CLIENT RAINBOW CONSTRUCTION LIMITED Date 10-Jun-15PROJECT EDEN GARDENS APARTMENTS By M V RampersadLocation 2-BEDROOM APARTMENT MODEL Project: 135-006Sub-Location Pad footing -F1, F4,
References:
OutputReference Calculation
1 - ACI 318M-05, Building Code requirements for Structural Concrete, 20052 - ASCE 7-10, Minimum Design loads for Buildings & Other Structures, 20103 - Preliminary Geotechnical report, Trintoplan Consultants Limited, October 20134 - STAAD output5 - ASTM A615-04, Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement
Summary of calculation checks Utilisation ratio (actual vs capacity)Soil bearing capacity 0.97 OK bearing capacity **this condition governs**
Two-way (punching) shear 0.37 OK two-way shearx-axis:
One-way (wide beam) shear 0.42 OK one-way shear (x-axis)Flexural 0.44 OK in flexure (x-axis)
Min. Flexural reinforcement 0.88 OK min. rfct flexure (x-axis)Shrinkage reinforcement 0.46 OK min. rfct shrinkage (x-axis)
z-axis:One-way (wide beam) shear 0.50 OK one-way shear (z-axis)
Flexural 0.46 OK in flexure (z-axis)Min. Flexural reinforcement 0.84 OK min. rfct flexure (z-axis)
Shrinkage reinforcement 0.46 OK min. rfct shrinkage (z-axis)
Starter bar reinforcement OK starter bar min. rfctStarter bar embedment OK embed. depth
Starter bar development length 0.13 OK dev't lengthStarter bar development length 0.13 OK dev t length
FOOTING GEOMTERY & MATERIAL PROPERTIES
Foundation geometrypedestal width (in X-direction), px = 580 mm 580
pedestal breadth (in Z-direction), pz = 760 mm 760pedestal height (in Y-direction), H 500 mm 500
Footing thickness, h 500 mm 500
Note for user and reader: Bordered cells denote user-input, all other cells are calculated via this spreadsheet using the relevant base data, material and guidance from the noted References
Founding depth below GL 1300 mmLength of footing, L (in X-direction) 6000 mm 6000
Breadth of footing, B (in Z-direction) 6000 mm 6000Footing shape: Square
Calculation of footing & soil surcharge weightRef 4: Tbl C3-2 Concrete density (kN/m3) 23.1 kN/m3
Pedestal volume 0.2 m3Pedestal weight 5.1 kNFooting volume 18.0 m3Footing weight 415.2 kN
3
500
580 760
500
Soil weight above pad (assumes =20kN/m3) = 928.9 kN Total footing & soil weight Ff = 1349.2 kN
Material properties28-day concrete comp. strength, f'c 30 N/mm2 f'c=30MPa
Ref 1: 7.7.1 Cover to reinforcement 75 mmRef 5 Main reinforcement to be used A615 Gr 60
Reinforcement yield strength, fy = 420 N/mm2Effective depth, d (for x-axis checks) 415 mm 208
Effective depth, dz (for z-axis checks) 395 mmRef 3 Allowable soil bearing capacity, qa 55.0 kN/m2
6000 6000
LOADING DATA
Serviceability Limit State resultsRef 4 From STAAD output, using Serviceability Limit state analysis:
Fx (kN) Fy (kN) Fz (kN) Mx (kNm) My (kNm) Mz (kNm) NodeMaximum FY occurrence (SLS) 4.5 565.1 70.7 14.3 0.6 1.7 4005
Note; Use Serviceability Limit state values when checking for soil bearing pressures. There is already a Factor of Safety built in to the allowable bearing pressure parameter as outlined in the geotehcnical report.Use Ultimate Limit State results for all other design checks.
