Box Girder Computations

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BOX GIRDER SUPER STRUCTURE

A3 A2 A1

A

T

B

M

D

G

P

C

F

E

L

H

N

O

K

I

J

I

Q

S

INPUT DIMENSION (mm)

(Designation as per above figure)

A = 430 G = 100 M = 300 S = 1800

(2)

C = 1800 I = 600 O = 150 A1 = 350

D = 400 J = 3000 P = 150 A2 = 330

E = 263.5 K = 200 Q = 430 A3 = 420

F = 315 L = 1700 R = 600

420

330 Clear Carriage way = 7500

350 430 0.065m Wearing Coat 350 200 300 400 100 150 1800 315 263.5 1700 250 315 150 200 600 3000 600 430 1800

(3)

400 300

150

685.16

650

200

GEOMETRY OF END CROSS GIRDER

DATA :

1. C/C of span (mm) 25000

2. Effective Span (mm) = C/C Dist.-2 ( Width of End cross girder) 24200 3. C/C of web for outer box span (mm) 3936.5 4. Clear Carriage way (mm) 15000 5. Overall width of decking (mm) 16460 6. Concrete Grade M 30 7. Grade of Steel 415 8. Thickness of wearing coat ( in m) = 0.065 9. Permissible stresses in steel 2000 10. Permissible stresses in concrete 101.94

11. Modular Ratio m 10

12. Density of parapet (t/m) 0.2



st (kg / cm2₎



cbc (kg / cm2₎

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Notes: This box indicate INPUT parameter. This indicate UDL load on span.

16460

OF FOUR LANE BRIDGE

7500 7500

CLEAR ROAD WAY CLEAR ROAD WAY

1931.8 3936.5 4723.5

c/c of web of Box girder 1800

1700 2200

Elastomeric Bearing RCC Pedestel

RCC Pier Cap

2260 mm c/c of 2260 mm c/c of pedestel

pedestel (All Dimensions are in mm)

25000 25000 mm c/c of Pier

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Elastomeric Bearing RCC Super Structure IN M

30

RCC Pedestal RCC Pier cap RCC Pier RCC Sub Structure Foundation GROUND LEVEL

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25000

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JAYESH DRG-2 BG/DAX/DRG-Section

400 200

100

1700 2200

200

C/C of Pier C/C Of Bearing SECTIONAL ELEVATION 1-1

400 600 2400 9100 OF SYMMETRY A B 263.5 685 315 1 1 3000 1843.0 c/c of 1630 OF BOX GIRDER Sofit Box 8660 315 c/c of Box 685 263.5

25000 Overall Span c/c of Bearing

OF bearing OF SYMMETRY

24200

A B Effective Span c/c of Bearing

PLAN AT SOFFIT LEVEL

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(2) DESIGN OF CANTILEVER DECK SLAB

430 Wearing Coat (m.) 0.065 X 350 KERB 200 400 1800 X

Dead Load bending moment @ XX,

(1) DL due to parapet 0.2 1.8 0.43 0.317 t.m. 2

(2) Parapet kerb = {A*A1 * 2.40 * (C-A/2)}

0.43 0.35 2.4 1.8 0.43 0.573 t.m.

2

(3) Wearing coat = { (C-A) * Thk. Of wearing coat* (C-A/2)}

1.8 0.43 0.065 2.4 1.8 0.43 0.146 t.m. 2

(4) Self weight of slab

(a) {(C*B*C/2)*2.40} 1.8 0.2 1.8 2.4 0.778 t.m. 2 (b) {1/2*C*(D-B)*(C/3)*2.40} 1 1.8 0.4 0.2 1.8 2.4 0.259 t.m. 2 3

TOTAL DEAD LOAD BENDING MOMENT 2.073 t.m.

0.43 Minimum Clarance (IRC - 6:2000)

2.1 DEAD LOAD BENDING MOMENT

2.2 LIVE LOAD BENDING MOMENT

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Ground contect Area

0.15 0.5

0.97 1.8

Effective Dispersion width = 1.2 a + b1 (Cl. 305.16.2, IRC-21:2000) 0.97 m.

0.38 m. Effective Dispersion width bf =1.2 a + b1

1.2 0.97 0.38 1.544 m. LIVE LOAD BENDING MOMENT = (Axle load/2) * a * Impact Factor

Impact factor 50% for cantilever slab as per Fig. 5 Cl. 211.2, IRC-6:2000

11.4 0.97 1.5 8.2935 t.m.

