il & fs
DESCRIPTION
limit state design.TRANSCRIPT
IL & FS TRANSPORTATION NETWORKS LTD. 402, Shivalik II, Nr. Shivranjani Cross Road, Satellite, Ahmedabad 380015 Tel: +91 79 29297388 Fax: +91 79 30420175
OFFICE OF ORIGIN
DNDA - Ahmedabad
OWNER
IL & FS Transportation Networks LTD.
CLIENT
NATIONAL HIGHWAY AUTHORITY OF INDIA
PROJECT
TITLE
Design of Superstructure of Minor BridgeAt Chainage: 134.203 & 132.610
DATE Rev. No. MODIFICATIONS/PURPOSE OF ISSUE Name Signature Name Signature Name Signature
21.01.2014 R0 For Approval NT BVR SCM
21.01.2014 DN- 08-2801 R0
Construction of 4-Laned Highways from Khed to Sinnar Section of NH-50 (KM 42.000 to 177.000) in the state of Maharashtra
PREPARED CHECKED APPROVED
DATE This note is property of IL & FS TRANSPORTATION NETWORKS LTD. it should not be used, copied or reproduced without their written permission.
Rev.No. NOTE NO.
S.No.
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Deflection Check
Interface Shear Check
Design of Diaphragms
Design of Deck Slab
Stress Check
Crack Width Check
Table of Contents
Serviceability Limit State
Title
Introduction
Design Basic Data
Properties of Longitudinal and Cross-girders
Design Methodology
Loads
Analysis Results
Design
Forces due to Differential Shrinkage
Temperature Stresses
1.0 INTRODUCTION
GENERAL ARRANGEMENT OF SUPERSTRUCTURE
This design note deals with the design of simply supported RCC precast T Girder at design chainage
134.203 The overall span is 18.70 m between C/C distances of expansion joints. RCC T Girder
is proposed under the pavement of 2 lanes of carriageway with footpath. The RCC T-Girder
is supported over RCC abutment.
The camber/superelevation is adjusted in pedestals supporting superstructure. The minimum height of
pedestal is considered as 0.25m. The pot PTFE bearings are provided over the pedestals below the
superstructure.
Expansion joint of 40mm has been provided between the spans. The clear cover for reinforcement is
considered as
NOTE : This design of super structure is also adopted for Minor bridge at Ch: 132.610
CODES
The superstructure shall be designed as per the following codes:
IRC: 6-2010 Standard specifications & Code of practice for road bridges, Section II
IRC: 112-2011 Code of practice for Concrete road bridges
MATERIALS
The materials used for the project are as under
Characteristic strength of concrete "fck" :
RCC Girder, Cross girder & Slab = M 40 N/mm2
Crash Barrier = M 40 N/mm2
Characteristic strength of steel "fyk" = Fe 500
Type of bearing = Elastomeric
0.04 m
Type of bearing = Elastomeric
Type of Expansion Joints = Strip seal exp joints
Environmental exposure = Moderate
Density of concrete = t/m3
Density of green concrete = t/m3
Density of wearing coat = t/m3
2.0 DESIGN BASIC DATA
Seismic Zone =
Overall span = m
C/C of Bearing & Expansion joint on LHS = m
C/C of Bearing & Expansion joint on RHS = m
C/C of bearing = m
O/O width of superstructure = m
Width of carriageway = m
Dimensions of footpath (b x h) = x m
Dimensions of crash barrier (b x h) = x m
Dimensions of railing (b x h) = x m
Dimensions of Kerb (b x h) = x m
Depth of slab = m
Depth of precast girder = m
Thickness of wearing coat = m
Clear cover = m
C/C dist between girders = m
Cantilever dist of slab from the centre of outer girder = m
No. of Longitudinal girders = Nos.
No. of Cross girders = Nos.
