RCC Design_Box Culvert

Beam Design

Beam Datawidth 200 mmdepth 600 mm d' 36 mm .= cc+ sdia + mdia/2

15 mm eff depth 565 mm .= d - d'

Material Grades

Concrete 20 MPaSteel 415 MPa

Moment 123 KN-m 1.93xumax 270 .= (700/(1100 * (0.87 * fy)) * dMulim 176 .= 0.36*fck*b*xumax*(d-(0.42*xumax))

2.76

Beam is designed as Singly Reinforced Beam

Area of Steel Tension (Ast) Compr (Asc)Percentage 0.613 % ------- Refer Table 2 SP 16 pg 48Area of Steel 692 sqmm

Tension Reinforcement Type Bar dia Nos Area of Steel

Layer 1 25 mm 2 982 sqmmLayer 2 16 mm 2 402 sqmmLayer 3 - 2

Total Steel Provided 1384 sqmm 1.226 %

Provided Steel OK

Compression ReinforcementType Bar dia Nos Area of Steel

Layer 1 12 mm 2Layer 2 -Layer 3

Total Steel Provided #VALUE!

Shear Force (Vu) 200 KNζv 1.771 .=Vu / (b * d)ζc 0.562 Refer Table 61 SP 16 pg 179ζcmax 2.8 Refer Table J SP 16 pg 175

Type Bar Dia Nos Area of SteelLayer 1 16 mm 2 402 sqmmLayer 2 12 mm 4 452 sqmmLayer 3 -

Total Steel Provided 855 sqmm 0.757 %

Sectional Dimensions OKShear Reinforcements required

Type of stirrup 2 leggedStirrup diameter 8 mmSpacing 150 c/c

clear cover to main reinf.

Mu/bd2

Mulim/bd2

or =(0.85*√(0.8*fck)*√(1+5β)-1)) / (6β)

Steel Calculation

Grade Check7.1

SRB DRBa 0.75 a 0.75b -3.611 b -3.611c 1.930 c 2.762-p 0.613 -p 0.955

Ast 692 .=(p*b*d)/100 Astlim 1079 .=(p*b*d)/100

Mu2 -53 .=Mu - MulimAst2 -278 .=Mu2/((0.87*fy)*(d-d'))Ast 801 .=Astlim+Ast2

0.0629 d'/d 0.100.1 fsc 353 Refer Table F SP 16 pg 13

fcc 8.92 .=0.466*fckAsc -291 .=Mu2/((fsc-fcc)*(d-d'))

Min steel % 0.205 .=0.85% / fyAst 692Asc -291

Min Steel 231 .=(0.85*b*d) / fyMax Steel 4516 .=0.04*b*d)

Ast 692Asc

Shear Calculations

Pt provided 0.757 .=(Ast*100)/(b*d)Pc provided .=(Asc*100)/(b*d)

β 3.068 .=(0.8*fck)/(6.89*Pt)

Shear Capacity of Concrete (Vs) 63 .=ζc*b*dShear Stg to be caried by Stirrup (Vus) 137 .=Vu-Vs

Spacingactual req 150 .=(Asv*0.87fy*d)/Vus

min 454 .=(Asv*0.87fy)/(b*0.4)max 423 .=0.75dmax 300 .=300mm

.=(0.87435/100) * (fy/fck)2 .=(0.87435/100) * (fy/fck)2

.=(0.87/100) * (fy) .=(0.87/100) * (fy)

.=Mu/bd2 .=Mulim/bd2

.=-(b±√(b2-4ac))/2a .=-(b±√(b2-4ac))/2a

pro

vid

e t

he

le

ast

of

the

4

Column Design

Design LoadsLoad Pu 2000 KN

Moment Mu 20 KN-m

Column Datawidth b 200 mmdepth d 200 mmlength l 3.00 meters

GradeConcrete fck 20 MPa

Steel fy 415 MPa

Pu/(fckbd) 2.50 Minimum eccentricity0.01 ex 1.27 mm OK

d'/d 0.05 ey 1.27 mm OK

Refer Chart 31 of SP 16, Page no: 116

pt/fck 0.18

pt 3.60%Ast 1440 sqmm

Number of bars dia nos ast

25 mm 4 1963 sqmm ● ● ● ● ● ● 4- ###

20 mm 4 1257 sqmm 4- ###

20 mm 4 1257 sqmm ● ● ● ● ● ● 4- ###

Total 12 4477 sqmm

Steel provided OK

Mu/(fckbd2)

04/17/2023 of 41

Column Design

Load Moment Column Data GradeDesign Constants

Ast Req RemarkArea of Steel

Check Figd'/d Type 1 Type 2 Total Reinf Provided

1 - - C1 R 1500 KN 30 KN-m 30 KN-m 200 mm 750 mm 750 mm 50 mm 3.60 m 20 MPa 415 MPa 0.50 0.01 0.1 0.02 0.40% 600 sqmm 1200 sqmm 4 12 mm 452 sqmm 2 12 mm 226 sqmm 6 679 sqmm

Sl No.

Grid No

Col Nos. Col type

Col Shape

Design

Paramenters

Final Ast

RequiredPu/(fckbdl) Mu/(fckbdl2)

Ast less than

min Ast req.

Steel provided NOT OK

Slab Design

Slab thickness t 150 mm Sunken Depth 325 mm

fck 20 MPa

fy 415 MPa

Loading

Slab Load Sunken Slab Load

Dead Load DL 3.750 KN/m Dead Load DL 3.750 KN/m

Live Load LL 2.000 KN/m Filler Load FL 5 KN/m

Finishes Load WL 1.000 KN/m Live Load LL 3.0 KN/m

Total Load Ws 6.750 KN/m Finishes Load WL 1.0 KN/m

Factored Load Wsu 10 KN/m Total Load Wsk 12.37 KN/m

Factored Load Wsku 19 KN/m

Slab Data

Slab Type Regular

Load 10 KN/m

Longer Span (ly) 9.50 m ly/lx ratio 2.02

Shorter Span (lx) 4.70 m Slab type -

Loading on edges one way two way

24 KN/m .=w*lx/2

.=w*lx/3

Moments one way two way

Mx 28 KN-m

Thickness Check OK .=Mulim > Mux or Muy

Deflection 10 mm

Area of SteelAstx Refer Chart 4 SP 16 pg 21 or

667 sqmm Refer Table 5-44 SP 16 pg 51-80

Spacing required in mm

x y x y x y x x

75 c/c 118 c/c 170 c/c 301 c/c

.=ast of bar*1000/ast req

x y

Concrete

Steel

Wlonger .=(w*lx/2) + (1-(1/3)*(lx/ly)2)

Wshorter

.=w*lx2/ 8 .=αx * w*lx2

.=αy * w*lx2

.= 5*W*l4/(384EI)

8# 10# 12# 16#

Final Ast provided

Design Calculations

ONE WAY TWO WAYa 0.75 a 0.75

b -3.611 b -3.611

cx 1.654 cy #VALUE!

