box girder computations
DESCRIPTION
Box GirderTRANSCRIPT
BOX GIRDER SUPER STRUCTURE
A3
A2
A1 AT
B MD
G P
C F
EL
H N
OK
I J I Q S
INPUT DIMENSION (mm) (Designation as per above figure)
A = 430 G = 100 M = 300 S = 1800B = 200 H = 250 N = 315 T = 350
C = 1800 I = 600 O = 150 A1 = 350D = 400 J = 3000 P = 150 A2 = 330E = 263.5 K = 200 Q = 430 A3 = 420F = 315 L = 1700 R = 600
420
330 Clear Carriage way = 7500
350 430 0.065 m Wearing Coat350
200 300400
100 150
1800 315
263.51700
250315
150200
600 3000 600 430 1800
400 300150
685.16
650
200
GEOMETRY OF END CROSS GIRDER
DATA :
1. C/C of span (mm) 250002. Effective Span (mm) = C/C Dist.-2 ( Width of End cross girder) 242003. C/C of web for outer box span (mm) 3936.54. Clear Carriage way (mm) 150005. Overall width of decking (mm) 164606. Concrete Grade M 307. Grade of Steel 4158. 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 1012. Density of parapet (t/m) 0.2
sst (kg / cm2)
scbc (kg / cm2)
Notes: This box indicate INPUT parameter.
This indicate UDL load on span.
16460OF FOUR LANE BRIDGE
7500 7500CLEAR ROAD WAY CLEAR ROAD WAY
1931.8 3936.5 4723.5c/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 pedestelpedestel (All Dimensions are in mm)
25000 25000 mm c/c of Piermm c/c of Pier
Elastomeric Bearing RCC Super Structure IN M 30RCC Pedestal
RCC Pier cap
RCC Pier
RCC Sub Structure
FoundationGROUND LEVEL
R
600
25000mm c/c of Pier
JAYESH DRG-2 BG/DAX/DRG-Section
400 200
100
1700 2200
200
C/C of Pier C/C Of Bearing SECTIONAL ELEVATION 1-1400 600 2400 9100 OF SYMMETRY
A B
263.5685
315
1 13000 1843.0c/c of 1630 OF BOX GIRDER
Sofit Box
8660315 c/c of Box
685263.5
25000 Overall Span c/c of Bearing OF bearing OF SYMMETRY
24200A B Effective Span c/c of Bearing
PLAN AT SOFFIT LEVEL
OF PIER
(2) DESIGN OF CANTILEVER DECK SLAB
430 Wearing Coat (m.)0.065 X
350 KERB
200
400
1800X
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)Ground contect Area
0.15 0.5
0.97
2.1 DEAD LOAD BENDING MOMENT
2.2 LIVE LOAD BENDING MOMENT
2.2.1 CLASS A Vehicle
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.
8.294 4.423 t.m/m1.544 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.
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. Hence class A governs the design.
LIVE LOAD BENDING MOMENT / m. Width =
28.294 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
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
LIVE LOAD BENDING MOMENT near expan. gap =
(3) SERVICES
Q = 1/2 * scbc * k* j =
cm2
cm2
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 = 2.390Live 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
JAYESH Steel Details
MAIN STEEL :Throughout Throughout
12 mm Tor 16 mm Tor 20 mm Tor 12280 mm c/c 280 mm c/c 280 mm c/c 280
10 mm Tor140 mm c/c 12 mm Tor 16 mm Tor 12
280 mm c/c 280 mm c/c 280Throughout
10 mm Tor 10 mm Tor150 mm c/c 150 mm c/c
10 mm Tor 8 mm Tor 8 mm Tor150 mm c/c at bottom 150 mm c/c 150 mm c/c
215 2185 3000 1030
DISTRIBUTION STEEEL :
JAYESH Steel Details
JAYESH ED-1 C/S Of End Diapharm
16460OF FOUR LANE BRIDGE
600 7500CLEAR ROAD WAY
6 250 20
A mm tor At Top.6 25
300 0 20mm tor At Top.
