Box Girder Computations
Short Description
Box Girder...
Description
BOX GIRDER SUPER STRUCTURE A3 A2
A
A1
T B
M D G C
P
F E L H N O K I
J
I
Q
INPUT DIMENSION (mm) (Designation as per above figure) A= B=
430 200
G= H=
100 250
M= N=
300 315
S= T=
1800 350
S
C= D= E= F=
1800 400 263.5 315
I= J= K= L=
600 3000 200 1700
O= P= Q= R=
150 150 430 600
A1 = A2 = A3 =
350 330 420
420 330 350
Clear Carriage way = 7500 430
0.065 m Wearing Coat 350
200
300 400 100 1800
150
315 263.5 1700 250 315 150 200 600
3000
600
430
1800
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 10. Permissible stresses in concrete 11. Modular Ratio m 12. Density of parapet (t/m)
st (kg / cm2) cbc (kg / cm2)
2000 101.94 10 0.2
Notes:
This box indicate INPUT parameter. This indicate UDL load on span.
16460 OF FOUR LANE BRIDGE
1931.8
7500
7500
CLEAR ROAD WAY
CLEAR ROAD WAY
3936.5 c/c of web of Box girder
4723.5 1800 1700
2200
Elastomeric Bearing RCC Pedestel RCC Pier Cap
2260
mm c/c of pedestel
25000 mm c/c of Pier
2260 mm c/c of pedestel (All Dimensions are in mm)
25000 mm c/c of Pier
Elastomeric Bearing RCC Pedestal RCC Pier cap RCC Pier
RCC Sub Structure
Foundation GROUND LEVEL
RCC Super Structure IN M
30
R
600
25000 mm c/c of Pier
400
200
100
1700
2200
200
C/C of Pier 400
C/C Of Bearing 600 A
SECTIONAL ELEVATION 1-1 2400
9100
OF SYMMETRY
B 263.5
685 315
1
1
3000 c/c of Sofit Box
1843.0 1630
OF BOX GIRDER
315
8660 c/c of Box
685 263.5 25000 Overall Span c/c of Bearing OF PIER
OF bearing A
OF SYMMETRY B
24200 Effective Span c/c of Bearing
PLAN AT SOFFIT LEVEL
JAYESH
DRG-2
BG/DAX/DRG-Section
(2) DESIGN OF CANTILEVER DECK SLAB 430 350
Wearing Coat (m.) 0.065 X
KERB
200
400
1800 X
2.1 DEAD LOAD BENDING MOMENT Dead Load bending moment @ XX, (1) DL due to parapet
0.2
1.8
0.43 2
(2) Parapet kerb = {A*A1 * 2.40 * (C-A/2)} 0.43 0.35 2.4
1.8
0.43 2
(3) Wearing coat = { (C-A) * Thk. Of wearing coat* (C-A/2)} 1.8 0.43 0.065 2.4 1.8 (4) Self weight of slab (a) {(C*B*C/2)*2.40} 1.8 0.2
1.8 2 (b) {1/2*C*(D-B)*(C/3)*2.40} 1 1.8 0.4 2
2.4
0.2
1.8 3
TOTAL DEAD LOAD BENDING MOMENT
2.2 LIVE LOAD BENDING MOMENT 2.2.1 CLASS A Vehicle 0.43
0.43 2
Minimum Clarance (IRC - 6:2000)
2.4
0.317
t.m.
0.573
t.m.
0.146
t.m.
0.778
t.m.
0.259
t.m.
2.073
t.m.
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) a = (C-A) - 0.15 - 0.50/2
=
b1 = 0.25 + 2 (Thk. Of Wearing coat)
0.97 m.
=
Effective Dispersion width bf =1.2 a + b1 1.2 0.97
0.38 m.
0.38
1.544 m.
LIVE LOAD BENDING MOMENT = (Axle load/2) * a * Impact Factor For Class A Axle load 11.40 t Impact factor 50% for cantilever slab as per Fig. 5 Cl. 211.2, IRC-6:2000 LIVE LOAD BENDING MOMENT = (11.40/2) * a * 1.50 11.4 0.97 2
1.5
8.2935 t.m.
2.2.2 CLASS AA Traked Vehicle 0.43
Minimum Clarance in m.(IRC - 6:2000)
Kerb
1.2
Ground contect Area 0.85
1.63
0.17
1.8 As c.g. of loads lying outside, No calculation of B.M. is reqd. Hence class A governs the design. 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 = So, Slab Thk. @ Load center =
0.2
0.43
0.4
0.4
0.2
0.5 2 0.83
0.83 m. 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.