III
0.000
0.500 0.900
0.200 0.700
1.500
0.300
4
2
2.5
2.2
0.065
18.700
17.200
1.600
0.225
0.040
2.7
12.000
9.000
1.500
0.750
0.750
3.000
0.500
Web tapering details:
Width of web in end portion of girder, bwe = m
Width of web at end of tapering, bw = m
Length of end portion of girder, le = m
Length of tapered portion, lt = m
Girder Details:
Width of top flange of girder = m
Depth of top flange of girder = m
Width of bottom flange of girder = m
Depth of bottom flange of girder = m
Top flange haunch depth at end portion of girder = m
Top flange haunch depth at mid portion of girder = m
Bottom flange haunch depth at end portion of girder = m
Bottom flange haunch depth at mid portion of girder = m
Cross-girder details:
Depth of end cross girder+slab = m
Width of top flange of end cross girder = m
Depth of top flange of end cross girder = m
Width of web of end cross girder = m
Width of top flange haunch of end cross girder = m
Depth of top flange haunch of end cross girder = m
0.450
0.250
0.064
0.100
0.000
0.000
0.000
0.100
0.400
0.000
0.400
0.450
0.250
0.900
0.900
1.575
0.800
0.150
Depth of intermediate cross girder = m
Width of top flange of intermediate cross girder = m
Depth of top flange of intermediate cross girder = m
Width of web of intermediate cross girder = m
Width of top flange haunch of intermediate cross girder = m
Depth of top flange haunch of intermediate cross girder = m
Span of cross girder in service condition = m
Mid-Span of cross girder in jacking condition = m
Total length of cross girder = m
c/c dist between cross girders in longitudinal direction = m
DESIGN CONSTANT
Partial mat. safety factor for conc "γm" = Basic (pg-49, IRC:112-2011)
Partial mat. safety factor for steel "γs" = Basic (pg-33, IRC:112-2011)
Ultimate Comp strain in conc "εcu2" = (tb:6.5, IRC:112-2011)
Modulus of elaticity of steel "E" = N/mm2
Modulus of elasticity of conc "Ecm" = N/mm2
(tb:6.5, IRC:112-2011)
Design compressive strength of conc "fcd" (0.67*fck/γm) = N/mm2
Design tensile strength of steel "fyd" (fyk/γs) = N/mm2
Design yield strength of shear rein. "fywd" (0.8*fyk/γs) = N/mm2
(pg-86, IRC:112-2011)
0.000
0.000
3.000
434.78
0.0035
200000
0.000
1.500
9.000
0.000
347.83
17.200
0.000
0.000
1.5
1.15
33000
17.867
DIAGRAM
beff1 beff2
b1 bw b2
b
As per clause 7.6.1.2 of IRC: 112-2011, the effective width of flange of a girder is as under:
Effective width of Longitudinal girder:
beff = beff1 + beff2 + bw
beff1 = 0.2*b1 + 0.1*lo ≤ 0.2*lo
beff2 = 0.2*b2 + 0.1*lo ≤ 0.2*lo
3.000
(CROSS SECTION OF SUPERSTRUCTURE)
b1 b2
beff
1.5
For inner girder:
lo = m
b1 = m
b2 = m
beff1 = < and
beff2 = < and
beff = m
For outer girder:
lo = m
b1 = m
b2 = m
beff1 = < and
beff2 = < and
beff = m
1.375
1.375
17.200
0.2lo = b1 =
0.2lo = b2 =
0.2lo =
0.2lo =
b1 =
b2 =
1.995 3.44
1.995 3.44
17.200
3
(LONGITUDINAL SECTION OF GIRDER)
0.900.900
1.375
1.375
1.375
0.900 15.100 0.90
1.995
3.44
3.44
3
1.375
1.375
1.375
1.995
Effective width of End Cross girder:
beff = beff1 + beff2 + bw
beff1 = 0.2*b1 + 0.1*lo ≤ 0.2*lo
beff2 = 0.2*b2 + 0.1*lo ≤ 0.2*lo
lo = m
b1 = m
b2 = m
beff1 = < and
beff2 = < and
beff = m
0.750
8.4
0.45 0.2lo =
0.750
0.400
1.450
0.6 b1 = 0.75
1.98 0.2lo = 0.6 b2 = 8.4
3.000
0.550
beff = m1.450
PROPERTIES OF LONGITUDINAL & CROSS GIRDERS
PROPERTIES OF OUTER GIRDER AT SECTION : = m
(A) GIRDER ALONE PROPERTY:
3.0
0.000 L
0.80
0.15
0.064
0.175
1.600
0.45
0
0
0.25
0
1
2
3
4
5
6
7
Extreme Fiber from bottom = 0.672 / 0.784
= m
M.I. (composite) = 0.0558 + 0.1273
= m4