2

0.43 Minimum Clarance in m.(IRC - 6:2000) Ground contect Area

Kerb 1.2 0.85

1.63 0.17

1.8

Effective Dispersion width (Cl. 305.16.3, IRC-21:2000)

= 0.50(Wheel contact Area) + 2*(Slab thk. + W.C.)

Distance between edge to center of load = 0.43 0.4 0.5 0.83 m. 2

So, Slab Thk. @ Load center = 0.2 0.4 0.2 0.83 0.292 m. 1.8

Effective Dispersion width = 0.50 + 2 ( Slab thk. + W.C.)

0.50 2 0.292 0.065 1.214 m.

a = (C-A) - 0.15 - 0.50/2 = b1 = 0.25 + 2 (Thk. Of Wearing coat) =

For Class A Axle load 11.40 t

LIVE LOAD BENDING MOMENT = (11.40/2) * a * 1.50

2.2.2 CLASS AA Traked Vehicle

As c.g. of loads lying outside, No calculation of B.M. is reqd.

(14)

8.294 4.423 t.m/m

1.544 1.214

When vehicals travels near expansion gap, Eff. Width available across the span. Effective width available across the span,

beff. = ( 1.2 x a)/2 + (0.25+W)

1.2 0.97 0.25 0.065 0.897 m. 2

8.294 7.613 t.m/m

0.897 1.214

Service load = 0.2 t/m (Assumed)

So, B.M. = 0.20 * (Width of Cantilever - Half width of kerb)

B.M. 0.20 1.8 0.43 0.317 t.m/m

2

TOTAL BENDING MOMENT (D.L. + L.L. + Services) = 2.073 4.423 0.317

(L.L.B.M./m. width taken) 6.813 t.m.

For M25 Concrete, m = 10

K = 0.338

j = 1- K/3 = 0.887 15.272

d reqd. = 21.121 cm. {d reqd. = ( Total BM / (Q*100)) }

d prov. = 36.2 cm d Prov. = 400 30(cover) - 16/2(half Dia.) 362 mm d reqd. < d prov. Hence OK... Ast Reqd. = 10.60 Provide 12 mm dia @ 280 mm c/c 16 mm dia @ 280 mm c/c

LIVE LOAD BENDING MOMENT / m. Width =

LIVE LOAD BENDING MOMENT near expan. gap =

(3) SERVICES

Q = 1/2 *



cbc * k* j =

(15)

Ast Provided 11.22 In Cantilever projection of Box slab. OK….

For End 1 m. near EXPANSION GAP.

TOTAL BENDING MOMENT (D.L. + L.L. + Services) = 10.003 t.m.

(L.L.B.M. taken at Expansion gap)

d reqd. = 25.593 cm. {d reqd. = Sqrt( Total BM / (Q*100)) }

d prov. = 36.2 cm d Prov. = 400 - 30(cover) - 16/2(half Dia.) = 362 mm d reqd. < d prov.

Hence OK...

Ast Reqd. = 15.57

Provide 12 mm dia @ 280 mm c/c

25 mm dia @ 280 mm c/c

Ast Provided 21.57 In Cantilever projection of Box slab. OK….

DISTRIBUTION STEEL

B.M. = 0.2 DLBM + 0.3 LLBM (Cl.305.18.2, IRC : 21-2000) Dead Load BM = DL + Service = 2.390

Live Load BM = 4.423 B.M. = 0.2 2.390 0.3 4.423

B.M. = 1.805 t.m.

Ast (Dist.) = 2.809

Ast Minimum = 3.6 ( 12% of gross area)

Ast Reqd. = 3.60

Provide 10 mm dia @ 150 mm c/c About top & bottom

Ast Provided 5.24 OK….

Provide 10 mm dia @ 140 mm c/c About bottom in span direction.