LIVE LOAD BENDING MOMENT / m. Width
=
8.294 1.544
4.423 t.m/m 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 2 LIVE LOAD BENDING MOMENT near expan. gap =
0.897 m. 8.294 0.897
7.613 t.m/m 1.214
(3) SERVICES 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 2
TOTAL BENDING MOMENT (D.L. + L.L. + Services)
0.317 t.m/m
=
(L.L.B.M./m. width taken)
2.073
4.423
6.813
t.m.
For M25 Concrete, m = 10 K=
0.338
j = 1- K/3
=
0.887
Q = 1/2 * cbc * k* j
=
15.272
d reqd. =
21.121 cm.
{d reqd. =
d prov. =
36.2 cm
d Prov. =
d reqd. Hence OK...
<
Ast Reqd. Provide
( Total BM / (Q*100)) } 400 362
d prov.
=
10.60 cm2
12
mm dia @
280
mm c/c
16
mm dia @
280
mm c/c
30(cover) - 16/2(half Dia.) mm
0.317
Ast Provided
11.22 cm2
In Cantilever projection of Box slab.
OK….
For End 1 m. near EXPANSION GAP. TOTAL BENDING MOMENT (D.L. + L.L. + Services) (L.L.B.M. taken at Expansion gap) d reqd. =
25.593 cm.
d prov. =
36.2 cm
d reqd. Hence OK...
<
Ast Reqd.
10.003 t.m.
{d reqd. = Sqrt( Total BM / (Q*100)) } d Prov. = 400 - 30(cover) - 16/2(half Dia.) = 362 mm
d prov.
=
Provide
=
15.57 cm2
12
mm dia @
280
mm c/c
25
mm dia @
280
mm c/c
Ast Provided
21.57 cm2
In Cantilever projection of Box slab.
DISTRIBUTION STEEL B.M. = 0.2 DLBM + 0.3 LLBM
(Cl.305.18.2, IRC : 21-2000)
Dead Load BM = DL + Service = Live Load BM = B.M. B.M.
= =
0.2
2.390
0.3
=
2.809 cm2
Ast Minimum
=
3.6 cm2
Ast Reqd.
=
3.60 cm2
10
Ast Provided Provide Ast Provided
4.423
1.805 t.m.
Ast (Dist.)
Provide
2.390 4.423
mm dia @
150
5.24 cm2 10
mm dia @
140
5.61 cm2
( 12% of gross area)
mm c/c
About top & bottom
OK…. mm c/c
About bottom in span direction.
(in Cantilever portion) OK….
OK….
MAIN STEEL : Throughout 12 mm Tor 280 mm c/c
16 mm Tor 280 mm c/c
Throughout 12
20 mm Tor 280 mm c/c
280
10 mm Tor 140 mm c/c
12 mm Tor
16 mm Tor
12
280 mm c/c
280 mm c/c
280
Throughout
DISTRIBUTION STEEEL :
10 mm Tor 150 mm c/c at bottom
215
2185 JAYESH
10 mm Tor
10 mm Tor
150 mm c/c
150 mm c/c
8 mm Tor
8 mm Tor
150 mm c/c
150 mm c/c
3000
1030 Steel Details
JAYESH
Steel Details
16460 OF FOUR LANE BRIDGE
600
7500 CLEAR ROAD WAY
6 0 A
25 20 mm tor At Top. 6 0
300 16 mm Tor 2 Legged Stirps 180 mm c/c.
16 mm Tor 2 Legged Stirrups 180 mm c/c.
25 20 mm tor At Top.
16 mm Tor 2 Legged Stirrups 180 mm c/c.
16 Tor 1900 180 mm c/c on both faces.
16 Tor 180 mm c/c on both faces. 0 6 1800
430
600
A 6 25 0 20 mm tor At bottom.
3000
600
20 25
1800
400 16 mm Tor 2 Legged Stirrups 180 mm c/c.
mm tor At bottom.
SECTION - AA
CROSS SECTION AT END DIAPHARM
JAYESH
ED-1
C/S Of End Diapharm
LONGITUDINAL GIRDER ( 4 ) LIVE LOAD BENDING MOMENT 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
Mid span moment =
391.63
t.m.