-px 0.513 -py #VALUE!

Ast 667 .=(p*b*d)/100 Ast #VALUE! .=(p*b*d)/100

Min Ast %0.12 180

Interpolation

Tabl

e 26

IS 4

56 p

g 91

1 0.056

ly/lx 1.1 0.064

1.2 0.072

0.00 0.00 2.02 #N/A #N/A #N/A 0.056 1.3 0.079

1.4 0.085

1.5 0.089

2 0.107

xumax 62 .= (700/(1100 * (0.87 * fy)) * d

Mulim 47 KN-m .= 0.36*fck*b*xumax*(d-(0.42*xumax))

2.76

1.65

#VALUE!

E 2.24E+07

I 2.81E-04Defln 10.23

.=(0.87435/100) * (fy/fck)2 .=(0.87435/100) * (fy/fck)2

.=(0.87/100) * (fy) .=(0.87/100) * (fy)

.=Mu/bd2 .=Mu/bd2

.=-(b±√(b2-4ac))/2a .=-(b±√(b2-4ac))/2a

mm2

αx αylower value

upper value

exact value

lower value

upper value

interptn. value

Mulim/bd2

Mux/bd2

Muy/bd2

.= bd3/12

.= 5*W*l4/(384EI)

Slab thickness t 150 mm

fck 20 MPa

fy 415 MPa Sunken Depth 450 mm

Loading

Slab Load Sunken Slab Load

Dead Load DL 3.75 KN/m Dead Load DL 3.75 KN/m

Live Load LL 3.00 KN/m Filler Load FL 6.39 KN/m

Floor Finish FF 1.00 KN/m Live Load LL 3.00 KN/m

Other Load OL 0.00 KN/m Floor Finish Load WL 1.00 KN/m

Total Load Ws 7.75 KN/m Total Load Wsk 14.14 KN/m

Factored Load Wsu 12 KN/m Factored Load Wsku 21 KN/m

Design & Reinforcement Details of Slabs

Slab Data

ly/lx

Sla

b ty

pe Loading on edges Moments Area of SteelSpacing required in mm

Sla

b ty

pe

Sla

b N

ame

Sl.No Sl. Id ThicknessLoad

Wsu / Wsku ly lx Mx Astx x y x y x y x y

1 Regular 150 mm 12 KN 7.20 m 3.00 m 2.40 - 18 KN/m 14 KN-m OK 302 sqmm 166 c/c 260 c/c 374 c/c -1a Regular 150 mm 12 KN 7.20 m 3.50 m 2.06 - 21 KN/m 18 KN-m OK 420 sqmm 120 c/c 187 c/c 269 c/c -2 Regular 150 mm 12 KN 9.20 m 1.50 m 6.13 - 9 KN/m 3 KN-m OK 180 sqmm 279 c/c 436 c/c 628 c/c -3 Regular 150 mm 12 KN 5.70 m 2.00 m 2.85 - 12 KN/m 6 KN-m OK 180 sqmm 279 c/c 436 c/c 628 c/c -4 Regular 150 mm 12 KN 3.60 m 2.00 m 1.80 + 11 KN/m 8 KN/m 5 KN-m 3 KN-m OK 180 sqmm 180 sqmm 279 c/c 279 c/c 436 c/c 436 c/c 628 c/c 628 c/c +5 Regular 150 mm 12 KN 15.00 m 2.60 m 5.77 - 16 KN/m 10 KN-m OK 224 sqmm 224 c/c 350 c/c 505 c/c -6 Regular 150 mm 12 KN 6.50 m 5.50 m 1.18 + 25 KN/m 22 KN/m 26 KN-m 20 KN-m OK 604 sqmm 468 sqmm 83 c/c 107 c/c 130 c/c 168 c/c 187 c/c 242 c/c +7 Regular 150 mm 12 KN 7.40 m 6.00 m 1.23 + 28 KN/m 24 KN/m 32 KN-m 24 KN-m OK 782 sqmm 567 sqmm 64 c/c 89 c/c 100 c/c 139 c/c 145 c/c 199 c/c +8 Regular 150 mm 12 KN 8.30 m 2.40 m 3.46 - 14 KN/m 9 KN-m OK 190 sqmm 265 c/c 414 c/c 596 c/c -9 Regular 150 mm 12 KN 6.70 m 3.70 m 1.81 + 20 KN/m 15 KN/m 17 KN-m 9 KN-m OK 379 sqmm 203 sqmm 133 c/c 248 c/c 207 c/c 388 c/c 298 c/c 558 c/c +

10 Sunken 150 mm 21 KN 6.50 m 5.00 m 1.30 + 42 KN/m 35 KN/m 41 KN-m 29 KN-m OK 1066 sqmm 706 sqmm 47 c/c 71 c/c 74 c/c 111 c/c 106 c/c 160 c/c +11 Sunken 150 mm 21 KN 5.80 m 4.80 m 1.21 + 39 KN/m 34 KN/m 35 KN-m 27 KN-m OK 869 sqmm 644 sqmm 58 c/c 78 c/c 90 c/c 122 c/c 130 c/c 176 c/c +

