundation Advanced V8i
Chapter — 7
7.6 Drilled Pier Foundation 6 Vesic
End bearing - 100%
Skin Friction - 100%
Neglected zone for skin friction
Top - 5ft
Bottom - Pier Dia = 4ft
Concrete Properties
fc= 4ksi
Ec= 3605ksi
Density= 150lb/ft3
Rebar Properties
fy= 60ksi
Es= 29000ksi
Figure 7-6: Pier Elevation
Section 7 Drilled Pier Foundations
7.6 Drilled Pier Foundation 6 Vesic
Verification Manual — 381
7.6.3 Solution
Critical Depth
Critical depth is set to be calculated by program
Effective Overburden Pressure
Po= (Soil Density of respective layer x Depth to the center of the layer)
Effects of water and critical depth are also considered calculating Po
Layer Effective Overburden Pres-sure (psf)
1 3152 13453 1874
Skin Friction
α Adhesion Factor for Drilled Pier in Cohesive Soil
α = 0.55 (All layers)
K Coefficient of lateral earth pressure
K=0.8 (for straight pier)
Lateral Earth Pressure and Friction Angle Factor, β = 0 (All layers)
δ Friction angle between soil and pier
Assumed to be same as soil friction angle
Shaft friction (f), from Alpha or Beta Method
For cohesive soil layerf = α x c
For cohesionless soil layerf = K xPo x tanδ
Layer Shaft Friction (psf)1 5502 6053 11004 1650
tan(δ1) = 0
382 — STAAD Foundation Advanced V8i
Chapter — 7
7.6 Drilled Pier Foundation 6 Vesic
Skin Friction Resistance (Qf), from FHWA-IF-99-025 Eqn 10.2
Rs = f x As
Layer Rs (kip)1 41.4692 98.8353 110.5844 248.814Σ (Total Skin Friction) 499.702
End Bearing for each layer (Qp), from FHWA-IF-99-025 Eqn 10.2
RB = q x Ap
Layer RB (kip)1 02 03 04 339.292
End Bearing for bottom Layer, RB_bott = 339.292 kip
Un-factored Capacity
Factored Capacity
Section 7 Drilled Pier Foundations
7.6 Drilled Pier Foundation 6 Vesic
Verification Manual — 383
7.6.4 Comparison
Value ofSTAAD Foun-
dationResult
ReferenceResult Difference
UnfactoredTip Resistance 339.429 kip 339.292 kip NegligibleUnfactored SkinResistance
382.360 kip 382.206 kip Negligible
Unfactored Total AxialCapacity
648.246 kip 164.149 kip Negligible
FactoredTip Resistance 113.143 kip 113.097 kip NegligibleFactored Skin Resistance 127.453 kip 127.402 kip NegligibleFactored Total AxialCapacity
216.082 kip 54.716 kip Negligible
Table 7-6: Drilled Pier (Vesic) verification example 6 comparison
384 — STAAD Foundation Advanced V8i
Chapter — 7
7.6 Drilled Pier Foundation 6 Vesic
Section 8
Plant Foundation8.1 Vertical Vessel Foundation 1
8.1.1 Input Parameters
Geometric Description
Vessel Geometry
Effective Height, Hve = 10ft
Effective Diameter, Dve = 4ft
Center of Gravity, CG = 10 ft
Pedestal Geometry
Height, Tp = 1 ft
Diameter, Dp = 5 ft
Footing Geometry
Minimum Footing Diameter = 10 ft
Maximum Footing Diameter = 10 ft
Minimum Footing Depth = 2 ft
Maximum Footing Depth = 2 ft
Verification Manual — 385
Figure 8-1: Tank and foundation elevation
Anchor Bolt Data
Figure 8-2: Anchor bolt plan
Bolt Circle Diameter, BCD = 14.875 ft
Bolt Diameter, BD = 1.5 in.
Sleeve Diameter, SD = 2 in
Number of Anchor Bolts, Nb = 16
Effective Embedment Depth, heff = 1.5 ft
386 — STAAD Foundation Advanced V8i
Chapter — 8
8.1 Vertical Vessel Foundation 1
Design Parameters
Soil
Soil Depth, Ts = 0 ft
Soil Density, Vsoil = 110 pcf
Allowable Soil Bearing Pressure, SBC = 3.8 ksf
Concrete
Cover, cc = 0.25 ft
Concrete Density, Vc = 15o pcf
Concrete strength, f'c = 4 ksi
Reinforcement
fy = 60 ksi
Bar Type : Imperial
Minimum Bar Diameter = 4
Maximum Bar Diameter = 11
Stability
Minimum Stability Ratio = 1.5
Primary Load Description
Load Types Axial Force(kip)
Base Moment(ft·kip)
Base Shear(kip)
Empty Load (De) 10 0 0Operating Load(Do)
20 0 0
Test Load (Dt) 0 0 0Erection Load(Dr)
0 0 0
Live Load (Dl) 0 0 0
Table 8-1: Primary load description
8.1.2 Solution
Wind Load
Wind Load Calculation per ASCE 7-05
Partial Wind Case: Percentage of wind = 50%
Section 8 Plant Foundation
8.1 Vertical Vessel Foundation 1
Verification Manual — 387
Wind Speed, V = 0 mph
Exposure category D, Case 2
Wind Directionality Factor, Kd = 0.95 ................................per ASCE 7-05 Table 6-4
Topographic Factor, Kzt = 1 ................................per ASCE 7-05 Fig. 6-4
Importance factor, IW = 1.15 ................................per ASCE 7-05 Table 6-1
Gust Effect Factor, G = 0.85 ................................per ASCE 7-05 Table 6.5.8
Net Force Coefficient, Cf = 0.9 ................................per ASCE 7-05 Gig. 6-20 & Fig. 6-21
Elevation Kz Pressure Width Area Shear Moment1 1.03023 0 4 4 0 011 1.03023 0 4 40 0 0
Table 8-2: Wind loads
Total Wind Shear = 0 kip
Total Wind Moment = 0 kip-ft
Seismic Load
Importance Factor, I = 1
Fundamental Period, T = 6 s
Long Period, TL = 12 s
Site Class C
Spectral Response Acc. Parameter at Short Period, Ss = 0
Spectral Response Acc. Parameter at 1 Sec, S1 = 0
Short Period Site Coefficient at 0.2s Period, Fa = 1.2
Long Period Site Coefficient at 1.0s Period, Fv = 1.7
Design Spectral Response Acc. Parameter st Short Period, SDS = 0
Design Spectral Response Acc. Parameter at 1 sec, SD1 = 0
Response Modification Factor, R = 2
Calculation Of Seismic Response Coefficient
Cs = 0
Empty Seismic = Cs x De = 0 kip
Operating Seismic = Cs x Do = 0 kip
Test Seismic = Cs x Dt = 0 kip
388 — STAAD Foundation Advanced V8i
Chapter — 8
8.1 Vertical Vessel Foundation 1
Load Combination Table
Load
CaseEmpty Operating Wind Seismic Test
Erection
LoadLiveLoad
UserLoad1
UserLoad2
UserLoad3
1 0 1 0 0 0 0 1 0 0 02 0 1 1 0 0 0 0 0 0 03 0 1 0 0.7 0 0 0 0 0 04 1 0 1 0 0 0 0 0 0 05 0 0.9 0 0.7 0 0 0 0 0 06 0.9 0 0 0.7 0 0 0 0 0 07 0 0 1 0 0 1 0 0 0 08 0 0 0.83 0 0.83 0 0 0 0 0
Table 8-3: Applied Load Combinations - Allowable Stress Level
Load
CaseEmpty Operating Wind Seismic Test
Erection
LoadLiveLoad
UserLoad1
UserLoad2
UserLoad3
1 1 0 0 0 0 0 0 0 0 02 0 0 0 0 0 0 0 0 0 03 0 0 0 0 0 0 0 0 0 04 0 0 0 0 0 0 0 0 0 05 0 0 0 0 0 0 0 0 0 06 0 0 0 0 0 0 0 0 0 07 0 0 0 0 0 0 0 0 0 08 0 0 0 0 0 0 0 0 0 0
Table 8-4: Applied Load Combinations - Strength Level
Load
CaseAxial Shear Moment(kips) (kips) (kip-ft)
1 20 0 02 2o 0 03 20 0 04 10 0 05 18 0 06 9 0 07 0 0 08 0 0 0
Table 8-5: Applied Load at Top ofPedestal - Allowable Stress Level
Governing Loads
Axial = 20 kip
Shear = 0 kip
Section 8 Plant Foundation
8.1 Vertical Vessel Foundation 1
Verification Manual — 389
Moment = 0 ft-kip
Load
CaseAxial Shear Moment(kips) (kips) (kip-ft)
1 10 0 02 o 0 03 0 0 04 0 0 05 0 0 06 0 0 07 0 0 08 0 0 0
Table 8-6: Applied Load at Top ofPedestal - Strength Level
Governing Loads
Axial = 10 kip
Shear = 0 kip
Moment = 0 kip
Pedestal Design
Fu = 56.64 kip
Check for minimum pedestal dimension is done in accordance with PIP STE 03350 Sect.4.5.1
Minimum Pedestal Dimension = 15.625 ft
Factored O.T.M. At Base Of Pedestal = 0 kip-ft
Seismic Load Governing, hence use Vessel Operating Weight
Nominal Axial Load (Empty/Operating), Du = 56.64 kip
Weight of Pedestal = 3.1066 kip
Dowel Circle Diameter, Dc = BCD
Number of Dowels, Nd = 32
Tensile Force In Each Dowel Per PIP STC03350 4.5.4
Fu = 4·Muped/(Nd·Dc) - 0.9·(Du + Wped)/Nd = -0.369 kip
Area of Dowel Bar Required
As_ped_req = Fu/(φ·fy) = -8.192(10)-3 in2
Minimum Dowel Reinforcement per PIP STC03350 4.5.5 : #5 - 32
Dowel Bar Size Provided = 5
Area of Steel Provided = -0.00819 in2
Area of steel required in pedestal, As, req = (dd)2 x pi/4 = 0.307 in2
Potential Conc. Failure Area per PIP STC03350 Fig. A, An = 5.5086 ft2
390 — STAAD Foundation Advanced V8i
Chapter — 8
8.1 Vertical Vessel Foundation 1
Compressive Force In Each Dowel Based on PIP STC03350 4.6.2
Pu = Muped/Dc + 0.9· (Du + Wped) = 11.769 kip
db = 0.625 in
Fc = Pu/An = 0.015 ksi
Beta = 1
Weight of Soil = 0 kip
Design Results
Stability Ratio is calculated based on PIP STE03350 Eqn. 15
LoadCase Eccentricity Stability
Ratio1 0 02 03 04 05 06 07 08 0
Table 8-7: Stability Ratio
Soil bearing calculations are per PIP STE03350 4.7.2
Load
CaseMax Soil
Bearing (ksf)Min Soil
Bearing (ksf)1 0.2414 0.24142 0.2414 0.24143 0.2414 0.24144 0.4582 0.45825 0.2173 0.21736 0.4123 0.41237 0 08 0 0
Table 8-8: Soil Bearing Check
Max Diagonal Soil Bearing Pressure, fdia = 0.4582 ksf
Max Diagonal Soil Bearing Pressure, fflat = 0.4233 ksf
Section 8 Plant Foundation
8.1 Vertical Vessel Foundation 1
Verification Manual — 391
Concrete Design
One Way Shear
Figure 8-3: One-way shear dimensions
Location of Pedestal Face from Face of Footing, X1 = 2.7246 ft
Location of Shear check from Face of Footing, X2 = 1.0006 ft
Shear Stress, Vu = 0.266 ksf
Factored Shear Stress Capacity per ACI318-05 Eqn. 11-3, φVC = 13.66 ksf
Two way Shear Check
Figure 8-4: Two-way shear check
Octagonal Perimeter, bo = 21.65 ft
Punching Shear Force, Vu = 6.463 kip
Factored Shear Capacity, φVc = 1019.8 kip
Reinforcement Calculations
Required development length for bars
392 — STAAD Foundation Advanced V8i
Chapter — 8
8.1 Vertical Vessel Foundation 1
Available development length for bars (From face of Pedestal to face of Footing) = 2.724551ft
m = fy / (0.85 fc) = 17.647
2·m·Rn / fy = 2.597(10)-3
Area of Steel Required
Ast,req = ρ·d·1ft = 0.018 in2
ρmin = 0.0018
Minimum Area of Steel Required
Ast,min = ρmin·d· 1 ft = 0.447 in2
Spacing Required, s = 8 in.
Area of Steel Provided
Ast_prov = (π·db2/4)·1ft/s = 0.205 in2
Bar Size = 5
Final Dimensions
Footing Diameter, Df = 10 ft
Footing Thickness, Tf = 2 ft
Section 8 Plant Foundation
8.1 Vertical Vessel Foundation 1
Verification Manual — 393
8.1.3 Comparison
Hand Cal-culations
STAAD Foun-dationResult
Percent Dif-ference
Footing Diagonal 10 10 noneFooting Thickness 2 2 noneFooting Soil Bear-ing
0.458 0.496 8%
Stability Check 0 0 n/aOne Way ShearCheck
0.266 0.266 0%
Punching ShearCheck
6.463 6.564 2%
Reinforcement Pro-vided
0.460 0.447 3%
Table 8-9: Vertical Vessel verification example 1 comparison
Note: Soil Bearing values are generated from graph; %diff also contains human errors.
8.2 Vertical Vessel Foundation Design8.2.1 Input Parameters
Geometrical Description
Vessel Geometry
Effective Height, Hve = 50 ft
Effective Diameter, Dve = 13 ft
Center of Gravity, CG = 8 ft
Pedestal Geometry
Height, Tp = 4 ft
Diameter, Dp = 14 ft
Footing Geometry
Minimum Footing Diameter = 16 ft
Maximum Footing Diameter = 24 ft
Minimum Footing Depth = 1 ft
Maximum Footing Depth = 16 ft
394 — STAAD Foundation Advanced V8i
Chapter — 8
8.2 Vertical Vessel Foundation Design
Figure 8-5: Tank and foundation elevation
Anchor Bolt Data
Figure 8-6: Anchor bolt plan
Bolt Circle Diameter, BCD = 1.333 ft
Bolt Diameter, BD = 168 in.
Sleeve Diameter, SD = 1.5 in
Number of Anchor Bolts, Nb = 14
Effective Embedment Depth, heff = 0.167 ft
Section 8 Plant Foundation
8.2 Vertical Vessel Foundation Design
Verification Manual — 395
Design Parameters
Soil
Soil Depth, Ts = 2 ft
Soil Density, Vsoil = 110 pcf
Allowable Soil Bearing Pressure, SBC = 4 ksf
Concrete
Cover, cc = 0.25 ft
Concrete Density, Vc = 15o pcf
Concrete strength, f'c = 4 ksi
Reinforcement
fy = 60 ksi
Bar Type : Imperial
Minimum Bar Diameter = 4
Maximum Bar Diameter = 11
Stability
Minimum Stability Ratio = 1.5
Primary Load Description
Load Types Axial Force(kip)
Base Moment (ft-kip)
Base Shear(kip)
Empty Load (De) -28 0 0Operating Load(Do)
-66 0 0
Test Load (Dt) -73 0 0Erection Load(Dr)
-70 0 0
Live Load (Dl) 0 0 0
Table 8-10: Primary load description
Wind Load
Wind Load Calculation per ASCE 7-05
Partial Wind Case: Percentage of wind = 50%
396 — STAAD Foundation Advanced V8i
Chapter — 8
8.2 Vertical Vessel Foundation Design
Wind Speed, V = 110 mph
Exposure category C, Case 2
Wind Directionality Factor, Kd = 0.95 ................................per ASCE 7-05Table 6-4
Topographic Factor, Kzt = 1 ................................per ASCE 7-05 Fig. 6-4
Importance factor, IW = 1.15 ................................per ASCE 7-05 Table 6-1
Gust Effect Factor, G = 0.85 ................................per ASCE 7-05 Table 6.5.8
Net Force Coefficient, Cf = 0.8 ................................per ASCE 7-05 Gig. 6-20& Fig. 6-21
Elevation Kz Pressure Width Area Shear Moment2 0.848884 0.028727 13 26 0.507899 0.50789915 0.848884 0.028727 13 169 3.301344 28.0614320 0.901885 0.030521 13 65 1.349026 23.6079625 0.945265 0.031989 13 65 1.413912 31.8130330 0.982253 0.033241 13 65 1.469238 40.4040540 1.043581 0.035316 13 130 3.121944 109.26850 1.093775 0.037015 13 130 3.272105 147.244752 1.102844 0.037322 13 26 0.659847 33.65219
Table 8-11: Wind loads
Total Wind Shear = 15.095 kip
Total Wind Moment = 414.449 ft-kip
Seismic Load
Importance Factor, I = 1
Fundamental Period, T = 4.1 s
Long Period, TL = 12 s
Site Class C
Spectral Response Acc. Parameter at Short Period, Ss = 0.105
Spectral Response Acc. Parameter at 1 Sec, S1 = 0.043
Short Period Site Coefficient at 0.2s Period, Fa = 1.2
Long Period Site Coefficient at 1.0s Period, Fv = 1.7
Design Spectral Response Acc. Parameter st Short Period, SDS = 0.084
Design Spectral Response Acc. Parameter at 1 sec, SD1 = 0.049
Response Modification Factor, R = 2
Calculation Of Seismic Response Coefficient
Cs = 5.973x10-3
Section 8 Plant Foundation
8.2 Vertical Vessel Foundation Design
Verification Manual — 397
Empty Seismic = Cs x De = 0.167 kip
Operating Seismic = Cs x Do = 0.394 kip
Test Seismic = Cs x Dt = 0.436 kip
Load Combination Table
Load
CaseEmpty Operating Wind Seismic Test
Erection
LoadLiveLoad
UserLoad1
UserLoad2
UserLoad3
1 0 1 0 0 0 0 1 0 0 02 0 1 1 0 0 0 0 0 0 03 0 1 0 0.7 0 0 0 0 0 04 1 0 1 0 0 0 0 0 0 05 0 0.9 0 0.7 0 0 0 0 0 06 0.9 0 0 0.7 0 0 0 0 0 07 0 0 1 0 0 1 0 0 0 08 0 0 0.83 0 0.83 0 0 0 0 0
Table 8-12: Applied Load Combination - Allowable Stress Level
Load
CaseEmpty Operating Wind Seismic Test
Erection
LoadLiveLoad
UserLoad1
UserLoad2
UserLoad3
1 0 1.4 0 0 0 0 0 0 0 02 0 1.2 0 0 0 0 1.6 0 0 03 0 1.2 1.6 0 0 0 0 0 0 04 0 1.2 0 1 0 0 0 0 0 05 0.9 0 1.6 0 0 0 0 0 0 06 0 0.9 0 1 0 0 0 0 0 07 0.9 0 0 1 0 0 0 0 0 08 0 0 1.6 0 0 0.9 0 0 0 09 0 0 0 0 0 0 0 0 0 010 0 0 0 0 0 0 0 0 0 0
Table 8-13: Applied Load Combination - Strength Level
Load
CaseAxial Shear Moment(kips) (kips) (kip-ft)
1 66 0 02 66 15.09532 414.55933 66 0.275945 2.2075634 28 15.09532 414.44935 59.4 0.275945 2.2075636 25.2 0.117068 0.9365427 70 7.547658 207.27978 60.59 6.264556 172.0421
Table 8-14: Applied Load at Top ofPedestal - Allowable Stress Level
398 — STAAD Foundation Advanced V8i
Chapter — 8
8.2 Vertical Vessel Foundation Design
Governing Loads
Axial = 70 kip
Shear = 15.09532 kip
Moment = 414.5593 ft-kip
Load
CaseAxial Shear Moment(kips) (kips) (kip-ft)
1 92.4 0 02 79.2 0 03 79.2 24.15251 663.29494 79.2 0.394208 3.1536615 25.2 24.15251 663.29496 59.4 0.394208 3.1536617 25.2 0.16724 1.3379178 63 12.07625 331.6474
Table 8-15: Applied Load at Top ofPedestal - Strength Level
Governing Loads
Axial = 92.4 kip
Shear = 24.15251 kip
Moment = 663.2949 kip
Pedestal Design
Fu = 56.64 kip
Check for minimum pedestal dimension is done in accordance with PIP STE 03350 Sect.4.5.1
Minimum Pedestal Dimension = 2.0833 ft
Factored O.T.M. At Base Of Pedestal = 759.9049 kip-ft
Seismic Load Governing, hence use Vessel Operating Weight
Nominal Axial Load (Empty/Operating), Du = 56.64 kip
Weight of Pedestal = 97.42292 kip
Dowel Circle Diameter, Dc = BCD = 1.333 ft
Number of Dowels, Nd = 32
Tensile Force In Each Dowel Per PIP STC03350 4.5.4
Fu = 4·Muped/(Nd·Dc) - 0.9·(Du + Wped)/Nd = 66.274 kip
Area of Dowel Bar Required
As_ped_req = Fu/(φ·fy) = 1.473 in2
Section 8 Plant Foundation
8.2 Vertical Vessel Foundation Design
Verification Manual — 399
Minimum Dowel Reinforcement per PIP STC03350 4.5.5 : #5 - 32
Dowel Bar Size Provided = 5
Area of Steel Provided = 1.472746 in.2
Potential Conc. Failure Area per PIP STC03350 Fig.