Ast Provided 5.61 (in Cantilever portion) OK….

cm2 cm2 cm2 cm2 cm2 cm2 cm2 cm2

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JAYESH Steel Details MAIN STEEL :

Throughout Throughout

12 mm Tor 16 mm Tor 20 mm Tor 12

280 mm c/c 280mm c/c 280 mm c/c 280 10 mm Tor 140mm c/c 12 mm Tor 16 mm Tor 12 280mm c/c 280mm c/c 280 Throughout 10 mm Tor 10 mm Tor 150mm c/c 150mm c/c

10 mm Tor 8 mm Tor 8 mm Tor

150mm c/c at bottom 150mm c/c 150mm c/c

215 2185 3000 1030

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JAYESH ED-1 C/S Of End Diapharm 16460

OF FOUR LANE BRIDGE

600 7500

CLEAR ROAD WAY

6 25 0 20 A mm tor At Top. 6 25 300 0 20 mm tor At Top. 16 mm Tor 16 mm Tor

2 Legged Stirps 2 Legged Stirrups

180 mm c/c. 180 mm c/c. 16 mm Tor 2 Legged Stirrups 16 Tor 1900 180 mm c/c. 180 mm c/c on both faces. 16 Tor 180 mm c/c on both faces. 0 20 6 25 1800 430 600 A 3000 600 1800 6 25 400 mm tor At bottom. 0 20 16 mm Tor

mm tor At bottom. 2 Legged Stirrups SECTION - AA

180 mm c/c.

(35)

LONGITUDINAL GIRDER

4.1 Max moment at mid span.

( i ) Class AA Tracked Vehicle

70 Tonne Total Load 70/3.6 = 19.444 t/m.

3.6

12.1

0.4 24.2 0.4

Mid span moment = 391.63 t.m.

Give value of impact factor = I. F. = 1.1 (cl.211.3(b), IRC:6-2000) Give value of Reaction factor = R. F. = 1.2

Moment With I.F. and R.F. = 516.9516 t.m.

( ii ) Class 70R wheeled Vehicle

17 17 17 17 12 12 8 6.6412 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 4.1588 A E B 12.1 0.4 24.2 0.4 RA RB

(36)

c.g. of load from right of first load = 5.1238 m. Coincide distance = 5.4588 m.

Moment @ E = 441.49 t.m.

Give value of impact factor = I. F. = 1.18 (From fig. 5 cl.211.3(b), IRC:6-2000) Give value of Reaction factor = R. F. = 1.2

Moment With I.F. and R.F. = 625.15 t.m.

( iii ) Class A Train (Two Lanes)

2.7 2.7 11.4 11.4 6.8 6.8 6.8 '6.8

2.66 . 1.10 . 3.20 . 1.20. . 4.3 . 3.0 .3.0 3 2.74

A E B

12.1

0.4 24.2 0.4

c.g. of load from right of first load = 9.09 m. Coincide distance = 9.44 m. Distance from A = 2.66 m.

Moment @ E = 193.28 t.m.

(37)

Quarter of load distance

(i.e. 1/4 X 3.6 m) = 0.9 70 T

3.6

6.05

0.4 24.2 0.4

Give value of impact factor = I. F. = 1.1 ( cl.211.3(b), IRC:6-2000) Give value of Reaction factor = R. F. = 1.2

17 17 17 17 12 12 8

4.68 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 6.1200

A E B

6.05

0.4 24.2 0.4

c.g. of load from right of first load = 5.1238 m. Coincide distance = 5.4588 m.

Moment @ E = 336.37 t.m.

(38)

1.75 2.7 2.7 11.4 11.4 6.8 6.8 6.8 '6.8 1.1 3.2 1.20. 4.3 3.0 . .3.0 3.0 3.65 A E B 6.05 0.4 24.2 0.4 23.1 Moment @ E = 164.65 t.m.

4.3 Max moment at 3 m from left of span.

70 T

3.6

3

0.4 24.2 0.4

(39)

Give value of Reaction factor = R. F. = 1.2

17 17 17 17 12 12 8

3 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 7.8000

A E B

3

0.4 24.2 0.4

c.g. of load from right of first load = 5.1238 m. Moment @ E = 190.91 t.m.

11.4 11.4 6.8 6.8 6.8 6.8

1.2 4.3 3.0 . 3.0 . .3.0 9.5

A E B

3 21.2

(40)

Moment @ E = 90.17 t.m.