Ultimate Limit State resultsRef 4 From STAAD output, using Ultimate Limit state analysis:
Fx (kN) Fy (kN) Fz (kN) Mx (kNm) My (kNm) Mz (kNm) NodeMaximum FY occurrence (ULS) 7.9 936.3 312.2 90.0 2.6 2.8 4005
Page 1 of 9
CLIENT RAINBOW CONSTRUCTION LIMITED Date 10-Jun-15PROJECT EDEN GARDENS APARTMENTS By M V RampersadLocation 2-BEDROOM APARTMENT MODEL Project: 135-006Sub-Location Pad footing -F1, F4,
OutputReference Calculation
CHECK ON SOIL BEARING PRESSURES
Bearing pressure along x-axisPressure distr. under base: qmax,min =
Ref 4 Use Fy (serviceability) = 565.1 kNLoad FV on underside of footing = Fy+Ft = 1914.4 kN
FV/LB = 53.2 kN/m2MZ+FXH/BL2 = 0.0 kN/m2
qmax= 53.2 kN/m2qmin= 53.2 kN/m2
1914.4
1.7
6000
4.5 2BLHFM
LBF XZV
Bearing pressure along z-axisPressure distr. under base: qmax,min =
Ref 4 Use Fy (serviceability) = 565.1 kNLoad FV on underside of footing = Fy+Ft = 1914.4 kN
FV/LB = 53.2 kN/m2MX+FZH/LB2 = 0.3 kN/m2
qmax= 53.5 kN/m2qmin= 52.8 kN/m2
1914.4
0.6 70.7
6000
2LBFzHMx
LBFV
Use max bearing pressure as pa = 53.5 kN/m2Ref 3 Allowable soil bearing capacity, qa 55.0 kN/m2
Ratio of pa to qa = 0.973 OK bearing capacity
CHECK FOR pedestal BEARING (transfer of load from pedestal into footing)
Nominal pedestal or bearing load capacity, PnRef 1: 10.17.1 Pn(0.85f'cA1)*[A2/A1]Ref 1: 9.3.2.4 0.65 [unitless]
A1 = 0 441 m2
936.3
415
A1 0.441 mA2 = (px+4d)*(pz+4d) = 5.421 m2
Ref 1: 10.17.1 A2/A1 (but max. 2.0)= 2.00 [unitless]f'c = 30.0 N/mm2
Pn 14,613 kNRef 4 Fy = 936.3 kN
Ratio of Fy to Pn 0.06 OK col bearing resistance
SHEAR CHECKSCheck for Two-way (punching) shear capacity Vn
Ref 1: 9.3.2.3 Where 0.75Ref 1: 11.1.1 VnVc Assuming that no shear reinforcement is used in the footing g g
Ref 1: 11.12.1.2 Shear perimeter is located at a distance of 1.0d outside of the pedestal/pedestal faceShear perimeter length, bo is given by
bo = 2(px+d)+(2(pz+d)px = 580 mmpz = 760 mmd = 415 mm
bo = 4340 mm
Factored net soil pressure qu = Pu/BLFy = Pu = 936.3 kN
qu = 26.0 kN/m2
Find the total shear force for two-way shear, VU2where VU2 = Pu-qu(px+d)(py+d)
VU2 = 905.9 kN
Page 2 of 9
CLIENT RAINBOW CONSTRUCTION LIMITED Date 10-Jun-15PROJECT EDEN GARDENS APARTMENTS By M V RampersadLocation 2-BEDROOM APARTMENT MODEL Project: 135-006Sub-Location Pad footing -F1, F4,
OutputReference Calculation
Calculate the nominal shear strength, VC of the footing(a) 0.17(1+2/)f'cbod
Ref 1: 11.12.2.1 (b) 0.083([sd/bo]+2)f'cbod(c) 0.33f'cbod
Condition (a)Ratio of long side to short side of col, = 1.00 [unitless]
f'c = 30.0 N/mm2bo = 4,340 mmd = 415 mm
Vc-condition (a) = 5,031.2 kNCondition (b)
Vc (kN) = min of
6000
208
pedestal location for determining as = EdgeRef 1: 11.12.2.1 s = 30
Vc-condition (b) = 3,986.4 kNCondition (c)
Vc-condition (c) = 3,255.5 kN
(a) 5,031.2 kN(b) 3,986.4 kN(c) 3,255.5 kN
Use Vc = 3,255.5 kNV = 2 441 6 kN
Vc = min of
580
415 208
760
Vc = 2,441.6 kNVU2 = 905.9 kN
Ratio of VU2/Vc = 0.37 OK two-way shear
Check for one-way (wide beam) shear:Ref 1: 11.12.1.1
One-way shear parallel to x-axisRef 1: 11.3.1.1 Vc = 0.17f'cBd
B = 6000 mmVc = 2,318.5 kN
The critical section for one-way (wide beam) shear extends across the width of the footing at a distance d from the face of the loaded area.