An = 0.060107
Compressive Force In Each Dowel Based on PIP STC03350 4.6.2
Pu = Muped/Dc + 0.9· (Du + Wped) = 728.889 kip
Fc = Pu/An = 84.211 ksi
Weight of Soil = 10.935 kip
Design Results
Stability Ratio is calculated based on PIP STE03350 Eqn. 15
LoadCase Eccentricity Stability
Ratio1 0 02 2.376857 3.365793 0.017400 459.7784 2.913937 2.745435 0.017975 445.0606 0.009203 869.2927 1.165810 6.862198 1.012977 7.89752
Table 8-16: Stability Ratio
Soil bearing calculations are per PIP STE03350 4.7.2
Max Diagonal Soil Bearing Pressure, fdia = 2.10298 ksf
Max Diagonal Soil Bearing Pressure, fflat = 1.94299 ksf
400 — STAAD Foundation Advanced V8i
Chapter — 8
8.2 Vertical Vessel Foundation Design
Concrete Design
One Way Shear
Figure 8-7: One-way shear dimensions
Location of Pedestal Face from Face of Footing (X1) = 1.62742 ft
Location of Shear check from Face of Footing (X2) = 0.904783 ft
Shear Stress, Vu = 4.185682 ksf
Factored Shear Stress Capacity φVC per ACI318-05 Eqn. 11-3 = 13.66104 ksf
Two way Shear Check
Figure 8-8: Two-way shear check
Octagonal Perimeter, bo = 52.41798 ft
Punching Shear Force, Vu = 17.5799 kip
Factored Shear Capacity, φVc = 661.6144 kip
Reinforcement Calculations
Required development length for bars
Section 8 Plant Foundation
8.2 Vertical Vessel Foundation Design
Verification Manual — 401
Available development length for bars (From face of Pedestal to face of Footing) =1.628742 ft
Rn = Mu / (0.9·1ft·d2) = 0.079 ksi
m = fy / (0.85· fc) = 17.647
2·m·Rn / fy = 0.047
Area of Steel Required
Ast_req = p·d·1ft = 0.139 in2
pmin = 0.0018
Minimum Area of Steel Req
Ast_min = pmin·d·1ft = 0.188 in2
Spacing Required
s = 18 in.
Area of Steel Provided
Ast_prov = (π·db2/4)·1ft/s = 0.205 in2
Bar Size = 5
Final Dimensions
Footing Diameter = 16 ft
Footing Thickness = 1 ft
402 — STAAD Foundation Advanced V8i
Chapter — 8
8.2 Vertical Vessel Foundation Design
8.2.2 Comparison
Hand Cal-culations
STAAD Foun-dationResult
Percent Dif-ference
Footing Diagonal 16 16 0Footing Thickness 1 1 0Footing Soil Bear-ing
2.1030 2.102 0
Stability Check 2.7454 2.748 0One Way ShearCheck
4.1857 4.193 0
Punching ShearCheck
17.58 17.951 2
Reinforcement Pro-vided
0.20453 0.18765 9
Table 8-17: Vertical Vessel verification example 2 comparison
8.3 Vertical Vessel Foundation Design8.3.1 Input Parameters
Geometric Description
Vessel Geometry
Effective Height, Hve = 30 ft
Effective Diameter, Dve - 10 ft
Center of Gravity, CG = 8 ft
Pedestal Geometry
Height = 2 ft
Diameter = 12 ft
Footing Geometry
Minimum Footing Diameter = 14 ft
Maximum Footing Diameter = 16 ft
Minimum Footing Depth = 1 ft
Maximum Footing Depth = 2 ft
Section 8 Plant Foundation
8.3 Vertical Vessel Foundation Design
Verification Manual — 403
Figure 8-9: Tank and foundation elevation
Anchor Bolt Data
Figure 8-10: Anchor bolt plan
Bolt Circle Diameter, BCD = 1.333 ft
Bolt Diameter, BD = 132 in.
Sleeve Diameter, SD = 1.5 in.
Number of Anchor Bolts, Nb = 11
Effective Embedment Depth, heff = 0.167 fyt
404 — STAAD Foundation Advanced V8i
Chapter — 8
8.3 Vertical Vessel Foundation Design
Design Parameters
Soil
Soil Depth, Ts = 2 ft
Soil Density, Vsoil = 110 pcf
Allowable Soil Bearing Pressure, SBC = 4 ksf
Concrete
Cover, cc = 0.25 ft
Concrete Density, Vc = 15o pcf
Concrete strength, f'c = 4 ksi
Reinforcement
fy = 60 ksi
Bar Type : Imperial
Minimum Bar Diameter = 4
Maximum Bar Diameter = 11
Stability
Minimum Stability Ratio = 1.5
Primary Load Description
Load Types Axial Force(kip)
Base Moment (ft-kip)
Base Shear(kip)
Empty Load (De) -20 0 0Operating Load(Do)
-40 0 0
Test Load (Dt) -60 0 0Erection Load(Dr)
-30 0 0
Live Load (Dl) 0 0 0
Table 8-18: Primary load description
8.3.2 Solution
Wind Load
Wind Load Calculation per ASCE 7-05
Partial Wind Case: Percentage of wind = 50%
Section 8 Plant Foundation
8.3 Vertical Vessel Foundation Design
Verification Manual — 405
Wind Speed, V = 90 mph
Exposure category B, Case 2
Wind Directionality Factor, Kd = 0.95 ................................per ASCE 7-05 Table 6-4
Topographic Factor, Kzt = 1 ................................per ASCE 7-05 Fig. 6-4
Importance factor, IW = 1.15 ................................per ASCE 7-05 Table 6-1
Gust Effect Factor, G = 0.85 ................................per ASCE 7-05 Table 6.5.8
Net Force Coefficient, Cf = 0.8 ................................per ASCE 7-05 Gig. 6-20 & Fig. 6-21
Elevation Kz Pressure Width Area Shear Moment1 0.57472 0.01302 10 10 0.088534 0.04426715 0.57472 0.01302 10 140 1.23948 9.91583820 0.623954 0.014135 10 50 0.480594 8.41039225 0.66503 0.015066 10 50 0.512232 11.5252230 0.700591 0.015871 10 50 0.539622 14.83962
Table 8-19: Wind loads
Total Wind Shear = 2.86 kip
Total Wind Moment = 44.735 ft-kip
Seismic Load
Importance Factor, I = 1
Fundamental Period, T = 4.1 s
Long Period, TL = 12 s
Site Class C
Spectral Response Acc. Parameter at Short Period, Ss = 1.997
Spectral Response Acc. Parameter at 1 Sec, S1 = 0.805
Short Period Site Coefficient at 0.2s Period, Fa = 1
Long Period Site Coefficient at 1.0s Period, Fv = 1.3
Design Spectral Response Acc. Parameter st Short Period, SDS = 1.332
Design Spectral Response Acc. Parameter at 1 sec, SD1 = 0.697
Response Modification Factor, R = 2
Calculation Of Seismic Response Coefficient
Cs = 0.805
Empty Seismic = Cs x De = 1.701 kip
Operating Seismic = Cs x Do = 3.402 kip
Test Seismic = Cs x Dt = 5.103 kip
406 — STAAD Foundation Advanced V8i
Chapter — 8
8.3 Vertical Vessel Foundation Design
Load Combination Table
Load
CaseEmpty Operating Wind Seismic Test
Erection
LoadLiveLoad
UserLoad1
UserLoad2
UserLoad3
1 0 1 0 0 0 0 1 0 0 02 0 1 1 0 0 0 0 0 0 03 0 1 0 0.7 0 0 0 0 0 04 1 0 1 0 0 0 0 0 0 05 0 0.9 0 0.7 0 0 0 0 0 06 0.9 0 0 0.7 0 0 0 0 0 07 0 0 1 0 0 1 0 0 0 08 0 0 0.83 0 0.83 0 0 0 0 0
Table 8-20: Applied Load Combination - Allowable Stress Level
Load
CaseEmpty Operating Wind Seismic Test
Erection
LoadLiveLoad
UserLoad1
UserLoad2
UserLoad3
1 0 1.4 0 0 0 0 0 0 0 02 0 1.2 0 0 0 0 1.6 0 0 03 0 1.2 1.6 0 0 0 0 0 0 04 0 1.2 0 1 0 0 0 0 0 05 0.9 0 1.6 0 0 0 0 0 0 06 0 0.9 0 1 0 0 0 0 0 07 0.9 0 0 1 0 0 0 0 0 08 0 0 1.6 0 0 0.9 0 0 0 09 0 0 0 0 0 0 0 0 0 010 0 0 0 0 0 0 0 0 0 0
Table 8-21: Applied Load Combination - Strength Level
Load
CaseAxial Shear Moment(kips) (kips) (kip-ft)
1 40 0 02 40 2.8605 44.7353 40 2.3816 19.0534 20 2.8605 44.7355 36 2.3816 19.0536 18 1.1908 9.52647 30 1.4302 22.3688 49.8 1.1871 18.565
Table 8-22: Applied Load at Top ofPedestal - Allowable Stress Level
Section 8 Plant Foundation
8.3 Vertical Vessel Foundation Design
Verification Manual — 407
Governing Loads
Axial = 49.8 kip
Shear = 2.86046 kip
Moment = 44.73534 kip-ft
Load
CaseAxial Shear Moment(kips) (kips) (kip-ft)
1 56 0 02 48 0 03 48 4.5767 71.5774 48 3.4023 27.2185 18 4.5767 71.5776 36 3.4023 27.2187 18 1.7011 13.6098 27 2.2884 35.788
Table 8-23: Applied Load atTop of Pedestal - Strength Level
Governing Loads
Axial = 56 kips
Shear 4.57674 kips
Moment = 71.5765 ft-kip
Pedestal Design
Fu = 56.64 kip
Check for minimum pedestal dimension is done in accordance with PIP STE 03350 Sect.4.5.1
Minimum Pedestal Dimension = 2.08333 ft
Factored O.T.M. At Base Of Pedestal = 80.730 kip-ft
Seismic Load Governing, hence use Vessel Operating Weight
Nominal Axial Load (Empty/Operating), Du = 56.64 kip
Weight of Pedestal = 35.788 kip
Dowel Circle Diameter, Dc = BCD = 1.333 ft
Number of Dowels, Nd = 32
Tensile Force In Each Dowel Per PIP STC03350 4.5.4
Fu = 4·Muped/(Nd·Dc) - 0.9·(Du + Wped)/Nd = 5.212 kip
Area of Dowel Bar Required
As_ped_req = Fu/(φ·fy) =0.116 in2
408 — STAAD Foundation Advanced V8i
Chapter — 8
8.3 Vertical Vessel Foundation Design
Minimum Dowel Reinforcement per PIP STC03350 4.5.5 : #5 - 32
Dowel Bar Size Provided = 5
Area of Steel Provided = 0.11582 in2
Area of steel required in pedestal, As, req = (dd)2 x pi/4 = 0.307 in2
Potential Conc. Failure Area per PIP STC03350 Fig. A, An = 0.075956ft2
Compressive Force In Each Dowel Based on PIP STC03350 4.6.2
Pu = Muped/Dc + 0.9· (Du + Wped) = 135.957 kip
db = 0.625 in
Fc = Pu/An = 12.43 ksi
Beta = 1
Weight of Soil, Wsoil = 9.477 kip
Design Results
Stability Ratio is calculated based on PIP STE03350 Eqn. 15
LoadCase Eccentricity Stability
Ratio1 0 02 0.4864 14.3923 0.2390 29.2914 0.5949 11.7665 0.2480 28.2226 0.1495 46.8257 0.2676 26.1598 0.1853 37.780
Table 8-24: Stability Ratio
Soil bearing calculations are per PIP STE03350 4.7.2
Load
CaseMax Soil
Bearing (ksf)Min Soil
Bearing (ksf)1 0.6751 0.24532 0.8672 0.31643 0.7695 0.28084 0.7440 0.74405 0.7449 0.25396 0.5402 0.54027 0.7100 0.21378 0.8152 0.3399
Table 8-25: Soil Bearing Check
Max Diagonal Soil Bearing Pressure, fdia = 0.8672 ksf
Max Diagonal Soil Bearing Pressure, fflat = 0.8012 ksf
Section 8 Plant Foundation
8.3 Vertical Vessel Foundation Design
Verification Manual — 409
Concrete Design
One Way Shear
Figure 8-11: One-way shear dimensions
Location of Pedestal Face from Face of Footing, X1 = 1.538921 ft
Location of Shear check from Face of Footing, X2 = 0.814963 ft
Shear Stress, Vu = 0.90518 ksf
Factored Shear Stress Capacity per ACI318-05 Eqn. 11-3, φVC = 13.66104 ksf
Two way Shear Check
Figure 8-12: Two-way shear check
Octagonal Perimeter, bo = 45.137 ft
Punching Shear Force, Vu = 12.085 kip
Factored Shear Capacity, φVc = 589.61 kip
Reinforcement Calculations
Required development length for bars
410 — STAAD Foundation Advanced V8i
Chapter — 8
8.3 Vertical Vessel Foundation Design
Available development length for bars (From face of Pedestal to face of Footing) = 1.538921ft
Rn = Mu / (0.9·1ft·d2) = 0.014 ksi
m = fy / (0.85· fc) = 17.647
2·m·Rn / fy = 7.944(10)-3
Area of Steel Required
Ast,req = ρ·d·1ft = 0.024 in2
ρmin = 0.0018
Minimum Area of Steel Req
Ast,min = ρmin·d·1 ft = 0.188 in2
Spacing Required, s = 18 in.
Area of Steel Provided
Ast_prov = (π·db2/4)·1ft/s = 0.205 in2
Bar Size = 5
Final Dimensions
Footing Diameter = 14 ft
Footing Thickness = 1 ft
Section 8 Plant Foundation
8.3 Vertical Vessel Foundation Design
Verification Manual — 411
8.3.3 Comparison
Hand Cal-culations
STAAD Foun-dationResult
Percent Dif-ference
Footing Diagonal 14 14 noneFooting Thickness 1 1 noneFooting Soil Bear-ing
0.8672 0.835 4%
Stability Check 11.766 12.898 9%One Way ShearCheck
0.9052 1.13 20%
Punching ShearCheck
12.085 12.338 2%
Reinforcement Pro-vided
0.2045 0.1878 9%
Table 8-26: Vertical Vessel verification example 3 comparison
8.4 Vertical Vessel Seismic Load Generation1
Location Santa Ana California
S1 = 0.5312, Spectral Response Acceleration at Short Periods determined in accordancewith ASCE 7 11.4.1
Ss = 1.378, Spectral Response Acceleration at Period of 1 sec determined in accordance withASCE 7 11.4.1
Site Class = A, Based On Soil Prorperties In Accordance With ASCE 7 Chapter 20
R = 2, Response modification Coefficient per ASCE 7 Tables 15.4-1 or 15.4-2
I = 1.25, Importance Factor per ASCE 7 11.5.1
T = 3 sec., Fundamental Period of Vessel
TL = 12 sec., Long-Period Transition Perios per ASCE 7 12.8.2
Empty Weight Of Vessel = 100 kips
Operating Weight of Vessel = 200 kips
Center of Gravity Of Vessel From Top Of Pedestal (CG) = 120 in.
Fa = 0.8 Short-Period Site Coeffiecient per ASCE 7 11.4.3
Fv = 0.8 Long-Period site Coefficient per ASCE 7 11.4.3
SDS = 0.735, Design Spectral Response Acceleration Parameter at short periods per ASCE 711.4.4
SD1 = 0.283, Design Spectral Response Acceleration Parameter at period of 1 sec per ASCE7 11.4.4
Cs = 0.059, Seismic Response Coefficient Per ASCE 7 12.8.1.1
Empty Load Case Base Shear = 5.902 kip
412 — STAAD Foundation Advanced V8i
Chapter — 8
8.4 Vertical Vessel Seismic Load Generation 1
Operating Load Case Base Shear = 11.804 kip
Empty Load Case Earthquake Moment = 59.021 kip ft
Operating Load Case Earthquake Moment = 118.043 kip ft
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Base Shear Empty Case(kip)
5.902132222 5.902 0.0022403
Base Shear Operating Case(kip)
11.80426444 11.804 0.0022403
Base Moment Empty Case(kip ft)
59.02132222 59.021 0.00054595
Base Moment OperatingCase (kip ft)
118.0426444 118.043 0.00030121
Table 8-27: Vertical Vessel verification example 4 comparison
8.5 Vertical Vessel Seismic Load Generation2
Location Yorba Linda California
Spectral Response Acceleration at Short Periods determined in accordance with ASCE 711.4.1, S1 = 0.857367
Spectral Response Acceleration at Period of 1 sec determined in accordance with ASCE 711.4.1, SS = 2.09511
Site Class = B, Based On Soil Properties In Accordance With ASCE 7 Chapter 20
Response modification Coefficient per ASCE 7 Tables 15.4-1 or 15.4-2, R = 2
Importance Factor per ASCE 7 11.5.1, I = 1.0
Fundamental Period of Vessel, T = 6 sec.
Long-Period Transition Period per ASCE 7 12.8.2, TL = 5 sec.
Empty Weight Of Vessel = 100 kip
Operating Weight of Vessel = 200 kip
Center of Gravity Of Vessel From Top Of Pedestal, CG = 10 ft
Short-Period Site Coefficient per ASCE 7 11.4.3, FA = 1
Long-Period site Coefficient per ASCE 7 11.4.3, FV = 1
SDS = 1.397, Design Spectral Response Acceleration Parameter at short periods per ASCE 711.4.4
SD1 = 0.572, Design Spectral Response Acceleration Parameter at period of 1 sec per ASCE 711.4.4
CS = 0.04, Seismic Response Coefficient Per ASCE 7 12.8.1.1
Section 8 Plant Foundation
8.5 Vertical Vessel Seismic Load Generation 2
Verification Manual — 413
Empty Load Case Base Shear
Shearempty = CS x Emptywt = 3.969 kips
Operating Load Case Base Shear
Shearoperating = CS x Operatingwt = 7.939 kips
Empty Load Case Earthquake Moment
Momentempty = Shearempty x CG = 39.693 kip*ft
Operating Load Case Earthquake Moment
Momentoperating = Shearoperating x CG = 79.386 kip*ft
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Base Shear Empty Case(kip)
3.9693 3.969 0.007
Base Shear Operating Case(kip)
7.9386 7.939 0.005
Base Moment Empty Case(kip ft)
39.693 39.69 0.007
Base Moment OperatingCase (kip ft)
79.3858 79.39 0.005
Table 8-28: Vertical Vessel verification example 5 comparison
8.6 Vertical Vessel Seismic Load Generation3
Location San Antonio, Texas
Spectral Response Acceleration at Short Periods determined in accordance with ASCE 711.4.1, S1 = 0.034656
Spectral Response Acceleration at Period of 1 sec determined in accordance with ASCE 711.4.1, SS = 0.12141
Site Class = C, Based On Soil Properties In Accordance With ASCE 7 Chapter 20
Response modification Coefficient per ASCE 7 Tables 15.4-1 or 15.4-2, R = 3
Importance Factor per ASCE 7 11.5.1, I = 1.5
Fundamental Period of Vessel, T = 4 sec.
Long-Period Transition Period per ASCE 7 12.8.2, TL = 12 sec.