Give value of impact factor = I. F. Give value of Reaction factor = R. F.
Moment With I.F. and R.F.
0.4
= =
1.1 1.2
=
(cl.211.3(b), IRC:6-2000)
516.9516 t.m.
( ii ) Class 70R wheeled Vehicle 17 6.6412
17 . 1.37
A
17 . 3.05
17 . 1.37
E
12 . 2.13
12 . 1.52
8 .
3.96
4.1588
B
12.1 0.4
24.2 RA
0.4 RB
c.g. of load from right of first load = Coincide distance = Moment @ E = 441.49 t.m.
5.1238 m. 5.4588 m.
Give value of impact factor = I. F. Give value of Reaction factor = R. F.
1.18 1.2
= =
Moment With I.F. and R.F.
=
625.15
(From fig. 5 cl.211.3(b), IRC:6-2000)
t.m.
( iii ) Class A Train (Two Lanes) 2.7 2.7 2.66
. 1.10
11.4 . 3.20
11.4 . 1.20.
6.8 . 4.3
A
6.8 . 3.0
6.8 .3.0
E
'6.8 3
2.74 B
12.1 0.4
24.2 c.g. of load from right of first load Coincide distance Distance from A
Moment @ E =
193.28
= = =
4.2 Max moment at quarter span.
9.09 m. 9.44 m. 2.66 m.
t.m.
Give value of impact factor = I. F. Give value of Reaction factor = R. F.
Moment With I.F. and R.F.
0.4
= =
=
1.18 1.2
547.37
(From fig. 5 cl.211.3(b), IRC:6-2000)
t.m.
( i ) Class AA Tracked Vehicle Quarter of load distance (i.e. 1/4 X 3.6 m) = 0.9
70 T
3.6
6.05 0.4
24.2 Mid span moment =
293.67
0.4
t.m.
Give value of impact factor = I. F. Give value of Reaction factor = R. F.
Moment With I.F. and R.F.
= =
1.1 1.2
=
( cl.211.3(b), IRC:6-2000)
387.6444 t.m.
( ii ) Class 70R wheeled Vehicle 17 4.68
17 . 1.37
17 . 3.05
17 . 1.37
A
12 . 2.13
12 . 1.52
E
8 .
3.96
6.1200
B
6.05 0.4
24.2
0.4
c.g. of load from right of first load = Coincide distance = Moment @ E = 336.37 t.m.
5.1238 m. 5.4588 m.
Give value of impact factor = I. F. Give value of Reaction factor = R. F.
1.18 1.2
= =
(From fig. 5 cl.211.3(b), IRC:6-2000)
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
1.1
11.4
3.2
6.8
1.20.
4.3
A
6.8 3.0 .
6.8 .3.0
'6.8 3.65
3.0
E
B
6.05 0.4
24.2
0.4 23.1
Moment @ E =
164.65
t.m.
Give value of impact factor = I. F. Give value of Reaction factor = R. F.
= =
Moment With I.F. and R.F.
=
1.18 1.2
(From fig. 5 cl.211.3(b), IRC:6-2000)
466.2888 t.m.
4.3 Max moment at 3 m from left of span. ( i ) Class AA Tracked Vehicle 70 T 3.6
3 0.4
24.2 Mid span moment =
162.80
Give value of impact factor = I. F.
0.4
t.m. =
1.1
(cl.211.3(b), IRC:6-2000)
Give value of Reaction factor = R. F.
=
Moment With I.F. and R.F.
1.2
=
214.90
t.m.
( ii ) Class 70R wheeled Vehicle 17 3
17 . 1.37
17 . 3.05
17 . 1.37
A
12 . 2.13
12 . 1.52
8 .
3.96
7.8000
E
B
3 0.4
24.2 c.g. of load from right of first load Moment @ E =
190.91
=
5.1238 m.
= =
1.18 1.2
t.m.
Give value of impact factor = I. F. Give value of Reaction factor = R. F.
Moment With I.F. and R.F.
0.4
=
270.33
(From fig. 5 cl.211.3(b), IRC:6-2000)
t.m.
( iii ) Class A Train (Two Lanes) 11.4
11.4 1.2
A
6.8 4.3
E 3
0.4
6.8 3.0 .
6.8 3.0 .
6.8 .3.0
9.5
B 21.2
24.2
0.4
Moment @ E =
90.17
t.m.