Concrete

Steel

Thickness Check

Spacing provided in mm c/cLonger

SpanShorter Span 8# 10# 12#

Wlonger Wshorter

Values of Moments and Shear force at different locations

Ma

rk Location (meters) Moments (KNm) Shear (KN)

x y0 0 0 0 9 0 0

1.5 0 0 0 9 0 153 0 0 0 7 0 27

4.5 0 0 0 4 0 366 0 0 0 0 0 39

7.5 0 0 0 -4 0 369 0 0 0 -7 0 27

10.5 0 0 0 -9 0 1512 0 0 0 -9 0 00 1.5 0 0 9 15 0

1.5 1.5 20 20 8 14 143 1.5 38 38 6 10 25

4.5 1.5 49 49 3 6 336 1.5 53 53 0 0 36

7.5 1.5 49 49 -3 -6 339 1.5 38 38 -6 -10 25

10.5 1.5 20 20 -8 -14 1412 1.5 0 0 -9 -15 00 3 0 0 7 27 0

1.5 3 38 38 6 25 103 3 69 69 5 19 19

4.5 3 91 91 3 10 256 3 98 98 0 0 27

7.5 3 91 91 -3 -10 259 3 69 69 -5 -19 19

10.5 3 38 38 -6 -25 1012 3 0 0 -7 -27 00 4.5 0 0 4 36 0

1.5 4.5 49 49 3 33 63 4.5 91 91 3 25 10

4.5 4.5 118 118 1 14 146 4.5 128 128 0 0 15

7.5 4.5 118 118 -1 -14 149 4.5 91 91 -3 -25 10

10.5 4.5 49 49 -3 -33 612 4.5 0 0 -4 -36 00 6 0 0 0 39 0

1.5 6 53 53 0 36 03 6 98 98 0 27 0

4.5 6 128 128 0 15 06 6 139 139 0 0 0

7.5 6 128 128 0 -15 09 6 98 98 0 -27 0

10.5 6 53 53 0 -36 012 6 0 0 0 -39 00 7.5 0 0 -4 36 0

1.5 7.5 49 49 -3 33 -63 7.5 91 91 -3 25 -10

4.5 7.5 118 118 -1 14 -146 7.5 128 128 0 0 -15

7.5 7.5 118 118 1 -14 -149 7.5 91 91 3 -25 -10

10.5 7.5 49 49 3 -33 -612 7.5 0 0 4 -36 00 9 0 0 -7 27 0

1.5 9 38 38 -6 25 -103 9 69 69 -5 19 -19

4.5 9 91 91 -3 10 -256 9 98 98 0 0 -27

7.5 9 91 91 3 -10 -259 9 69 69 5 -19 -19

10.5 9 38 38 6 -25 -1012 9 0 0 7 -27 00 10.5 0 0 -9 15 0

1.5 10.5 20 20 -8 14 -143 10.5 38 38 -6 10 -25

4.5 10.5 49 49 -3 6 -336 10.5 53 53 0 0 -36

7.5 10.5 49 49 3 -6 -339 10.5 38 38 6 -10 -25

10.5 10.5 20 20 8 -14 -1412 10.5 0 0 9 -15 00 12 0 0 -9 0 0

1.5 12 0 0 -9 0 -153 12 0 0 -7 0 -27

4.5 12 0 0 -4 0 -366 12 0 0 0 0 -39

7.5 12 0 0 4 0 -369 12 0 0 7 0 -27

10.5 12 0 0 9 0 -1512 12 0 0 9 0 0

Mx My Mxy Qx Qy

Staircase Design

DataEffective Span (l) 3.00 mmRiser (R) 150 mmThread (T) 300 mmWaist Slab thickness (t) 150 mmClear Cover 15 mmEffective Depth of Waist Slab (d) 135 mm

Grade of Concrete (fck) 20 MPaGrade of Steel (fy) 415 MPa

LoadingLoads on going Loads on waist slabSelf weight of waist slab 4.19 KN/m Self weight of landing slab 3.75 KN/mSelf weight of steps 1.88 KN/m Live Load 2.00 KN/mLive Load 3.00 KN/m Floor Finish Load 1.00 KN/mFloor Finish Load 1.00 KN/m Total Load 6.75 KN/m

Total Load 10.07 KN/m Factored Load 10.13 KN/mFactored Load 15.10 KN/m

Bending Moment

###Bending Moment = 17 KN-m

Reactionto be used as UDL = 23 KN ###

60 KN-m

Area of Main SteelAst 370 sqmm

Spacing

Diameter of barSpacing across x 306 c/c 544 c/c

Provded Main Steel:

Area of Distribution SteelAst 180 sqmm

Spacing

Diameter of barSpacing across y 279 c/c 436 c/c

Provided Distridution Steel:

12ø 16ø

8ø 10ø

Calculate Bending Moment using the equation (W*L*L )/8

Seismic Zone II Table 2 IS 1893 2002 pg 16Seismic Intensity z 0.1

Importance factor I 1.5 Table 6 IS 1893 2002 pg 18

Response Reduction Factor R 3 Table 7 IS 1893 2002 pg 23

Lateral Dimension of Building d 65.6 metersHeight of the of Building h 50.4 meters

with brick infill

Fundamental Natural Period 0.560

Type of Soil Medium Soil

Spectral Acceleration Coefficient 0.000

Design Horizontal Seismic Coefficient 0

Seismic Weight of Building W 680034 KN

Design Seismic Base Shear 0 KN

Ta

Sa/g

Ah

VB

Combined Footing

1 Footing Size Design

Load 1 Pu1 2000 KNLoad 2 Pu2 1850 KNCombine load Pcu 3850 KNDesign Load Pc 2823 KN