Empty Weight Of Vessel = 100 kips
Operating Weight of Vessel = 200 kips
Center of Gravity Of Vessel From Top Of Pedestal, CG = 10 ft
Short-Period Site Coefficient per ASCE 7 11.4.3, FA = 1.2
414 — STAAD Foundation Advanced V8i
Chapter — 8
8.6 Vertical Vessel Seismic Load Generation 3
Long-Period site Coefficient per ASCE 7 11.4.3, FV = 1.7
SDS = 0.097, Design Spectral Response Acceleration Parameter at short periods per ASCE 711.4.4
SD1 = 0.039, Design Spectral Response Acceleration Parameter at period of 1 sec per ASCE 711.4.4
CS = 4.91x10-3, Seismic Response Coefficient Per ASCE 7 12.8.1.1
Empty Load Case Base Shear
Shearempty = CS x Emptywt = 0.491 kips
Operating Load Case Base Shear
Shearoperating = CS x Operatingwt = 0.982 kips
Empty Load Case Earthquake Moment
Momentempty = Shearempty x CG =4.91 kip*ft
Operating Load Case Earthquake Moment
Momentoperating = Shearoperating x CG = 9.819 kip*ft
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Base Shear Empty Case(kip)
0.49096 0.491 0.0081
Base Shear Operating Case(kip)
0.98192 0.982 0.0081
Base Moment Empty Case(kip ft)
4.9096 4.91 0.0081
Base Moment OperatingCase (kip ft)
9.8192 9.82 0.0081
Table 8-29: Vertical Vessel verification example 6 comparison
8.7 Vertical Vessel Seismic Load Generation4
Location New York, New York
Spectral Response Acceleration at Short Periods determined in accordance with ASCE 711.4.1, S1 = 0.0937194
Spectral Response Acceleration at Period of 1 sec determined in accordance with ASCE 711.4.1, SS = 0.42416
Site Class = D
Site Class Based On Soil Properties In Accordance With ASCE 7 Chapter 20
Response modification Coefficient per ASCE 7 Tables 15.4-1 or 15.4-2, R = 3
Section 8 Plant Foundation
8.7 Vertical Vessel Seismic Load Generation 4
Verification Manual — 415
Importance Factor per ASCE 7 11.5.1, I = 1.0
Fundamental Period of Vessel, T = 4 sec.
Long-Period Transition Period per ASCE 7 12.8.2, TL = 12 sec.
Empty Weight Of Vessel = 100 kips
Operating Weight of Vessel = 200 kips
Center of Gravity Of Vessel From Top Of Pedestal, CG = 10 ft
Short-Period Site Coefficient per ASCE 7 11.4.3, FA = 1.461
Long-Period site Coefficient per ASCE 7 11.4.3, FV = 2.4
SDS = 0.413, Design Spectral Response Acceleration Parameter at short periods per ASCE 711.4.4
SD1 = 0.15 Design Spectral Response Acceleration Parameter at period of 1 sec per ASCE 711.4.4
CS = 0.012, Seismic Response Coefficient Per ASCE 7 12.8.1.1
Empty Load Case Base Shear
Shearempty = CS x Emptywt = 1.25 kips
Operating Load Case Base Shear
Shearoperating = CS x Operatingwt = 2.499 kips
Empty Load Case Earthquake Moment
Momentempty = Shearempty x CG = 12.496 kip*ft
Operating Load Case Earthquake Moment
Momentoperating = Shearoperating x CG =24.992 kip*ft
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Base Shear Empty Case(kip)
1.249592 1.25 0.03264
Base Shear Operating Case(kip)
2.499184 2.499 0.00736295
Base Moment Empty Case(kip ft)
12.49592 12.496 0.0006402
Base Moment OperatingCase (kip ft)
24.99184 24.992 0.0006402
Table 8-30: Vertical Vessel verification example 7 comparison
8.8 Vertical Vessel Seismic Load Generation5
Location Nashville, Tennessee
416 — STAAD Foundation Advanced V8i
Chapter — 8
8.8 Vertical Vessel Seismic Load Generation 5
Spectral Response Acceleration at Short Periods determined in accordance with ASCE 711.4.1, S1 = 0.145056
Spectral Response Acceleration at Period of 1 sec determined in accordance with ASCE 711.4.1, SS = 0.32156
Site Class = E, Based On Soil Properties In Accordance With ASCE 7 Chapter 20
Response modification Coefficient per ASCE 7 Tables 15.4-1 or 15.4-2, R = 2
Importance Factor per ASCE 7 11.5.1, I = 1.0
Fundamental Period of Vessel, T = 12 sec.
Long-Period Transition Period per ASCE 7 12.8.2, TL = 8 sec.
Empty Weight Of Vessel = 100 kips
Operating Weight of Vessel = 200 kips
Center of Gravity Of Vessel From Top Of Pedestal, CG = 10 ft
Short-Period Site Coefficient per ASCE 7 11.4.3, FA = 2.271
Long-Period site Coefficient per ASCE 7 11.4.3, FV = 3.365
SDS = 0.487, Design Spectral Response Acceleration Parameter at short periods per ASCE 711.4.4
SD1 = 0.325, Design Spectral Response Acceleration Parameter at period of 1 sec per ASCE 711.4.4
CS = 9.039x10-3, Seismic Response Coefficient Per ASCE 7 12.8.1.1
Empty Load Case Base Shear
Shearempty = CS x Emptywt = 0.904 kips
Operating Load Case Base Shear
Shearoperating = CS x Operatingwt = 1.808 kips
Empty Load Case Earthquake Moment
Momentempty = Shearempty x CG = 9.039 kip*ft
Operating Load Case Earthquake Moment
Momentoperating = Shearoperating x CG =18.077 kip*ft
Section 8 Plant Foundation
8.8 Vertical Vessel Seismic Load Generation 5
Verification Manual — 417
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Base Shear Empty Case(kip)
0.903868649 0.904 0.01452995
Base Shear Operating Case(kip)
1.807737298 1.808 0.01452995
Base Moment Empty Case(kip ft)
9.038686492 9.039 0.00346839
Base Moment OperatingCase (kip ft)
18.07737298 18.077 0.00206331
Table 8-31: Vertical Vessel verification example 8 comparison
8.9 Vertical Vessel Seismic Load Generation6
Location Santa Ana California
S1 = 0.5312, Spectral Response Acceleration at Short Periods determined in accordancewith ASCE 7 11.4.1
Ss = 1.378, Spectral Response Acceleration at Period of 1 sec determined in accordance withASCE 7 11.4.1
Site Class = A; Based On Soil Properties In Accordance With ASCE 7 Chapter 20
R = 2, Response modification Coefficient per ASCE 7 Tables 15.4-1 or 15.4-2
I = 1.0, Importance Factor per ASCE 7 11.5.1
TL = 12 sec., Fundamental Period of Vessel
Long-Period Transition Period per ASCE 7 12.8.2
Empty Weight Of Vessel, Ewt = 100 kip
Operating Weight of Vessel, Operatingwt = 200 kip
Center of Gravity Of Vessel From Top Of Pedestal, CG = 9 ft
Fa = 0.9, Short-Period Site Coefficient per ASCE 7 11.4.3
Fv =0.8, Long-Period site Coefficient per ASCE 7 11.4.3
SDS = 0.735, Design Spectral Response Acceleration Parameter at short periods per ASCE 711.4.4
SD1 = 0.283, Design Spectral Response Acceleration Parameter at period of 1 sec per ASCE7 11.4.4
CS = 0.024, Seismic Response Coefficient Per ASCE 7 12.8.1.1
Base Shear Based on Operating Load Condition
V = Cs·Operatingwt = 4.722 kip
418 — STAAD Foundation Advanced V8i
Chapter — 8
8.9 Vertical Vessel Seismic Load Generation 6
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Seismic Response Coef-ficient (Cs)
0.02361 0.024 1.631
Base Shear OperatingCase (kip)
4.722 4.722 0.006
Table 8-32: Vertical Vessel verification example 9 comparison
8.10 Vertical Vessel Seismic LoadGeneration 7
Location Yorba Linda California 92887
S1, 0.8574, Spectral Response Acceleration at Short Periods determined in accordance withASCE 7 11.4.1
SS = 2.0951, Spectral Response Acceleration at Period of 1 sec determined in accordancewith ASCE 7 11.4.1
Site Class = B, Based On Soil Properties In Accordance With ASCE 7 Chapter 20
R = 2, Response modification Coefficient per ASCE 7 Tables 15.4-1 or 15.4-2
I = 1.0, Importance Factor per ASCE 7 11.5.1
T = 4 sec., Fundamental Period of Vessel
TL = 12 sec., Long-Period Transition Period per ASCE 7 12.8.2
Empty Weight Of Vessel = 100 kip
Operating Weight of Vessel = 200 kip
Center of Gravity Of Vessel From Top Of Pedestal, CG = 2.5 ft
Fa = 1, Short-Period Site Coefficient per ASCE 7 11.4.3
Fv = 1, Long-Period site Coefficient per ASCE 7 11.4.3
SDS = 1.397, Design Spectral Response Acceleration Parameter at short periods per ASCE 711.4.4
SD1 = 0.572, Design Spectral Response Acceleration Parameter at period of 1 sec per ASCE 711.4.4
CS = 0.071, Seismic Response Coefficient Per ASCE 7 12.8.1.1
Base Shear Based on Operating Load Condition
V = Cs·Operatingwt = 14.289 kip
Section 8 Plant Foundation
8.10 Vertical Vessel Seismic Load Generation 7
Verification Manual — 419
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Seismic Response Coef-ficient (Cs)
0.0715 0.071 0.63
Base Shear OperatingCase (kip)
14.289 14.289 0.002
Table 8-33: Vertical Vessel verification example 10 comparison
8.11 Vertical Vessel Seismic LoadGeneration 8
Location Mountain Valley 73062
S1 = 0.0884, Spectral Response Acceleration at Short Periods determined in accordancewith ASCE 7 11.4.1
SS = 0.329, Spectral Response Acceleration at Period of 1 sec determined in accordancewith ASCE 7 11.4.1
Site Class = C, Based On Soil Properties In Accordance With ASCE 7 Chapter 20
R = 2, Response modification Coefficient per ASCE 7 Tables 15.4-1 or 15.4-2
I = 1.0, Importance Factor per ASCE 7 11.5.1
T = 3 sec., Fundamental Period of Vessel
TL = 12 sec., Long-Period Transition Period per ASCE 7 12.8.2
Empty Weight Of Vessel = 100 kip
Operating Weight of Vessel = 200 kip
Center of Gravity Of Vessel From Top Of Pedestal, CG = 2.5 ft
Fa = 1.2, Short-Period Site Coefficient per ASCE 7 11.4.3
Fv = 1.7, Long-Period site Coefficient per ASCE 7 11.4.3
SDS 0.263, Design Spectral Response Acceleration Parameter at short periods per ASCE 711.4.4
SD1 = 0.1, Design Spectral Response Acceleration Parameter at period of 1 sec per ASCE 711.4.4
CS = 0.017, Seismic Response Coefficient Per ASCE 7 12.8.1.1
Base Shear Based on Operating Load Condition
V = Cs·Operatingwt =3.339 kip
420 — STAAD Foundation Advanced V8i
Chapter — 8
8.11 Vertical Vessel Seismic Load Generation 8
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Seismic Response Coef-ficient (Cs)
0.0167 0.017 1.787
Base Shear OperatingCase (kip)
3.339 3.339 0.007
Table 8-34: Vertical Vessel verification example 11 comparison
8.12 Vertical Vessel Seismic LoadGeneration 9
Location San Bernadino 92411
S1 = 1.415, Spectral Response Acceleration at Short Periods determined in accordance withASCE 7 11.4.1
SS = 2.984, Spectral Response Acceleration at Period of 1 sec determined in accordance withASCE 7 11.4.1
Site Class = D, Based On Soil Properties In Accordance With ASCE 7 Chapter 20
R =2, Response modification Coefficient per ASCE 7 Tables 15.4-1 or 15.4-2
I = 1.0, Importance Factor per ASCE 7 11.5.1
T = 3.5 sec., Fundamental Period of Vessel
TL = 12 sec., Long-Period Transition Period per ASCE 7 12.8.2
Empty Weight Of Vessel = 100 kip
Operating Weight of Vessel = 200 kip
Center of Gravity Of Vessel From Top Of Pedestal, CG = 9 ft
Fa = 1, Short-Period Site Coefficient per ASCE 7 11.4.3
Fv = 1.5, Long-Period site Coefficient per ASCE 7 11.4.3
SDS = 1.989, Design Spectral Response Acceleration Parameter at short periods per ASCE 711.4.4
SD1 = 1.415, Design Spectral Response Acceleration Parameter at period of 1 sec per ASCE 711.4.4
Cs = 0.202, Seismic Response Coefficient Per ASCE 7 12.8.1.1
Base Shear Based on Operating Load Condition
V = Cs·Operatingwt = 40.429 kip
Section 8 Plant Foundation
8.12 Vertical Vessel Seismic Load Generation 9
Verification Manual — 421
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Seismic Response Coef-ficient (Cs)
0.2021 0.202 none
Base Shear OperatingCase (kip)
40.429 40.429 none
Table 8-35: Vertical Vessel verification example 12 comparison
8.13 Vertical Vessel Wind Load Generation 1Vessel Data
Height of Vessel, H = 60 ft
Diameter of Vessel, D = 15 ft
Vessel Time Period, t = 5 sec.
Pedestal height Above Ground = 1 ft
Vessel Frequency, f = 1/t = 0.2 Hz
Wind Parameters
Wind Speed = 80 mph
Wind Directional Factor, Kd = 0.95, per ASCE 7-05 6.5.6.6
Wind Exposure = C
Exposure Case = 2
Topographic Factor, Kzt = 1.0, per ASCE 7-05 6.5.7.2
Importance factor, I = 1.15, per ASCE 7-05 6.5.5
Gust Wind Effect Factor, G = 0.85, per ASCE 7-05 6.5.8
Net Force Coefficient, Cf = 1, per ASCE 7-05 Fig. 6-20 & 6-21
Velocity Pressure
Exposure Coefficient, Kz, per ASCE 7-05 6.5.6.6
Design Wind Pressure per ASCE 7-05 6.5.10
qz = 0.00256·Kd·Kz·V·I·G·CfShear Force on Top of Pier
F = qz·G·Cf·A
Moment on Top of Pier
M = F x Moment Arm
422 — STAAD Foundation Advanced V8i
Chapter — 8
8.13 Vertical Vessel Wind Load Generation 1
Kzqz(psf)
A(ft2) F (kip) M
(ft·kip)0.849 15.195 15 0.194 0.0970.849 15.195 210 2.712 21.6980.902 16.143 75 1.029 18.0100.945 16.920 75 1.079 24.2690.982 17.582 75 1.121 30.8231.044 18.680 150 2.382 83.8231.094 19.578 150 2.496 112.3291.137 20.344 150 2.594 142.6631.141 20.415 15 0.260 15.748
Σ 13.867 448.995
Total Shear Force at Top of Pier = 13.867 kip
Total Moment at Top of Pier = 448.995 ft·kip
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Wind Shear on Top of Pier(kip)
13.867 13.867 none
Wind Moment of Top ofPier (ft·kip)
448.995 448.898 negligible
Table 8-36: Vertical Vessel verification example 13 comparison
8.14 Vertical Vessel Wind Load Generation 2Vessel DataHeight of Vessel, h = 74 ft
Diameter of Vessel, D = 20 ft
Vessel Time Period, t = 5 sec.
Pedestal height Above Ground = 3 ft
Vessel Frequency, f = 1/t = 0.2 Hz
Wind ParametersWind Speed = 90 mph
Wind Directional Factor, Kd = 0.95, per ASCE 7-05 6.5.6.6
Wind Exposure = D
Exposure Case = 2
Topographic Factor, Kzt = 1.0, per ASCE 7-05 6.5.7.2
Importance factor, I = 1.15, per ASCE 7-05 6.5.5
Section 8 Plant Foundation
8.14 Vertical Vessel Wind Load Generation 2
Verification Manual — 423
Gust Wind Effect Factor, G = 0.85, per ASCE 7-05 6.5.8
Net Force Coefficient, Cf = 0.8, per ASCE 7-05 Fig. 6-20 & 6-21
Velocity Pressure
Exposure Coefficient, Kz, per ASCE 7-05 6.5.6.6
Design Wind Pressure per ASCE 7-05 6.5.10
qz = 0.00256·Kd·Kz·V·I·G·CfShear Force on Top of Pier
F = qz·G·Cf·A
Moment on Top of Pier
M = F x Moment Arm
Kzqz(psf)
A(ft2)
F(kip) M (ft·kip)
1.030 23.339 20 0.317 0.1591.030 23.339 280 4.444 35.5501.083 24.536 100 1.668 29.1981.126 25.507 100 1.734 39.0261.162 26.329 100 1.790 49.2351.222 27.680 200 3.764 131.7561.270 28.775 200 3.913 176.1031.311 29.702 200 4.039 222.1711.347 30.509 200 4.149 269.7001.369 31.019 140 2.953 217.046
Σ 28.77 1169.945
Total Shear Force at Top of Pier = 28.774 kip
Total Moment at Top of Pier = 1169.945 ft·kip
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Wind Shear on Top ofPier (kip)
28.774 28.774 none
Wind Moment of Top ofPier (ft·kip)
1169.945 1168.516 0.12
Table 8-37: Vertical Vessel verification example 14 comparison
8.15 Vertical Vessel Wind Load Generation 3Vessel DataHeight of Vessel = 74 ft
424 — STAAD Foundation Advanced V8i
Chapter — 8
8.15 Vertical Vessel Wind Load Generation 3
Diameter of Vessel = 20 ft
Vessel Time Period, t = 5 sec.
Pedestal height Above Ground = 3 ft
Vessel Frequency, f = 1/t = 0.2 Hz
Wind ParametersWind Speed = 110 mph
Wind Directional Factor, Kd = 0.95, per ASCE 7-05 6.5.6.6
Wind Exposure = B
Exposure Case = 2
Topographic Factor, Kzt = 1.0, per ASCE 7-05 6.5.7.2
Importance factor, I = 1.15, per ASCE 7-05 6.5.5
Gust Wind Effect Factor, G = 0.85, per ASCE 7-05 6.5.8
Net Force Coefficient, Cf = 0.8, per ASCE 7-05 Fig. 6-20 & 6-21
Velocity Pressure
Exposure Coefficient, Kz, per ASCE 7-05 6.5.6.6
Design Wind Pressure per ASCE 7-05 6.5.10
qz = 0.00256·Kd·Kz·V·I·G·CfShear Force on Top of Pier
F = qz·G·Cf·A
Moment on Top of Pier
M = F x Moment Arm
Kzqz(psf)
A(ft2) F (kip) M
(ft·kip)0.575 19.449 20 0.265 0.1320.575 19.449 280 3.703 29.6250.624 21.115 100 1.436 25.1270.665 22.505 100 1.530 34.4330.701 23.709 100 1.612 44.3360.761 25.740 200 3.501 122.5220.811 27.434 200 3.731 167.8990.854 28.901 200 3.931 216.1830.892 30.203 200 4.108 266.9930.917 31.037 140 2.955 217.169
Σ 26.771 1124.42
Total Shear Force at Top of Pier 26.771 kip
Total Moment at Top of Pier = 1124.42 ft·kip
Section 8 Plant Foundation
8.15 Vertical Vessel Wind Load Generation 3
Verification Manual — 425
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Wind Shear on Top ofPier (kip)
26.771 26.771 none
Wind Moment of Top ofPier (ft·kip)
1124.42 1123.23 0.11
Table 8-38: Vertical Vessel verification example 15 comparison
8.16 Vertical Vessel Wind Load Generation 4Vessel Data
Height of Vessel = 22 ft
Diameter of Vessel = 6 ft
Vessel Time Period, t = 5 sec.