Give value of impact factor = I. F. Give value of Reaction factor = R. F.
Moment With I.F. and R.F.
= =
=
1.18 1.2
(From fig. 5 cl.211.3(b), IRC:6-2000)
255.3614 t.m.
RECAPITULATION OF LIVE LOAD BENDING MOMENTS Load Discription
BENDING MOMENT (in tm) .@ Mid Span
@ Quarter Span
@ Widening.
Beginning of
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
625.150
476.30
270.33
DESIGN BM
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.
0.3612
t/m.
0.2
t/m.
3.3012
t/m.
Kerb
=
= Area X Density
=
Services = 0.1 t/m
= Total SIDL
=
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) Bending Moment at quarter span (D) Bending Moment at Widening (C)
= = =
241.4003 t.m. 180.9842 t.m. 104.7141 t.m.
Dead Load Bending Moment due to self wt. of Super Structure C/S Area of box at mid span = udl
A
C
=
D
8.069
m2
19.37
t/m.
19.37
t/m.
E
3.00 0.4
6.05 12.1 24.2 12.5 25 Reaction at A & B =
242.07
t
B
Bending Moment at mid span (E) Bending Moment at quarter span (D) Bending Moment at Widening (C)
= = =
1416.11 t.m. 1061.695 t.m. 614.2768 t.m.
Dead Load Bending Moment due to widening C/S Area of box at End span C/S Area of box at mid span
= =
10.86 8.069
m2 m2
Difference of C/S Area
=
2.791
m2
Wt./R.m.(A X Density)
=
6.6984
t/m.
1 2.4
m. m.
Total Length of END Beam Length of Taperd Section of Beam
= =
6.6984 t/m.
A
C
6.6984
D 2.4
0.6
E
B
3.0 0.4
6.05 12.1 24.2 12.5 25 Reaction at A & B =
14.74
t
Bending Moment at mid span (E) Bending Moment at quarter span (D) Bending Moment at Widening (C)
= = =
11.92315 t.m. 11.92315 t.m. 11.92315 t.m.
Total Reaction @ A & B ( i.e. Total DL due to half Span ) = Total DL of Super Structure =
NOTE :
298.07 t 597 t
Put All Geometry in STAAD Analysis and Varify above data.
Summary of DLBM
Sr .No.
LOAD
1
SIDL
2 3
At At MID Quarter At Span (E) Span (D) Widening 't.m' 't.m' (C) 't.m' 241.4003
180.9842 104.71406
Self Wt.of Box (Running Section)
1416.11
1061.695 614.27683
Widning (Self Weight)
11.92315
11.92315 11.923152
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.
0.3612
t/m.
0.2
t/m.
3.3012
t/m.
Kerb
=
= Area X Density
=
Services = 0.1 t/m
= Total SIDL
=
3.3012 t/m. Y X 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
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 Shear Force, .@ A .@ Y .@ X .@ C .@ D
41.265 39.945 39.945 39.945 39.945
3.3012 3.3012 3.3012 3.3012 3.3012
0.4 0.6 1.8 3.0 6.05
39.945 37.964 34.002 30.041 19.972
0.6 1.8 3.00 6.05
t t t t t
Dead Load Shear Force due to self wt. of Super Structure 19.37 t/m. Y X A
C
D
E
B
3.00 0.4
6.05 12.1 24.2 12.5 25 Reaction at A & B =
242.07
Shear Force, .@ A 242.07 .@ Y 234.324 .@ X 234.324 .@ C 234.324 .@ D 234.324
t
19.37 19.37 19.37 19.37 19.37
0.4 0.6 1.8 3.00 6.05
234.324 222.704 199.466 176.227 117.162
t t t t t
Dead Load Shear Force due to widening 6.698 t/m. Y A
6.698 t/m.
X C
D 2.4
0.6
E
B
3.0 0.4
6.05 12.1 24.2 12.5 25 Reaction at A & B = Shear Force, .@ A 14.74 .@ Y 12.057 .@ X 8.038 .@ C 8.038 .@ D 0.000
14.74
6.70 6.70 5.02 3.35 0.00
t
0.4 0.6 1.2 2.4 6.05
12.057 8.038 2.010 0.000 0.000
t t t t t
Total Reaction @ A & B ( i.e. Total DL due to half Span ) = Total DL of Super Structure =
NOTE :
298.07 t 597 t
Put All Geometry in STAAD Analysis and Varify above data.