RECAPITULATION OF LIVE LOAD BENDING MOMENTS

Load Discription BENDING MOMENT (in tm)

.@ Mid @ @

Span Quarter Beginning of

Span Widening. Live load Class AA 516.95 387.64 214.90 Class 70R 625.15 476.30 270.33 Class A 547.37 466.29 255.36

DESIGN BM

625.150 476.30

270.33

(41)

Beginning of Widening of section from support (m) = 3

Dead Load Bending Moment

Super Imposed Dead Load (SIDL) of Super Structure

Wearing Coat ( t ) =Ht.X Clear carriage way X Density= 2.34 t/m. Parapet ( t ) = 0.2 t/m = 0.4 t/m. Kerb = Area X Density = 0.3612 t/m. Services = 0.1 t/m = 0.2 t/m. Total SIDL = 3.3012 t/m. 3.3012 t/m. A C D E B 3.00 0.4 6.05 12.1 24.2 12.5 25 Reaction at A & B = 41.265 t

Bending Moment at mid span (E) = 241.4003 t.m.

Bending Moment at quarter span (D) = 180.9842 t.m.

Bending Moment at Widening (C) = 104.7141 t.m. Dead Load Bending Moment due to self wt. of Super Structure

C/S Area of box at mid span = 8.069

u d l = 19.37 t/m. 19.37 t/m. A C D E B 3.00 0.4 6.05 12.1 24.2 12.5 25 Reaction at A & B = 242.07 t m2

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Bending Moment at Widening (C) = 614.2768 t.m. Dead Load Bending Moment due to widening

C/S Area of box at End span = 10.86

C/S Area of box at mid span = 8.069

Difference of C/S Area = 2.791

Wt./R.m.(A X Density) = 6.6984 t/m. Total Length of END Beam = 1 m. Length of Taperd Section of Beam = 2.4 m.

6.6984 t/m. 6.6984 A C D E B 0.6 2.4 3.0 0.4 6.05 12.1 24.2 12.5 25 Reaction at A & B = 14.74 t

Bending Moment at Widening (C) = 11.92315 t.m.

Total Reaction @ A & B ( i.e. Total DL due to half Span ) = 298.07 t

Total DL of Super Structure = 597 t

NOTE :

Summary of DLBM

Sr .No. LOAD

1 SIDL 241.4003 180.9842 104.71406

2 Self Wt.of Box (Running Section) 1416.11 1061.695 614.27683

3 Widning (Self Weight) 11.92315 11.92315 11.923152

m2

Put All Geometry in STAAD Analysis and Varify above data.

At MID Span (E) 't.m' At Quarter Span (D) 't.m' At Widening (C) 't.m'

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SHEAR FORCE

Give Value of No. of GIRDER 4

Due To Dead Load

Due To SIDL

Super Imposed Dead Load (SIDL) of Super Structure

Wearing Coat ( t ) =Ht.X Clear carriage way X Density= 2.34 t/m. Parapet ( t ) = 0.2 t/m = 0.4 t/m. Kerb = Area X Density = 0.3612 t/m. Services = 0.1 t/m = 0.2 t/m. Total SIDL = 3.3012 t/m. 3.3012 t/m. A C D E B 3.00 0.4 6.05 12.1 24.2 12.5 25 Reaction at A & B = 41.265 t 0.6 1.8 3.00 6.05 Shear Force, .@ A 41.265 3.3012 0.4 39.945 t .@ Y 39.945 3.3012 0.6 37.964 t .@ X 39.945 3.3012 1.8 34.002 t .@ C 39.945 3.3012 3.0 30.041 t .@ D 39.945 3.3012 6.05 19.972 t

Dead Load Shear Force due to self wt. of Super Structure

19.37 t/m.

A C D E B

Y X

Section Y = Distance from support to edge of END BEAM Section X = Distance from support to centre of WIDENING Section C = Distance from support to Starting of WIDENING Section D = Distance from support to Quarter Span

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3.00 0.4 6.05 12.1 24.2 12.5 25 Reaction at A & B = 242.07 t Shear Force, .@ A 242.07 19.37 0.4 234.324 t .@ Y 234.324 19.37 0.6 222.704 t .@ X 234.324 19.37 1.8 199.466 t .@ C 234.324 19.37 3.00 176.227 t .@ D 234.324 19.37 6.05 117.162 t

Dead Load Shear Force due to widening

6.698 t/m. 6.698 t/m. Y X A C D E B 0.6 2.4 3.0 0.4 6.05 12.1 24.2 12.5 25 Reaction at A & B = 14.74 t Shear Force, .@ A 14.74 6.70 0.4 12.057 t .@ Y 12.057 6.70 0.6 8.038 t .@ X 8.038 5.02 1.2 2.010 t .@ C 8.038 3.35 2.4 0.000 t .@ D 0.000 0.00 6.05 0.000 t

Total Reaction @ A & B ( i.e. Total DL due to half Span ) = 298.07 t

Total DL of Super Structure = 597 t

NOTE :

Summary of DLSF

Sr .No. LOAD

1 SIDL 39.94 37.96 34.00

Put All Geometry in STAAD Analysis and Varify above data.