Pedestal height Above Ground = 2 ft
Vessel Frequency, f = 1/t = 0.2 Hz
Wind Parameters
Wind Speed = 110 mph
Wind Directional Factor, Kd = 0.95, per ASCE 7-05 6.5.6.6
Wind Exposure = B
Exposure Case = 2
Topographic Factor, Kzt = 1.0, per ASCE 7-05 6.5.7.2
Importance factor, I = 1.15, per ASCE 7-05 6.5.5
Gust Wind Effect Factor, G = 0.85, per ASCE 7-05 6.5.8
Net Force Coefficient, Cf = 0.8, per ASCE 7-05 Fig. 6-20 & 6-21
Velocity Pressure
Exposure Coefficient, Kz, per ASCE 7-05 6.5.6.6
Design Wind Pressure per ASCE 7-05 6.5.10
qz = 0.00256·Kd·Kz·V·I·G·CfShear Force on Top of Pier
F = qz·G·Cf·A
Moment on Top of Pier
M = F x Moment Arm
426 — STAAD Foundation Advanced V8i
Chapter — 8
8.16 Vertical Vessel Wind Load Generation 4
Kzqz(psf)
A(ft2)
F(kip)
M(ft·kip)
0.575 19.449 6 0.079 0.0400.575 19.449 84 1.111 8.8880.624 21.115 30 0.431 7.5380.657 22.245 24 0.363 7.987
Σ 1.984 24.452
Total Shear Force at Top of Pier = 1.984 kip
Total Moment at Top of Pier = 24.452 ft·kip
Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Wind Shear on Top of Pier(kip)
1.984 1.984 none
Wind Moment of Top ofPier (ft·kip)
24.452 24.293 negligible
Table 8-39: Vertical Vessel verification example 16 comparison
8.17 Horizontal Vessel Applied Loads 1Pier Design Philosophy
Vessel Loads
You are provided an option of making both piers identical, engineering and installationerrors can be avoided by doing so. If making them identical does not lead to economicalsolution, then check applied load distribution, follow PIP 4.3
Operating Load = 106 kip
Empty Load = 92 kip
Test Load = 118 kip
A major difference between pier loads is caused by longitudinal seismic load (i.e., whenvessel is located in higher seismic area). Thermal load and bundle pull force also contributetowards the difference.
Thermal Load = 0 kip
Live Load = 0 kip
Erection Load = 110 kip
Anchor Bold data
Anchor bold dia., Db = 1 in
BP = 0 kip
Section 8 Plant Foundation
8.17 Horizontal Vessel Applied Loads 1
Verification Manual — 427
Bolt spacing = 9 in
Bolt edge dist. = 6 in
center-to-center = 2 in
Horizontal vessel Data
Vessel CG from Top of Pier = 7 ft - 5ft/2 = 4.5 ft
Tan to Tan Length, L = 23.5 ft
CL to CL of AB, Lab = 11 ft
Vertical Load DistributionVessel Outer Dim including Insulation = 42 in
% Distribution For Vertical Loads At Fixed End = 40%
% Distribution For Vertical Loads At Sliding End = 60%
CG to Bott of Baseplate = 10 ft
Empty Load at fixed end = 36.8 kip
Operating Load at fixed end = 42.4 kip
Earthquake LoadsTransverse Earthquake Load Operating Condition
Bottom of the Base Plate to HPFS (est) = 10 kip
Longitudinal Earthquake Load Operating Condition = 15 kip
Transverse Earthquake Load Empty Condition = 9 kip
Longitudinal Earthquake Load Empty Condition= 10 kip
X = long
Z = trans
Wind Loadsμ = 0.4
Transverse Wind Load on Vessel = 10 kip
Longitudinal Wind Load on Vessel = 3.5 kip
Longitudinal Wind Load on Pier = 0.5 kip
428 — STAAD Foundation Advanced V8i
Chapter — 8
8.17 Horizontal Vessel Applied Loads 1
PIP Load combinations
LoadComb. Empty Operating Test Thermal Bundle EQ Trans EQ Long W
TransW
Long Live Erection
1 0 1 0 1 0 0 0 0 0 0 02 0 1 0 1 0 0 0 0 0 1 03 0 1 0 0 0 0 0 1 0 0 04 0 1 0 0 0 0 0 0 1 0 05 0 1 0 0 0 1 0 0 0 0 06 0 1 0 0 0 0 1 0 0 0 07 1 0 0 0 0 0 0 1 0 0 08 1 0 0 0 0 0 0 0 1 0 09 0 0.9 0 0 0 0.7 0 0 0 0 010 0 0.9 0 0 0 0 0.7 0 0 0 011 0.9 0 0 0 0 0.7 0 0 0 0 012 0.9 0 0 0 0 0 0.7 0 0 0 013 0 0 0 0 0 0 0 1 0 0 114 0 0 0 0 0 0 0 0 1 0 115 0 0 0.83 0 0 0 0 0.415 0 0 016 0 0 0.83 0 0 0 0 0 0.415 0 017 1 0 0 0 1 0 0 0 0 0 0
Table 8-40: Service level load combinations per PIP
LoadComb. Empty Operating Test Thermal Bundle EQ Trans EQ Long W
TransWLong Live Erection
1 0 1.4 0 1.4 0 0 0 0 0 0 02 0 1.2 0 1.2 0 0 0 0 0 1.6 03 0 1.2 0 0 0 0 0 1.6 0 0 04 0 1.2 0 0 0 0 0 0 1.6 0 05 0 1.2 0 0 0 1 0 0 0 0 06 0 1.2 0 0 0 0 1 0 0 0 07 0.9 0 0 0 0 0 0 1.6 0 0 08 0.9 0 0 0 0 0 0 0 1.6 0 09 0 0.9 0 0 0 1 0 0 0 0 010 0 0.9 0 0 0 0 1 0 0 0 011 0.9 0 0 0 0 1 0 0 0 0 012 0.9 0 0 0 0 0 1 0 0 0 013 0 0 0 0 0 0 0 1.6 0 0 0.914 0 0 0 0 0 0 0 0 1.6 0 0.915 0 0 1.2 0 0 0 0 0.8 0 0 016 0 0 1.2 0 0 0 0 0 0.8 0 017 0.9 0 0 0 1.6 0 0 0 0 0 0
Table 8-41: Strength level load combinations per PIP
Section 8 Plant Foundation
8.17 Horizontal Vessel Applied Loads 1
Verification Manual — 429
LoadComb.
AxialLoad(kip)
LongitudinalShear (kip)
TransverseShear (kip)
TransverseMoment(ft-kip)
LongitudinalMoment (ft-
kip)1 42.4 0 0 0 02 42.4 0 0 0 03 42.4 0 5 0 04 42.4 2.25 0 0 05 42.4 0 7 0 06 42.4 10.5 0 0 07 36.8 0 5 0 08 36.8 2.25 0 0 09 38.16 0 4.9 0 010 38.16 7.35 0 0 011 33.12 0 4.41 0 012 33.12 4.9 0 0 013 44.0 0 5 0 014 44.0 2.25 0 0 015 39.176 0 2.075 0 016 39.176 0.9338 0 0 017 36.8 0 0 0 0
Table 8-42: Service level loads applied at the top of the top of the fixedpier
LoadComb.
AxialLoad(kip)
LongitudinalShear (kip)
TransverseShear (kip)
TransverseMoment(ft-kip)
LongitudinalMoment (ft-
kip)1 59.36 0 0 0 02 50.88 0 0 0 03 50.88 0 4 0 04 50.88 3.6 0 0 05 50.88 0 7 0 06 50.88 10.5 0 0 07 33.12 0 4 0 08 33.12 3.6 0 0 09 38.16 0 7 0 010 38.16 10.5 0 0 011 33.12 0 6.3 0 012 33.12 7 0 0 013 39.60 0 4 0 014 39.60 3.6 0 0 015 56.64 0 2 0 016 56.64 1.8 0 0 017 33.12 0 0 0 0
Table 8-43: Strength level loads applied at the top of the top of thefixed pier
430 — STAAD Foundation Advanced V8i
Chapter — 8
8.17 Horizontal Vessel Applied Loads 1
ComparisonHand Calculation results exactly match the results of STAAD Foundation analysis.
8.18 Horizontal Vessel Applied Loads 2Pier Design Philosophy
Vessel LoadsYou are provided an option of making both piers identical, engineering and installationerrors can be avoided by doing so. If making them identical does not lead to economicalsolution, then check applied load distribution, follow PIP 4.3
Operating Load = 150 kip
Empty Load = 100 kip
Test Load = 160 kip
A major difference between pier loads is caused by longitudinal seismic load (i.e., whenvessel is located in higher seismic area). Thermal load and bundle pull force also contributetowards the difference.
Thermal Load = 0
Bundle Pull Force = 0
Live Load = 0
Erection Load = 110 kip
Anchor Bold data
Anchor bold dia., Db = 1 in
BP = 0 kip
Bolt spacing = 9 in
Bolt edge dist. = 6 in
center-to-center = 2 in
Horizontal vessel Data
Vessel CG from Top of Pier = 7 ft - 6.5ft/2 = 3.75 ft
Tan to Tan Length, L = 23.5 ft
CL to CL of AB, Lab = 11 ft
Vertical Load DistributionVessel Outer Dim including Insulation = 42 in
% Distribution For Vertical Loads At Fixed End = 40%
% Distribution For Vertical Loads At Sliding End = 60%
Section 8 Plant Foundation
8.18 Horizontal Vessel Applied Loads 2
Verification Manual — 431
CG to Bott of Baseplate = 10 ft
Empty Load at fixed end = 40 kip
Operating Load at fixed end = 60 kip
Earthquake LoadsLocation Corona 92880
S1 = 0.882, Spectral Response Acceleration at Short Periods determined in accordance withASCE 7 11.4.1
SS = 2.296, Spectral Response Acceleration at Period of 1 sec determined in accordancewith ASCE 7 11.4.1
Site Class = D, Based On Soil Properties In Accordance With ASCE 7 Chapter 20
R = 1, Response modification Coefficient per ASCE 7 Tables 15.4-1 or 15.4-2
I = 1.15, Importance Factor per ASCE 7 11.5.1
T = 6 sec., Fundamental Period of Vessel
TL = 12 sec., Long-Period Transition Periods per ASCE 7 12.8.2
Center of Gravity Of Vessel From Top Of Pedestal = 7 ft + 10.416 ft - 5 ft =
fa = , Short-Period Site Coefficient per ASCE 7 11.4.3
fv = , Long-Period site Coefficient per ASCE 7 11.4.3
SDS = 1.53, Design Spectral Response Acceleration Parameter at short periods per ASCE 711.4.4
SD1 = 0.882, Design Spectral Response Acceleration Parameter at period of 1 sec per ASCE7 11.4.4
CS = 0.074, Seismic Response Coefficient Per ASCE 7 12.8.1.1
Base Shear Based on Operating Load Condition = 11.029 kip
Base Shear Based on Empty Load Condition = 7.352 kip
Transverse Earthquake Load Operating Condition = 11.029 kip
Longitudinal Earthquake Load Operating Condition
Transverse Earthquake Load Empty Condition= 7.352 kip
Longitudinal Earthquake Load Empty Condition= 7.352 kip
Wind LoadsTransverse Wind Load on Vessel = 10 kip
Bottom of the Base Plate to HPFS (est)
μ = 0.4
Longitudinal Wind Load on Vessel = 3.5 kip
Longitudinal Wind Load on Pier = 0.5 kip
Transverse Wind Moment at top of pedestal = 20 ft-kip
X = long
432 — STAAD Foundation Advanced V8i
Chapter — 8
8.18 Horizontal Vessel Applied Loads 2
Z = trans
Longitudinal Wind Load at top of pedestal = 10 ft-kip
PIP Load combinations
LoadComb. Empty Operating Test Thermal Bundle EQ Trans EQ Long W
TransW
Long Live Erection
1 0 1 0 1 0 0 0 0 0 0 02 0 1 0 1 0 0 0 0 0 1 03 0 1 0 0 0 0 0 1 0 0 04 0 1 0 0 0 0 0 0 1 0 05 0 1 0 0 0 1 0 0 0 0 06 0 1 0 0 0 0 1 0 0 0 07 1 0 0 0 0 0 0 1 0 0 08 1 0 0 0 0 0 0 0 1 0 09 0 0.9 0 0 0 0.7 0 0 0 0 010 0 0.9 0 0 0 0 0.7 0 0 0 011 0.9 0 0 0 0 0.7 0 0 0 0 012 0.9 0 0 0 0 0 0.7 0 0 0 013 0 0 0 0 0 0 0 1 0 0 114 0 0 0 0 0 0 0 0 1 0 115 0 0 0.83 0 0 0 0 0.415 0 0 016 0 0 0.83 0 0 0 0 0 0.415 0 017 1 0 0 0 1 0 0 0 0 0 0
Table 8-44: Service level load combinations per PIP
LoadComb. Empty Operating Test Thermal Bundle EQ Trans EQ Long W
TransWLong Live Erection
1 0 1.4 0 1.4 0 0 0 0 0 0 02 0 1.2 0 1.2 0 0 0 0 0 1.6 03 0 1.2 0 0 0 0 0 1.6 0 0 04 0 1.2 0 0 0 0 0 0 1.6 0 05 0 1.2 0 0 0 1 0 0 0 0 06 0 1.2 0 0 0 0 1 0 0 0 07 0.9 0 0 0 0 0 0 1.6 0 0 08 0.9 0 0 0 0 0 0 0 1.6 0 09 0 0.9 0 0 0 1 0 0 0 0 010 0 0.9 0 0 0 0 1 0 0 0 011 0.9 0 0 0 0 1 0 0 0 0 012 0.9 0 0 0 0 0 1 0 0 0 013 0 0 0 0 0 0 0 1.6 0 0 0.914 0 0 0 0 0 0 0 0 1.6 0 0.915 0 0 1.2 0 0 0 0 0.8 0 0 016 0 0 1.2 0 0 0 0 0 0.8 0 017 0.9 0 0 0 1.6 0 0 0 0 0 0
Table 8-45: Strength level load combinations per PIP
Section 8 Plant Foundation
8.18 Horizontal Vessel Applied Loads 2
Verification Manual — 433
LoadComb.
AxialLoad(kip)
LongitudinalShear (kip)
TransverseShear (kip)
TransverseMoment(ft-kip)
LongitudinalMoment (ft-
kip)1 60 0 0 0 02 60 0 0 0 03 60 0 2.5 5 04 60 1.125 0 0 105 60 0 5.404 20.27 06 60 5.404 0 0 20.277 40 0 2.5 5 08 40 1.125 0 0 109 54 0 3.783 14.19 010 54 3.783 0 0 14.1911 36 0 2.522 9.457 012 36 2.522 0 0 9.45713 44 0 2.5 5 014 44 1.125 0 0 1015 53.12 0 1.038 2.075 016 53.12 0.467 0 0 4.15017 40 0 0 0 0
Table 8-46: Service level loads applied at the top of the top of thefixed pier
LoadComb.
AxialLoad(kip)
LongitudinalShear (kip)
TransverseShear (kip)
TransverseMoment(ft-kip)
LongitudinalMoment (ft-
kip)1 84 0 0 0 02 72 0 0 0 03 72 0 4 8 04 72 1.8 0 0 165 72 0 5.404 20.27 06 72 5.404 0 0 20.277 36 0 4 8 08 36 1.8 0 0 169 54 0 5.404 20.27 010 54 5.404 0 0 20.2711 36 0 3.602 13.509 012 36 3.602 0 0 13.50913 39.6 0 4 8 014 39.6 1.8 0 0 1615 76.8 0 2 4 016 76.8 0.9 0 0 817 36 0 0 0 0
Table 8-47: Strength level loads applied at the top of the top of thefixed pier
434 — STAAD Foundation Advanced V8i
Chapter — 8
8.18 Horizontal Vessel Applied Loads 2
ComparisonHand Calculation results exactly match the results of STAAD Foundation analysis.
Section 8 Plant Foundation
8.18 Horizontal Vessel Applied Loads 2
Verification Manual — 435
436 — (Undefined variable: Primary.ProductName)
Chapter 8
8.18 Horizontal Vessel Applied Loads 2
Section 9
Chinese Code (GB50007-2002)
The manual test cases in accordance with Chinese standard GB50007-2002 design. PKPMand the Foundation of the input data consistent, easy to check the results
9.1 Cone Footing DesignIndependent bases for design details
This example is included in the \VERIFICATION\CHINESE\ISO_CHN.AFS example file forreference.
Overview of tapered design results based on
NodeNumber
GroupNumber
Basic Geometry (Conical Base)Length(X Dir.)
Width (ZDir.) Thickness Edge height
(should be > 0.2 m)1 1 3.000 m 3.000 m 1.000 m 0.500 m
Table 9-1: Overview of cone footing design results
BaseNumber
Foundation Reinforcement Base Rein-forcement
Bottom Reinf.(Mz)
Bottom Reinf.(Mx)
MainBars Stirrups
1 # 10 @ 60 mm c /c
# 10 @ 60 mm c /c
N / A N / A
Table 9-2: Reinforcement details
Verification Manual — 437
9.1.1 Problem
Characteristics of Concrete and Steel
Heavy concrete units: 18.000 kN/m3
Compressive strength of concrete: 11.900 N/mm2
Reinforcement strength: 210.000 N/mm2
Minimum bar size: # 6
Maximum bar size: # 50
Minimum bar spacing: 50.00 mm
Maximum bar spacing: 500.00 mm
Clear Cover
Reinforcement layer thickness (F, CL): 50.00 mm
Soil Characteristics
Unit Weight: 18.00 kN/m3
Foundation bearing capacity: 180.00 kPa
Surcharge: 0.00 kN/m2
Height of soil above footing: 2000.00 mm
Geometry Information
Initial size of base
Thickness (Ft) : 1000.00 mm
Length - X (Fl) : 3000.00 mm
Width - Z (Fw) : 3000.00 mm
Edge height of the cone footing (St) : 500.00 mm
Column Dimension
Column Shape: Rectangular
Column length - X (Pl) : 600.00 mm
Column width - Z (Pw) : 600.00 mm
Column Cap
Column cap length - X : N/A
Column cap width - Z : N/A
438 — STAAD Foundation Advanced V8i
Chapter — 9
9.1 Cone Footing Design
9.1.2 Solution
ConditionNo.
VerticalForce (KN)
Shear X(KN)
Shear Z(KN)
Moment X(kN·m)
Moment Z(kN·m)
101 1000.000 0.000 0.000 99.998 99.998
Table 9-3: Loads for foundation base size estimation -For foundationbase (1)
LC Vertical Force(KN)
Shear X(KN)
Shear Z(KN)
Moment X(kN·m)
Moment Z(kN·m)
102 1000.000 0.000 0.000 99.998 99.998
Table 9-4: Loads for Punching shear check and reinforcements- For foun-dation base (1)
Basic dimensions
Initial size (Lo) = 3.00 m
Initial size (Wo) = 3.00 m
Net buoyancy = -0.00 kN
Adhesion = 0.00 kN
The minimum required base area, Amin = P / fa = 7.356 m2
The initial design area , Ao = Lo·Wo = 9.00 m2
Final design size
Length (L2) = 3.00 m
No. of control condition: # 101
Width (W2) = 3.00 m
No. of control condition: # 101
Area (A2) = 9.00 m2
Figure 9-1: Four corners of the calculated stress
Section 9 Chinese Code (GB50007-2002)
9.1 Cone Footing Design
Verification Manual — 439
LoadCase
Pressure atCorner1(q1)
(KN/m2)
Pressure atCorner2(q2)
(KN/m2)
Pressure atCorner3(q3)
(KN/m2)
Pressure atCorner4(q4)
(KN/m2)
Zero-pres-sure area(Au) (m2)
101 147.1111 102.6667 147.1111 191.5556 0.00101 147.1111 102.6667 147.1111 191.5556 0.00101 147.1111 102.6667 147.1111 191.5556 0.00101 147.1111 102.6667 147.1111 191.5556 0.00
If Au equals zero, that means it is small eccentricity, and do not need to adjust thepressure. Otherwise, the pressure needs to be adjusted. The negative pressure shouldalways set as 0. Keep adjusting if necessary.
Four corners of the stress adjusted data (if any).
No. LoadCondition
Pressure atCorner1 (q1)(KN/m2)
Pressure atCorner2 (q2)(KN/m2)
Pressure atCorner3 (q3)(KN/m2)
Pressure atCorner4 (q4)(KN/m2)
101 147.1111 102.6667 147.1111 191.5556101 147.1111 102.6667 147.1111 191.5556101 147.1111 102.6667 147.1111 191.5556101 147.1111 102.6667 147.1111 191.5556
If necessary, the bottom will be adjusted accordingly based on size.
Zero-pressure area ( if any )
Control the condition number = N / A
Foundation area = 9.00 m2
Zero-pressure area = 0.00 m2
Zero-pressure area percentage = 0.00%
9.1.3 Check Overturning and Sliding StabilityFigure 9-2: Elevation of stability forces
440 — STAAD Foundation Advanced V8i
Chapter — 9
9.1 Cone Footing Design
Load Case No. Sliding Factor of Safety Overturning Factor of SafetyX Dir. Z Dir. X Dir. Z Dir.