16 mm Tor 16 mm Tor2 Legged Stirps 2 Legged Stirrups
180 mm c/c. 180 mm c/c. 16 mm Tor2 Legged Stirrups
16 Tor 1900 180 mm c/c.180 mm c/c on both faces.
16 Tor180 mm c/c on both faces.
0 206 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 - AA180 mm c/c.
CROSS SECTION AT END DIAPHARM
LONGITUDINAL GIRDER
4.1 Max moment at mid span.
( i ) Class AA Tracked Vehicle70 Tonne Total Load
70/3.6 = 19.444 t/m.3.6
12.10.4 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 86.6412 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 4.1588
A E B12.1
0.4 24.2 0.4RA RB
( 4 ) LIVE LOAD BENDING MOMENT
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 '6.82.66 . 1.10 . 3.20 . 1.20. . 4.3 . 3.0 .3.0 3 2.74
A E B12.1
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.
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. = 547.37 t.m.
4.2 Max moment at quarter span.
( i ) Class AA Tracked Vehicle
Quarter of load distance (i.e. 1/4 X 3.6 m) = 0.9 70 T
3.6
6.050.4 24.2 0.4
Mid span moment = 293.67 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. = 387.6444 t.m.
( ii ) Class 70R wheeled Vehicle
17 17 17 17 12 12 84.68 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 6.1200
A E B6.05
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.
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. = 476.30 t.m.
( iii ) Class A Train (Two Lanes)
1.75 2.7 2.7 11.4 11.4 6.8 6.8 6.8 '6.81.1 3.2 1.20. 4.3 3.0 . .3.0 3.0 3.65
A E B6.05
0.4 24.2 0.423.1
Moment @ E = 164.65 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. = 466.2888 t.m.
4.3 Max moment at 3 m from left of span.
( i ) Class AA Tracked Vehicle70 T
3.6
30.4 24.2 0.4
Mid span moment = 162.80 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. = 214.90 t.m.
( ii ) Class 70R wheeled Vehicle
17 17 17 17 12 12 83 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 7.8000
A E B3
0.4 24.2 0.4
c.g. of load from right of first load = 5.1238 m.
Moment @ E = 190.91 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. = 270.33 t.m.
( iii ) Class A Train (Two Lanes)
11.4 11.4 6.8 6.8 6.8 6.81.2 4.3 3.0 . 3.0 . .3.0 9.5
A E B3 21.2
0.4 24.2 0.4
Moment @ E = 90.17 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. = 255.3614 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
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 B3.00
0.4 6.0512.1
24.212.5
25
Reaction at A & B = 41.265 t
Bending Moment at mid span (E) = 241.4002 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 B3.00
0.4 6.0512.1
24.212.5
25
Reaction at A & B = 242.07 t
m2
Bending Moment at mid span (E) = 1416.11 t.m.Bending Moment at quarter span (D) = 1061.695 t.m.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 B0.6 2.4
3.00.4 6.05
12.124.2
12.525
Reaction at A & B = 14.74 t
Bending Moment at mid span (E) = 11.92315 t.m.Bending Moment at quarter span (D) = 11.92315 t.m.Bending Moment at Widening (C) = 11.92315 t.m.