Summary of DLSF
Sr .No.
LOAD
1
SIDL
Section A Section Y Section X (t) (t) (t) 39.94
37.96
34.00
2
Self Wt.of Box (Running Section)
234.32
222.70
199.47
3
Widning (Self Weight)
12.06
8.04
2.01
286.33
268.71
235.48
TOTAL DLSF ( t ) =
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 . 1.20.
6.8 . 4.3
6.8 . 3.0
6.8 .3.0
'6.8 9.7
3
B 24.2
RA
=
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
RA
=
70
22.4 24.2 64.79 t
S.F.@support with R.F. & I.F. (For Two Lane) 64.79 85.527 t
1.1
1.2
( C ) Class 70R Wheeled Vehicle 17
17 . 1.37
17 . 3.05
17 . 1.37
12 . 2.13
12 . 1.52
8 .
3.96
10.800
B 24.2 RA
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 RECAPITULATION OF LIVE LOAD SHEAR FORCE At SUPPORT Sr. No. 1 2 3
LOADING
S.F. ( t )
Class A ( 2 lane) Class AA Traked 70R wheeled Vehicle
AT Section - ' Y '
(
0.6
108.168 85.527 111.619
) m. From support
( A ) Class A Two Lane Vehicle 11.4
11.4
0.6 . 1.20.
6.8 . 4.3
6.8 . 3.0
6.8 .3.0
'6.8 9.1
3
B 24.2
RA
=
11.4
23.6
22.4
6.8 24.2
36.96 t S.F.@support with R.F. & I.F. (For Two Lane)
18.1
15.1
12.1
36.96
1.18
1.2
2
104.658 t
( B ) Class AA Traked Vehicle 70 t 0.6 A
B 3.60 24.2
RA
=
70
21.8 24.2 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
0.60 . 1.37
17 . 3.05
17 . 1.37
12 . 2.13
12 . 1.52
8 .
3.96
10.200
B 24.2 RA
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 RECAPITULATION OF LLSF At Sr. No.
LOADING
0.6
m.From Support. S.F. ( t )
1 2 3
Class A ( 2 lane) Class AA Traked 70R wheeled Vehicle
AT Section - ' X '
(
1.8
104.658 83.236 108.109
) m. From support
( A ) Class A Two Lane Vehicle 11.4
11.4
1.8 . 1.20.
6.8 . 4.3
6.8 . 3.0
6.8
'6.8
.3.0
7.9
3
B 24.2
RA
=
11.4
22.4
21.2
6.8
16.9
13.9
10.9
24.2 34.48 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 Vehicle 70 t 1.8 A
B 3.60 24.2
RA
=
70
20.6 24.2 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 1.80 . 1.37
17
17 . 3.05
17 . 1.37
12 . 2.13
12 . 1.52
8 .
3.96
9.000
B 24.2 RA
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 RECAPITULATION OF LLSF At Sr. No. 1 2 3
1.8
m.From Support.
LOADING
S.F. ( t )
Class A ( 2 lane) Class AA Traked 70R wheeled Vehicle
AT Section - ' C '
(
3.00
97.636 78.655 101.087
) m. From support
( A ) Class A Two Lane Vehicle 11.4
11.4
3.00 . 1.20.
6.8 . 4.3
6.8 . 3.0
6.8 .3.0
'6.8 6.7
3
B 24.2
RA
=
11.4
21.2
20
6.8 24.2
32.00 t S.F.@support with R.F. & I.F. (For Two Lane) 32.00
1.18
90.615 t
( B ) Class AA Traked Vehicle
1.2
2
15.7
12.7
9.7
70 t 3.0 A
B 3.60 24.2
RA
=
70
19.4 24.2 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
3.00 . 1.37
17 . 3.05
17 . 1.37
12 . 2.13
12 . 1.52
8 .
3.96
7.800
B 24.2 RA
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 RECAPITULATION OF LLSF At Sr. No. 1 2 3
AT Section - ' D '
3
LOADING Class A ( 2 lane) Class AA Traked 70R wheeled Vehicle
(
6.05
) m. From support
m.From Support. S.F. ( t ) 90.615 74.073 94.066
( A ) Class A Two Lane Vehicle 11.4
11.4
6.05 . 1.20.