101 N / A N / A 19.763 19.763
Table 9-5: Factor of safety
Critical load cases and governing factor of safety ofoverturning
Along the X Direction
Critical sliding load case along the X direction: 101
Governing sliding force : 0.000 kN
Resisting Force for Sliding: 658.760 kN
Minimum sliding coefficient under critical load case: 0.000
Critical Overturning load case along X direction: 101
Critical overturning moment: 99.998 kN·m
Resisting moment for Overturning: 1976.244 kN·m
Minimum overturning coefficient under critical load case: 19.763
Along the Z Direction
Critical sliding load case along the Z direction : 101
Governing sliding force : 0.000 kN
Resisting Force for Sliding: 658.760 kN
Minimum sliding coefficient under critical load case: 0.000
Critical Overturning load case along Z direction : 101
Critical overturning moment: 99.998 kN·m
Resisting Moment for Overturning: 1976.244 kN·m
Minimum overturning coefficient under critical load case: 19.763
9.1.4 Check ShearFollowing formulae are used per GB50007 - 2002 code for design of building foundations.
Fl ≤ 0.7·βhpftamh0 (Ref. clause 8.2.7 - 1)
am = (At + ab) / 2 (Ref. clause 8.2.7 - 2)
Fl = Pj·Al (Ref. clause 8.2.7 - 3)
Punching One-way Check
Positive X Side
Control condition = # 102
Section 9 Chinese Code (GB50007-2002)
9.1 Cone Footing Design
Verification Manual — 441
Punching shear
Fl = Pj·Al = 88.889·724774.976 = 64.424 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7·0.92·1.270·(0.600 +2.470) / 2·0.935 = 1169.589 kN
Fl < 0.7·βhpftamh0Hence, Safe
Negative X Side
Control condition = # 102
Punching shear
Fl = Pj·Al = 133.333·724774.976 = 96.637 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7·0.92·1.270·(0.600 +2.470) / 2·0.935 = 1169.589 kN
Fl < 0.7·βhpftamh0Hence, Safe
Positive Z Side
Control condition = # 102
Punching shear
Fl = Pj·Al = 133.333·724774.976 = 96.637 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7·0.917·1.270·(0.600 +2.470) / 2·0.935 = 1169.589 kN
Fl < 0.7·βhpftamh0Hence, Safe
Negative Z Side
Control condition = # 102
Punching shear
Fl = Pj·Al = 88.889·724774.976 = 64.424 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7·0.92·1.270·(0.600 +2.470) / 2·0.935 = 1169.589 kN
Fl < 0.7·βhpftamh0Hence, Safe
Two-way punching test (four sides)
Control condition = # 102
442 — STAAD Foundation Advanced V8i
Chapter — 9
9.1 Cone Footing Design
Punching shear
Fl = Pj·Al = 111.111·2899099.905 = 322.122 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7·0.917·1.270·(2.400 +9.880) / 2·0.935 = 4678.355 kN
Fl < 0.7·βhpftamh0Hence, Safe
9.1.5 Reinforcement
Reinforcement Along the X DirectionFigure 9-3: Reinforcement parallel to the X-direction
A simplified formula for reinforcement is used per GB50010 – 2002.
No control condition = # 102
Minimum reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15%
Cross-sectional area about X-axis, A cross = 2,425,000.005
Minimum reinforcement area
Astmin = Ρmin·A cross- = 0.15 · 2,425,000.005 = 3,637.500
Calculate moment
MI = (A1) 2 [(2·l + a ')·(pmax + p - 2·G / A) + (pmax - p)·l] / 12
= 1,200.0002·[(2·3,000.000 +600.000) (0.169 +0.152 - 2·324,000.000/9,000,000.000) + (0.169 -0.152)·3,000.000] / 12 = 20,3519,997.379 kN·m
Calculate area required
Ast = MI / (0.9·h0·fy) = 20,3519,997.379 / (0.9·935.000·210.000) = 1,139.498
Select rebar size, db = 10.000
Minimum allowable reinforcement spacing, Smin = 50.000 mm
Section 9 Chinese Code (GB50007-2002)
9.1 Cone Footing Design
Verification Manual — 443
Maximum allowable reinforcement spacing, Smax = 500.000 mm
With actual spacing, S = 60.000 mm
Actual area, Ast (Actual) = 3637.500 mm2
Smin ≤ S ≤ Smax
Selected Reinforcement satisfy the requirements.
Astmin ≤ Ast, with real
Selected Reinforcement satisfy the requirements.
Reinforcement Along the Z DirectionFigure 9-4: Reinforcement parallel to the Z-direction
A simplified formula for reinforcement is used per GB50010 – 2002.
No control condition = # 102
Minimum reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15%
Cross-sectional area about Z-axis, A cross = 2425000.005
Minimum reinforcement area
Astmin = Ρmin·A cross = 0.15%·2425000.005 = 3637.500
Calculate moment
MI = (A1) 2 [(2·l + a ')·(pmax + p - 2·G / A) + (pmax - p)·l] / 12
= 1200.0002·[(2·3000.000 +600.000) (0.169 +0.152 - 2·324000.000/9000000.000) + (0.169 -0.152)·3000.000] / 12 = 203519997.379 kN·m
Calculate area required
Ast = MI / (0.9·h0·fy) = 203519997.379 / (0.9·935.000·210.000) = 1151.685
Select rebar size, db = 10.000
Minimum allowable reinforcement spacing, Smin = 50.000 mm
444 — STAAD Foundation Advanced V8i
Chapter — 9
9.1 Cone Footing Design
Maximum allowable reinforcement spacing, Smax = 500.000 mm
With actual spacing, S = 60.000 mm
Actual area, Ast (Actual) = 3637.500 mm2
Smin ≤ S ≤ SmaxReinforced selected to meet the requirements .
Astmin ≤ Ast, with realReinforcement meet the requirements
Reinforcements should be placed at the base bottom.
9.2 PKPM Isolated Footing Design9.2.1 Problem
Elevation and Plan
Foundation type: cast-in-site cone footing
Initial iteration base dimensions:
Length = 3000 mm
Width = 3000 mm
Section 9 Chinese Code (GB50007-2002)
9.2 PKPM Isolated Footing Design
Verification Manual — 445
Height = 500 mm
Second iteration
Length = 700 mm
Width = 700 mm
Height = 500 mm
Bottom elevation of the basis: -2.0 m
Shifts of the base: S Direction: 0 mm B direction: 0 mm
Reinforcement at the bottom of the base:
Y direction : 10 @ 200
X direction : 10 @ 200
Weight of the foundation and soil:: 18.0 kPa
Column section information
High column section: 600 mm
Column section width: 600 mm
Eccentric x : 0 mm
Eccentric y : 0 mm
Column angle: 0°
Loading information
Basic values of vertical load: Nk = 1000 kN
Basic value of the moment along X dir.: Mx = 100 kN·M
Basic value of the moment along Y dir.: My = 100 kN·M
9.2.2 Solution
Check Shear
Following formula Per GB5007 - 2002 code for design of building foundation:
Fl ≤ 0.7·βhpftamh0 (Ref. clause 8.2.7 - 1)
am = (At + ab) / 2 (Ref. clause 8.2.7 - 2)
Fl = Pj·Al (Ref. clause 8.2.7 - 3)
Resisting Shear force calculation:
X + direction , height H = 1000
Fl = Pj·Al = 133.33·0.69 = 91.67
Fl ≤ 0.7·βhpft (At + ab)·h0/2 = 0.7·0.98·1270.94·(0.60 +2.50)·0.95 / 2 = 1288.19 KN
Punching Shear check is satisfied in this direction.
X- direction , height H = 1000
446 — STAAD Foundation Advanced V8i
Chapter — 9
9.2 PKPM Isolated Footing Design
Fl = Pj·Al = 92.59·0.69 = 63.66
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7·0.98·1270.94·(0.60 +2.50)·0.95 / 2 = 1288.19 KN
Punching Shear check is satisfied in this direction.
Y + direction , height H = 1000
Fl = Pj·Al = 92.59·0.69 = 63.66
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7·0.98·1270.94·(0.60 +2.50)·0.95 / 2 = 1288.19 KN
Punching Shear check is satisfied in this direction.
Y- direction , height H = 1000
Fl = Pj·Al = 133.33·0.69 = 91.67
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7·0.98·1270.94·(0.60 +2.50)·0.95 / 2 = 1288.19 KN
Punching Shear check is satisfied in this direction.
Check Shear Edges
H = 1000.
Fl = N - pk·(bc +2·h0)·(hc +2·h0) = 1000.00 - 111.1·(600.0 + 2·950.0)·(600.0 +2·950.0)·1e-6 =305.56 Kn
Fr = 0.7·βhp·ft·am·h0 = 0.7·0.98·1270.9·(600.0 + 600.0 + 2·950.0)·950.0·1e-6 = 5152.76 Kn
Punching Shear check at edges is satisfied.
X + direction , height H = 1000 mm
Fl = Pj·Al = 133.33·0.56 = 74.67
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7·0.98·1270.94·(0.70 + 2.60)·0.95 / 2 = 1371.30 KN
Punching Shear check at edges is satisfied.
X- direction , height H = 1000 mm
Fl = Pj·Al = 91.85·0.56 = 51.44
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7·0.98·1270.94·(0.70 + 2.60)·0.95 / 2 = 1371.30 KN
Punching Shear check at edges is satisfied.
Y + direction , height H = 1000 mm
Fl = Pj·Al = 91.85·0.56 = 51.44
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7·0.98·1270.94·(0.70 + 2.60)·0.95 / 2 = 1371.30 KN
Punching Shear check at edges is satisfied.
Y- direction , height H = 1000 mm
Fl = Pj·Al = 133.33·0.56 = 74.67
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7·0.98·1270.94·(0.70 + 2.60)·0.95 / 2 = 1371.30 KN
Punching Shear check at edges is satisfied.
Section 9 Chinese Code (GB50007-2002)
9.2 PKPM Isolated Footing Design
Verification Manual — 447
Bending Reinforcement
The following formula are used Per GB5007 - 2002 code for design of building foundation:
M = (1/12)a12·[(2·l + a')(Pjmax + Pj) + (Pjmax + Pj)·l ]
Moment calculations
x direction, h0 = 940 mm
M = (1.20)2·[(2·3.00 + 0.60)·(133333.33 + 115555.55) + (133333.33 - 115555.55)·3.00] / 12 = 203.52kN·m
M =(1.20)2·[(2·3.00 + 0.60)·(88888.89 + 106666.66) + (88888.89 - 106666.66)·3.00] / 12 =148.48 kN·m
y direction , h0 = 940 mm
M = (1.20)2·[(2·3.00 + 0.60)·(88888.89 + 106666.66) + (88888.89 - 106666.66)·3.00] / 12 =148.48 kN·m
M = (1.20)2·[(2·3.00 + 0.60)·(133333.33 + 115555.55) + (133333.33 - 115555.55)·3.00] / 12 = 203.52kN·m
x direction , h0 = 940 mm
M = (1.20)2·[(2·3.00 + 0.60)·(133333.33 + 115555.55) + (133333.33 - 115555.55)·3.00] / 12 = 203.52kN·m
M = (1.20)2·[(2·3.00 + 0.60)·(88888.89 + 106666.66) + (88888.89 - 106666.66)·3.00] / 12 =148.48 kN·m
y direction , h0 = 940 mm
M = (1.20)2·[(2·3.00 + 0.60)·(88888.89 + 106666.66) + (88888.89 - 106666.66)·3.00] / 12 =148.48 kN·m
M = (1.20)2·[(2·3.00 + 0.60)·(133333.33 + 115555.55) + (133333.33 - 115555.55)·3.00] / 12 = 203.52kN·m
Reinforcement calculation:
M1 = 203.520
AGx = M1 / (0.9·h0·fy) = 203520.016 / (0.9·0.940·210.) = 1145.559 mm2
M2 = 203.520
AGy = M2 / (0.9·h0·fy) = 203520.016 / (0.9·0.940·210.) = 1145.559 mm2
M1 = 203.520
AGx = M1 / (0.9·h0·fy) = 203520.016 / (0.9·0.940·210.) = 1145.559 mm2
M2 = 203.520
AGy = M2 / (0.9·h0·fy) = 203520.016 / (0.9·0.940·210.) = 1145.559 mm2
The area of steel at X direction: 1145.559
The area of steel at Y direction: 1145.559
The initial area of steel along X direction is satisfied.
448 — STAAD Foundation Advanced V8i
Chapter — 9
9.2 PKPM Isolated Footing Design
The initial area of steel along Y direction is satisfied.
The area of steel required:
AgX: 10 @ 200
AgY: 10 @ 200
9.3 Stepped Foundation Design
NodeNumber
GroupNumber
Basic Geometry Dimension (Base Level)
Order Length X Dir.(M)
Width Z Dir.(M)
Height(M)
1 1 Total 3.000 m 3.000 m 1.200 m- - Article
(1)Order3.000 m 3.000 m 0.400 m
- - Article (2)order 2.000 m 2.000 m 0.400 m
- - Article (3)order 1.000 m 1.000 m 0.400 m
Table 9-6: Overview of the stepped foundation design
NodeNumber
Foundation Reinforcement Base Rein-forcement
Bottom Reinf.(Mz)
Bottom Reinf.(Mx)
MainBars Stirrups
1 # 10 @ 60 mm c /c
# 10 @ 60 mm c /c
N / A N / A
Table 9-7: Reinforcement details
9.3.1 Problem
Basic Geometry
Height of the base - (Ft): 1200.00 mm
Length of the base - X (Fl): 3000.00 mm
Width of the base - Z (Fw): 3000.00 mm
Column Dimension
Column Shape : Rectangular
Length of the Column section - X (Pl): 600.00 mm
Width of the column section - Z (Pw): 600.00 mm
Base
Base length - X: N / A
Base width - Z: N / A
Section 9 Chinese Code (GB50007-2002)
9.3 Stepped Foundation Design
Verification Manual — 449
Concrete and Steel Parameters
Concrete density: 18.000 kN/m3
Concrete strength: 11.900 N/mm2
Reinforcement strength: 210.000 N/mm2
Minimum bar Size: # 6
Maximum bar size: # 40
Minimum bar spacing : 50.00 mm
Maximum bar spacing : 500.00 mm
Clear cover (F, CL): 50.00 mm
Soil Properties
Soil type: Drained
Density: 18.00 kN/m3
Foundation bearing capacity : 180.00 kPa
Surcharge: 0.00 kN/m2
Embedment depth of foundation: 2,000.00 mm
Adhesion: 0.00 kN/m2
Factor of Safety for sliding and overturning
Basal friction coefficient: 0.50
Safety factor of sliding: 1.50
Safety factor of overturning: 1.50
ConditionNo.
VerticalForce (KN)
Shear X(KN)
Shear Z(KN)
Moment X(kN·m)
Moment Z(kN·m)
101 1000.000 0.000 0.000 99.998 99.998
Table 9-8: Critical loads for base size estimation - standard combination
LC Vertical Force(KN)
Shear X(KN)
Shear Z(KN)
Moment X(kN·m)
Moment Z(kN·m)
102 1000.000 0.000 0.000 99.998 99.998
Table 9-9: Loads for foundation design- the basic combination
9.3.2 Solution
Foundation Dimensions
The initial length (Lo) = 76.20 m
The initial width (Wo) = 76.20 m
Buoyancy = -0.00 KN
450 — STAAD Foundation Advanced V8i
Chapter — 9
9.3 Stepped Foundation Design
Adhesion = 0.00 kN
Minimum area of steel required
Bearing pressure, Amin = P / qmax = 7.356 m2
Initial foundation area , Ao = Lo x Wo = 5806.44 m2
Final Design Sizes
Length of the Base (L2) = 3.00 m
Number of load case: # 101
Width of the base (W2) = 3.00 m
Number of load case: # 101
Height of the base (D2) = 1.20 m
Number of load case: # 101
Area (A2) = 9.00 m2
Corner Stresses
Initial pressure at four corners ( before adjustment )
Figure 9-5: Four corners of the calculated stress
LoadCase
Pressure atCorner1 (q1)(KN/m2)
Pressure atCorner2 (q2)(KN/m2)
Pressure atCorner3 (q3)(KN/m2)
Pressure atCorner4 (q4)(KN/m2)
Zero-pressurearea (Au) (m2)
101 147.1111 102.6667 147.1111 191.5556 0.00101 147.1111 102.6667 147.1111 191.5556 0.00101 147.1111 102.6667 147.1111 191.5556 0.00101 147.1111 102.6667 147.1111 191.5556 0.00
If Au equals zero, that means it is small eccentricity, and do not need to adjust thepressure. Otherwise, the pressure needs to be adjusted. The negative pressure should alwaysset as 0. Keep adjusting if necessary.
Section 9 Chinese Code (GB50007-2002)
9.3 Stepped Foundation Design
Verification Manual — 451
four corners of the stress of adjustment ( if necessary )
No. LoadCondition
Pressure atCorner1 (q1)(KN/m2)
Pressure atCorner2 (q2)(KN/m2)
Pressure atCorner3 (q3)(KN/m2)
Pressure atCorner4 (q4)(KN/m2)
101 147.1111 102.6667 147.1111 191.5556101 147.1111 102.6667 147.1111 191.5556101 147.1111 102.6667 147.1111 191.5556101 147.1111 102.6667 147.1111 191.5556
If necessary, the bottom will be adjusted accordingly based on size.
Details of the Zero-pressure zone ( if any )
Design condition number = N / A
Area of Foundation Base = 9.00 sq.m
Zero-pressure area = 0.00 sq.m
Zero-pressure area percentage = 0.00%
Check overturning and sliding stability
Factor of Safety table
Load Case No. Sliding Factor of Safety Overturning Factor of SafetyX Dir. Z Dir. X Dir. Z Dir.
101 N / A N / A 19.782 19.782
Table 9-10: Safety factors
Critical loads and governing factor of safety ofoverturning and sliding
Along the X Direction
Critical sliding load case along X direction: 101
Governing sliding force: 0.000 kN
Resisting Force for Sliding: 659.408 kN
Minimum sliding coefficient under critical load case: 0.000
Critical Overturning load case along X direction: 101
Critical overturning moment: 99.998 kN·m
Resisting moment for Overturning: 1978.188 kN·m
Minimum overturning coefficient under critical load case 19.782
452 — STAAD Foundation Advanced V8i
Chapter — 9
9.3 Stepped Foundation Design
Along the Z Direction
Critical sliding load case along Z direction: 101
Critical sliding force: 0.000
Resisting Force for Sliding: 659.408 kN
Minimum sliding coefficient under critical load case: 0.000
Critical Overturning load case along Z direction: 101
Critical overturning moment: 99.998 kN·m
Resisting Moment for Overturning: 1978.188 kN·m
Minimum overturning coefficient under critical load case: 19.782
9.3.3 Check ShearThe following formulae are used per GB50007 - 2002 code for design of buildingfoundations.
Fl ≤ 0.7·βhpftamh0 (Ref. clause 8.2.7 - 1)
am = (At + ab) / 2 (Ref. clause 8.2.7 - 2)
Fl = Pj·Al (Ref. clause 8.2.7 - 3)
Punching One-way Check
Positive X Direction
Control condition = # 102
Punching shear
Fl = Pj·Al = 88.889·190774.972 = 16.958 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 0.933 · 1.270 · (0.600 + 2.870) / 2 · 1.135 = 1633.932 kN
Fl < 0.7·βhpftamh0Hence, Safe
Negative X Direction
Control condition = # 102
Punching shear
Fl = Pj·Al = 133.333 · 190774.972 = 25.437 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 =0.7 · 0.933 · 1.270 ·(0.600 +2.870) / 2 · 1.135 = 1633.932 kN
Fl < 0.7·βhpftamh0Hence, Safe
Section 9 Chinese Code (GB50007-2002)
9.3 Stepped Foundation Design
Verification Manual — 453
Positive Z Direction
Control condition = # 102
Punching shear
Fl = Pj·Al = 133.333 · 190774.972 = 25.437 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 0.933 · 1.270 · (0.600 +2.870) / 2 · 1.135 = 1633.932 kN
Fl < 0.7·βhpftamh0Hence, Safe
Negative Z Direction
Control condition = # 102
Punching shear
Fl = Pj·Al = 88.889 · 190774.972 = 16.958 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 0.933 · 1.270 · (0.600 +2.870) / 2 · 1.135 = 1633.932 kN
Fl < 0.7·βhpftamh0Hence, Safe
Two-way punching test (four sides)
Control condition = # 102
Punching shear
Fl = Pj·Al = 111.111 · 763099.890 = 84.789 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 0.933 · 1.270 · (2.400 +11.480) / 2 · 1.135 = 6535.727 kN
Fl < 0.7·βhpftamh0Hence, Safe
454 — STAAD Foundation Advanced V8i
Chapter — 9
9.3 Stepped Foundation Design
9.3.4 Reinforcement Calculations
Along the X AxisFigure 9-6: Reinforcement parallel to the X-direction
A simplified formula for reinforcement is used per GB50010 – 2002.