Moment in x dir Mux 40 KN-mMoment in y dir Muy 40 KN-m

c/c dist b/w col in x dir 2.725 metersc/c dist b/w col in y dir 0.000 meters

Col Dim x dir 0.20 metersy dir 0.20 meters

SBC q 150 KNm2

Footing Size required A req 18.82 sqmm

Footing Size ProvidedL 6.00 metersB 3.20 meters

Area Provided A prvd 19.20 meters

x bar 1.309y bar 0.000

Zx 10.24Zx 19.20

Nup 151 KNm2

Increase the Footing Size

2 Beam Design

Total Load W 151 KNm2Factored Load Wu 725 KNm2

1.691 meters 2.725 meters 1.584 meters

3.20 meters

6.00 meters

725 KNm2


Beam Size width 600 mmdepth 900 mm

Moment Mb 898 KN-m

Design the beam from the BEAM DESIGN SHEET

Bottom ReinforcementType Bar dia Nos Area of Steel

Layer 1 25 mm 6 2945 sqmmLayer 2 25 mm 6 2945 sqmmLayer 3 -

Total Steel Provided 5890 sqmmPercentage of Steel 1.148 %

Top ReinforcementType Bar dia Nos Area of Steel

Layer 1 25 mm 6 2945 sqmmLayer 2 20 mm 6 1885 sqmmLayer 3 -

Total Steel Provided 4830 sqmm

3 Slab Design

Net upward pressure Nup 151 KNm2l 1.30 meters /=width of footing from col face

Bending Moment Ms 128 KN-mFactored Moment Mus 191 KN-m 1.5*Ms

Concrete fck 20 MPafy 415 MPa

Minimum Depth Required dmin 264 d=sqrt(Ms/Rumax*1000*b)

Depth Provided D 600 mmClear Cover c 50 mmEffective Cover d' 56 mmEffective Depth d' 544 mm

Area of Steel across x dir Spacing c/c in mm 20#

1014 sqmm 112 c/c 198 c/c 310 c/c

Ast across x direction 12 mm dia @ 100 mm c/c 1131 sqmmDist Ast across y direction 8 mm dia @ 175 mm c/c 287 sqmm

4 Shear Check for Slab

Vu1 171 KNζv 0.315 MPa

ζc 0.316 MPa

Shear Check OK

M=Nup*l2/2

Steel

12# 16#

E110

d'= clear cover + stirrup dia + ø/2

E126

ζv=Shear Force/(bd)

E128

refer Table 61 SP 16 pg 178

56.00 meters

3.20 meters 600 mm


600 mm

6 - 25 mm dia6 - 20 mm dia

90

0 m

m

6 - 25 mm dia6 - 25 mm dia

60

0 m

m

250 mm

8 mm dia @ 175 mm c/c 12 mm dia @ 100 mm c/c

6 - 25 mm dia6 - 20 mm dia

6 - 25 mm dia6 - 25 mm dia

Design Of Isolated Footing 16 of 41

1 Footing Size Design

Load Pu 1500 KNDesign Load P 1100 KN

Moment in x dir Mux 30 KN-mMoment in y dir Muy 30 KN-m

Column size cx 450 mmcy 450 mm

SBC q 150 KN/sqm

Footing Size required A req 7.33 sqmm

Footing Size ProvidedL 3.30 metersB 2.40 meters

Area Provided A prvd 7.92 meters

Zx 3.17Zx 4.36

Net upward pressure Nup 150 KNm2

Footing Size OK

2 Slab Design

lx 1.425ly 0.975

Bending Moment in x dir Mx 228 KN-mBending Moment in y dir My 107 KN-m

Concrete fck 20 MPafy 415 MPa

Minimum Depth Required dmin 288

Depth Provided D 650 mmClear Cover c 50 mmEffective Cover d' 58 mmEffective Depth d' 592 mm

Area of SteelSpacing c/c in mm

20#1111 sqmm 102 c/c 181 c/c 283 c/c710 sqmm 159 c/c 283 c/c 442 c/c

Minimum Ast required across y direcion

Ast across x direction 16 mm dia @ 125 mm c/c 1608 sqmm

Ast across y direction 16 mm dia @ 125 mm c/c 1608 sqmm

Steel

12# 16#

E47

d'= clear cover + stirrup dia + ø/2


3 One Way Shear along x direction


ζc 0.317 MPa

Vc1 451 KN

One Way Shear Check OK

4 One Way Shear along y direction


ζc 0.260 MPaVc1 508 KN

One Way Shear Check OK

5 Two Way ShearVu2 1536 KNζv 0.622 MPa

ks*ζc 1.118 MPaVc1 2759 KN

Two Way Shear Check OK

E65


E67


E75


E77



L= 3.30 meters

450

B= 2.40 meters 450

65

0 m

m250 mm

16 mm dia @ 125 mm c/c 16 mm dia @ 125 mm c/c

Dome Design

Dimensions of DomeDiameter d = 12600 mmHeight h = 3000 mmThickness t = 150 mm

Radius of Sphere r = 8115 mm

h =

3.0

0 m

Φ = 50.93Ѳ = 0 to 50.93

Loading d = 12.60 mDead Load DL = 3.75 KN/m

Live Load LL = 0.10 KN/m 50.93 r = 8.12 mWind Load WL = 0.10 KN/mTotal Load W = 3.95 KN/mFactored Load Wu = 5.93 KN/m

Meridional Stress Hoop StressѲ Mt Ѳ Mt

50.93 0.197 MPa 50.93 0.003 MPa45.00 0.188 MPa 45.00 0.025 MPa40.00 0.182 MPa 40.00 0.041 MPa35.00 0.176 MPa 35.00 0.055 MPa30.00 0.172 MPa 30.00 0.067 MPa25.00 0.168 MPa 25.00 0.077 MPa20.00 0.165 MPa 20.00 0.086 MPa15.00 0.163 MPa 15.00 0.093 MPa5.00 0.161 MPa 5.00 0.100 MPa0.00 0.160 MPa 0.00 0.101 MPa

Maximum Meridional Stress 0.197 MPa Maximum Hoop Stress 0.101 MPa

fck 20 MPaFy 415 MPa

230.00

Area of steel 128 sqmm Area of steel 66 sqmm

Bar Dia 10 mm Bar Dia 10 mmSpacing 613 c/c Spacing 1187 c/c

Meridional Thrust @ Base 29 KN/mHorizontal Component on Ring Beam 19 KN/mHoop Tension on Ring Beam 117 KN

Area of steel 509 sqmm

Bar Dia 16 mmNo of Bars 3 nos

бst

r = 8115.00 m

3 Hinged Arch Design

19.7 KNm2

Dimensions of DomeDiameter d = 12600 mmHeight h = 5000 mm

Radius of Sphere r = 6469 mmΦ = 76.87Ѳ = 0 to 76.87

LoadingDead Load DL = 3.00 KN/m

Live Load LL = 0.10 KN/mOther Load OL = 10.00 KN/mTotal Load W = 13 KN/mFactored Load Wu = 20 KN/m