Section A

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2 Self Wt.of Box (Running Section) 234.32 222.70 199.47

3 Widning (Self Weight) 12.06 8.04 2.01

TOTAL DLSF ( t ) = 286.33 268.71 235.48

Due To Live Load

FOR Twin Box Take R.F. = 1.2

AT Support Section

( A ) Class A Two Lane Vehicle

11.4 11.4 6.8 6.8 6.8 '6.8 . 1.20. . 4.3 . 3.0 .3.0 3 9.7 B 24.2 11.4 24.2 23 6.8 18.7 15.7 12.7 24.2 38.20 t

S.F.@support with R.F. & I.F. (For Two Lane)

38.20 1.18 1.2 2

108.168 t

( B ) Class AA Traked Vehicle

70 t A B 3.60 24.2 70 22.4 24.2 64.79 t

S.F.@support with R.F. & I.F. (For Two Lane) 64.79 1.1 1.2

85.527 t R_A =

(50)

( C ) Class 70R Wheeled Vehicle 17 17 17 17 12 12 8 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 10.800 B 24.2 RA RB 17 24.2 22.83 19.78 18.41 12 16.28 8 10.8 24.2 78.83 t

S.F.@support with R.F. & I.F. (For Two Lane) 78.83 1.18 1.2 111.619 t Sr. No. LOADING S.F. ( t ) 1 Class A ( 2 lane) 108.168 2 Class AA Traked 85.527 3 70R wheeled Vehicle 111.619

AT Section - ' Y ' ( 0.6 ) m. From support

11.4 11.4 6.8 6.8 6.8 '6.8 0.6 . 1.20. . 4.3 . 3.0 .3.0 3 9.1 B 24.2 11.4 23.6 22.4 6.8 18.1 15.1 12.1 24.2 36.96 t

S.F.@support with R.F. & I.F. (For Two Lane) R_A =

RECAPITULATION OF LIVE LOAD SHEAR FORCE At SUPPORT

(51)

36.96 1.18 1.2 2 104.658 t

70 t 0.6 A B 3.60 24.2 70 21.8 24.2 63.06 t

83.236 t

( C ) Class 70R Wheeled Vehicle

17 17 17 17 12 12 8 0.60 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 10.200 B 24.2 RA RB 17 23.60 22.23 19.18 17.81 12 15.68 8 10.20 24.2 76.35 t

S.F.@support with R.F. & I.F. (For Two Lane) 76.35 1.18 1.2 108.109 t 0.6 m.From Support. Sr. No. LOADING S.F. ( t ) R_A = R_A = RECAPITULATION OF LLSF At

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1 Class A ( 2 lane) 104.658

2 Class AA Traked 83.236

3 70R wheeled Vehicle 108.109

AT Section - ' X ' ( 1.8 ) m. From support

11.4 11.4 6.8 6.8 6.8 '6.8 1.8 . 1.20. . 4.3 . 3.0 .3.0 3 7.9 B 24.2 11.4 22.4 21.2 6.8 16.9 13.9 10.9 24.2 34.48 t

34.48 1.18 1.2 2

97.636 t

70 t 1.8 A B 3.60 24.2 70 20.6 24.2 59.59 t

78.655 t

17 17 17 17 12 12 8

1.80 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 9.000

R_A =

(53)

B 24.2 RA RB 17 22.40 21.03 17.98 16.61 12 14.48 8 9.00 24.2 71.39 t

S.F.@support with R.F. & I.F. (For Two Lane) 71.39 1.18 1.2 101.087 t 1.8 m.From Support. Sr. No. LOADING S.F. ( t ) 1 Class A ( 2 lane) 97.636 2 Class AA Traked 78.655 3 70R wheeled Vehicle 101.087

AT Section - ' C ' ( 3.00 ) m. From support

11.4 11.4 6.8 6.8 6.8 '6.8 3.00 . 1.20. . 4.3 . 3.0 .3.0 3 6.7 B 24.2 11.4 21.2 20 6.8 15.7 12.7 9.7 24.2 32.00 t

32.00 1.18 1.2 2

90.615 t

R_A =

RECAPITULATION OF LLSF At

(54)