Critical load case number = # 102
Minimum reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15%
Cross-sectional area about X-axis, A cross = 2400000.000
Minimum reinforcement area
Astmin = 0.15(A cross)- = 0.15(2,400,000.000) = 3600.000
Calculate moment
MI = (A1) 2 [(2·l + a ') · (pmax + p-2·G / A) + (pmax - p)·l] / 12
= 1,200.0002 · [(2 · 3,000.000 + 600.000) (0.169 + 0.152 - 2 · 324,000.000/9,000,000.000) +(0.169 - 0.152) · 3000.000] / 12 = 203,519,997.379 kN·m
Calculate the area required
Ast = MI / (0.9·h0·fy) = 203,519,997.379 / (0.9 · 1,135.000 · 210.000) = 1, 069.687
Select Rebar size, db = 10.000
Minimum allowable reinforcement spacing, Smin = 50.000 mm
Maximum allowable reinforcement spacing, Smax = 500.000 mm
Actual spacing, S = 60.000 mm
Actual area, Ast (Actual) = 3,600.000 mm2
Smin ≤ S ≤ Smax
Selected Reinforcements satisfy the requirements.
Section 9 Chinese Code (GB50007-2002)
9.3 Stepped Foundation Design
Verification Manual — 455
Astmin ≤ Ast, with real
Selected Reinforcements satisfy the requirements.
Along the Z AxisFigure 9-7: Reinforcement parallel to the Z-direction
A simplified formula for reinforcement is used per GB50010 – 2002.
Critical load case number = # 102
Minimal reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15%
Cross-sectional area about Z-axis, A cross = 2400000.000
Minimum reinforcement area
Astmin = Ρmin · A cross- = 0.15% · 2400000.000 = 3600.000
Calculate moment
MI = (A1) 2 [(2·l + a ') · (pmax + p-2·G / A) + (pmax - p)·l] / 12
= 1,200.0002 · [(2 · 3,000.000 + 600.000) (0.169 + 0.152 - 2 · 324,000.000/9,000,000.000) +(0.169 - 0.152) · 3000.000] / 12 = 203,519,997.379 kN·m
Calculate the area required
Ast = MI / (0.9·h0·fy) = 203,519,997.379 / (0.9 · 1,135.000 · 210.000) = 1,084.241
Reinforced selected size, db = 10.000
Minimum allowable reinforcement spacing, Smin = 50.000 mm
Maximum allowable reinforcement spacing, Smax = 500.000 mm
With actual spacing, S = 60.000 mm
Actual area, Ast (Actual) = 3600.000 mm2
Smin ≤ S ≤ Smax
Selected Reinforcements satisfy the requirements.
456 — STAAD Foundation Advanced V8i
Chapter — 9
9.3 Stepped Foundation Design
Astmin ≤ Ast, with real
Selected Reinforcements satisfy the requirements.
Reinforcements should be placed at the base bottom.
9.4 PKPM Stepped Footing Design9.4.1 ProblemFoundation type : Cast-in-place, stepped footing
Initial Single base dimensions:
Length = 3,000 mm
Width = 3,000 mm
Height = 400 mm
Second
Length = 2,000 mm
Width = 2,000 mm
Height = 400 mm
Third
Length = 1,000 mm
Width = 1,000 mm
Height = 400 mm
Bottom elevation of the base: -2.0 m
Shift the basis of the heart: S Direction : 0 mm B direction : 0 mm
Bottom Reinforcement:
Y direction : 10 @ 200
X direction : 10 @ 200
Unit self weight of the soil and footing: 18.0 kPa
Column section information:
Height of the column section: 600 mm
Width of the Column section: 600 mm
Eccentricity x : 0 mm
Eccentricity y : 0 mm
Column angle: 0 °
Loading information
The basic values of vertical load: Nk = 1,000 kN
X direction of the basic value of the moment: Mx = 100 kN·m
Y direction of the basic value of the moment: My = 100 kN·m
Section 9 Chinese Code (GB50007-2002)
9.4 PKPM Stepped Footing Design
Verification Manual — 457
Elevation and plan
9.4.2 Solution
Check Shear
The following formulae are used per GB5007 - 2002 code of design of buildingfoundations:
Fl ≤ 0.7·βhpftamh0 (Ref. clause 8.2.7 - 1)
am = (At + ab) / 2 (Ref. clause 8.2.7 - 2)
Fl = Pj·Al (Ref. clause 8.2.7 - 3)
Calculate resisting Shear force:
X + direction , height H = 1000
Fl = Pj·Al = 133.33·0.69 = 91.67
Fl ≤ 0.7·βhpft (At + ab)·h0/2 = 0.7 · 0.97 · 1270.94 · (0.60 +2.90) · 1.15 / 2 = 1,730.76 KN
Punching shear check is satisfied along this direction
X- direction , height H = 1200
Fl = Pj·Al = 89.63 · 0.15 = 13.22
458 — STAAD Foundation Advanced V8i
Chapter — 9
9.4 PKPM Stepped Footing Design
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7 · 0.97 · 1270.94 · (0.60 +2.90) · 1.15 / 2 = 1,730.76 KN
Punching shear check is satisfied along this direction
Y + direction , height H = 1200
Fl = Pj·Al = 89.63 · 0.15 = 13.22
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7 · 0.97 · 1270.94 · (0.60 +2.90) · 1.15 / 2 = 1,730.76 KN
Punching shear check is satisfied along this direction
Y- direction , height H = 1200
Fl = Pj·Al = 133.33 · 0.15 = 19.67
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7 · 0.97 · 1270.94 · (0.60 +2.90) · 1.15 / 2 = 1,730.76 KN
Punching shear check is satisfied along this direction
Check Shear Edges
H = 1200.
Fl = N-pk · (bc +2 · h0) · (hc +2 · h0) = 1000.00-111.1 · (600.0 +2 ******)*( 600.0 +2 ******)*1e-6 = 65.56 Kn
Fl = 0.7·βhpftamh0 = 0.7 · 0.97 · 1270.9 · (600.0 +600.0 +2 ******)******* 1e-6 = 6923.04 Kn
Sides punching checking meet
X + direction , height H = 800 mm
Fl = Pj·Al = 133.33 · 0.69 = 91.67
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7 · 1.00 · 1270.94 · (1.00 +2.50) · 0.75 / 2 = 1167.68 KN
Punching shear check is satisfied along this direction
X- direction , height H = 800 mm
Fl = Pj·Al = 92.59 · 0.69 = 63.66
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7 · 1.00 · 1270.94 · (1.00 +2.50) · 0.75 / 2 = 1167.68 KN
Punching shear check is satisfied along this direction
Y + direction , height H = 800 mm
Fl = Pj·Al = 92.59 · 0.69 = 63.66
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7 · 1.00 · 1270.94 · (1.00 +2.50) · 0.75 / 2 = 1167.68 KN
Punching shear check is satisfied along this direction
Y- direction , height H = 800 mm
Fl = Pj·Al = 133.33 · 0.69 = 91.67
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7 · 1.00 · 1270.94 · (1.00 +2.50) · 0.75 / 2 = 1167.68 KN
Punching shear check is satisfied along this direction
X + direction , height H = 400 mm
Fl = Pj·Al = 91.11 · 0.43 = 38.95
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7 · 1.00 · 1270.94 · (2.00 +2.70) · 0.35 / 2 = 731.75 KN
Section 9 Chinese Code (GB50007-2002)
9.4 PKPM Stepped Footing Design
Verification Manual — 459
Punching shear check is satisfied along this direction
X- direction , height H = 400 mm
Fl = Pj·Al = 133.33 · 0.43 = 57.00
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7 · 1.00 · 1270.94 · (2.00 +2.70) · 0.35 / 2 = 731.75 KN
Punching shear check is satisfied along this direction
Y + direction , height H = 400 mm
Fl = Pj·Al = 91.11 · 0.43 = 38.95
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7 · 1.00 · 1270.94 · (2.00 +2.70) · 0.35 / 2 = 731.75 KN
Punching shear check is satisfied along this direction
Y- direction , height H = 400 mm
Fl = Pj·Al = 133.33 · 0.43 = 57.00
0.7·βhp·ft·(at + ab)·ho / 2 = 0.7 · 1.00 · 1270.94 · (2.00 +2.70) · 0.35 / 2 = 731.75 KN
Punching shear check is satisfied along this direction
Bending Reinforcement
The following formula is used per GB50007 - 2002 code for design of building foundations:
M = (1/12)a12·[(2·l + a')(Pjmax + Pj) + (Pjmax + Pj)·l ]
Moment calculations
x direction , h0 = 340 mm
M = 0.50 · 0.50 [(2 · 3.00 +0.60) · (133,333.33 + 125,925.92) + (133,333.33 - 125,925.92) · 3.00] /12 = 36.11 kN·m
M = 0.50 · 0.50 [(2 · 3.00 +0.60) · (88,888.89 + 96,296.30) + (88,888.89 - 96,296.30) · 3.00]/ 12 = 25.00 kN·m
y direction , h0 = 340 mm
M = 0.50 · 0.50 [(2 · 3.00 +0.60) · (88,888.89 + 96,296.30) + (88,888.89 - 96,296.30) · 3.00]/ 12 = 25.00 kN·m
M = 0.50 · 0.50 [(2 · 3.00 +0.60) · (133,333.33 + 125,925.92) + (133,333.33 - 125,925.92) · 3.00] /12 = 36.11 kN·m
x direction , h0 = 740 mm
M = 1.00 · 1.00 [(2 · 3.00 +0.60) · (133,333.33 + 118,518.52) + (133,333.33 - 118,518.52) · 3.00] /12 = 142.22 kN·m
M = 1.00 · 1.00 [(2 · 3.00 +0.60) · (88,888.89 + 103,703.70) + (88,888.89 - 103,703.70) · 3.00]/ 12 = 102.22 kN·m
y direction , h0 = 740 mm
M = 1.00 · 1.00 [(2 · 3.00 +0.60) · (88,888.89 + 103,703.70) + (88,888.89 - 103,703.70) · 3.00]/ 12 = 102.22 kN·m
460 — STAAD Foundation Advanced V8i
Chapter — 9
9.4 PKPM Stepped Footing Design
M = 1.00 · 1.00 [(2 · 3.00 +0.60) · (133,333.33 + 118,518.52) + (133,333.33 - 118,518.52) · 3.00] / 12= 142.22 kN·m
x direction , h0 = 1140 mm
M = 1.20 · 1.20 [(2 · 3.00 +0.60) · (133,333.33 + 115,555.55) + (133,333.33 - 115,555.55) · 3.00] / 12= 203.52 kN·m
M = 1.20 · 1.20 [(2 · 3.00 +0.60) · (88,888.89 + 106,666.66) + (88,888.89 - 106,666.66) · 3.00]/ 12 = 148.48 kN·m
y direction , h0 = 1140 mm
M = 1.20 · 1.20 [(2 · 3.00 +0.60) · (88,888.89 + 106,666.66) + (88,888.89 - 106,666.66) · 3.00]/ 12 = 148.48 kN·m
M = 1.20 · 1.20 [(2 · 3.00 +0.60) · (133,333.33 + 115,555.55) + (133,333.33 - 115,555.55) · 3.00] / 12= 203.52 kN·m
Reinforcement calculation:
M1 = 36.111
AGx = M1 / (0.9·h0·fy) = 36,111.113 / (0.9 · 0.340 · 210.) = 561.953 mm2
M2 = 36.111
AGy = M2 / (0.9·h0·fy) = 36,111.113 / (0.9 · 0.340 · 210.) = 561.953 mm2
M1 = 142.222
AGx = M1 / (0.9·h0·fy) = 142,222.219 / (0.9 · 0.740 · 210.) = 1,016.890 mm2
M2 = 142.222
AGy = M2 / (0.9·h0·fy) = 142,222.219 / (0.9 · 0.740 · 210.) = 1,016.890 mm2
M1 = 203.520
AGx = M1 / (0.9·h0·fy) = 203,520.016 / (0.9 · 1.140 · 210.) = 944.584 mm2
M2 = 203.520
AGy = M2 / (0.9·h0·fy) = 203,520.016 / (0.9 · 1.140 · 210.) = 944.584 mm2
The area of steel at X direction: 1,016.890
The area of steel at Y direction: 1,016.890
The original area of steel at X direction is satisfied.
The original area of steel at Y direction is satisfied.
Calculated the areas of steel are:
AgX: 10 @ 200
AgY: 10 @ 200
9.5 Combined FoundationPer Chinese standard GB50007-2002.
Section 9 Chinese Code (GB50007-2002)
9.5 Combined Foundation
Verification Manual — 461
BaseNumber
Left Can-tilever (M)
Right Can-tilever (M)
Length(M)
Width(M)
Height(M)
1 0.150 2.150 8.300 3.100 0.700
Table 9-11: Overview of the design results
BaseNumber
Top Lon-gitudinal Rein-forcement
Bottom Lon-gitudinal Rein-forcement
Top Trans-verse Rein-forcement
Bottom Trans-verse Rein-forcement
1 #12 @ 55 mmc / c
#12 @ 105 mmc / c
#12 @ 105 mmc / c
#12 @ 105 mmc / c
Table 9-12: Foundation reinforcement details
Elevation and plan
462 — STAAD Foundation Advanced V8i
Chapter — 9
9.5 Combined Foundation
9.5.1 Problem
Basic Geometry
Column 1
Column dimensions
Column Shape : Rectangle
Length of the column - X (Pl): 0.30 m
Width of the column - Z (Pw): 0.30 m
No Column caps
Column 2
Column section size
Column Shape : Rectangle
Length of the Column - X (Pl): 0.30 m
Width of the Column - Z (Pw): 0.40 m
No Column cap
Left overhanging length : 0.15 m
Right cantilevered length : 2.15 m
Whether the length of the left cantilever needs design ( or enter a fixed value )? Yes
Whether the length of the right cantilever needs design ( or enter a fixed value )? Yes
The initial input length (Lo) of the foundation: 1500.00 mm
The initial input width (Wo) of the foundation: 3.10 m
The initial input of height (Do) of the foundation: 700.00 mm
Clear Cover and Soil Properties
The thickness of the clear cover for cap : 50.00 mm
The thickness of the clear cover for foundation : 50.00 mm
Density of the Soil: 25.00 kN/m3
Foundation bearing capacity : 200.00 kN/m2
Additional ground pressure : 0.00 kip/in2
Weight of soil about foundation : 1500.00 mm
Groundwater depth : -0.00 KN
Concrete and Steel Properties
Concrete density: 25.000 kN/m3
Section 9 Chinese Code (GB50007-2002)
9.5 Combined Foundation
Verification Manual — 463
Compressive strength of concrete : 11.900 N/mm2
Reinforcement strength : 210.000 N/mm2
Minimum bar Size : 12.0 mm
Maximum bar size : 50.0 mm
Minimum bar spacing : 50.00 mm
Maximum bar spacing : 400.00 mm
9.5.2 SolutionBuoyancy generated on the ground = -0.00 kN
Minimum area of steel required
Amin = Pc / qmax: 13.80 m2
Specify the initial cross-sectional area
Ao = L x W: 25.73 m2
Final provided foundation dimensions:
Length of base , L: 8.30 m
Width of base, W: 3.10 m
Height of base, Do: 0.70 m
Area of base, A: 25.73 m2
Left Cantilever length , Llo: 0.15 m
Right Cantilever length , Lro: 2.15 m
ConditionNo.
ColumnNo.
AxialForce (KN)
ShearX (KN)
ShearZ (KN)
MomentX (kN·m)
MomentZ (kN·m)
1 1 105076.125 0.000 0.000 0.000 0.0001 2 210152.249 0.000 0.000 0.000 0.000
Table 9-13: Load cases for base dimensions estimation - standard com-bination
ConditionNo.
ColumnNo.
AxialForce (KN)
ShearX (KN)
ShearZ (KN)
MomentX (kN·m)
MomentZ (kN·m)
1 1 105076.125 0.000 0.000 0.000 0.0001 2 210152.249 0.000 0.000 0.000 0.000
Table 9-14: Load cases for foundation design - basic combinationn
Four corners of the calculated stress
LoadCase
Pressureat Corner1
(q1)(KN/m2)
Pressureat Corner2
(q2)(KN/m2)
Pressureat Corner3
(q3)(KN/m2)
Pressureat Corner4
(q4)(KN/m2)
Zero-pres-sure area(Au) (m2)
1 107.2940 107.2940 107.2940 107.2940 0.001 107.2940 107.2940 107.2940 107.2940 0.001 107.2940 107.2940 107.2940 107.2940 0.001 107.2940 107.2940 107.2940 107.2940 0.00
464 — STAAD Foundation Advanced V8i
Chapter — 9
9.5 Combined Foundation
If Au equals zero, that means it is small eccentricity, and do not need to adjust thepressure. Otherwise, the pressure needs to be adjusted. The negative pressure should alwaysset as zero. Keep adjusting if necessary.
Adjusted pressure at corners (if necessary)
ConditionNo.
Pressure atCorner1 (q1)(KN/m2)
Pressure atCorner2 (q2)(KN/m2)
Pressure atCorner3 (q3)(KN/m2)
Pressure atCorner4 (q4)(KN/m2)
1 107.2940 107.2940 107.2940 107.29401 107.2940 107.2940 107.2940 107.29401 107.2940 107.2940 107.2940 107.29401 107.2940 107.2940 107.2940 107.2940
Overturning Stability Test
ConditionNo.
MomentX
(kN·m)
MomentZ
(kN·m)
ResistanceMoment X(kN·m)
ResistanceMoment Z(kN·m)
OverturningStabilityFactor X
Overturning Sta-bility Factor Z
1 0.000 0.000 4273.272 11441.341 N / A 633,778,703.608
9.5.3 Check ShearThe following formulae are used per GB50007 - 2002 code for design of buildingfoundations.
Formula is as follows :
Fl ≤ 0.7·βhpftamh0 (Ref. clause 8.2.7 - 1)
am = (At + ab) / 2 (Ref. clause 8.2.7 - 2)
Fl = Pj·Al (Ref. clause 8.2.7 - 3)
One-way Punching Shear Check
Column 1, +X Direction
Control condition = # 1
Punching shear
Fl = Pj·Al = 69.96 · 5,097,642.75 = 356.62 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 1.00 · 1270.00 · (0.30 · 1.56) / 2 · 0.64 = 523.64 kN
Fl < 0.7·βhpftamh0Hence, safe.
Column 1, -X Direction
Control condition = # 1
Punching shear
Fl = Pj·Al = 69.96 · 0.00 = 0.0 kN
Section 9 Chinese Code (GB50007-2002)
9.5 Combined Foundation
Verification Manual — 465
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 1.00 · 1270.00 · (0.30 · 1.56) / 2 · 0.64 = 523.64 kN
Fl < 0.7·βhpftamh0Hence, safe.
Column 1, +Z Direction
Control condition = # 1
Punching shear
Fl = Pj·Al = 69.96 · 1,010,688.00 = 70.70 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 1.00 · 1270.00 · (0.30 · 1.56) / 2 · 0.64 = 523.64 kN
Fl < 0.7·βhpftamh0Hence, safe.
Column 1, -Z Direction
Control condition = # 1
Punching shear
Fl = Pj·Al = 69.96 · 1,010,688.00 = 70.70 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 1.00 · 1270.00 · (0.30 · 1.56) / 2 · 0.64 = 523.64 kN
Fl < 0.7·βhpftamh0Hence, safe.
Column 2, +X Direction
Control condition = # 1
Punching shear
Fl = Pj·Al = 69.96 · 3,725,275.99 = 260.61 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 1.00 · 1270.00 · (0.30 · 1.66) / 2 · 0.64 = 579.83 kN
Fl < 0.7·βhpftamh0Hence, safe.
Column 2, -X Direction
Control condition = # 1
Punching shear
Fl = Pj·Al = 69.96 · 7,548,609.37 = 528.08 kN
466 — STAAD Foundation Advanced V8i
Chapter — 9
9.5 Combined Foundation
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 1.00 · 1270.00 · (0.30 · 1.66) / 2 · 0.64 = 579.83 kN
Fl < 0.7·βhpftamh0Hence, safe.
Column 2, +Z Direction
Control condition = # 1
Punching shear
Fl = Pj·Al = 69.96 · 163,8475.99 = 114.62 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 1.00 · 1270.00 · (0.40 · 1.56) / 2 · 0.64 = 551.73 kN
Fl < 0.7·βhpftamh0Hence, safe.