Vertical Reaction VA = VB = 123.8 KNHorizontal Reaction HA = HB = 234.0 KN

Ѳ x y Moment76.87 0.00 0.00 075.00 0.05 0.21 -4260.00 0.70 1.77 -33150.00 1.34 2.69 -48140.00 2.14 3.49 -59630.00 3.07 4.13 -68020.00 4.09 4.61 -73710.00 5.18 4.90 -7695.00 5.74 4.98 -7770.00 6.30 5.00 -780

Max Values 780 KN-m

3 Hinged Arch Designh

= 5

.00

m

d = 12.60 m

76.87 r = 6.47 m

Radial Shear Normal Thrust 0 67 17467 174 42 59 18059 180 331 10 224-10 224 481 56 245-56 245 596 100 259

-100 259 680 141 265-141 265 737 178 262-178 262 769 209 252-209 252 777 222 244-222 244 780 234 234-234 234

234 KN 265 KN

r = 6469.00 m

Circular Beam

Dimensions of Ring BeamRadius r = 6.30 mtsNo of supports n = 8 nos

Constants Ѳ = 23 deg 0.3927 radians

9 1/2 0.1658 radians

C1 = 0.066C2 = 0.03C3 = 0.005

LoadingWu = 10 KN/m

Shear Force

deg KN KN-m KN-m0 24.74 -20.62 0.009 1/2 14.29 -0.05 1.57

22 1/2 0.00 10.39 0.00

Beam Datawidth 300 mmdepth 600 mm

Equivalent Shear

Ve = V+1.6(T/b) = 33 KN

Equivalent MomentMt = T((1+D/b)/1.7) = 1 KN-m Mt = BM due to torsion

22 KN-m

20 KN-m

Φm =

ΦFΦ MΦ Mm

t

Bending Moment

Torsional Moment

T=MΦ

Me1 = M+Mt = Me1 = Equivalent BM on tension side

Me2 = M-Mt = Me2 = Equivalent BM on compression side

A Load 2700Moment x-dir y-dirBottom 0 29Top 6 137

Col Type Rectangular Column (reinf. on 2 sides)

x-dir y-dirUnsupported Length 8250 8250Col Size 200 900

d'/D 0.05 0.20d' 40

Concrete 20Steel 415

D

Effective Length Ratio0.80 from IS Code0.90 manual Calculation

Effective Length to be considered from Manual CalculationEffective Length (le) lex Ley

7425 7425E Slenderness Ratio

le/D 8 Short Columnle/b 37 Slender ColumnMoment due to Slen Muax 0

Muay 372

Min Ecc ex 46.5ey 23.2

Moment due to ecc Mux 125.55Muy 62.55

G Reduction of MomentsPercentage assumed 2.18

Asc 3924

Puz 2841

k1 K2 Pbx-x 0.219 0.096 367y-y 0.184 -0.022 291

Kx 0.06Ky 0.06

Additional Moments due to ecc Max 0May 21

Modified Initial Moments Mux 3.6Muy 70.6

Summary of MomentsA Moment due to eccentricity + Modified additional moments

Mux 126Muy 83

B Modified initial moments + Modified additional momentsMux 4Muy 91

C 0.4Muz + Modified additional momentsMux 0Muy 32

Final Design LoadsPu 2700Mux 126Muy 91

Bi-Axial Column

Design LoadsPu = 2400 KN

Mux = 192 KN-mMuy = 517 KN-m

Col Datab = 600 mmD = 750 mmd' = 40.0 mm

d'/D = 0.10d'/b = 0.10

Material Gradesfck = 20 MPafy = 415 MPa

Design ConstantsSteel % pt = 1.2 Ast = 5400 sqmm

pt/fck = 0.06 Min Ast = 3600 sqmmPu/fck*b*D = 0.27

0.11

0.11

Puz = 5682

743

594

Pu/Puz = 0.42

0.26

0.87

1.37

0.98

Steel Percentage OK

Steel Detailsnos dia ast

Type 1 4 20 mm 1257 sqmmType 2 8 16 mm 1608 sqmm

Total Steel 12 - 2865 sqmmPercentage 0.64%

Mux/fck*b*D2 =

Muy/fck*b*D2 =

Mux1 =

Muy1 =

Mux/Mux1 =

Muy/Muy1 =

αn =

(Mux/Mux1)αn + (Muy/Muy1)αn

Deflection Calculation

Load W 8 KN/m 70 KN/mLength l 2.60 m 3.00 m

Ec 22000000 MPa 22000000 MPa

Width b 0.20 m 0.20 mDepth d 0.45 m 0.60 mMoment M 8.66 m 82.13 mReaction R 13.33 m 109.50 m

Ixx 0.0015 mm4 0.0036 mm4

Deflectiondy

0.1 mm 0.5 mmFormula

Simply supported beam with UDL

Simply supported beam with Point Load

Elasticity of Concrete = 5000(√fck)

Moment of Inertia = bd3/12

5Wl4/384EI Wl3/48EI

Deflection Calculation

1400 KN/m 10 KN/m3.80 m 5.00 m

22000000 MPa 22000000 MPa

1.50 m 0.20 m1.10 m 0.60 m2601.46 m 40.63 m2738.38 m 32.50 m

0.1664 mm4 0.0036 mm4

10.0 mm 5.3 mm

Cantilever beam with UDL

Cantilever beam with Point Load

Wl4/8EI Wl3/3EI

DESIGN OF RETAINING WALL

1 Preliminary Datai) Height of RW h 3.00 meters

ii) Soil Density 18 KN/cum

iii) SBC 250 KN/sqm

iv) Angle of repose Ø30 degrees

0.524 radians

v) Surcharge Angle Ө0 degrees

0.000 radiansvi) Coefficient of friction µ 0.5

vii) Surcharge Load 4 KN/sqm

2 Pressure Coefficients

i)Active Pressure Coefficients

Ca 0.333

ii)Passive Pressure Coefficients

Cp 3.00 = (1+SinØ) / (1+SinØ)