70 t 3.0 A B 3.60 24.2 70 19.4 24.2 56.12 t

74.073 t

17 17 17 17 12 12 8 3.00 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 7.800 B 24.2 RA RB 17 21.20 19.83 16.78 15.41 12 13.28 8 7.80 24.2 66.43 t

S.F.@support with R.F. & I.F. (For Two Lane) 66.43 1.18 1.2 94.066 t 3 m.From Support. Sr. No. LOADING S.F. ( t ) 1 Class A ( 2 lane) 90.615 2 Class AA Traked 74.073 3 70R wheeled Vehicle 94.066

AT Section - ' D ' ( 6.05 ) m. From support

R_A =

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( A ) Class A Two Lane Vehicle 11.4 11.4 6.8 6.8 6.8 '6.8 6.05 . 1.20. . 4.3 . 3.0 .3.0 3 3.65 B 24.2 11.4 18.15 16.95 6.8 12.65 9.65 6.65 24.2 25.70 t

25.70 1.18 1.2 2

72.768 t

70 t 6.1 A B 3.60 24.2 70 16.35 24.2 47.29 t

62.427 t

17 17 17 17 12 12 8 6.05 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 4.750 B 24.2 RA RB R_A = R_A =

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17 18.15 16.78 13.73 12.36 12 10.23

8 4.75

24.2 53.83 t

S.F.@support with R.F. & I.F. (For Two Lane) 53.83 1.18 1.2 76.219 t 6.05 m.From Support. Sr. No. LOADING S.F. ( t ) 1 Class A ( 2 lane) 72.768 2 Class AA Traked 62.427 3 70R wheeled Vehicle 76.219

RECAPITULATION OF DL & LL SHEAR @ VARIOUS SECTION

Sr. No. S.F. Due To Shear Force At Section in Tonne

Support Sect - Y Sect - X Sect - C Sect - D

1 DL + SIDL 286.33 268.71 235.48 206.27 137.13

2 LIVE LOAD 111.619 108.109 101.087 94.066 76.219

DESIGN S.F.( t ) 397.94 376.81 336.56 300.33 213.35

CHECK FOR SHEAR STRESS & REINFORCEMENT CALCULATION

At Support Section :

MAX. Shear force = 397.94 t

SF / Girder = 397.94 99.49 t 4 Shear Stress = 99.49 1000 65 220 6.96 < 21.582 OK….

Providing 12 mm dia. 4 legged stirrups, R_A =

RECAPITULATION OF LLSF At

Kg / Cm2

(57)

Spacing ' S ' = 196.672 mm

Provide 12 mm dia. 4 legged stirrups, @ 180 mm C/C. Shear Force Taken = 108.70 > 99.49 Hence OK….

At Section ' Y ':

Providing 12 mm dia. 4 legged stirrups, Spacing ' S ' = 207.700 mm

At Section ' X ':

Kg / Cm2

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At Section ' C ' :

At Section ' D ' :

SHEAR REIFOREMENT DETAILS:

{ 1 } { 2 } { 3 } { 4 } { 5 } Y X C D Kg / Cm2 Kg / Cm2 Kg / Cm2 Kg / Cm2

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0.4 0.6 1.8 2.4 3.00

6.05

Portion Dia. Legged C/C Dist.

(No.) (mm) (No.) (mm) 1 12 4 180 2 12 4 180 3 16 2 180 4 16 2 180 5 16 2 200

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m. m. m. m.

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30.04 19.97

Section C

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176.23 117.16 0.00 0.00

206.27 137.13

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14.76

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12.96

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5.1 AT MID SPAN

Dead Load B.M. = 1669.43 t.m. for twin box (D.L. + S.I.D.L.)

Design B.M. = 1459.87 t.m. per box.

(All Dimensions are in mm.)