Total Reaction @ A & B ( i.e. Total DL due to half Span ) = 298.07 tTotal DL of Super Structure = 597 t
NOTE :
Summary of DLBM
Sr .No. LOAD
1 SIDL 241.4002 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
m2
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'
TOTAL DLBM = 1669.433 1254.602 730.91405
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 B3.00
0.4 6.0512.1
24.212.5
25
Reaction at A & B = 41.265 t
0.61.8
3.006.05
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 Structure19.37 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
Y X
3.000.4 6.05
12.124.2
12.525
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 B0.6 2.4
3.00.4 6.05
12.124.2
12.525
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 tTotal 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 ( t )
Section Y ( t )
Section X ( t )
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
24.238.20 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 Vehicle70 t
A B3.60
24.2
70 22.424.2
64.79 t
S.F.@support with R.F. & I.F. (For Two Lane)
64.79 1.1 1.2
85.527 t
RA =
RA =
( 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
24.2RA RB
17 24.2 22.83 19.78 18.41 12 16.28
8 10.824.2
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) 108.1682 Class AA Traked 85.5273 70R wheeled Vehicle 111.619
AT Section - ' Y ' ( 0.6 ) m. From support
( A ) Class A Two Lane Vehicle
11.4 11.4 6.8 6.8 6.8 '6.80.6 . 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
24.236.96 t
S.F.@support with R.F. & I.F. (For Two Lane)
RA =
RECAPITULATION OF LIVE LOAD SHEAR FORCE At SUPPORT
RA =
36.96 1.18 1.2 2
104.658 t
( B ) Class AA Traked Vehicle70 t
0.6
A B3.60
24.2
70 21.824.2
63.06 t
S.F.@support with R.F. & I.F. (For Two Lane)
63.06 1.1 1.2
83.236 t
( C ) Class 70R Wheeled Vehicle
17 17 17 17 12 12 80.60 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 10.200
B
24.2RA RB
17 23.60 22.23 19.18 17.81 12 15.68
8 10.2024.2
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 )
RA =
RA =
RECAPITULATION OF LLSF At
1 Class A ( 2 lane) 104.6582 Class AA Traked 83.2363 70R wheeled Vehicle 108.109
AT Section - ' X ' ( 1.8 ) m. From support
( A ) Class A Two Lane Vehicle
11.4 11.4 6.8 6.8 6.8 '6.81.8 . 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
24.234.48 t
S.F.@support with R.F. & I.F. (For Two Lane)
34.48 1.18 1.2 2
97.636 t
( B ) Class AA Traked Vehicle70 t
1.8
A B3.60
24.2
70 20.624.2
59.59 t
S.F.@support with R.F. & I.F. (For Two Lane)
59.59 1.1 1.2
78.655 t
( C ) Class 70R Wheeled Vehicle
17 17 17 17 12 12 81.80 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 9.000
RA =
RA =
B
24.2RA RB
17 22.40 21.03 17.98 16.61 12 14.48
8 9.0024.2
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) 97.6362 Class AA Traked 78.6553 70R wheeled Vehicle 101.087
AT Section - ' C ' ( 3.00 ) m. From support
( A ) Class A Two Lane Vehicle
11.4 11.4 6.8 6.8 6.8 '6.83.00 . 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
24.232.00 t
S.F.@support with R.F. & I.F. (For Two Lane)
32.00 1.18 1.2 2
90.615 t
( B ) Class AA Traked Vehicle
RA =
RECAPITULATION OF LLSF At
RA =
70 t3.0
A B3.60
24.2
70 19.424.2
56.12 t
S.F.@support with R.F. & I.F. (For Two Lane)
56.12 1.1 1.2
74.073 t
( C ) Class 70R Wheeled Vehicle
17 17 17 17 12 12 83.00 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 7.800
B
24.2RA RB
17 21.20 19.83 16.78 15.41 12 13.28
8 7.8024.2
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) 90.6152 Class AA Traked 74.0733 70R wheeled Vehicle 94.066
AT Section - ' D ' ( 6.05 ) m. From support
RA =
RA =
RECAPITULATION OF LLSF At
( A ) Class A Two Lane Vehicle
11.4 11.4 6.8 6.8 6.8 '6.86.05 . 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
24.225.70 t
S.F.@support with R.F. & I.F. (For Two Lane)
25.70 1.18 1.2 2
72.768 t
( B ) Class AA Traked Vehicle70 t
6.1
A B3.60
24.2
70 16.3524.2
47.29 t
S.F.@support with R.F. & I.F. (For Two Lane)
47.29 1.1 1.2
62.427 t
( C ) Class 70R Wheeled Vehicle
17 17 17 17 12 12 86.05 . 1.37 . 3.05 . 1.37 . 2.13 . 1.52 . 3.96 4.750
B
24.2RA RB
RA =
RA =
17 18.15 16.78 13.73 12.36 12 10.23
8 4.7524.2
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) 72.7682 Class AA Traked 62.4273 70R wheeled Vehicle 76.219
RECAPITULATION OF DL & LL SHEAR @ VARIOUS SECTION
Sr. No. S.F. Due To Shear Force At Section in TonneSupport 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 t4
Shear Stress = 99.49 100065 220
6.96
< 21.582 OK….