6000
c 2,318.5 kN Vc = 1,738.9 kN
Find the projection noted as L'Footing shape: Square
L' = 2295 mmShear force on shear plane, Vu1 = BL'qu = 732.5 kN
Ratio of Vu1/Vc = 0.42
OK one-way shear (x-axis)One-way shear parallel to z-axis
Vc = 0.17f'cLdz6
00
0
415
L = 6000 mmVc = 2,206.8 kN
Vc = 1,655.1 kN
Find the projection noted as L'Footing shape: Square
L' = 2585 mmShear force on shear plane, Vu1 = BL'qu = 829.9 kN
Ratio of Vu1/Vc = 0.50 [unitless] Note: sketch also holds for one-way shear in the z-axis OK one-way shear (z-axis)
2295
415
Page 3 of 9
CLIENT RAINBOW CONSTRUCTION LIMITED Date 10-Jun-15PROJECT EDEN GARDENS APARTMENTS By M V RampersadLocation 2-BEDROOM APARTMENT MODEL Project: 135-006Sub-Location Pad footing -F1, F4,
OutputReference Calculation
MOMENT AND REINFORCEMENT CHECKS
Bending parallel to x-axisFind the projection noted as Lm
Lm = 2710 mmmoment on the bending plane, Mux = quBL2m/2
qu = 26.0 kN/m2 Mux = 573.0 kNm
Required steel ratio, =
'
'
85.021185.0
c
u
y
c
fR
ff
Coefficient of resistance Ru = Mux / (bd2)Ref 1: 9.3.2.1 = 0.9
Ru = 0.6162 0.85f'c / fy = 0.061
2RU/((0.85f'c) = 0.054 = 0.0017
Area of steel required As req = Bd As req = 4,115 mm2
Check for minimum reinforcement required for flexureR f 1 10 5 1 0 25Bdf' / f
60
00
6000
Ref 1: 10.5.1 0.25Bdf c / fy1.4Bd/ fy
0.25Bdf'c / fy = 8,118 mm21.4Bd/ fy = 8,300 mm2
Use As min (flexure) = 8,300 mm2
Check for minimum reinforcement required for shrinkageRef 1: 7.12.2.1 As, min (shrinkage) = 0.0018 (times gross sectional area)
0.0018Bh = 5,400 mm2Reinforcement selection
Bottom TopSelect bar diameter (mm) 20 10
As min (flexure) max of
2710
Select bar diameter (mm) 20 10Select number of bars 30 30
Provide bar spacing (to nearest 25mm) 200 200 mmAs prov 9,425 2,356 mm2
As total = 11,781 mm2Ratio of As (flexure) / As prov = 0.44 [unitless] OK in flexure (x-axis)
Ratio of As min (flexure) / As prov = 0.88 [unitless] OK min. rfct flexure (x-axis)Ratio of As min (shrinkage) / As prov = 0.46 [unitless] OK min. rfct shrinkage (x-axis
Page 4 of 9
CLIENT RAINBOW CONSTRUCTION LIMITED Date 10-Jun-15PROJECT EDEN GARDENS APARTMENTS By M V RampersadLocation 2-BEDROOM APARTMENT MODEL Project: 135-006Sub-Location Pad footing -F1, F4,
OutputReference Calculation
Bending parallel to z-axisFind the projection noted as Lm
Lm = 2710 mmmoment on the bending plane, Muz = quLL2m/2
qu = 26.0 kN/m2 Muz = 573.0 kNm
Required steel ratio, =
Coefficient of resistance Ru = Muz / (Ldz2)Ref 1: 9.3.2.1 = 0.9
R 6000
''
85.021185.0
c
u
y
c
fR
ff
Ru = 0.6801 0.85f'c / fy = 0.061
2RU/((0.85f'c) = 0.059 = 0.0018
Area of steel required As req = Ldz As req = 4,329 mm2
Check for minimum reinforcement required for flexureRef 1: 10.5.1 0.25Bdzf'c / fy
1.4Bdz/ fy0.25Ldzf'c / fy = 7,727 mm2
1 4Ld / f = 7 900 2
As min (flexure) max of
60
00
6000
2710
1.4Ldz/ fy = 7,900 mm2 Use As min (flexure) = 7,900 mm2
Check for minimum reinforcement required for shrinkageRef 1: 7.12.2.1 As, min (shrinkage) = 0.0018 (times gross sectional area)
0.0018Lh = 5,400 mm2Reinforcement selection