6.8 . 4.3
6.8 . 3.0
6.8
'6.8
.3.0
3.65
3
B 24.2
RA
=
11.4
18.15
16.95
6.8
12.65
9.65
6.65
24.2 25.70 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 Vehicle 70 t 6.1 A
B 3.60 24.2
RA
=
70
16.35 24.2 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 6.05 . 1.37
17
17 . 3.05
17 . 1.37
12 . 2.13
12 . 1.52
8 .
3.96
4.750
B 24.2 RA
RB
RA
=
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 RECAPITULATION OF LLSF At Sr. No. 1 2 3
6.05
m.From Support.
LOADING
S.F. ( t )
Class A ( 2 lane) Class AA Traked 70R wheeled Vehicle
72.768 62.427 76.219
RECAPITULATION OF DL & LL SHEAR @ VARIOUS SECTION Sr. No.
S.F. Due To Support
Shear Force At Section in Tonne 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
SF / Girder
=
397.94 4
Shear Stress
=
99.49 65 6.96 21.582
<
Providing
12
mm dia.
4
t 99.49 t
1000 220 Kg / Cm2 Kg / Cm2
OK….
legged stirrups,
Spacing Provide
12
'S'
=
mm dia.
Shear Force Taken =
196.672 mm 4
legged stirrups, @
108.70
>
99.49
180
mm C/C.
Hence OK….
At Section ' Y ': MAX. Shear force =
376.81
SF / Girder
=
376.81 4
Shear Stress
=
94.20 65 6.59 21.582
<
Providing
12 Spacing
Provide
12
mm dia. 'S'
=
mm dia.
Shear Force Taken =
4
t 94.20 t
1000 220 Kg / Cm2 Kg / Cm2
OK….
legged stirrups,
207.700 mm 4
legged stirrups, @
108.70
>
94.20
180
mm C/C.
Hence OK….
At Section ' X ': MAX. Shear force =
336.56
SF / Girder
=
336.56 4
Shear Stress
=
84.14 45 8.50 21.582
<
Providing
16 Spacing
Provide
16
mm dia. 'S'
=
mm dia.
Shear Force Taken =
2
t 84.14 t
1000 220 Kg / Cm2 Kg / Cm2
OK….
legged stirrups,
206.701 mm 2 96.62
legged stirrups, @ >
84.14
180
mm C/C.
Hence OK….
At Section ' C ' : MAX. Shear force =
300.33
SF / Girder
=
300.33 4
Shear Stress
=
75.08 25 13.65 21.582
<
Providing
16 Spacing
Provide
16
mm dia. 'S'
2
=
t 75.08 t
1000 220 Kg / Cm2 Kg / Cm2
OK….
legged stirrups,
231.637 mm
mm dia.
2
Shear Force Taken =
legged stirrups, @
96.62
>
75.08
180
mm C/C.
Hence OK….
At Section ' D ' : MAX. Shear force =
213.35
SF / Girder
=
213.35 4
Shear Stress
=
53.34 25 9.70 21.582
<
Providing
16 Spacing
Provide
16
mm dia. 'S'
2
=
t 53.34 t
1000 220 Kg / Cm2 Kg / Cm2
OK….
legged stirrups,
326.071 mm
mm dia.
2
Shear Force Taken =
86.96
legged stirrups, @ >
53.34
200
Hence OK….
SHEAR REIFOREMENT DETAILS: {1}
{2}
Y
{3}
X
{4}
C
{5}
D
mm C/C.
0.4
0.6
1.8 2.4 3.00 6.05
Portion (No.) 1 2 3 4 5
Dia. (mm) 12 12 16 16 16
Legged (No.) 4 4 2 2 2
C/C Dist. (mm) 180 180 180 180 200
m. m. m. m.
Section C Section D (t) (t) 30.04
19.97
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
5.0 Reiforcement calculations and checking stresses at various section. 5.1 AT MID SPAN Dead Load B.M. Design B.M.
= =
1669.43
t.m. for twin box (D.L. + S.I.D.L.)
1459.87
t.m. per box.
(All Dimensions are in mm.) 250
315
79.057 150
25.46
237.2 270.9431
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
48
Nos. of
Ast =
32
Tor in
3
rows
385.991 cm2
Provide Clear Cover
=
30
mm
Provide dia. Of Stirups
=
12
mm
Provide no. Of bar in 1st Row Provide no. Of bar in 2nd Row Provide no. Of bar in 3rd Row Total
= = = =
18 16 14 48
no. no. no. OK…….