0.858
0.1831
T O T A L 0.784 0.672 0.1273 0.055798
0.45 x 0.064 0.029 1.418 0.041 0.0090 0.000010
0.45 x 0 0.000 0.250 0.000 0.0000 0.000000
0.8 x 0.15 0.120 1.525 0.183 0.0535 0.000225
0.175 x 0.064 0.011 1.429 0.016 0.0037 0.000003
1.136 x 0.45 0.511 0.818 0.418 0.0008 0.054975
0 x 0 0.000 0.250 0.000 0.0000 0.000000
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.0604 0.000586
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
A.yb A.yb2
0.45
Section modulus (bottom) Zb = 0.183 / 0.858
= m3
Section modulus (top) Zt = 0.183 / 0.742
= m3
(B) PROPERTY OF COMPOSITE SECTION:
0.8 0.15
0.064
0.175
0.214
0.247
3
0.225
1
2
3
4
5
6
7
8
T O T A L 1.459 1.828 0.3924 0.058646
3 x 0.225 0.675 1.713 1.156 0.1424 0.002848
0.45 x 0.064 0.029 1.418 0.041 0.0008 0.000010
0.45 x 0 0.000 0.250 0.000 0.0000 0.000000
0.8 x 0.15 0.120 1.525 0.183 0.0089 0.000225
0.175 x 0.064 0.011 1.429 0.016 0.0003 0.000003
1.136 x 0.45 0.511 0.818 0.418 0.0968 0.054975
0 x 0 0.000 0.250 0.000 0.0000 0.000000
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.1432 0.000586
0
0
0.25
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
1.600
0.45
Extreme Fiber from bottom = 1.828 / 1.459
= m
M.I. (composite) = 0.0586 + 0.3924
= m4
Section modulus (bottom of girder) Zgb = 0.451 / 1.253
= m3
Section modulus (top of slab) Zst = 0.451 / 0.572
= m3
Section modulus (bottom of slab) Zsb = 0.451 / 0.347
1.253
0.4510
0.36
0.789
= m3
First moment of Area of girder above N.A. = ( 0.12 x 0.272 ) + ( 0.011 x 0.175 ) + ( 0.029 x 0.165)
( 0.06 x 0.066 )
= m3
First Moment of Area of composite secton above N.A.
= ( 0.12 x 0.272 ) + ( 0.011 x 0.175 ) + ( 0.029 x 0.165)
( 0.06 x 0.066 ) ( 0.675 x 0.459 )
= m3
0.353
1.3
0.043
PROPERTIES OF OUTER GIRDER AT SECTION : = m
(A) GIRDER ALONE PROPERTY:
0.25
0.174 L
0.80
0.15
0.1
0.275
1.600
0.25
0.1
0.1
2.99
1
2
3
4
5
6
7
Extreme Fiber from bottom = 0.494 / 0.57
= m
M.I. (composite) = 0.0217 + 0.1408
= m4
0.866
0.1625
T O T A L 0.570 0.494 0.1408 0.021707
0.25 x 0.1 0.025 1.400 0.035 0.0071 0.000021
0.25 x 0.1 0.025 0.300 0.008 0.0080 0.000021
0.8 x 0.15 0.120 1.525 0.183 0.0520 0.000225
0.275 x 0.1 0.028 1.417 0.039 0.0083 0.000015
1 x 0.25 0.250 0.850 0.213 0.0001 0.020833
0.003 0.0034 0.000006
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.0618 0.000586
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
0.1 x 0.1 0.010 0.283
Section modulus (bottom) Zb = 0.163 / 0.866
= m3
Section modulus (top) Zt = 0.163 / 0.734
= m3
(B) PROPERTY OF COMPOSITE SECTION:
0.8 0.15
0.1
0.275
0.188
0.222
3
0.225
1
2
3
4
5
6
7
8
T O T A L 1.245 1.650 0.3620 0.024554
3 x 0.225 0.675 1.713 1.156 0.1013 0.002848
0.25 x 0.1 0.025 1.400 0.035 0.0001 0.000021
0.25 x 0.1 0.025 0.300 0.008 0.0263 0.000021
0.8 x 0.15 0.120 1.525 0.183 0.0048 0.000225
0.275 x 0.1 0.028 1.417 0.039 0.0002 0.000015
1 x 0.25 0.250 0.850 0.213 0.0564 0.020833
0.1 x 0.1 0.010 0.283 0.003 0.0109 0.000006
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.1620 0.000586
0.1
0.1
0.25
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
1.600
0.25
Extreme Fiber from bottom = 1.65 / 1.245
= m
M.I. (composite) = 0.0246 + 0.362
= m4
Section modulus (bottom of girder) Zgb = 0.387 / 1.325
= m3
Section modulus (top of slab) Zst = 0.387 / 0.5
= m3
Section modulus (bottom of slab) Zsb = 0.387 / 0.275
1.325
0.3866
0.292
0.773
= m3
First moment of Area of girder above N.A. = ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 )
= m3
First Moment of Area of composite secton above N.A.
= ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 ) ( 0.675 x 0.387 )
= m3
0.29
1.407
0.028
PROPERTIES OF OUTER GIRDER AT SECTION : = m
(A) GIRDER ALONE PROPERTY:
0.25
0.283 L
0.80
0.15
0.1
0.275
1.600
0.25
0.1
0.1
4.86
1
2
3
4
5
6
7
Extreme Fiber from bottom = 0.494 / 0.57
= m
M.I. (composite) = 0.0217 + 0.1408
= m4
0.866
0.1625
T O T A L 0.570 0.494 0.1408 0.021707
0.25 x 0.1 0.025 1.400 0.035 0.0071 0.000021
0.25 x 0.1 0.025 0.300 0.008 0.0080 0.000021
0.8 x 0.15 0.120 1.525 0.183 0.0520 0.000225
0.275 x 0.1 0.028 1.417 0.039 0.0083 0.000015
1 x 0.25 0.250 0.850 0.213 0.0001 0.020833
0.003 0.0034 0.000006
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.0618 0.000586
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
0.1 x 0.1 0.010 0.283
Section modulus (bottom) Zb = 0.163 / 0.866
= m3
Section modulus (top) Zt = 0.163 / 0.734
= m3
(B) PROPERTY OF COMPOSITE SECTION:
0.8 0.15
0.1
0.275
0.188
0.222
3
0.225
1
2
3
4
5
6
7
8
T O T A L 1.245 1.650 0.3620 0.024554
3 x 0.225 0.675 1.713 1.156 0.1013 0.002848
0.25 x 0.1 0.025 1.400 0.035 0.0001 0.000021
0.25 x 0.1 0.025 0.300 0.008 0.0263 0.000021
0.8 x 0.15 0.120 1.525 0.183 0.0048 0.000225
0.275 x 0.1 0.028 1.417 0.039 0.0002 0.000015
1 x 0.25 0.250 0.850 0.213 0.0564 0.020833
0.1 x 0.1 0.010 0.283 0.003 0.0109 0.000006
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.1620 0.000586
0.1
0.1
0.25
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
1.600
0.25
Extreme Fiber from bottom = 1.65 / 1.245
= m
M.I. (composite) = 0.0246 + 0.362
= m4
Section modulus (bottom of girder) Zgb = 0.387 / 1.325
= m3
Section modulus (top of slab) Zst = 0.387 / 0.5
= m3
Section modulus (bottom of slab) Zsb = 0.387 / 0.275
1.325
0.3866
0.292
0.773
= m3
First moment of Area of girder above N.A. = ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 )
= m3
First Moment of Area of composite secton above N.A.
= ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 ) ( 0.675 x 0.387 )
= m3
0.29
1.407
0.028
PROPERTIES OF OUTER GIRDER AT SECTION : = m
(A) GIRDER ALONE PROPERTY:
0.25
0.391 L
0.80
0.15
0.1
0.275
1.600
0.25
0.1
0.1
6.73
1
2
3
4
5
6
7
Extreme Fiber from bottom = 0.494 / 0.57
= m
M.I. (composite) = 0.0217 + 0.1408
= m4
0.866
0.1625
T O T A L 0.570 0.494 0.1408 0.021707
0.25 x 0.1 0.025 1.400 0.035 0.0071 0.000021
0.25 x 0.1 0.025 0.300 0.008 0.0080 0.000021
0.8 x 0.15 0.120 1.525 0.183 0.0520 0.000225
0.275 x 0.1 0.028 1.417 0.039 0.0083 0.000015
1 x 0.25 0.250 0.850 0.213 0.0001 0.020833
0.003 0.0034 0.000006
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.0618 0.000586
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
0.1 x 0.1 0.010 0.283
Section modulus (bottom) Zb = 0.163 / 0.866
= m3
Section modulus (top) Zt = 0.163 / 0.734
= m3
(B) PROPERTY OF COMPOSITE SECTION:
0.8 0.15
0.1
0.275
0.188
0.222
3
0.225
1
2
3
4
5
6
7
8
T O T A L 1.245 1.650 0.3620 0.024554
3 x 0.225 0.675 1.713 1.156 0.1013 0.002848
0.25 x 0.1 0.025 1.400 0.035 0.0001 0.000021
0.25 x 0.1 0.025 0.300 0.008 0.0263 0.000021
0.8 x 0.15 0.120 1.525 0.183 0.0048 0.000225
0.275 x 0.1 0.028 1.417 0.039 0.0002 0.000015
1 x 0.25 0.250 0.850 0.213 0.0564 0.020833
0.1 x 0.1 0.010 0.283 0.003 0.0109 0.000006
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.1620 0.000586
0.1
0.1
0.25
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
1.600
0.25
Extreme Fiber from bottom = 1.65 / 1.245
= m
M.I. (composite) = 0.0246 + 0.362
= m4
Section modulus (bottom of girder) Zgb = 0.387 / 1.325
= m3
Section modulus (top of slab) Zst = 0.387 / 0.5
= m3
Section modulus (bottom of slab) Zsb = 0.387 / 0.275
1.325
0.3866
0.292
0.773
= m3
First moment of Area of girder above N.A. = ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 )
= m3
First Moment of Area of composite secton above N.A.
= ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 ) ( 0.675 x 0.387 )
= m3
0.29
1.407
0.028
PROPERTIES OF OUTER GIRDER AT SECTION : = m
(A) GIRDER ALONE PROPERTY:
0.500 L
0.80
0.15
0.1
0.275
1.600
0.25
0.1
0.1
0.25
8.6
1
2
3
4
5
6
7
Extreme Fiber from bottom = 0.494 / 0.57
= m
M.I. (composite) = 0.0217 + 0.1408
= m4
0.866
0.1625
T O T A L 0.570 0.494 0.1408 0.021707
0.25 x 0.1 0.025 1.400 0.035 0.0071 0.000021
0.25 x 0.1 0.025 0.300 0.008 0.0080 0.000021
0.8 x 0.15 0.120 1.525 0.183 0.0520 0.000225
0.275 x 0.1 0.028 1.417 0.039 0.0083 0.000015
1 x 0.25 0.250 0.850 0.213 0.0001 0.020833
0.1 x 0.1 0.010 0.283 0.003 0.0034 0.000006
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.0618 0.000586
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
A.yb A.yb2
0.45
Section modulus (bottom) Zb = 0.163 / 0.866
= m3
Section modulus (top) Zt = 0.163 / 0.734
= m3
(B) PROPERTY OF COMPOSITE SECTION:
0.8 0.15
0.1
0.275
0.188
0.222
3
0.225
1
2
3
4
5
6
7
8
T O T A L 1.245 1.650 0.3620 0.024554
3 x 0.225 0.675 1.713 1.156 0.1013 0.002848
0.25 x 0.1 0.025 1.400 0.035 0.0001 0.000021
0.25 x 0.1 0.025 0.300 0.008 0.0263 0.000021
0.8 x 0.15 0.120 1.525 0.183 0.0048 0.000225
0.275 x 0.1 0.028 1.417 0.039 0.0002 0.000015
1 x 0.25 0.250 0.850 0.213 0.0564 0.020833
0.1 x 0.1 0.010 0.283 0.003 0.0109 0.000006
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.1620 0.000586
0.1
0.1
0.25
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
1.600
0.25
Extreme Fiber from bottom = 1.65 / 1.245
= m
M.I. (composite) = 0.0246 + 0.362
= m4
Section modulus (bottom of girder) Zgb = 0.387 / 1.325
= m3
Section modulus (top of slab) Zst = 0.387 / 0.5
= m3
Section modulus (bottom of slab) Zsb = 0.387 / 0.275
1.325
0.3866
0.292
0.773
= m3
First moment of Area of girder above N.A. = ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 )
= m3
First Moment of Area of composite secton above N.A.
= ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 ) ( 0.675 x 0.387 )
= m3
0.29
1.407
0.028
PROPERTIES OF INNER GIRDER AT SECTION : = m
(A) GIRDER ALONE PROPERTY:
00.000 L
0.80
0.15
0.064
0.175
0
0.45
1.600
0
0.25
1
2
3
4
5
6
7
Extreme Fiber from bottom = 0.672 / 0.784
= m
M.I. (composite) = 0.0558 + 0.1273
= m4
0.45 x 0.25 0.113 0.125 0.014 0.0604 0.000586
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45
0.418 0.0008 0.054975
0 x 0 0.000 0.250 0.000 0.0000 0.000000
0.016 0.0037 0.000003
0.000 0.250 0.000 0.0000 0.000000
0.8 x 0.15 0.120 1.525 0.183 0.0535 0.000225
0.1273 0.055798
0.0090
T O T A L 0.784
0.858
0.1831
0.45 x 0.064 0.029 1.418
0.175 x 0.064 0.011 1.429
1.136 x 0.45 0.511 0.818
0.000010
0.45 x 0
0.672
0.041
Section modulus (bottom) Zb = 0.183 / 0.858
= m3
Section modulus (top) Zt = 0.183 / 0.742
= m3
(B) PROPERTY OF COMPOSITE SECTION:
0.225
3
0.214
0.247
0.8 0.15
0.064
0.175
1
2
3
4
5
6
7
8
1.600
0
0
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
A.yb A.yb2
0.45
0.0968 0.054975
0 x 0 0.000
0.000000
0.8 x 0.15 0.120 1.525 0.183 0.0089 0.000225
0.175 x 0.064 0.011 1.429 0.016 0.0003 0.000003
0.45 x 0 0.000 0.250 0.000 0.0000
0.058646
3 x 0.225 0.675 1.713 1.156 0.1424 0.002848
0.45 x 0.064 0.029 1.418 0.041 0.0008 0.000010
0.3924T O T A L 1.459 1.828
1.136 x 0.45 0.511 0.818 0.418
0.25
0.45
0.250 0.000 0.0000 0.000000
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.1432 0.000586
Extreme Fiber from bottom = 1.828 / 1.459
= m
M.I. (composite) = 0.0586 + 0.3924
= m4
Section modulus (bottom of girder) Zgb = 0.451 / 1.253
= m3
Section modulus (top of slab) Zst = 0.451 / 0.572
= m3
Section modulus (bottom of slab) Zsb = 0.451 / 0.347
1.253
0.4510
0.36
0.789
= m3
First moment of Area of girder above N.A. = ( 0.12 x 0.272 ) + ( 0.011 x 0.175 ) + ( 0.029 x 0.165)
( 0.06 x 0.066 )
= m3
First Moment of Area of composite secton above N.A.