Providing 12 mm dia. 4 legged stirrups,
RA =
RECAPITULATION OF LLSF At
Kg / Cm2
Kg / Cm2
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 ':
MAX. Shear force = 376.81 t
SF / Girder = 376.81 94.20 t4
Shear Stress = 94.20 100065 220
6.59
< 21.582 OK….
Providing 12 mm dia. 4 legged stirrups,
Spacing ' S ' = 207.700 mm
Provide 12 mm dia. 4 legged stirrups, @ 180 mm C/C.
Shear Force Taken = 108.70 > 94.20 Hence OK….
At Section ' X ':
MAX. Shear force = 336.56 t
SF / Girder = 336.56 84.14 t4
Shear Stress = 84.14 100045 220
8.50
< 21.582 OK….
Providing 16 mm dia. 2 legged stirrups,
Spacing ' S ' = 206.701 mm
Provide 16 mm dia. 2 legged stirrups, @ 180 mm C/C.
Shear Force Taken = 96.62 > 84.14 Hence OK….
Kg / Cm2
Kg / Cm2
Kg / Cm2
Kg / Cm2
At Section ' C ' :
MAX. Shear force = 300.33 t
SF / Girder = 300.33 75.08 t4
Shear Stress = 75.08 100025 220
13.65
< 21.582 OK….
Providing 16 mm dia. 2 legged stirrups,
Spacing ' S ' = 231.637 mm
Provide 16 mm dia. 2 legged stirrups, @ 180 mm C/C.
Shear Force Taken = 96.62 > 75.08 Hence OK….
At Section ' D ' :
MAX. Shear force = 213.35 t
SF / Girder = 213.35 53.34 t4
Shear Stress = 53.34 100025 220
9.70
< 21.582 OK….
Providing 16 mm dia. 2 legged stirrups,
Spacing ' S ' = 326.071 mm
Provide 16 mm dia. 2 legged stirrups, @ 200 mm C/C.
Shear Force Taken = 86.96 > 53.34 Hence OK….
SHEAR REIFOREMENT DETAILS:
{ 1 } { 2 } { 3 } { 4 } { 5 }
Y X C D
Kg / Cm2
Kg / Cm2
Kg / Cm2
Kg / Cm2
0.4 0.6 1.82.4
3.006.05
Portion Dia. Legged C/C Dist.(No.) (mm) (No.) (mm)
1 12 4 1802 12 4 1803 16 2 1804 16 2 1805 16 2 200
m.m.m.m.
30.04 19.97
Section C ( t )
Section D ( t )
176.23 117.16
0.00 0.00
206.27 137.13
9.7
14.76
9.1
14.16
7.9
12.96
6.7
11.76
3.65
8.71
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
79.057150
237.2 a = 25.46270.9431
200
146.990.31 461.86 420
881.86
q = 71.565051X = 237.17082 mmY = 79.056942 mmZ = 270.94306 mm
X1 = 90.314353 mmT = 146.85647 mm
T1 = 461.85647 mm
5.0 Reiforcement calculations and checking stresses at various section.
a = 25.463345a = 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 mmClear Side Cover = 40 mmDiameter of stirrups = 12 mmDiameter 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 mmOK….
cm2
Provide no. Of bar in 1st Row =
Provide no. Of bar in 2nd Row =
Provide no. Of bar in 3rd Row =
Rein. Spacing (Betwn. In to In ) =
58 mm
64 mm
64 mm
c.g. of steel from bottom of girder, = 11.67 cm
d eff. = 208.33 cm
180 420 22320 3020
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 2nd row =
Distance between centre of 2nd row to centre of 3rd row =
cm2
Sum = 27687.41 1176785
1107.50 47071.39
1107.496 n - 47071.39 4.553E-08Don'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.,
18020
40.99 40 n20
-0.9920.99
(All Dimensions are in cm.)
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
n2 + .= 0
cm4 cm2 h2 (A x h2)
cm4
cm3
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 1930.41882167.35
= 1998.093
214.2 < 2000 OK…….167.35
1930.425.87
(All Dimensions are in cm.)