250 315 79.057 150 237.2  25.46 270.9431 200 146.9 90.31 461.86 420 881.86



71.565051 X = 237.17082 mm Y = 79.056942 mm Z = 270.94306 mm X1 = 90.314353 mm T = 146.85647 mm T1 = 461.85647 mm

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 25.463345 a = 420 mm

Provide 48 Nos. of 32 Tor in 3 rows Ast = 385.991

Provide Clear Cover = 30 mm Provide dia. Of Stirups = 12 mm 18 no. 16 no. 14 no. Total = 48 OK……. Provision of No. of BAR in First Row

50 mm

Clear Side Cover = 40 mm Diameter of stirrups = 12 mm Diameter of Main Bar = 32 mm NO. OF BAR in First raw = 9

Total Distance,

9 32 8 50 2 12 2 40

792 mm < 881.86 mm

OK….

cm2

Provide no. Of bar in 1st_{Row =}

Provide no. Of bar in 2nd_{Row =}

Provide no. Of bar in 3rd_{Row =}

(75)

58 mm 64 mm 64 mm

c.g. of steel from bottom of girder, =

11.67 cm

d eff. = 208.33 cm

180 420 223 20 30 20 31.5 n [2] 10 [1] [5] 43 15 [3] [4] 25 [6] [7]

(All Dimensions are in cm.)

Portion Length Depth c.g. from REMARK NO. AREA

cm cm Top (cm) X n [1] 420 30 15 Rectangle 1 12600 189000 [2] 180 20 10 Rectangle 1 3600 36000 [3] 223 30 15 Rectangle 1 6690 100350 [4] 180 20 26.67 Triangle 1 1800 48000 [5] 31.5 10 33.33 Triangle 2 315.00 10500 [6] 43 15 35 Triangle 1 322.5 11287.5 [7] 25 30 2 -1500 22500 Due to Reinforcement 3859.9066 804147.2 Distance between end of Soffit to centre of 1st_{row =}

Distance between centre of 1st_{row to centre of 2}nd_{row =}

Distance between centre of 2nd_{row to centre of 3}rd_{row =}

(76)

Sum = 27687.41 1176785

1107.50 47071.39

1107.496

n -

47071.39 4.55E-008

Don't Delete this cell, it is useful for operation of Goal Seek…

N.A. from Top of girder =

40.9857

cm For finding out Value of n.

M.I. Of section @ N.A.,

180 20 40.99 40

n

20 -0.99 20.99

Portion Length Depth c.g. from REMARK M.I. AREA M.I. +

cm cm Top (cm) [1] 420 30 15 Rectangle 945000 12600 675.2588 9453261.2 [2] 180 20 10 Rectangle 120000 3600 960.1163 3576418.5 [3] 223 30 15 Rectangle 501750 6690 675.2588 5019231.5 [4] 85.56416 20.985743 Eq. Rectn. 65899.73 1795.6274 220.2007 461298.14 180 20 26.67 Triangle 40000 1800 205.0359 409064.69 Due to Reinforcement = 108097517

M.I. Of section @ N.A., = 126555493

Section Modulus at Compression, Zc = 3087793

n

2

₊

_{.= 0}

cm4 _cm2 _h2 _{(A x h}2₎

cm4

(77)

Section Modulus at Tension, Zt = 756243.29 Stresses in Concrete = 47.278631 < 101.94 OK……. Stresses in Steel = 1930.4188 < 2000 OK……. 47.28

40.99 Stress in Outer layer, 167.35 + 5.87 1930.41882 167.35 = 1998.093 214.2 < 2000 OK……. 167.35 1930.42 5.87

5.2 AT QUARTER SPAN

250 315 237.17 79.057 150 cm3 kg/cm2 kg/cm2 kg/cm2 kg/cm2 kg/cm2 kg/cm2

(78)

 25.46 270.9431 200 146.9 90.31 461.86 420 881.86



71.565051 X = 237.17082 mm Y = 79.056942 mm Z = 270.94306 mm X1 = 90.314353 mm T = 146.85647 mm T1 = 461.85647 mm  25.463345 a = 420 mm

Provide 38 Nos. of 32 Tor in 3 rows Ast = 305.576

Provide Cover = 30 mm Provide dia. Of Stirups = 12 mm 18 no. 16 no. 4 no. Total = 38 OK…….

cm2

(79)

58 mm 64 mm 64 mm

c.g. of steel from bottom of box, =

9.84 cm

d eff. = 210.16 cm

180 420 223

20 30

n

420 x n x n/2 + 223 x n x n/2 + 180 x n x n/2 + .= 10 x 305.576 x ( 210.16 .-n )

411.5 3055.7594

n -

642192 .= 0

N.A. from Top of girder = 35.97 cm 0

M.I. Of the section @ N.A., For finding out Value of n.