Column 2, -Z Direction
Control condition = # 1
Punching shear
Fl = Pj·Al = 69.96 · 163,8475.99 = 114.62 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 1.00 · 1270.00 · (0.40 · 1.56) / 2 · 0.64 = 551.73 kN
Fl < 0.7·βhpftamh0Hence, safe.
Column 1, Four Edges
Control condition = # 1
Punching shear
Fl = Pj·Al = 139.91 · 3,559,509.38 = 498.03 kN
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 1.00 · 1270.00 · (1.20 · 4.99) / 2 · 0.64 = 1,739.48 kN
Fl < 0.7·βhpftamh0Hence, safe.
Column 2, Four Edges
Control condition = # 1
Punching shear
Fl = Pj·Al = 139.91 · 7,275,418.66 = 1,017.94 kN
Section 9 Chinese Code (GB50007-2002)
9.5 Combined Foundation
Verification Manual — 467
Punching shear capacity
Fu = 0.7·βhpftamh0 = 0.7 · 1.00 · 1270.00 · (1.20 · 6.46) / 2 · 0.64 = 2,206.94 kN
Fl < 0.7·βhpftamh0Hence, safe.
9.5.4 Reinforcement Design
Top Longitudinal Reinforcement
A simplified formula for reinforcement is used in accordance with GB50010-2002.
No control condition = # 1
Minimum reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15%
Minimum area of steel, Astmin = 3,255.000 mm2
The area of steel required
Ast = MI / (0.9 · h0 · fy) = 740,000,006.857 / (0.9 · 6,44.000 · 210.000) = 6,079.727 mm2
Selected rebar size,db = 12.000 mm
Minimum allowable reinforcement spacing, Smin = 50.00 mm
Maximum allowable reinforcement spacing, Smax = 400.00 mm
Actual spacing, S = 55.00 mm
Actual area of steel required, Ast (Actual) = 6220.353 mm2
Smin ≤ S ≤ Smax
Selected Reinforcements satisfy the requirements.
Astmin ≤ Ast, with actual
Selected Reinforcements satisfy the requirements.
Bottom Longitudinal Reinforcement
A simplified formula for reinforcement is used in accordance with GB50010-2002.
No control condition = # 1
Minimum reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15%
Minimum area of steel, Astmin = 3,255.000 mm2
The area of steel required
Ast = MI / (0.9 · h0 · fy) = -479,467,391.579 / (0.9 · 644.000 · 210.000) = -3,939.231 mm2
Selected rebar size,db = 12.000 mm
Minimum allowable reinforcement spacing, Smin = 50.00 mm
Maximum allowable reinforcement spacing, Smax = 400.00 mm
Actual spacing, S = 105.00 mm
Actual area of steel required, Ast (Actual) = 3279.823 mm2
Smin ≤ S ≤ Smax
468 — STAAD Foundation Advanced V8i
Chapter — 9
9.5 Combined Foundation
Selected Reinforcements satisfy the requirements.
Astmin ≤ Ast, with actual
Selected Reinforcements satisfy the requirements.
Top Transverse Reinforcement
A simplified formula for reinforcement is used in accordance with GB50010-2002.
No control condition = # 1
Minimum reinforcement ratio [per Cl. 9.5.2], min = 0.15%
Minimum area of steel, Astmin = 8715.000 mm2
The area of steel required
Ast = MI / (0.9 · h0 · fy) = 0.000 / (0.9 · 644.000 · 210.000) = 0.000 mm2
Selected rebar size,db = 12.000 mm
Minimum allowable reinforcement spacing, Smin = 50.00 mm
Maximum allowable reinforcement spacing, Smax = 400.00 mm
Actual spacing, S = 105.00 mm
Actual area of steel required, Ast (Actual) = 8821.592 mm2
Smin ≤ S ≤ Smax
Selected Reinforcements satisfy the requirements.
Astmin ≤ Ast, with actual
Selected Reinforcements satisfy the requirements.
Bottom Transverse Reinforcement
A simplified formula for reinforcement is used in accordance with GB50010-2002.
No control condition = # 1
Minimum reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15%
Minimum area of steel, Astmin = 8,715.000 mm2
The area of steel required
Ast = MI / (0.9 · h0 · fy) = 569,032,250.186 / (0.9 · 644.000 · 210.000) = 4,675.082 mm2
Selected rebar size,db = 12.000 mm
Minimum allowable reinforcement spacing, Smin = 50.00 mm
Maximum allowable reinforcement spacin, Smax = 400.00 mm
Actual spacing, S = 105.00 mm
Actual area of steel required, Ast (Actual) = 8,821.592 mm2
Smin ≤ S ≤ Smax
Selected Reinforcements satisfy the requirements.
Astmin ≤ Ast, with actual
Section 9 Chinese Code (GB50007-2002)
9.5 Combined Foundation
Verification Manual — 469
Selected Reinforcements satisfy the requirements.
9.6 Pile Foundation DesignA typical pile foundation design example is provided here to verify the pile foundationdesign per Chinese codes in the program. The Chinese codes implemented are " GB50007-2002 code for design of building foundations "," GB50009-2001 Load code for design ofbuilding structures "," GB50010-2002 Code for design of Concrete Structures "," TechnicalCode for Building Pile Foundations”
9.6.1 Problem
Basic conditions
Rectangular column foundation. Length of the column is 0.5000 m and the width of thecolumn is 0.5000 m. The height of the base is 0.5000 m , the length of the base is 0.8 m,and the width of the base is 0.8.
Loads: vertical load is 1500 kN and the basic combination distribution factor is 1.4 ( 1500X 1.4 will involve in all members and reinforcements design).
Basic design parameters
Concrete strength: 25 N/mm2
Concrete density: 25 kN/m3
Steel yield strength: 210 N/mm2
Clear cover thickness on sides: 50 mm
Clear cover thickness on bottom: 50 mm
Depth of pile cap: 75 mm
The initial depth of pile cap: 300 mm
Minimum bar diameter: 10
Maximum bar diameter: 45
Pile Parameters
Pile layout: 3 row x 3 row = total 9 piles, spacing 1.5 m , center to edge of pile cap edge 0.5m , pile diameter and 0.5 m , thus base of the cap is 4 m in length and 4 m in width.
Pile bearing capacity: lateral capacity is 100 kN , vertical capacity is 500 kN , upliftcapacity is 300 kN (both single pile). So the reactions of the pile can be calculated as:
Vertical Uplift Lateral-180.888 0.000 0.000-180.888 0.000 0.000-180.888 0.000 0.000-180.888 0.000 0.000
Table 9-15: Pile capacities under load case no. 101
470 — STAAD Foundation Advanced V8i
Chapter — 9
9.6 Pile Foundation Design
Vertical Uplift Lateral-180.888 0.000 0.000-180.888 0.000 0.000-180.888 0.000 0.000-180.888 0.000 0.000-180.888 0.000 0.000
Vertical Uplift Lateral-247.555 0.000 0.000-247.555 0.000 0.000-247.555 0.000 0.000-247.555 0.000 0.000-247.555 0.000 0.000-247.555 0.000 0.000-247.555 0.000 0.000-247.555 0.000 0.000-247.555 0.000 0.000
Table 9-16: Pile capacities under load case no. 102
9.6.2 Solution
Pile layout
Column Dimension
Column Shape : Rectangular
Column length - X (Pl): 0.500 m
Column width - Z (Pw): 0.500 m
Base
A base ? Yes
Base Shape : Rectangular
Base height (Ph): 0.500 m
Base length - X (Pl): 0.800 m
Base width - Z (Pw): 0.800 m
Cap geometry
Pile length P CL = 4.000 m
Cap width P CW = 4.000 m
Initial cap height t I = 0.300 m
Section 9 Chinese Code (GB50007-2002)
9.6 Pile Foundation Design
Verification Manual — 471
Pile geometry
Pile spacing, P s = 1.500 m
Distance from the edge of the Pile cap to the center of pile, e = 0.500 m
Pile diameter, d P = 0.500 m
Bearing capacity of pile
Vertical bearing capacity of P P = 500.000 kN
Lateral bearing capacity of P L = 100.000 kN
Pullout capacity of P L = 300.000 kN
Material Properties
Concrete f ' c = 25,000.004 kN/m2
Concrete f ' t = 1,890.000 kN/m2
Steel f y = 210,000.035 kN/m2
Concrete clear cover
Concrete clear cover on the bottom, CC B = 0.050 m
Concrete clear cover on the sides, CC S = 0.050 m
Depth of pile cap depth, PC P = 0.075 m
LoadCase
Fx(kN) Fy (kN) Fz
(kN)Mx (kN-
m)My (kN-
m)Mz (kN-
m)101 0.000 -
1500.000.000 0.000 0.000 0.000
102 0.000 -2100.00
0.000 0.000 0.000 0.000
Table 9-17: Load about the pile cap
Pile Design Calculations
The total number of piles N = 9
Coordinates ofPiles Reactions
Pile No. X (m) Y (m) Vertical(kN)
Lateral(kN)
Uplift(kN)
1 -1.500 -1.500 -247.555 0.000 0.0002 -1.500 0.000 -247.555 0.000 0.0003 -1.500 1.500 -247.555 0.000 0.0004 0.000 -1.500 -247.555 0.000 0.000
472 — STAAD Foundation Advanced V8i
Chapter — 9
9.6 Pile Foundation Design
Coordinates ofPiles Reactions
Pile No. X (m) Y (m) Vertical(kN)
Lateral(kN)
Uplift(kN)
5 0.000 0.000 -247.555 0.000 0.0006 0.000 1.500 -247.555 0.000 0.0007 1.500 -1.500 -247.555 0.000 0.0008 1.500 0.000 -247.555 0.000 0.0009 1.500 1.500 -247.555 0.000 0.000
Check Depth of Pile Cap
One Way Punching Shear Along Length
Critical Load Case #102
Influential factor of sectional height
βhs = (800/h0)1/4 = (800/0)1/4 = 1.000
Shear Span-to-Depth Ratios
λx = ax/h0 = 1.050/0.300 = 3.000
Punching Shear Factor of Pile Cap
α = 1.75/(λx + 1) = 1.75/(3.000 + 1) = 0.438
Shear Capacity of Pile Cap
dVc = βhs · α · ft · b0 · h0 = 1.000 · 0.438 · 1,890.000 · 4.000 · 0.300 = 992.250 kN
Maximum Shear Design Value, V = 742.665 kN
V < dVc
Hence, Safe
One Way Punching Shear Along Width
Critical Load Case #102
Influential factor of sectional height
βhs = (800/h0)1/4 = (800/0)1/4 = 1.000
Shear Span-to-Depth Ratios
λy = ay/h0 = 1.050/0.300 = 3.000
Punching Shear Factor of Pile Cap
α = 1.75/(λy + 1) = 1.75/(3.000 + 1) = 0.438
Shear Capacity of Pile Cap
dVc = βhs · α · ft · b0 · h0 = 1.000 · 0.438 · 1,890.000 · 4.000 · 0.300 = 992.250 kN
Maximum Shear Design Value, V = 742.665 kN
V < dVc
Section 9 Chinese Code (GB50007-2002)
9.6 Pile Foundation Design
Verification Manual — 473
Hence, Safe
Punching Shear Check for Column
Critical Load Case #102
Shear Span-to-Depth Ratios
λ0x = a0x/h0 = (1.050/0.300) = 1.000
Shear Span-to-Depth Ratios
λ0y = a0y/h0 = (1.050/0.300) = 1.000
Influential factor of sectional height
β0x = 0.84/(λ0x + 0.2) = 0.84/(1.000 + 0.2) = 0.700
Influential factor of sectional height
β0y = 0.84/(λ0y + 0.2) = 0.84/(1.000 + 0.2) = 0.700
Shear Capacity of Pile Cap
dVc = 2 · [β0x · (bc + a0y) + β0y · (hc + a0x)] · βhp · ft · h0 = 2 · [0.700 · (0.500 + 1.050) +0.700 · (0.500 + 1.050)] · 1.000 · 1,890.000 · 0.300 = 2460.780 kN
Maximum Punching Shear Design Value Fl = 1980.440kN
Fl < dVcHence, Safe
Punching Shear Check for Corner Column
Critical Load Case #102
Shear Span-to-Depth Ratios
λ1x = a1x/h0 = (0.300/0.300) = 1.000
Shear Span-to-Depth Ratios
λ1y = a1y/h0 = (0.300/.0.300) = 1.000
Shear Span-to-Depth Ratios
β1x = 0.56/(λ1x + 0.2) = 0.56/(1.000 + 0.2) = 0.467
Shear Span-to-Depth Ratios
β1y = 0.56/(λ1y + 0.2) = 0.56/(1.000 + 0.2) = 0.467
Shear Capacity of Pile Cap
dVc = [β1x · (c2 + a1y/2) + β1y · (c1 + a1x/2)] · βhp · ft · h0 = [0.467 · (0.700 + 0.300/2) + 0.467· (0.700 + 0.300/2)] · 1.000 · 1,890.000 · 0.300 = 449.820 kN
Maximum Punching Shear Design Value Nl = 247.555kN
Nl < dVcHence, Safe
474 — STAAD Foundation Advanced V8i
Chapter — 9
9.6 Pile Foundation Design
Reinforcement Calculations
Use the same reinforcement along both top and bottom.
Along X Direction
Critical Load Case #102
Critical Moment
My = ∑Nixi = 816.931 kN·m
Area of Steel Required
Asy = My/(0.9 · fy · h0) = 816.931/(0.9 · 210,000.035 · 0.300 = 14,407 mm2
Minimum Area of Steel Required
As,min = 0.15 · B · H = 0.15 · 4,000 · 300 = 1,800 mm2
Bar Diameter, ds = 20 mm
Bar Space, S = 80 mm
Min Bar Space, Smin = 50 mm
Max Bar Space, Smax = 500 mm
Actual Bar Area required, As,actual = 49 · π · 10 · 10 = 15,393 mm2
Smin< S < SmaxAs,min < As,actual & Asy < As,actual
Hence, Safe
Along Y Direction
Critical Load Case #102
Critical Moment
My = ∑Nixi = 816.931 kN·m
Area of Steel Required
Asy = My/(0.9 · fy · h0) = 816.931/(0.9 · 210,000.035 · 0.300 = 14,407 mm2
Minimum Area of Steel Required
As,min = 0.15 · B · H = 0.15 · 4,000 · 300 = 1,800 mm2
Bar Diameter, ds = 20 mm
Bar Space, S = 80 mm
Min Bar Space, Smin = 50 mm
Max Bar Space, Smax = 500 mm
Actual Bar Area required, As,actual = 49 · π · 10 · 10 = 15,393 mm2
Smin< S < SmaxAs,min < As,actual & Asy < As,actual
Section 9 Chinese Code (GB50007-2002)
9.6 Pile Foundation Design
Verification Manual — 475
Hence, Safe
Comparing Results with PKPM***********************************************************-**************************************
Design Iterm: Pile Cap-1
***********************************************************-**************************************
Basic Information
1, cap information
Section shape: Stepped Cast-on-site
Plane Shape: Rectangular
Number of steps: 1-step
Elevation at Cap bottom: 0.0m
Number of cap edges: 4
Pile height: 300mm
Cap eccentric at X direction: 0mm
Cap eccentric at X direction: 0mm
2 pile information
Pile Diameter: 500mm
Pile bearing Capacity: 500.00Kn
Pile Coordinate:
NUm X Y
1 -1500 -1500
2 0 -1500
3 1500 -1500
4 -1500 0
5 0 0
6 1500 0
7 -1500 1500
8 0 1500
9 1500 1500
3, Load information
476 — STAAD Foundation Advanced V8i
Chapter — 9
9.6 Pile Foundation Design
Vertical Load: N = 1500.
Moment at x direction: Mx = 0.00knm
Moment at y direction: My = 0.00knm
Shear force at x direction: Qx = 0.00knm
Shear force at y direction: Qy = 0.00knm
4, column information
Column width: 800mm
Column height: 800mm
5, concrete information
Concrete class: C50
Concrete density: 25.00kn/m3
[Design Results]
6、Pile Reactions Calculation
The following formula is used:
Section 9 Chinese Code (GB50007-2002)
9.6 Pile Foundation Design
Verification Manual — 477
Self weight of pile cap and the soil Gk = B * S *H * γ+ B * S * futu
=( 4000.0* 4000.0* 300.0*25.0*1.E-9+ 4000.0* 4000.0* 0.0*1.E-6)
= 120.0(kn)
∑Xi*Xi = 13500000.0 ∑Yi*Yi =13500000.0
Pile No. X Y Pile ReactionQ(KN) Net Reaction QN(KN)
1 -1500.0 -1500.0 180.00 166.67
2 0.0 -1500.0 180.00 166.67
3 1500.0 -1500.0 180.00 166.67
4 -1500.0 0.0 180.00 166.67
5 0.0 0.0 180.00 166.67
6 1500.0 0.0 180.00 166.67
7 -1500.0 1500.0 180.00 166.67
8 0.0 1500.0 180.00 166.67
9 1500.0 1500.0 180.00 166.67
QP= 1620.0(kN); QAVE= 180.0(kN)
7、Punching Shear Check
Step 1: H = 300.00MM
**Punching Shear Check for the Corner Pile***
478 — STAAD Foundation Advanced V8i
Chapter — 9
9.6 Pile Foundation Design
No.=1
h0= 300. α1x=900.λ1x=1.00 c1=700.
h0= 300. α1y=900.λ1y=1.00 c2=700.
β1x=0.4667 β1y= 0.467βhp=1.00 ft= 1.888
QPC=(β1x*(C2+α1y/2)+β1y*(c1+α1x/2))*βhp*ft*ho
= 449.37KN > QPD = 166.67(*1.35) KN
No.=2
h0= 300. α1x=900.λ1x=1.00 c1=700.
h0= 300. α1y=900.λ1y=1.00 c2=700.
β1x=0.4667 β1y= 0.467βhp=1.00 ft= 1.888
QPC=(β1x*(C2+α1y/2)+β1y*(c1+α1x/2))*βhp*ft*ho
= 449.37KN > QPD = 166.67(*1.35) KN
No.=3
h0= 300. α1x=900.λ1x=1.00 c1=700.
h0= 300. α1y=900.λ1y=1.00 c2=700.
β1x=0.4667 β1y= 0.467βhp=1.00 ft= 1.888
QPC=(β1x*(C2+α1y/2)+β1y*(c1+α1x/2))*βhp*ft*ho
= 449.37KN > QPD = 166.67(*1.35) KN
Section 9 Chinese Code (GB50007-2002)
9.6 Pile Foundation Design
Verification Manual — 479
No.=4
h0= 300. α1x=900.λ1x=1.00 c1=700.
h0= 300. α1y=900.λ1y=1.00 c2=700.