3 Preliminary DimensionsProposed Adopted

i) Thickness of Stem - 0.20 meters

ii) Thickness of footing base slab 0.24 meters 0.30 meters

iii)Length of base slab L = 1.5 * √(Ca/3) * (h + hs) 1.61 meters

2.00 metersor L = 0.6h to 0.65h 2.09 meters

iv) Extra Height of Retaining Wall due to Surcharge 0.22 meters

v) Total Height of Retaining Wall due to Surcharge 3.22 meters

vi) Extra Height of RW due to inclined back fill 0.00 meters

vii) Total Height of RW due to inclined back fill 3.00 meters

viii) 3.22 meters

4 Stability against Overturning

i) Active pressure due Surcharge Load 4 KN

ii) Active pressure due Backfill Load 27 KN

iii) Total Load on stem 31 KN

iv) Overturning Moment 33 KNm

v) Load Lever arm from end of stem Moment

Backfill Load = (L-ts)*(h-tb)*γs 87 KN 0.90 meters 79 KNm

Surcharge Load = Ca*Ws*h 4 KN 0.90 meters 4 KNm

Inclined Backfill Load = ((L-ts)*hi)/2*γs 0 KN 0.60 meters 0 KNm

= ts*(h-tb)*γconc 14 KN 0.95 meters 13 KNm

Base self weight = L*tb*γconc 15 KN 1.00 meters 15 KNm

Downward component = Pa*sinӨ 0 KN 0 KNm

Other Load 0 KNm∑W 120 KN 110 KNm

vi) Distance of Resultant Vertical Force from end of heel 0.92 meters

vii) Stabilizing Moment 130 KNm

viii) Factor of Safety against OVERTURNING

3.54 > 1.4 Safe against Overturning

5 Stability against Slidingi) Sliding Force Pa*CosӨ 31 KNii) Resisting Force 60 KN

iii) Factor of Safety against SLIDING

1.74 > 1.4 Safe against Sliding

Shear Key not required

iv) Shear key Design

a) Shear Key Sizex 0.00 metersy 0.00 meters

b) Distance from stem z 0.00 meters

c) Heigth of exacavation 0.00 meters

d) Heigth of exacavation 0.00 meters

e) Passive Pressure 0 KN

v) Revised Factor of Safety against SLIDING

1.74 > 1.4Safe against Sliding

6 Soil Pressures at footing basei) Resultant Vertical Reaction ∑W = R 120 KNii) Distance of R from heel Lr = (Mw+Mo)/R 1.19 metersiii) Eccentricity e = Lr- L/2 0.19 meters

Eccentricity lies within middle third of the base hence OK

iv) Pressure Distridution on soil 95 KN/sqm

25 KN/sqmMax Pressure qmax<SBC hence pressure on base is OK

v) 88 KN/sqm

γs

qo

Ws

=(cosӨ-√(cos2Ө-cos2Ø)*cosӨ) / (cosӨ+√(cos2Ө-cos2Ø))

ts

tb = 0.08 * (h + hs)

hs = Ws/γs

Hs = h+hs

hi = (L-ts)* tanӨ

Hi = h+hi

Design Height of RW considered H = Max of H1 & H2

Pa1 = Ca*Ws*h

Pa2 = Ca*γs*h2 / 2

Pa = Pa1 + Pa2

Mo= (Pa1 * h/2) +(( Pa2*CosӨ)* h/3)

W1 (L-ts) / 2

W2 (L-ts) / 2

W3 (L-ts) / 3

W4 Stem self weight (L- (ts/2))/2

W5 L / 2

W6

W6

∑Mw

xw=∑Mw/∑W

Mr =∑W * (L - xw)

(FS)OT = 0.9 * (Mr/Mo)

F = µ*∑W

(FS)SL=0.9*(F/(Pa*CosӨ))

h1

h2 = h1 + y + (z * tanØ)

Pp = Cp*γs*(h12-h2

2) / 2

(FS)sliding = 0.9 * ((F+Pp)/(Pa*CosӨ))

qmax = R/L * (1+(6*e/L))

qmin = R/L * (1-(6*e/L))

Pressure at junction of stem and heel

qsh=qmax-((qmax-qmin)/L)*ts)

DESIGN OF L Shaped Cantilever RETAINING WALL

1 Preliminary Datai) Height of Retaining Wall h 3.60 meters

ii) Soil Density 18 KN/cum

iii) SBC 150 KN/sqm

iv) Angle of repose Ø 30 degrees

0.524 radians

v) Surcharge Angle Ө 0 degrees

0.000 radiansvi) Coefficient of friction µ 0.5


2 Pressure Coefficientsi) Active Pressure Coefficients Ca 0.333

ii) Passive Pressure Coefficients Cp 3.00 = (1+SinØ) / (1+SinØ)


i) Thickness of Stem min 200mm 0.20 meters

ii) Thickness of footing base slab 0.29 meters 0.25 metersiii) Length of base slab L = 1.5 * √(Ca/3) * (h + hs) 1.86 meters

2.50 metersL = 0.6h to 0.65h 2.41 meters





viii) 3.71 meters




iii) Total Load on stem (Force) 44 KN

iv) Overturning Moment due to Imposed load 5 KN

v) Overturning Moment due to Backfill load 51 KN

vi) Overturning Moment 68 KN

v) Load Lever arm at end of stem Moment

Backfill Load = (L-ts)*(h-tb)*γs 143 KN 1.35 meters 193 KNm

Inclined Backfill Load = ((L-ts)*hi)/2*γs 0 KN 0.97 meters 0 KNm


Base self weight = L*tb*γconc 16 KN 1.25 meters 20 KNm∑W 176 KN 215 KNm

viii) Safe against Overturning -clause 20.1 page 33 of IS 456 2000

5 Stability against Sliding

i) Sliding Force 44 KNii) Resisting Force 88 KN

iii) 1.81 > 1.4 Safe against Sliding -clause 20.2 page 33 of IS 456 2000

6 Soil Pressures at footing basei) Net Moment at toe Mn = Mw - Mo 159 KNii) Point of application of Resultant R x = Mn/W 0.90 metersiii) Eccentricity e = (L/2) - x 0.35 meters L/6= 0.42

e<L6 Eccentricity lies within middle third of the base hence OK


12 KN/sqmMax Pressure qmax<SBC hence pressure on base is OK

v) 120 KN/sqm

γs

qo

Ws


ts

tb = 0.08 * (h + hs)

hs = Ws/γs

Hs = h+hs

hi = (L-ts)* tanӨ

Hi = h+hi


PHS = Ca*Ws*h

PH = Ca*γs*h2 / 2

Pa = PHS + PH

MOIL = PHS*h/2

MODL = PH*h/3

Mo = (1.2*MDIL) + (1.4*MOIL)

