Detailed Analysis of Single Cell Box Culvert

PROJECT:

TITLE:

DOCUMENT NO.

DESIGNED BY:

DESIGN BOX CULVERT

Top Member= Bottom Member Side Member

550 750 750

Garde of concrete

DATE

CHECKED

mm mm mm

M20 2 22361 N/mm 2 210000 N/mm 2.5 t/sq.m

Youngs Modulous of Concrete Youngs Modulous of steel gc=Unit weight of the concrete Finished assumed size Thickness at top Thickness on sides Unit weight of the over burden soil Unit weight of water K for soil at rest f=angle of repose of the soil/rock= Effective span Load on Top member:

4.31m x 0.55 0.8 2.00 1.00 0.50

1.64 m m m t/cum t/cum

(saturated)

25 o 4.69 m

UDL due to traffick, stackings etc= Add 25% for impact Add for weight of water Load due to wt of submerged earth Dead weight of slab= Total UDL on roof Say

2.00 0.50 -15.82 5.00 1.38 -6.94 -7.00

t/m t/m t/m t/sq.m t/m t/m t/m

SHEET NO.

PROJECT:

TITLE:

DOCUMENT NO.

DESIGN BOX CULVERT

DATE

DESIGNED BY:

CHECKED

IRC eqivalent Load+Weigt of water Horizontal force due to rock + water load 50% release

-7.00t/sq.m -5.4t/sq.m

-5.4t/sq.m -2.00t/sq.m Uniform vertical reaction due to 1.Weight of lining 2. Rock load 3. water

Load on bottom member: Reaction due to subgrade Load due to wt of walls= Load due to self weight= Uplift = Total UDL

t/sq.m 1.84 t/sq.m 1.88 t/m -5.41 t/sq.m -1.69 -2.00 t/sq.m

SHEET NO.

PROJECT:

DOCUMENT NO.

TITLE:

DESIGNED BY:

DESIGN BOX CULVERT

Loads:

w2=Reaction at the base=

-2.00 t/sq.m

w3=Uniform surcharge load on sides= w12=UDL on the top beam member= w4= -2.00

-5.41 t/sq.m

Assume thick ness at top=d1= Thickness at bottom Assume thick ness on sides=d2= Le=L+d1= He=h+d2=

-7.00 t/sq.m

0.55 m 0.75 m 0.75 m 4.86 m 2.39 m

W12

j= A

B

L=4.31 m h=1.64 m D

C

W2

W3W2 W4

FIXED END MOMENTS  w11  w12 L 2 MAB= =

13.79

12

MDC=

=

w4 L2 12

3.94

MDA=MCB=

w  w =  2  3 h 2  20 12 

-2.57

MAD=MBC=

w  w =  2  3 h2  30 12 

-2.57

BENDING MOMENT AT MID SPAN Moment at centre on span AB= Moment at centre on span DC=

-20.68 t-m -5.91 t-m

W3

DATE

CHECKED

SHEET NO.

PROJECT:

DOCUMENT NO.

TITLE:

DESIGN BOX CULVERT

LH1

4.86

I1

0.013865

LV2

2.39

I2

0.03516

I1/LH1

0.003

r_1

0.838

I2/LV2

0.0147

r_2

0.162

JOINT

A

MEMBER DF F.E.M BALANCE C.O BALANCE C.O BALANCE C.O BALANCE C.O BALANCE C.O BALANCE C.O BALANCE TOTAL

AD 0.8377 -2.5707 -9.3983 0.5735 -1.2430 2.0149 -1.7888 0.4238 -0.5002 0.4090 -0.3832 0.1379 -0.1466 0.0914 -0.0885 -12.4687

B AB 0.1623 13.7894 -1.8204 0.9102 -0.2408 0.1204 -0.3465 0.1732 -0.0969 0.0484 -0.0742 0.0371 -0.0284 0.0142 -0.0171 12.4687

BA 0.1623 -13.7894 1.8204 -0.9102 0.2408 -0.1204 0.3465 -0.1732 0.0969 -0.0484 0.0742 -0.0371 0.0284 -0.0142 0.0171 -12.4687

DESIGNED BY:

CHECKED

C BC 0.8377 2.5707 9.3983 -0.5735 1.2430 -2.0149 1.7888 -0.4238 0.5002 -0.4090 0.3832 -0.1379 0.1466 -0.0914 0.0885 12.4687

CB 0.8377 -2.5707 -1.1470 4.6992 -4.0297 0.6215 -0.8476 0.8944 -0.8180 0.2501 -0.2759 0.1916 -0.1829 0.0733 -0.0763 -3.2180

CD 0.1623 3.9398 -0.2222 0.1111 -0.7805 0.3903 -0.1642 0.0821 -0.1584 0.0792 -0.0534 0.0267 -0.0354 0.0177 -0.0148 3.2180

Reaction at A(hor) Reaction A due to UDL= Reaction A due to Triangular Load= Reaction A due to FE M= Net reaction at A:

-2.388 -2.153 -3.874 -8.415

Reaction at D(hor)

-2.820 t

t t t t

Reaction at A(ver) -15.092 0.000 0.000 -15.092

SHEET NO.