β1x=0.4667 β1y= 0.467βhp=1.00 ft= 1.888
QPC=(β1x*(C2+α1y/2)+β1y*(c1+α1x/2))*βhp*ft*ho
= 449.37KN > QPD = 166.67(*1.35) KN
***Punching Shear Check for Column***
H00= 300.mm
x+ h0= 300. αox= 300. λox=1.000
x- h0= 300. αox= 300. λox=1.000
y+ h0= 300. αoy= 300. λoy=1.000
y+ h0= 300. αoy= 300. λoy=1.000
Step 1 H = 400.00MM
***Punching Shear Check for Column***
H00= 350.mm
x+ h0= 350. αox= 350. λox=1.000
x- h0= 350. αox= 350. λox=1.000
y+ h0= 350. αoy= 350. λoy=1.000
y+ h0= 350. αoy= 350. λoy=1.000
hc= 800. bc= 800. βox= 0.70 βoy= 0.70
480 — STAAD Foundation Advanced V8i
Chapter — 9
9.6 Pile Foundation Design
ft= 1.89 βhp=1.000
QCC = 2*(βox*(bc+αoy)+βoy(hc+αox))βhp*ft*ho
= 2127.89KN
QCC= 2127.89KN > QCD= 1333.33 (* 1.35) KN
***Sheack Check***
VPL = βhs*1.75/(λ+1.0)*b0*h0*ft
=1.000*1.75/(2.571+1.0)*4000.*350.*1.8881*1.e-3
= 1295.2KN
VCI1= 1295.24KN > VDI1= 500.00 (* 1.35)KN
Right h0= 350. αx= 900. λx=2.571
VPL = βhs*1.75/(λ+1.0)*b0*h0*ft
=1.000*1.75/(2.571+1.0)*4000.*350.*1.8881*1.e-3
= 1295.2KN
VCI2= 1295.24KN > VDI2= 500.00 (* 1.35)KN
Down h0= 350. αy= 900. λy=2.571
VPL = βhs*1.75/(λ+1.0)*b0*h0*ft
=1.000*1.75/(2.571+1.0)*4000.*350.*1.8881*1.e-3
= 1295.2KN
VCJ1= 1295.24KN > VDJ1= 500.00 (* 1.35)KN
Top h0= 350. αy= 900. λy=2.571
VPL = βhs*1.75/(λ+1.0)*b0*h0*ft
Section 9 Chinese Code (GB50007-2002)
9.6 Pile Foundation Design
Verification Manual — 481
=1.000*1.75/(2.571+1.0)*4000.*350.*1.8881*1.e-3
= 1295.2KN
VCJ2= 1295.24KN > VDJ2= 500.00 (* 1.35)KN
8、Steel Area Calculation
DMX1 = 742.500
AGX = DMX1/(0.9*h0*fy)/YS = 742.500/(0.9*350.0*210.0)/4.0= 2806.123mm*mm/M
DMX2 = 742.500
AGX = DMX2/(0.9*h0*fy)/YS = 742.500/(0.9*350.0*210.0)/4.0= 2806.123mm*mm/M
DMY1 = 742.500
AGY = DMY1/(0.9*h0*fy)/XS = 742.500/(0.9*350.0*210.0)/4.0= 2806.123mm*mm/M
DMY2 = 742.500
AGY = DMY2/(0.9*h0*fy)/XS = 742.500/(0.9*350.0*210.0)/4.0= 2806.123mm*mm/M
ASX=2806.1mm*mm/M ASY=2806.1mm*mm/M
The Area of Steel at x direction is satisfied,hence, safe.
The Area of Steel at y direction is satisfied,hence, safe.
Actual Areas of Steel required:
AGx: 16@100 AGy: 16@100
Com No ASX ASY H(1)H(2)
1 2806.1 2806.1 400.0
2 2455.4 2455.4 450.0
3 2182.5 2182.5 500.0
4 1964.3 1964.3 550.0
482 — STAAD Foundation Advanced V8i
Chapter — 9
9.6 Pile Foundation Design
5 1785.7 1785.7 600.0
6 1636.9 1636.9 650.0
7 1511.0 1511.0 700.0
9.6.3 Comparison
Value of ReferenceResult
STAAD Foun-dationResult
Percent Dif-ference
Bearing Pressure 108.94 KN/m2 108.63 KN/m2 NegligibleResisting force for sliding (x) 313.74 KN 312.867 KN NegligibleResisting Moment for Overturning(z)
752.98 KNm 750.87 KNm Negligible
Resisting force for sliding (z) 313.74 KN 312.867 KN NegligibleResisting Moment for Overturning(x)
752.98 KNm 750.87 KNm Negligible
Table 9-18: Chinese verification example 6 comparison
Section 9 Chinese Code (GB50007-2002)
9.6 Pile Foundation Design
Verification Manual — 483
484 — (Undefined variable: Primary.ProductName)
Chapter 9
9.6 Pile Foundation Design
Section 10
Technical SupportThese resources are provided to help you answer support questions:
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Verification Manual — 485
486 — (Undefined variable: Primary.ProductName)
Chapter 10
IndexA
ACI 318 201, 321
AS3600 3
Australian 3
General Combined Footing 14,16
General Isolated Footing 3, 6
B
British
Combined Foundation 71, 77
Isolated Foundation 23, 26, 32,38, 44, 53,
62, 88
Mat Combined Foundation 83
British Code 23
BS8110 23
C
Canadian Code 99
Chinese Code 437
CSA A23.3 99
D
Deadman Anchors 321
Drilled Pier 357
E
Eccentricity 88
G
GB50007-2002 437
I
Indian Code 125
IS 456 125
P
Pile Cap
Chinese Code 470
Plant Foundation 385
U
United States Code 201
V
Vertical Vessel Foundation 1 385
Verification Manual — 487
List of Figures & TablesFigures
Figure 1-1: Australian code General isolated foundation 4
Figure 1-2: Plan and Elevation 6
Figure 1-3: Plan and Elevation 15
Figure 1-4: Plan and Elevation 17
Figure 1-5: Graphs of combined strip footing internal forces 20
Figure 2-1: Bending section considered 24
Figure 2-2: One way shear section considered 24
Figure 2-3: Two way shear section considered 24
Figure 2-4: Plan and Elevation 27
Figure 2-5: Sections considered for bending in both directions 28
Figure 2-6: Sections considered for one-way shear in both directions 30
Figure 2-7: Section considered for punching shear 31
Figure 2-8: Plan and Elevation 33
Figure 2-9: Section considered for bending about the Z axis 47
Figure 2-10: Section considered for bending about the Z axis 48
Figure 2-11: Section considered for one-way shear along X direction 50
Figure 2-12: Section considered for one-way shear along z direction 51
Figure 2-13: Section considered for punching shear 52
Figure 2-14: Plan and Elevation 63
Figure 2-15: Section considered for punching shear 69
Verification Manual — 489
Figure 2-16: Plan and Elevation 72
Figure 2-17: Shear force and Bending Moment diagrams 76
Figure 2-18: Plan and Elevation 78
Figure 2-19: Shear force and Bending Moment diagrams 82
Figure 2-20: Plan and Elevation 84
Figure 2-21: Plan and Elevation 89
Figure 2-22: Bending about major axes 91
Figure 3-1: Plan and Elevation 100
Figure 3-2: Plan and Elevation 106
Figure 3-3: Plan and Elevation 113
Figure 3-4: Elevation and Plan, with dimension and loads 116
Figure 3-5: Bending sections considered 117
Figure 3-6: Shear sections considered 119
Figure 3-7: Two-way shear sections considered 120
Figure 3-8: Plan and Elevation 123
Figure 4-1: Plan and Elevation 126
Figure 4-2: Plan of Reinforcement 128
Figure 4-3: Cross Section showing Reinforcement 129
Figure 4-4: Plan and Elevation 130
Figure 4-5: Elevation and Plan showing reinforcement design 132
Figure 4-6: Plan and Elevation 134
Figure 4-7: Plan and Elevation 139
Figure 4-8: Plan and Elevation 141
Figure 4-9: Plan and Elevation 146
Figure 4-10: Plan and Elevation 151
Figure 4-11: Final Plan Dimensions 158
Figure 4-12: Plan and Elevation 159
Figure 4-13: Dimension, Moment, and Shear and diagrams 162
Figure 4-14: Plan and Elevation 165
Figure 4-15: Shear Force and Bending Moment diagrams 169
Figure 4-16: Plan and Elevation 171
Figure 4-17: Shear Force and Bending Moment diagrams 174
Figure 4-18: Plan and Elevation 177
Figure 4-19: Shear Force and Bending Moment diagrams 181
Figure 4-20: Plan and Elevation 183
490 — STAAD Foundation Advanced V8i
Chapter — 12
Figures
Figure 4-21: Plan, Elevation, and Pedestal dimensions 190
Figure 4-22: Footing Plan 198
Figure 4-23: >Loads on Footing 198
Figure 4-24: Shear Force (kN, top) and Bending Moment (kNm, bottom) dia-grams
200
Figure 5-1: Elevation and loads 202
Figure 5-2: Considered sections for two-way (bo) and beam (bw) action 203
Figure 5-3: Critical section for moment (long projection) 204
Figure 5-4: Elevation and Plan 207
Figure 5-5: Elevation and Plan 211
Figure 5-6: Elevation and Plan 216
Figure 5-7: Section considered for two-way shear 218
Figure 5-8: Elevation and Plan 221
Figure 5-9: Elevation and Plan 230
Figure 5-10: Elevation and Plan 234
Figure 5-11: Corner pressure values on plan for punching shear 236
Figure 5-12: One-way shear pressure values along x-direction 237
Figure 5-13: One-way shear pressure values along z-direction 238
Figure 5-14: Bending pressure about Z axis 239
Figure 5-15: Bending pressure about X axis 239
Figure 5-16: Elevation and Plan 241
Figure 5-17: Shear Force and Bending Moment diagrams 243
Figure 5-18: Elevation and Plan 247
Figure 5-19: Shear Force and Bending Moment diagrams 252
Figure 5-20: Elevation and Plan 254
Figure 5-21: Shear Force and Bending Moment diagrams 255
Figure 5-22: Elevation and Plan 259
Figure 5-23: Shear Force and Bending Moment diagrams 261
Figure 5-24: Elevation and Plan 265
Figure 5-25: Section considered for punching shear 267
Figure 5-26: Elevation and Plan 272
Figure 5-27: Section considered for two-way shear 274
Figure 5-28: Section considered for one-way shear 276
Figure 5-29: Section considered for bending 278
Figure 5-30: Elevation and Plan 281
Figure 5-31: Section considered for punching shear 282
List of Figures & Tables
Figures
Verification Manual — 491
Figure 5-32: Section considered for one-way shear 283
Figure 5-33: Section considered for moment 285
Figure 5-34: Elevation and Plan 288
Figure 5-35: Section considered for punching shear 290
Figure 5-36: Section considered for one-way shear 291
Figure 5-37: Section considered for moment 293
Figure 5-38: Elevation and dimensions 296
Figure 5-39: Forces on foundation 298
Figure 5-40: Shear and Bending diagrams 298
Figure 5-41: Plan and Elevation 303
Figure 5-42: Critical section for punching shear is at d/2 305
Figure 5-43: Critical section for moment is at the face of column 307
Figure 5-44: Plan and Elevation 313
Figure 5-45: Critical section for punching shear at d/2 315
Figure 6-1: Deadman Anchor Guy Tension Block section 324
Figure 6-2: Dispersion of soil against vertical uplift diagram 325
Figure 6-3: Dispersion line diagram 326
Figure 6-4: Top rebar force diagram 328
Figure 6-5: Bending moment diagram - top 328
Figure 6-6: Bending moment diagram - front face 329
Figure 6-7: Deadman Anchor Guy Tension Block section 331
Figure 6-8: Dispersion of soil against vertical uplift 333
Figure 6-9: Top rebar force diagram 336
Figure 6-10: Bending moment diagram - top 336
Figure 6-11: Bending moment diagram - front face 337
Figure 6-12: Deadman Anchor Guy Tension Block section 341
Figure 6-13: Dispersion of soil against vertical uplift diagram 342
Figure 6-14: Dispersion line diagram 344
Figure 6-15: Top rebar force diagram 345
Figure 6-16: Bending moment diagram - top 346
Figure 6-17: Bending moment diagram - front face 346
Figure 6-18: Deadman Anchor Guy Tension Block section 348
Figure 6-19: Dispersion of soil against vertical uplift diagram 350
Figure 6-20: Top rebar force diagram 353
Figure 6-21: Bending moment diagram - top 353
492 — STAAD Foundation Advanced V8i
Chapter — 12
Figures
Figure 6-22: Bending moment diagram - front face 354
Figure 7-1: Pier Elevation 358
Figure 7-2: Pier Elevation 363
Figure 7-3: Pier Elevation 368
Figure 7-4: Pier Elevation 372
Figure 7-5: Pier Elevation 377
Figure 7-6: Pier Elevation 381
Figure 8-1: Tank and foundation elevation 386
Figure 8-2: Anchor bolt plan 386
Figure 8-3: One-way shear dimensions 392
Figure 8-4: Two-way shear check 392
Figure 8-5: Tank and foundation elevation 395
Figure 8-6: Anchor bolt plan 395
Figure 8-7: One-way shear dimensions 401
Figure 8-8: Two-way shear check 401
Figure 8-9: Tank and foundation elevation 404
Figure 8-10: Anchor bolt plan 404
Figure 8-11: One-way shear dimensions 410
Figure 8-12: Two-way shear check 410
Figure 9-1: Four corners of the calculated stress 439
Figure 9-2: Elevation of stability forces 440
Figure 9-3: Reinforcement parallel to the X-direction 443
Figure 9-4: Reinforcement parallel to the Z-direction 444
Figure 9-5: Four corners of the calculated stress 451
Figure 9-6: Reinforcement parallel to the X-direction 455
Figure 9-7: Reinforcement parallel to the Z-direction 456
Tables
Table 1-1: Australian verification example 1 comparison 5
Table 1-2: Australian verification example 2 comparison 14
Table 1-3: Australian verification example 3 comparison 16
Table 1-4: Australian verification example 4 comparison 22
Table 2-1: British verification example 1 comparison 26
Table 2-2: Table BS2.1 - Column loads 26
Table 2-3: British verification example 2 comparison 32
List of Figures & Tables
Tables
Verification Manual — 493
Table 2-4: British verification example 3 comparison 38
Table 2-5: British verification example 4 comparison 44
Table 2-6: British verification example 5 comparison 53
Table 2-7: British verification example 6 comparison 62
Table 2-8: British verification example 7 comparison 71
Table 2-9: British verification example 8 comparison 77
Table 2-10: British verification example 9 comparison 83
Table 2-11: British verification example 10 comparison 88
Table 2-12: British verification example 13 comparisons 98
Table 3-1: CSA verification example 1 comparison 105
Table 3-2: CSA verification example 2 comparison 112
Table 3-3: CSA verification example 3 comparison 115
Table 3-4: CSA verification example 5 comparison 122
Table 3-5: CSA verification example 5 comparison 124
Table 4-1: IS verification example 1 comparison 129
Table 4-2: IS verification example 2 comparison 133
Table 4-3: IS verification example 3 comparison 138
Table 4-4: IS verification example 4 comparison 140
Table 4-5: IS verification example 5 comparison 145
Table 4-6: IS verification example 6 comparison 150
Table 4-7: IS verification example 7 comparison 158
Table 4-8: IS verification example 8 comparison 164
Table 4-9: IS verification example 9 comparison 170
Table 4-10: IS verification example 10 comparison 176
Table 4-11: IS verification example 11 comparison 182
Table 4-12: Pile Locations in Plan 183
Table 4-13: IS verification example 12 comparison 189
Table 4-14: Pile Coordinates in Plan 191
Table 4-15: IS verification example 13 comparison 197
Table 4-16: IS verification example 14 comparison 200
Table 5-1: US verification example 1 comparison 206
Table 5-2: US verification example 2 comparison 210
Table 5-3: US verification example 3 comparison 215
Table 5-4: US verification example 4 comparison 220
Table 5-5: US verification example 5 comparison 229
494 — STAAD Foundation Advanced V8i
Chapter — 12
Tables
Table 5-6: US verification example 6 comparison 233
Table 5-7: US Verification problem 9 comparison 240
Table 5-8: US verification example 7 comparison 246
Table 5-9: US verification example 8 comparison 253
Table 5-10: US verification example 7 comparison 258
Table 5-11: US verification example 7 comparison 264
Table 5-12: Pile Coordinates in Plan 266
Table 5-13: US verification example 10 comparison 271
Table 5-14: Pile Coordinates in Plan 273
Table 5-15: US verification example 11 comparison 280
Table 5-16: Pile Coordinates in Plan 281
Table 5-17: US verification example 11 comparison 287
Table 5-18: Pile Coordinates in Plan 289
Table 5-19: US verification example 13 comparison 295
Table 5-20: US verification example 12 comparison 302
Table 5-21: US verification example 14 comparison 311
Table 5-22: US verification example 15 comparison 320
Table 6-1: Soil Test Report Summary 322
Table 6-2: Deadman Anchor (US) verification example 1 comparison 330
Table 6-3: Soil test report summary 331
Table 6-4: Soil layers 334
Table 6-5: Deadman Anchor (US) verification example 2 comparison 338
Table 6-6: Soil test report summary 339
Table 6-7: Soil layers 342
Table 6-8: Deadman Anchor (US) verification example 3 comparison 347
Table 6-9: Soil layers 348
Table 6-10: Deadman Anchor (US) verification example 4 comparison 355
Table 7-1: Drilled Pier (API) verification example 1 comparison 361
Table 7-2: Drilled Pier (API) verification example 2 comparison 366
Table 7-3: Drilled Pier (FHWA) verification example 3 comparison 371
Table 7-4: Drilled Pier (FHWA) verification example 4 comparison 375
Table 7-5: Drilled Pier (Vesic) verification example 5 comparison 380
Table 7-6: Drilled Pier (Vesic) verification example 6 comparison 384
Table 8-1: Primary load description 387
Table 8-2: Wind loads 388
List of Figures & Tables
Tables
Verification Manual — 495
Table 8-3: Applied Load Combinations - Allowable Stress Level 389
Table 8-4: Applied Load Combinations - Strength Level 389
Table 8-5: Applied Load at Top of Pedestal - Allowable Stress Level 389
Table 8-6: Applied Load at Top of Pedestal - Strength Level 390
Table 8-7: Stability Ratio 391
Table 8-8: Soil Bearing Check 391
Table 8-9: Vertical Vessel verification example 1 comparison 394
Table 8-10: Primary load description 396
Table 8-11: Wind loads 397
Table 8-12: Applied Load Combination - Allowable Stress Level 398
Table 8-13: Applied Load Combination - Strength Level 398
Table 8-14: Applied Load at Top of Pedestal - Allowable Stress Level 398
Table 8-15: Applied Load at Top of Pedestal - Strength Level 399
Table 8-16: Stability Ratio 400
Table 8-17: Vertical Vessel verification example 2 comparison 403
Table 8-18: Primary load description 405
Table 8-19: Wind loads 406
Table 8-20: Applied Load Combination - Allowable Stress Level 407
Table 8-21: Applied Load Combination - Strength Level 407
Table 8-22: Applied Load at Top of Pedestal - Allowable Stress Level 407
Table 8-23: Applied Load at Top of Pedestal - Strength Level 408
Table 8-24: Stability Ratio 409
Table 8-25: Soil Bearing Check 409
Table 8-26: Vertical Vessel verification example 3 comparison 412
Table 8-27: Vertical Vessel verification example 4 comparison 413
Table 8-28: Vertical Vessel verification example 5 comparison 414
Table 8-29: Vertical Vessel verification example 6 comparison 415
Table 8-30: Vertical Vessel verification example 7 comparison 416
Table 8-31: Vertical Vessel verification example 8 comparison 418
Table 8-32: Vertical Vessel verification example 9 comparison 419
Table 8-33: Vertical Vessel verification example 10 comparison 420
Table 8-34: Vertical Vessel verification example 11 comparison 421
Table 8-35: Vertical Vessel verification example 12 comparison 422
Table 8-36: Vertical Vessel verification example 13 comparison 423
Table 8-37: Vertical Vessel verification example 14 comparison 424
496 — STAAD Foundation Advanced V8i
Chapter — 12
Tables
Table 8-38: Vertical Vessel verification example 15 comparison 426
Table 8-39: Vertical Vessel verification example 16 comparison 427
Table 8-40: Service level load combinations per PIP 429
Table 8-41: Strength level load combinations per PIP 429
Table 8-42: Service level loads applied at the top of the top of the fixed pier 430
Table 8-43: Strength level loads applied at the top of the top of the fixed pier 430
Table 8-44: Service level load combinations per PIP 433
Table 8-45: Strength level load combinations per PIP 433
Table 8-46: Service level loads applied at the top of the top of the fixed pier 434
Table 8-47: Strength level loads applied at the top of the top of the fixed pier 434
Table 9-1: Overview of cone footing design results 437
Table 9-2: Reinforcement details 437
Table 9-3: Loads for foundation base size estimation -For foundation base (1) 439
Table 9-4: Loads for Punching shear check and reinforcements- For foundationbase (1)
439
Table 9-5: Factor of safety 441
Table 9-6: Overview of the stepped foundation design 449
Table 9-7: Reinforcement details 449
Table 9-8: Critical loads for base size estimation - standard combination 450
Table 9-9: Loads for foundation design- the basic combination 450
Table 9-10: Safety factors 452
Table 9-11: Overview of the design results 462
Table 9-12: Foundation reinforcement details 462
Table 9-13: Load cases for base dimensions estimation - standard combination 464
Table 9-14: Load cases for foundation design - basic combinationn 464
Table 9-15: Pile capacities under load case no. 101 470
Table 9-16: Pile capacities under load case no. 102 471
Table 9-17: Load about the pile cap 472
Table 9-18: Chinese verification example 6 comparison 483
List of Figures & Tables
Tables
Verification Manual — 497
498 — (Undefined variable: Primary.ProductName)
Chapter 12
Tables
Bentley Systems, Incorporated
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Verification Manual — 499