W1 ((L-ts) / 2) + ts

W2 ((L-ts) / 3) + ts

W3 Stem self weight ts / 2

W4 L / 2

∑Mw

Mw not less than (1.2*MODL) +(1.4*MOIL)

Pa = PHS + PH

F = µ*∑W

(FS)SL= (0.9*F)/(Pa)

qmax = W/L * (1+(6*e/L))

qmin = W/L * (1-(6*e/L))



7 Constants for Working Stress Method

Design Constantsi) Grade of concrete 20 MPaii) Grade of steel 415 MPa

iii) Compr stress in concrete c 7.0 table 21 page 81 IS 456iv) Tensile stress in steel t 230v) Modular ratio m = 280/3c 13.33vi) Neutral axis depth factor k=mc/(mc+t) 0.289vii) Lever arm j = 1 - k/3 0.904viii) Factor R= cjk / 2 0.913

8 Design

A) Stem

i) Beanding Moment at base of stem 56 KN/m

ii) Thickness required 0.01 metersiii) Thickness provided ts 0.20 meters

Thickness of Stem is OK

iv) Ast required 1914 sqmm

v) Ast provided 16 mm dia @ 105 mm c/c 1915 sqmm

vi) Percentage of Steel 1.37 %

Steel OK

B) Base SlabForce Lever arm from end of stem Moment

i) Force due to backfill+surcharge 143 1.15 meters 165 KNm

ii) Force due to inclined backfill 0 0.77 meters 0 KNm

iii) Self Weight of base slab 16 1.25 meters 20 KNm∑Ws 159 Md 184 KNm

vi) Upward soil pressure 151 0.83 meters 126 KNmDownward Pressure is greater Mu 126 KNm

v) Bending Moment Msh = Mu-Md 58

vi) Thickness required 0.25 metersThickness of Stem is OK

vii) Thickness provided ts 0.25 meters

viii) Ast required 1440 sqmm

ix) Ast provided 16 mm dia @ 125 mm c/c 1608 sqmm

x) Percentage of Steel 0.74 %

Steel OK

C) Reinforcement Details

M = MODL + MOIL

dreq=√(Ms/(R*b)

Ast = M/(t*j*tse)

pt = Ast/(b*d)

= (H2-tb)*(L-ts)*γs (L-ts) / 2

= hi/2*(L-ts)*γs (L-ts) / 3

=L *tb*γconc L / 2

Nup = ((qsh+qmin)/2)*(L-ts) ((qsh+(2*qmin))/(qsh+qmin)) * ((L-ts)/3)

dreq=√(Ms/(R*b)

Ast = M/(t*j*tse)

pt = Ast/(b*d)

FILL

DESIGN OF Reverse L Shaped Cantilever RETAINING WALL

1 Preliminary Datai) Height of Retaining Wall h 3.00 metersii) Height of Plinth Fill hp 0.50 meters

iii) Soil Density 18 KN/cum

iv) SBC 250 KN/sqm

v)Angle of repose Ø 30 degrees

0.524 radians

vi)Surcharge Angle Ө 0 degrees

0.000 radiansvii) Coefficient of friction µ 0.5


2 Pressure Coefficientsi) Active Pressure Coefficients Ca 0.333

ii) Passive Pressure Coefficients Cp 3.000 = (1+SinØ) / (1+SinØ)


i) Thickness of Stem min 200mm 0.20 meters

ii) Thickness of footing base slab 0.24 meters 0.45 meters

iii) Length of base slabif sloped backfill

-0.60 meters

2.45 meters0.00 meters

if horizontal backfill-0.96 meters0.00 meters

L = 0.6h to 0.65h 2.09 meters





viii) 3.22 meters




iii) Total Load on stem (Force) 35 KN

iv) Overturning Moment due to Imposed load 7 KN

v) Overturning Moment due to Backfill load 33 KN

vi) Overturning Moment 50 KN

v) Load Lever arm at start of heel Moment

Front fill Load = (L-ts)*(hp-tb)*γs 2 KN 1.13 meters 2 KNm


Base self weight = L*tb*γconc 28 KN 1.23 meters 34 KNm

Other Load PT Beam Load 0 KN∑W 43 KN 69 KNm

viii) Safe against Overturning -clause 20.1 page 33 of IS 456 2000

5 Stability against Sliding

i) Sliding Force 35 KNii) Resisting Force 22 KN

iii) 0.55 < 1.4 Unsafe against Sliding -clause 20.2 page 33 of IS 456 2000

5a Shear key Design

a) Shear Key Sizex 0.30 metersy 0.30 meters

b) Distance from stem z 0.30 meters

c) Heigth of exacavation 0.60 meters

d) Heigth of earth mobilization 1.07 meters

e) Passive Pressure 21 KN

v) Revised Factor of Safety against SLIDING

γs

qo

Ws


ts

tb = 0.08 * (h + hs)

α = 1 - (q0/2.7*γs*H)L = H*sqrt((Ca*cosβ)/((1-α)*(1+3α))

α = 1 - (q0/2.2*γs*H)L = 0.95*H*sqrt((Ca)/((1-α)*(1+3α))

hs = Ws/γs

Hs = h+hs

hi = (L-ts)* tanӨ

Hi = h+hi


PHS = Ca*Ws*h

PH = Ca*γs*h2 / 2

Pa = PHS + PH

MOIL = PHS*h/2

MODL = PH*h/3

Mo = (1.2*MDIL) + (1.4*MOIL)

W1 ((L-ts) / 2)