Rein. Spacing (Betwn. In to In ) = Clear Side Cover = Diameter of stirrups = Diameter of Main Bar =
50 40 12 32
mm mm mm mm
NO. OF BAR in First raw
9
Provision of No. of BAR in First Row
=
Total Distance, 9
32 792 mm
8
50 <
2 881.86 mm OK….
12
2
40
Distance between end of Soffit to centre of 1 st row Distance between centre of 1st row to centre of 2nd row
= =
58 64
mm mm
Distance between centre of 2nd row to centre of 3rd row
=
64
mm
c.g. of steel from bottom of girder, = d eff. 180
11.67
cm
= 208.33 cm
420
223
20 20
30 31.5 [2]
n 10
[1]
[5]
43
15
[4] 25 [6] [7]
(All Dimensions are in cm.)
Portion
Length cm
Depth cm
c.g. from Top (cm)
REMARK
NO.
[1] [2] [3] [4] [5] [6] [7]
420 180 223 180 31.5 43
30 20 30 20 10 15 25
15 10 15 26.67 33.33 35 30
Rectangle Rectangle Rectangle Triangle Triangle Triangle
1 1 1 1 2 1 2
Due to Reinforcement
AREA cm2 X n 12600 3600 6690 1800 315.00 322.5 -1500
189000 36000 100350 48000 10500 11287.5 22500
3859.9066 804147.2
[3]
Sum
n2 + 1107.496 n
=
27687.41
1176785
1107.50
47071.39
- 47071.39 .= 0
N.A. from Top of girder =
4.55E-008 Don't Delete this cell, it is useful for
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 (All Dimensions are in cm.) Portion
[1] [2] [3] [4]
Length cm
Depth cm
420 30 180 20 223 30 85.56416 20.985743 180 20
Section Modulus at Compression,
c.g. from Top (cm) 15 10 15 26.67
Zc =
REMARK
M.I. cm4
AREA cm2
M.I. + (A x h2)
h
2
Rectangle 945000 12600 675.2588 Rectangle 120000 3600 960.1163 Rectangle 501750 6690 675.2588 Eq. Rectn. 65899.73 1795.6274 220.2007 Triangle 40000 1800 205.0359
9453261.2 3576418.5 5019231.5 461298.14 409064.69
Due to Reinforcement
=
108097517
M.I. Of section @ N.A.,
=
126555493 cm4
3087793 cm3
Section Modulus at Tension, Stresses in Concrete
Stresses in Steel
Zt =
756243.29 cm3
=
47.278631 kg/cm2 < 101.94 kg/cm2
OK…….
1930.4188 kg/cm2 < 2000 kg/cm2
OK…….
= 47.28
40.99
Stress in Outer layer,
167.35
+ 167.35
5.87
= 1998.093 kg/cm2 < 2000 kg/cm2
214.2 167.35 1930.42 5.87 (All Dimensions are in cm.)
5.2 AT QUARTER SPAN Dead Load B.M. Design B.M.
= =
1254.6021 t.m. for twin box (D.L. + S.I.D.L.) 1103.601 t.m. per box.
(All Dimensions are in mm.) 250
315
237.17 79.057 150
1930.41882
OK…….
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 Ast =
Nos. of
32
Tor in
305.576 cm2
Provide Cover
=
30
mm
Provide dia. Of Stirups
=
12
mm
18 16 4 38
no. no. no. OK…….
Provide no. Of bar in 1st Row = Provide no. Of bar in 2nd Row = Provide no. Of bar in 3rd Row = Total =
3
rows
Distance between end of beam to centre of 1 st row Distance between centre of 1st row to centre of 2nd row
= =
58 64
mm mm
Distance between centre of 2nd row to centre of 3rd row
=
64
mm
c.g. of steel from bottom of box,
=
d eff. 180
9.84
cm
= 210.16 cm
420
223
20
n
30
(All Dimensions are in cm.) 420 x n x n/2 +
223 411.5
x n x n/2 +
n2
+
180 3055.7594
N.A. from Top of girder
x n x n/2 +
n
-
=
35.97
+
420
.= 10 x
305.576
x(
210.16 .-n )