5.2 AT QUARTER SPAN
Dead Load B.M. = 1254.6021 t.m. for twin box (D.L. + S.I.D.L.)
Design B.M. = 1103.601 t.m. per box.
(All Dimensions are in mm.)250 315
237.1779.057
150
cm3
kg/cm2
kg/cm2
kg/cm2
kg/cm2
kg/cm2
kg/cm2
a = 25.46270.9431
200
146.990.31 461.86 420
881.86
q = 71.565051X = 237.17082 mmY = 79.056942 mmZ = 270.94306 mm
X1 = 90.314353 mmT = 146.85647 mm
T1 = 461.85647 mm
a = 25.463345a = 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
Provide no. Of bar in 1st Row =
Provide no. Of bar in 2nd Row =
Provide no. Of bar in 3rd Row =
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
(All Dimensions are in cm.)
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 0Don't Delete this cell, it is useful for operation of Goal Seek…
M.I. Of the section @ N.A., For finding out Value of n.2
420 x 30.0 ^3 + 420 30 35.966 -15 .= 648348212
2
Distance between end of beam to centre of 1st row =
Distance between centre of 1st row to centre of 2nd row =
Distance between centre of 2nd row to centre of 3rd row =
n2 +
223 x 30.0 ^3 + 223 30 35.966 -15 .= 915549412
2180 x 20 ^3 + 180 20 35.966 -10 .= 1560000
122
36.31 x 15.97 ^3 + 36.31 15.97 15.97 .= 4925512 2
2143.69 x 15.97 ^3 + 1/2 143.69 15.97 15.97 x 2 .= 146197
36 32
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 1745.79797174.19
174.19 214.2
= 1786.309
cm4
cm3
cm3
kg/cm2
kg/cm2
kg/cm2
kg/cm2
kg/cm2
< 2000 OK…….1745.80 4.04
5.3 AT BEGINNING OF WIDENING SECTION
Dead Load B.M. = 730.91405 t.m. for twin box (D.L. + S.I.D.L.)
Design B.M. = 635.78558 t.m. per box.
(All Dimensions are in mm.)250 315
237.1779.057
150a = 25.46
270.9431
200
146.990.31 461.86 420
881.86
q = 71.565051X = 237.17082 mmY = 79.056942 mmZ = 270.94306 mm
X1 = 90.314353 mmT = 146.85647 mm
T1 = 461.85647 mm
kg/cm2
a = 25.463345a = 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 1st Row =
Provide no. Of bar in 2nd Row =
Provide no. Of bar in 3rd Row =
Distance between end of beam to centre of 1st row =
Distance between centre of 1st row to centre of 2nd row =
Distance between centre of 2nd row to centre of 3rd row =
(All Dimensions are in cm.)
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 0.0006016Don't Delete this cell, it is useful for operation of Goal Seek…
M.I. Of the section @ N.A., For finding out Value of n.2
420 x 30 ^3 + 420 30 30.319 -15 .= 3902026.6812
2223 x 30 ^3 + 223 30 30.319 -15 .= 2071790.35
122
180 x 20 ^3 + 180 20 30.319 -10 .= 1606363.9212
287.13 x 10.32 ^3 + 87.13 10.32 10.32 .= 31914.5388
12 2
292.87 x 10.32 ^3 + 1/2 92.87 10.32 10.32 x 2 .= 25515.4848
12 32
10 x 209.078 x 211.25 -30.31942 .= 68440690.8
M.I. Of the section @ N.A., = 75850791 76078301.7
n2 +
cm4
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 1512.00284180.93
214.2
180.93 = 1536.688
< 2000 OK…….1512.00
2.95
CALCULATION OF WEB REIFORCEMENT : (Skin Reinforcement)
2 2Skew 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.
mm2
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 10On Each Faces.
Third raw 7 32Second ra 8 32First raw 9 32
mm2
Don't Delete this cell, it is useful for operation of Goal Seek…
For finding out Value of n.
Don't Delete this cell, it is useful for operation of Goal Seek…For finding out Value of n.
Don't Delete this cell, it is useful for operation of Goal Seek…For finding out Value of n.