Governing area of steel required = 7,900 mm2Bottom Top
Select bar diameter (mm) 20 10Select number of bars 30 30Select number of bars 30 30
Provide bar spacing (to nearest 25mm) 200 200 mmAs prov 9,425 2,356 mm2
As prov (total) = 11,781 mm2Ratio of As (flexure) / As prov = 0.46 [unitless] OK in flexure (z-axis)
Ratio of As min (flexure) / As prov = 0.84 [unitless] OK min. rfct flexure (z-axis)Ratio of As min (shrinkage) / As prov = 0.46 [unitless] OK min. rfct shrinkage (z-axis
REINFORCEMENT SUMMARYAlong x-axis, bottom mat 31-T20-200 B
Along x-axis, top mat 31-T10-200 TAlong z-axis, bottom mat 31-T20-200 Bg ,
Along z-axis, top mat 31-T10-200 T
Ref 1: 7.12.2.1 Check on distribution of steel parallel to the x-axis:Centre band zone, s = 2/(+1)
= 1.00s = 1.00 No special reinforcement distribution needed over the length of the footing
Page 5 of 9
CLIENT RAINBOW CONSTRUCTION LIMITED Date 10-Jun-15PROJECT EDEN GARDENS APARTMENTS By M V RampersadLocation 2-BEDROOM APARTMENT MODEL Project: 135-006Sub-Location Pad footing -F1, F4,
OutputReference Calculation
CHECK ON STARTER BARS
Check on minimum % reinforcement to starter barsdiameter of starter bar, db = 20 mm
Number of starter bars = 8 Nr (note: minimum 4)Cross sectional area of bars = 2,513 mm2
Ref 1: 15.8.2.1 Minimum As-starter = 0.005Agpedestal cross-section area Ag=(px*pz) = 440,800 mm2
As-starter / Ag = 0.006 OK starter bar min. rfct
Check on starter bar embedment into footingRef 1: 12.3.2 Min of 200 mm
(0.24fy/f'c)db0.043fydb
fy = 420 N/mm2db = 20 mmf'c = 30 N/mm2
(0.24fy/f'c)db = 368 mm0.043fydb = 361 mm
Use ldc as = 368 mm Say 370 mm (rounded up)Check on ldc versus depth of footing, h, and effective depth, d
d = 415 mmh 500 OK b d d th
larger oflength of embedment ldc =
h = 500 mm OK embed. depth
Check on development length of starter barsCritical sections for the development length (ld) of the starter bars occur at the pedestal/footing interface
Ref 1: 12.2.2 ld =
For tdepth of freshly cast concrete below ld
CLIENT RAINBOW CONSTRUCTION LIMITED Date 10-Jun-15PROJECT EDEN GARDENS APARTMENTS By M V RampersadLocation 2-BEDROOM APARTMENT MODEL Project: 135-006Sub-Location Pad footing -F1, F4,
OutputReference Calculation
SUMMARY OUTPUT
500
500
580
31-T10-200 T
31-T10-200 T
8-T20
370
760 6000
6000
31-T20-200 B
735
580
31-T20-200 B
f'c=30MPa
Page 7 of 9
CLIENT RAINBOW CONSTRUCTION LIMITED Date 10-Jun-15PROJECT EDEN GARDENS APARTMENTS By M V RampersadLocation 2-BEDROOM APARTMENT MODEL Project: 135-006Sub-Location Pad footing -F1, F4,
OutputReference Calculation
APPENDIX
Ref 4
Horizontal Vertical Horizontal Moment Node L/C Fx kN Fy kN Fz kN Mx kNm My kNm Mz kNm
Max Fx 4005 1 1.0DL+1.0 4.51 565.14 -70.74 -14.29 0.57 1.73Min Fx 1005 1 1.0DL+1.0 4.38 534.17 56.90 9.67 -0.47 1.56
SERVICEABILITY LIMIT STATE (1.0DL+1.0LL)
STAAD ANALYSIS OUTPUT
The user is to carry out the analysis in STAAD and use the post-processing results to obtain the values shown in these tables. Note that two limit state Envelopes are used, Serviceability Limit State and Ultimate Limit State.