642192 .= 0
cm
0 Don't Delete this cell, it is useful for For finding out Value of n.
M.I. Of the section @ N.A., 2 420
x 12
30.0
^3
30
35.966
-15
.= 2
6483482
223
x 12
180
30.0
^3
+
223
30
35.966
-15
x 12
20 ^3
+
180
20
35.966
-10
36.31
x 12
15.97 ^3
+
36.31
15.97
15.97 2
143.69
x 36
15.97 ^3
+ 1/2
143.69
15.97
x
210.16 -35.96574
.=
9155494
.=
1560000
.=
49255
.=
146197
2
2
2 15.97 x 2 3
2 10 x
305.576
.= 92720625.3 M.I. Of the section @ N.A., =
Section Modulus at Compression, Section Modulus at Tension, Stresses in Concrete
Stresses in Steel
Zc = Zt =
3061665 cm3 632147 cm3
=
36.04577 kg/cm2 < 101.94 kg/cm2
OK…….
1745.798 kg/cm2 < 2000 kg/cm2
OK…….
=
110115054 cm4
36.05 35.97 Stress in Outer layer, 174.19
174.19
+ 174.19
4.04
214.2 = 1786.309 kg/cm2
1745.79797
< 2000 kg/cm2 1745.80
4.04
5.3 AT BEGINNING OF WIDENING SECTION Dead Load B.M. Design B.M.
= =
730.91405 t.m. for twin box (D.L. + S.I.D.L.) 635.78558 t.m. per box.
(All Dimensions are in mm.) 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
OK…….
25.463345 a= 420 mm Provide
26 Ast =
Nos. of
32
Tor in
Provide Cover
=
30
mm
Provide dia. Of Stirups
=
12
mm
Provide no. Of bar in 1st Row Provide no. Of bar in 2nd Row Provide no. Of bar in 3rd Row Total
= = = =
14 12 0 26
no. no. no. OK…….
c.g. of steel from bottom of box, d eff.
20
rows
209.078 cm2
Distance between end of beam to centre of 1 st row Distance between centre of 1st row to centre of 2nd row Distance between centre of 2nd row to centre of 3rd row
180
3
=
8.75
= = =
58 64 64
mm mm mm
cm
= 211.25 cm
420
223 30
n
(All Dimensions are in cm.) 420 x n x n/2 +
223 411.5
x n x n/2 +
n2
+
180 2090.7827
N.A. from Top of girder
=
x n x n/2 +
.= 10 x
n
441669.8 .= 0
-
209.078
x(
211.25 .-n )
30.3194 cm
0.0006016 Don't Delete this cell, it is useful for For finding out Value of n.
M.I. Of the section @ N.A., 2 420
x 12
30
^3
+
420
30
30.319
-15
223
x 12
30
^3
+
223
30
30.319
-15
180
x 12
20 ^3
+
180
20
30.319
-10
87.13
x 12
10.32 ^3
+
87.13
10.32
10.32 2
92.87
x 12
10.32 ^3
+ 1/2
92.87
10.32
.= 3902026.68 2 .= 2071790.35 2 .= 1606363.92
2 .= 31914.5388
2 10.32 x 2 3
.= 25515.4848
2 10 x
209.078
x
M.I. Of the section @ N.A., =
211.25 -30.31942 75850791 cm4
.= 68440690.8 76078301.7
Section Modulus at Compression, Section Modulus at Tension,
Zc = Zt =
2509227 cm3 420492.3 cm3
=
25.33791 kg/cm2 < 101.94 kg/cm2
OK…….
1512.003 kg/cm2 < 2000 kg/cm2
OK…….
Stresses in Concrete
Stresses in Steel
=
25.34 30.32 Stress in Outer layer,
180.93
+ 180.93
2.95
1512.00284
214.2 180.93
= 1536.688 kg/cm2 < 2000 kg/cm2
1512.00 2.95
CALCULATION OF WEB REIFORCEMENT : (Skin Reinforcement)
As per Cl.305.10, IRC - 21:2000, Min. Shrinkage reiforcement shall be 250 mm 2 of Steel area per metre. 2 Skew Web Dimension : Length = Width = Total Steel Req.
=
1897.37
2
1800 250 250
600
1897.3666 mm
mm 474.34
mm2
OK…….
1000 Provide
7
Numebrs
10
mm
at top and bottom.
0
mm
at top and bottom.
+ Provide
0
Ast provided
Numebrs
=
549.710
mm2
7 10 On Each Faces.
Third raw Second ra First raw
7 8 9
32 32 32
OK….
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.
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