D

REACTIONS:

Reaction A due to UDL= Reaction A due to Triangular Load= Reaction A due to FE M= Net reaction at A:

DATE

t t t t

DC 0.1623 -3.9398 0.2222 -0.1111 0.7805 -0.3903 0.1642 -0.0821 0.1584 -0.0792 0.0534 -0.0267 0.0354 -0.0177 0.0148 -3.2180

DA 0.8377 2.5707 1.1470 -4.6992 4.0297 -0.6215 0.8476 -0.8944 0.8180 -0.2501 0.2759 -0.1916 0.1829 -0.0733 0.0763 3.2180

PROJECT:

DOCUMENT NO.

TITLE:

DESIGN BOX CULVERT

Reactio At Bottom(Ver)

DESIGNED BY:

DATE

CHECKED

SHEET NO.

-4.862 t -8.215t-m 12.47t-m

-12.47t-m

12.47t-m

12.47t-m

-8.41 t

x

2.388 m

-2.69t-m -2.82 t 3.22t-m

-3.22t-m -5.91t-m

-3.22t-m

3.22t-m 4.862 m

-4.31 t

-4.31 t

-8.42x2x.x/2--5.41/Hx.x.x/6-12.47=0 x= M=

2.365 m -21.78t-m

Computation of thickness: Member Location Top Member Side Member Bottom Member

M1 t-m 12.47t-m -3.22t-m -3.22t-m

Mc t-m -8.215t-m -21.78t-m -2.69t-m

Thcikness at Thickness supports at centre cm cm 32.63 26.49 16.58 43.13 16.58 15.16

Overall Overall depth depth provided cm t-m 41.13 45.00 51.63 75.00 25.08 75.00

Overall thickness: The thickness provided is 750 mm as the supporting members are to resist the moments due to horizontal forces due to braking effect, temperature change and differentail water pressures when adjecent vents get blocked. De 75.00 cm b= 1000.00 mm Depth on deflection criteria=1/8x Span

539 mm

PROJECT:

DOCUMENT NO.

TITLE:

DESIGN BOX CULVERT

DATE

DESIGNED BY:

CHECKED

-7.00t/sq.m M1=12.47t-m

M2=12.47t-m B

A

4.36m

-15kN

-15.25kN

M2=12.47t-m -20.684t-m

-8.215t-m 2.39m

Es Ec= fck fy I Cover

N/mm2

200000

2

22360.68

2

M20

2

415

N/mm N/mm N/mm 4

m mm

xumax/d

0.479

Qlim=

2.77 2 2.770 bd kN-m

Mu_lim Pmax= Ptmin=

0.03516 50

0.956 % 0.205 %

SHEET NO.

PROJECT:

DOCUMENT NO.

TITLE:

DESIGNED BY:

DESIGN BOX CULVERT

DETAILS Depth Reaction at supports Shear (Factored) Moment from analysis k1 k2 Pt= Pt adopted=

unit mm t kN t-m

%

Ast Nominal reinforcement Dia of bar Area Spacing Spacing adopted Area provided= Area provided= Distribution steel F= Area Spacing Spacing provided

DATE

CHECKED

SHEET NO.

Top member(AB) Bottom member(CD) Side members(AD & BC) @centre @ support @centre @ support @centre @ support 387.5 387.5 687.5 687.5 687.5 687.5 -15.25 -4.31 -2.82 -224.40 -63.45 -41.50 -8.22 12.47 -2.69 3.22 -21.78 -3.22 SRB SRB SRB SRB SRB SRB -0.048 -0.048 -0.048 -0.048 -0.048 -0.048 0.000108 0.000163 0.000011 0.000013 0.000091 0.000013 0.23 0.37 0.20 0.20 0.20 0.20 0.23 0.37 0.20 0.20 0.20 0.20

mm2 mm2 mm mm2 mm mm mm2

938.04

1466

1433.73

1434

1433.73

1434

1550.00 20

1550.00 20

2750.00 25

2750.00 25

2750.00 25

2750.00 25

314.16 203 190

314.16 203 190

490.87 178 170

490.87 178 170

490.87 178 170

490.87 178 170

1653

1653

2887

2887

2887

2887

2

1257

1885

1963

1963

1963

1963

2

525 12

525 12

885 16

885 16

885 16

1106.25 16

113.10 215 210

113.10 215 210

201.06 227 220

201.06 227 220

201.06 227 220

201.06 182 175

mm

mm mm mm2 mm mm

* SRB SINGLY REINFORCED, DRB DOUBLY REINFORCED

Check for Shear: Shear force Thickness of haunch Shear stress Atx100/bd Permissible shear= Balance shear stress= Balance Shear force= Maximum shear Provide haunch bars dia spacing

kN N/mm2 % N/mm2 N/mm2 N N/mm2 mm mm

Deflection permissble deflection=

-152.50 0.00 -0.39 0.37 0.42 0.00 0.00 2.80

-43.12 375.00 -0.04 0.31 0.39 0.00 0.00 2.80

-28.20 0.00 -0.04 0.31 0.39 0.00 0.00 2.80

16 150

16 150

` 150

-0.42 mm 12.45 mm

PROJECT:

DOCUMENT NO.