2

420 x 30.0 ^3 + 420 30 35.966 -15 .= 6483482

12

2 Distance between end of beam to centre of 1st_{row =}

Distance between centre of 2nd_{row to centre of 3}rd_{row =}

(80)

223 x 30.0 ^3 + 223 30 35.966 -15 .= 9155494 12 2 180 x 20 ^3 + 180 20 35.966 -10 .= 1560000 12 2 36.31 x 15.97 ^3 + 36.31 15.97 15.97 .= 49255 12 2 2 143.69 x 15.97 ^3 + 1/2 143.69 15.97 15.97 x 2 .= 146197 36 3 2 10 x 305.576 x 210.16 -35.96574 .= 92720625.3

M.I. Of the section @ N.A., = 110115054

Section Modulus at Compression, Zc = 3061665 Section Modulus at Tension, Zt = 632147 Stresses in Concrete = 36.04577 < 101.94 OK……. Stresses in Steel = 1745.798 < 2000 OK……. 36.05 35.97

Stress in Outer layer, 174.19 + 4.04 1745.79797 174.19 174.19 214.2 = 1786.309 cm4 cm3 cm3 kg/cm2 kg/cm2 kg/cm2 kg/cm2 kg/cm2

(81)

< 2000 OK…….

1745.80 4.04

5.3 AT BEGINNING OF WIDENING SECTION

250 315 237.17 79.057 150  25.46 270.9431 200 146.9 90.31 461.86 420 881.86



71.565051 X = 237.17082 mm Y = 79.056942 mm Z = 270.94306 mm X1 = 90.314353 mm T = 146.85647 mm T1 = 461.85647 mm kg/cm2

(82)

 25.463345 a = 420 mm

Provide 26 Nos. of 32 Tor in 3 rows Ast = 209.078

Provide Cover = 30 mm Provide dia. Of Stirups = 12 mm 14 no. 12 no. 0 no. Total = 26 OK……. 58 mm 64 mm 64 mm

c.g. of steel from bottom of box, =

8.75 cm

d eff. = 211.25 cm

180 420 223

20 30

n

cm2

Provide no. Of bar in 3rd_{Row =}

Distance between end of beam to centre of 1st_{row =}

(83)

420 x n x n/2 + 223 x n x n/2 + 180 x n x n/2 + .= 10 x 209.078 x ( 211.25 .-n )

411.5 2090.7827

n -

441669.8 .= 0

N.A. from Top of girder =

30.3194

cm

0.0006016

M.I. Of the section @ N.A., For finding out Value of n.

2 420 x 30 ^3 + 420 30 30.319 -15 .= 3902026.68 12 2 223 x 30 ^3 + 223 30 30.319 -15 .= 2071790.35 12 2 180 x 20 ^3 + 180 20 30.319 -10 .= 1606363.92 12 2 87.13 x 10.32 ^3 + 87.13 10.32 10.32 .= 31914.5388 12 2 2 92.87 x 10.32 ^3 + 1/2 92.87 10.32 10.32 x 2 .= 25515.4848 12 3 2 10 x 209.078 x 211.25 -30.31942 .= 68440690.8

M.I. Of the section @ N.A., = 75850791 76078301.7

n

2

₊

(84)

Section Modulus at Compression, Zc = 2509227 Section Modulus at Tension, Zt = 420492.3 Stresses in Concrete = 25.33791 < 101.94 OK……. Stresses in Steel = 1512.003 < 2000 OK……. 25.34 30.32

Stress in Outer layer, 180.93 + 2.95 1512.00284 180.93 214.2 180.93 = 1536.688 < 2000 OK……. 1512.00 2.95

CALCULATION OF WEB REIFORCEMENT : (Skin Reinforcement)

2 2

Skew Web Dimension : Length = 1800 600 1897.3666 mm Width = 250 mm

Total Steel Req. = 1897.37 250 474.34

cm3 cm3 kg/cm2 kg/cm2 kg/cm2 kg/cm2 kg/cm2 kg/cm2

As per Cl.305.10, IRC - 21:2000, Min. Shrinkage reiforcement shall be 250 mm2_{of Steel area per metre.}

(85)

1000

Provide 7 Numebrs 10 mm at top and bottom.

+

Provide 0 Numebrs 0 mm at top and bottom.

Ast provided = 549.710 OK….

7 10 On Each Faces. Third raw 7 32 Second ra 8 32 First raw 9 32 mm2

(86)

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Don't Delete this cell, it is useful for operation of Goal Seek… For finding out Value of n.

(90)

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