W3 Stem self weight (ts/2) + (L-ts)

W4 L / 2

W5

∑Mw

Mw not less than (1.2*MODL) +(1.4*MOIL)

Pa = PHS + PH

F = µ*∑W

(FS)SL= (0.9*F)/(Pa)

h1

h2 = h1 + y + (z * tanØ)

Pp = Cp*γs*(h12-h2

2) / 2

v)1.09 > 1.4

Unsafe against Sliding. Shear Key Required

6 Soil Pressures at footing base

i) Net Moment at toe 28 KNii) Point of application of Resultant R x = Mn/W 0.65 metersiii) Eccentricity e = (L/2) - x 0.58 meters L/6= 0.41

e>L6 Eccentricity lies outside the middle third of the base. Revise the base dimensions


-7 KN/sqmMax Pressure qmax<SBC hence pressure on base is OK

v) 39 KN/sqm

(FS)sliding = 0.9 * ((F+Pp)/(Pa*CosӨ))

Mn = Mw - (MOIL+MODL)

qmax = W/L * (1+(6*e/L))

qmin = W/L * (1-(6*e/L))



7 Constants for Working Stress Method

Design Constantsi) Grade of concrete 20 MPaii) Grade of steel 415 MPa

iii) Compr stress in concrete c 7.0 table 21 page 81 IS 456iv) Tensile stress in steel t 230v) Modular ratio m = 280/3c 13.33vi) Neutral axis depth factor k=mc/(mc+t) 0.289vii) Lever arm j = 1 - k/3 0.904viii) Factor R= cjk / 2 0.913

8 Design

A) Stem

i) Beanding Moment at base of stem 40 KN/m

ii) Thickness required 0.01 metersiii) Thickness provided ts 0.20 meters


iv) Ast required 1387 sqmm

v) Ast provided 16 mm dia @ 120 mm c/c 1676 sqmm

vi) Percentage of Steel 0.99 %

Steel OK

B) Base SlabForce Lever arm from end of stem Moment

i) Force due to Frontfill 2 1.13 meters 2 KNm

iii) Self Weight of base slab 28 1.23 meters 34 KNm∑Ws 30 Md 36 KNm

vi) Upward soil pressure 35 0.58 meters 20 KNm

Upward Pressure is greater Mu 20 KNm

v) Bending Moment Msh = Mu-Md 16

vi) Thickness required 0.13 meters Thickness of Stem is OK

vii) Thickness provided ts 0.45 meters

viii) Ast required 193 sqmm

ix) Ast provided 12 mm dia @ 150 mm c/c 754 sqmm

x) Percentage of Steel 0.05 %

Steel OK

C) Reinforcement Details

M = MODL + MOIL

dreq=√(Ms/(R*b)

Ast = M/(t*j*tse)

pt = Ast/(b*d)

= (L-ts)*(hp-tb)*γs (L-ts) / 2

= L* tb * γconc L / 2

Nup = ((qsh+qmin)/2)*(L-ts) ((qsh+(2*qmin))/(qsh+qmin)) * ((L-ts)/3)

dreq=√(Ms/(R*b)

Ast = M/(t*j*tse)

pt = Ast/(b*d)

FILL

DESIGN OF Reverse L Shaped Cantilever RETAINING WALL

Design Constants for Working Stress Method

i) Grade of concrete 20 MPaii) Grade of steel 250 MPa

iii) Compr stress in concrete c 7.0iv) Tensile stress in steel t 140v) Modular ratio m = 280/3c 13.33vi) Neutral axis depth factor k=mc/(mc+t) 0.400vii) Lever arm j = 1 - k/3 0.867viii) Factor R= cjk / 2 1.213

Design

i) Height of Tank h 3.00 meters

ii) Saturated Soil Density 18 KN/cum

iii) Water Density 9.81 KN/cum

iv) Dry Soil Density 8.19 KN/cum

v) SBC 250 KN/sqm

vi)Angle of repose Ø 30 degrees

0.524 radians

vii)Active Pressure Coefficients

Ka 0.33 = (1-SinØ) / (1+SinØ)

A) Design of Long Walls

a) Tank empty with pressure of saturated soil from sidei) Active pressure pa = (Ka*γ'*H) + (γw*H) 38 KNii) Beanding Moment at base of wall M = (pa) *H/3 38 KN/m

iii) Thickness required 0.176 metersiv) Thickness provided ts 0.230 meters


v) Ast required

vi) Ast provided 16 mm dia @ 100 mm c/c

vii) Percentage of Steel

Steel OK

viii)50 % bars to be Curtailed from base 0.62 meters

plus 12 dia or thickness12dia 0.19 meters

thinkness 0.23 metersTotal curtaliment length from base 0.85 meters

ix) Ast required

Ast provided is more than mimimun Ast required hence OK

γs

γw

γ' = γ - γw

qo

dreq=√(Ms/(R*b)

Ast = M/(t*j*tse)

pt = Ast/(b*d)

h1 = h - h*(1/2)1/3

Ast min = 12 % of area

b) Tank full with water and no earth fill outsidei) Active pressure pa = (γw*H) 29 KNii) Beanding Moment at base of wall M = (pa) *H/3 29 KN/m

iii) Thickness required 0.156 metersiv) Thickness provided ts 0.230 meters


v) Ast required

vi) Ast provided 12 mm dia @ 100 mm c/c

vii) Percentage of Steel

Steel OK

viii)50 % bars to be Curtailed from base 0.62 meters

plus 12 dia or thickness12dia 0.14 meters

thinkness 0.23 metersTotal curtaliment length from base 0.85 meters

ix) Ast required


dreq=√(Ms/(R*b)

Ast = M/(t*j*tse)

pt = Ast/(b*d)

h1 = h - h*(1/2)1/3

Ast min = 12 % of area

table 21 page 81 IS 456

pa = w*l/2

1369 sqmm

2011 sqmm

0.70 %

Steel OK

IS 456 caluse 26.2.3.1 page 44

276 sqmm


pa = w*l/2

1071 sqmm

1131 sqmm

0.55 %

Steel OK

IS 456 caluse 26.2.3.1 page 44

276 sqmm


RCC Design_Box Culvert

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