Max Fy 4005 1 1.0DL+1.0 4.51 565.14 -70.74 -14.29 0.57 1.73Min Fy 1005 1 1.0DL+1.0 4.38 534.17 56.90 9.67 -0.47 1.56Max Fz 1005 1 1.0DL+1.0 4.38 534.17 56.90 9.67 -0.47 1.56Min Fz 4005 1 1.0DL+1.0 4.51 565.14 -70.74 -14.29 0.57 1.73Max Mx 1005 1 1.0DL+1.0 4.38 534.17 56.90 9.67 -0.47 1.56Min Mx 4005 1 1.0DL+1.0 4.51 565.14 -70.74 -14.29 0.57 1.73Max My 4005 1 1.0DL+1.0 4.51 565.14 -70.74 -14.29 0.57 1.73Min My 1005 1 1.0DL+1.0 4.38 534.17 56.90 9.67 -0.47 1.56Max Mz 4005 1 1.0DL+1.0 4.51 565.14 -70.74 -14.29 0.57 1.73Min Mz 1005 1 1.0DL+1.0 4.38 534.17 56.90 9.67 -0.47 1.56
Maximum values 4.51 565.14 56.90 9.67 0.57 1.73Corresponding values at F max 4005 4 51 565 14 70 74 14 29 0 57 1 73Corresponding values at Fy max 4005 4.51 565.14 70.74 14.29 0.57 1.73
Horizontal Vertical Horizontal Moment Node L/C Fx kN Fy kN Fz kN Mx kNm My kNm Mz kNm
Max Fx 4005 DL+1.0EQ(-X 53.59 647.54 -80.34 -16.17 0.93 -12.57Min Fx 4005 0.9DL+1.0EQ -45.51 364.81 -42.81 -8.38 0.06 15.67Max Fy 4005 1.0WL(+Z)+1 7.88 936.32 -312.19 -89.96 2.64 2.77Min Fy 1005 0.9DL+1.0W 0.04 52.79 -196.10 -67.27 1.69 0.25Max Fz 1005 1.0WL(-Z)+1 7.84 904.98 298.53 85.42 -2.54 2.56Min Fz 4005 1.0WL(+Z)+1 7.88 936.32 -312.19 -89.96 2.64 2.77Max Mx 1005 1 0WL(-Z)+1 7 84 904 98 298 53 85 42 -2 54 2 56
ULTIMATE LIMIT STATE (All Load Combs)
Max Mx 1005 1.0WL( Z)+1 7.84 904.98 298.53 85.42 2.54 2.56Min Mx 4005 1.0WL(+Z)+1 7.88 936.32 -312.19 -89.96 2.64 2.77Max My 4005 1.0WL(+Z)+1 7.88 936.32 -312.19 -89.96 2.64 2.77Min My 1005 1.0WL(-Z)+1 7.84 904.98 298.53 85.42 -2.54 2.56Max Mz 4005 DL+1.0EQ(+X -43.27 645.37 -80.19 -16.14 0.36 16.52Min Mz 4005 0.9DL+1.0EQ 51.35 366.98 -42.97 -8.40 0.63 -13.43
Maximum values 53.59 936.32 298.53 85.42 2.64 16.52Corresponding values at Fy max 4005 7.88 936.32 312.19 89.96 2.64 2.77
This is achieved with Load Combination: 106 1.2DL+1.0WL(+Z)+1.0LL+0.5LR
Ref 2 Listing of Load combinations used: 100: 1.0DL 101: 1.0DL+1.0LL 102: 1.4DL 103: 1.2DL+1.6LL+0.5LR 104: 1.2DL+1.6LR+1.0LL 105: 1.2DL+1.0WL(+X)+1.0LL+0.5LR 106: 1.2DL+1.0WL(+Z)+1.0LL+0.5LR 107: 1.2DL+1.0WL(-X)+1.0LL+0.5LR 108: 1.2DL+1.0WL(-Z)+1.0LL+0.5LR 109: 1.2DL+1.0EQ(+X)+1.0LL 110: 1.2DL+1.0EQ(+Z)+1.0LL 111: 1.2DL+1.0EQ(-X)+1.0LL 112: 1.2DL+1.0EQ(-Z)+1.0LL 113: 0.9DL+1.0WL(+X) 114: 0.9DL+1.0WL(+Z) 115: 0.9DL+1.0WL(-X) 116: 0.9DL+1.0WL(-Z) 117: 0.9DL+1.0EQ(+X) 118: 0.9DL+1.0EQ(+Z) 119: 0.9DL+1.0EQ(-X) 120: 0.9DL+1.0EQ(-Z)
Page 8 of 9
CLIENT RAINBOW CONSTRUCTION LIMITED Date 10-Jun-15PROJECT EDEN GARDENS APARTMENTS By M V RampersadLocation 2-BEDROOM APARTMENT MODEL Project: 135-006Sub-Location Pad footing -F1, F4,
OutputReference Calculation
SUMMARY OF MAIN QUANTITIESExcavation 46.80 m3Concrete
Pedestal 0.22 m3Footing 18.00 m3
Total concrete 18.22 m3
ReinforcementBottom mat (x-axis) 484.6 kgTop mat (x-axis) 121.1 kgBottom mat (z-axis) 484.6 kgTop mat (z-axis) 121.1 kg
Total reinforcement 1211.5 kg
FormworkPedestal (x-axis) 0.58 m2Pedestal (z-axis) 0.76 m2Length 6.00 m2Breadth 6.00 m2
Total formwork 13.34 m2
Section analysis (x-axis)Depth of stress block a = A f /0 85f BDepth of stress block, a = Asfy/0.85f cB
10.2.7.3 1 (stress block depth to neutral axis depth) = 0.84 [unitless] a = 25.9 mm
c = a/1 c = 31.0 mm
c/d ratio = 0.075