TITLE:

DATE

DESIGNED BY:

DESIGN BOX CULVERT

#12@210 c/c

CHECKED

SHEET NO.

450mm #20@200 c/c

#20@190 c/c

#25@170 c/c #20@200 c/c 750mm #16@175 c/c #20@200 c/c

750mm

#16@220 c/c

#25@170 c/c

WORKING SRTRESS METHOD MEMBER A-B Permissible stresses: N/mm

Grade of concrete

2

20 2 415 N/mm 2 7 N/mm

Grade steel Permissible stress in concrete

2 150 N/mm 13.33 0.384 0.872 1.171 mm2 6000.00 50 25 490.9

Permissible stress in steel m= k= j= Q= Min. Steel= Cover F(mm) Area Location @supports @centre

M(kN-m) 124.687 -82.155 Overall depth

d(mm)

D(mm)

326 265

380 320 800

Effective depth=

Ast

Spacing(m m) 12.22 80 1.73 250

Ast adopted No. of rods

1290.16 850.07

748.75 mm

6000.00 850.07

PROJECT:

DOCUMENT NO.

TITLE:

DESIGN BOX CULVERT

Main reinforcement; B.M Dia of main bar

DESIGNED BY:

DATE

CHECKED

12.47 t-m 32 mm 2 804.25 mm 134.04 mm 130 mm 2 6186.52 mm

Area Spacing Spacing provided Area of steel provided Distribution Steel: Area of steel (0.12%) Dia of main bar

900.00 16 mm 2 201.06 mm 223.40 mm 220 mm 2 913.92 mm

Area Spacing Spacing provided Area of steel provided To find tension in the members At top= Tensile/compressive stress= At botttom= Tensile stress= Ast= Dia bars Area Spacing Spacing provided= Check for shear shear force= Shear stress % of steel= correction factor=

-8.41 -1.122 -2.82 -0.376 -7.992 25 4.909 -61.421 15

t kg/sqcm t kg/sqcm sq.cm mm sq.cm cm c/c

152.50 0.47 1.37 1.00

kN N/mm2 % k 2 0.81 N/mm 2 0.81 N/mm

Permissible shear stress= Permissible Shear stress kt

2 - N/mm

Balance shear Development Length:

Codal requirement of development length of diameter of bar should be such that;

M1  Lo ³ L d V Tensile bars are at support= Moment of resistence due to this steel= Shear force= V

Lo =

ls - c'  4f 2

2 6186.5 mm 124.69 kN-m 152.50 kN

2281.5 mm

SHEET NO.

PROJECT:

TITLE:

DOCUMENT NO.

DESIGN BOX CULVERT

Lo =

ls - c'  4f 2 M1  Lo = V

t

For HYSD bars

t

bd

CHECKED

3099.1 mm

=

bd

= 1 . 4t

DESIGNED BY:

DATE

bd

Ld =

fs st = 4t bd

2 0.60 N/mm 2 0.84 N/mm

1428.57 mm OKAY

SHEET NO.

PROJECT:

DOCUMENT NO.

TITLE:

DATE

DESIGNED BY:

DESIGN BOX CULVERT

CHECKED

SHEET NO.

Checkfor effective depth of slab from the consideration of stiffness/Deflection Effectve depth as per above= mm K(=20 FOR SIMPLY SUPPORTED, =7 FOR CANTILEVER,=26 FOR CONTINUOUS) Pt= Modification factor Effective depth=

L/{K x Modification factor} 20 % 1.37 0.89 mm 245 OKAY

2.34

2.19

2.05

1.90

1.75

1.61

1.46

1.32

1.17

1.02

0.88

0.73

0.58

0.44

0.29

0.15

0.00

8.00 6.00 4.00 2.00 0.00 -2.00 -4.00 -6.00 -8.00

1.00 0.50 0.00 -0.50

-1.00 2.34

2.19

2.05

1.90

1.75

1.61

1.46

1.32

1.17

1.02

0.88

0.73

0.58

0.44

0.29

0.15

0.00

-1.50

2.50

2.00

1.50

1.00

0.50

-1.6

0.00

10.0

2.34

CHECKED

2.34

2.19

DOCUMENT NO.

2.24

2.14

2.05

1.90

1.75

1.61

DESIGNED BY:

2.05

1.95

1.85

1.75

1.66

1.46

1.32

1.17

1.02

0.88

0.73

0.58

0.44

0.29

DESIGN BOX CULVERT

1.56

1.46

1.36

1.27

1.17

1.07

0.97

0.88

0.78

0.68

0.58

0.15

0.00

TITLE:

0.49

0.39

0.29

0.19

0.10

0.00

PROJECT: DATE

SHEET NO.

-13.3

8.00 6.00 4.00 2.00 0.00 -2.00 -4.00 -6.00 -8.00 -10.00

0.0

-11.6

-23.3