= ( 0.12 x 0.272 ) + ( 0.011 x 0.175 ) + ( 0.029 x 0.165)
( 0.06 x 0.066 ) ( 0.675 x 0.459 )
= m3
0.353
1.3
0.043
PROPERTIES OF INNER GIRDER AT SECTION : = m
(A) GIRDER ALONE PROPERTY:
0.125 L
0.80
0.15
0.1
0.275
1.600
0.25
0.1
0.1
2.99
0.25
1
2
3
4
5
6
7
Extreme Fiber from bottom = 0.494 / 0.57
= m
M.I. (composite) = 0.0217 + 0.1408
= m4
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
A.yb
0.1 x 0.1 0.010 0.283 0.003 0.0034 0.000006
A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.0618 0.000586
0.275 x 0.1 0.028 1.417 0.039 0.0083 0.000015
1 x 0.25 0.250 0.850 0.213 0.0001 0.020833
0.25 x 0.1 0.025 0.300 0.008 0.0080 0.000021
0.8 x 0.15 0.120 1.525 0.183 0.0520 0.000225
T O T A L 0.570 0.494 0.1408 0.021707
0.25 x 0.1 0.025 1.400 0.035 0.0071 0.000021
0.866
0.1625
Section modulus (bottom) Zb = 0.163 / 0.866
= m3
Section modulus (top) Zt = 0.163 / 0.734
= m3
(B) PROPERTY OF COMPOSITE SECTION:
0.225
0.15
0.1
0.275
0.188
0.222
3
0.8
1
2
3
4
5
6
7
8
1.600
0.25
0.1
0.1
0.25
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.1620 0.000586
1 x 0.25 0.250 0.850 0.213 0.0564 0.020833
0.1 x 0.1 0.010 0.283 0.003 0.0109 0.000006
0.8 x 0.15 0.120 1.525 0.183 0.0048 0.000225
0.275 x 0.1 0.028 1.417 0.039 0.0002 0.000015
0.25 x 0.1 0.025 1.400 0.035 0.0001 0.000021
0.25 x 0.1 0.025 0.300 0.008 0.0263 0.000021
T O T A L 1.245 1.650 0.3620 0.024554
3 x 0.225 0.675 1.713 1.156 0.1013 0.002848
Extreme Fiber from bottom = 1.65 / 1.245
= m
M.I. (composite) = 0.0246 + 0.362
= m4
Section modulus (bottom of girder) Zgb = 0.387 / 1.325
= m3
Section modulus (top of slab) Zst = 0.387 / 0.5
= m3
Section modulus (bottom of slab) Zsb = 0.387 / 0.275
1.325
0.3866
0.292
0.773
= m3
First moment of Area of girder above N.A. = ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 )
= m3
First Moment of Area of composite secton above N.A.
= ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 ) ( 0.675 x 0.387 )
= m3
0.29
1.407
0.028
PROPERTIES OF INNER GIRDER AT SECTION : = m
(A) GIRDER ALONE PROPERTY:
0.174 L
0.80
0.15
0.1
0.275
1.600
0.25
0.1
0.1
4.86
0.25
1
2
3
4
5
6
7
Extreme Fiber from bottom = 0.494 / 0.57
= m
M.I. (composite) = 0.0217 + 0.1408
= m4
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
A.yb
0.1 x 0.1 0.010 0.283 0.003 0.0034 0.000006
A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.0618 0.000586
0.275 x 0.1 0.028 1.417 0.039 0.0083 0.000015
1 x 0.25 0.250 0.850 0.213 0.0001 0.020833
0.25 x 0.1 0.025 0.300 0.008 0.0080 0.000021
0.8 x 0.15 0.120 1.525 0.183 0.0520 0.000225
T O T A L 0.570 0.494 0.1408 0.021707
0.25 x 0.1 0.025 1.400 0.035 0.0071 0.000021
0.866
0.1625
Section modulus (bottom) Zb = 0.163 / 0.866
= m3
Section modulus (top) Zt = 0.163 / 0.734
= m3
(B) PROPERTY OF COMPOSITE SECTION:
0.225
0.15
0.1
0.275
0.188
0.222
3
0.8
1
2
3
4
5
6
7
8
1.600
0.25
0.1
0.1
0.25
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.1620 0.000586
1 x 0.25 0.250 0.850 0.213 0.0564 0.020833
0.1 x 0.1 0.010 0.283 0.003 0.0109 0.000006
0.8 x 0.15 0.120 1.525 0.183 0.0048 0.000225
0.275 x 0.1 0.028 1.417 0.039 0.0002 0.000015
0.25 x 0.1 0.025 1.400 0.035 0.0001 0.000021
0.25 x 0.1 0.025 0.300 0.008 0.0263 0.000021
T O T A L 1.245 1.650 0.3620 0.024554
3 x 0.225 0.675 1.713 1.156 0.1013 0.002848
Extreme Fiber from bottom = 1.65 / 1.245
= m
M.I. (composite) = 0.0246 + 0.362
= m4
Section modulus (bottom of girder) Zgb = 0.387 / 1.325
= m3
Section modulus (top of slab) Zst = 0.387 / 0.5
= m3
Section modulus (bottom of slab) Zsb = 0.387 / 0.275
1.325
0.3866
0.292
0.773
= m3
First moment of Area of girder above N.A. = ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 )
= m3
First Moment of Area of composite secton above N.A.
= ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 ) ( 0.675 x 0.387 )
= m3
0.29
1.407
0.028
PROPERTIES OF INNER GIRDER AT SECTION : = m
(A) GIRDER ALONE PROPERTY:
0.391 L
0.80
0.15
0.1
0.275
1.600
0.25
0.1
0.1
6.73
0.25
1
2
3
4
5
6
7
Extreme Fiber from bottom = 0.494 / 0.57
= m
M.I. (composite) = 0.0217 + 0.1408
= m4
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
A.yb
0.1 x 0.1 0.010 0.283 0.003 0.0034 0.000006
A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.0618 0.000586
0.275 x 0.1 0.028 1.417 0.039 0.0083 0.000015
1 x 0.25 0.250 0.850 0.213 0.0001 0.020833
0.25 x 0.1 0.025 0.300 0.008 0.0080 0.000021
0.8 x 0.15 0.120 1.525 0.183 0.0520 0.000225
T O T A L 0.570 0.494 0.1408 0.021707
0.25 x 0.1 0.025 1.400 0.035 0.0071 0.000021
0.866
0.1625
Section modulus (bottom) Zb = 0.163 / 0.866
= m3
Section modulus (top) Zt = 0.163 / 0.734
= m3
(B) PROPERTY OF COMPOSITE SECTION:
0.225
0.15
0.1
0.275
0.188
0.222
3
0.8
1
2
3
4
5
6
7
8
1.600
0.25
0.1
0.1
0.25
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.1620 0.000586
1 x 0.25 0.250 0.850 0.213 0.0564 0.020833
0.1 x 0.1 0.010 0.283 0.003 0.0109 0.000006
0.8 x 0.15 0.120 1.525 0.183 0.0048 0.000225
0.275 x 0.1 0.028 1.417 0.039 0.0002 0.000015
0.25 x 0.1 0.025 1.400 0.035 0.0001 0.000021
0.25 x 0.1 0.025 0.300 0.008 0.0263 0.000021
T O T A L 1.245 1.650 0.3620 0.024554
3 x 0.225 0.675 1.713 1.156 0.1013 0.002848
Extreme Fiber from bottom = 1.65 / 1.245
= m
M.I. (composite) = 0.0246 + 0.362
= m4
Section modulus (bottom of girder) Zgb = 0.387 / 1.325
= m3
Section modulus (top of slab) Zst = 0.387 / 0.5
= m3
Section modulus (bottom of slab) Zsb = 0.387 / 0.275
1.325
0.3866
0.292
0.773
= m3
First moment of Area of girder above N.A. = ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 )
= m3
First Moment of Area of composite secton above N.A.
= ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 ) ( 0.675 x 0.387 )
= m3
0.29
1.407
0.028
PROPERTIES OF INNER GIRDER AT SECTION : = m
(A) GIRDER ALONE PROPERTY:
0.500 L
0.80
0.15
0.1
0.275
1.600
0.25
0.1
8.6
0.1
0.25
1
2
3
4
5
6
7
Extreme Fiber from bottom = 0.494 / 0.57
= m
M.I. (composite) = 0.0217 + 0.1408
= m4
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
A.yb
0.1 x 0.1 0.010 0.283 0.003 0.0034 0.000006
A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.0618 0.000586
0.275 x 0.1 0.028 1.417 0.039 0.0083 0.000015
1 x 0.25 0.250 0.850 0.213 0.0001 0.020833
0.25 x 0.1 0.025 0.300 0.008 0.0080 0.000021
0.8 x 0.15 0.120 1.525 0.183 0.0520 0.000225
T O T A L 0.570 0.494 0.1408 0.021707
0.25 x 0.1 0.025 1.400 0.035 0.0071 0.000021
0.866
0.1625
Section modulus (bottom) Zb = 0.163 / 0.866
= m3
Section modulus (top) Zt = 0.163 / 0.734
= m3
(B) PROPERTY OF COMPOSITE SECTION:
0.225
0.15
0.1
0.275
0.188
0.222
3
0.8
1
2
3
4
5
6
7
8
1.600
0.25
0.1
0.1
0.25
0.45
No. Dimension of
Element
Area Distance of C.G.
from bottom (m)
A.yb A.yb2
M.I. (self) m4
A (m2)
0.45 x 0.25 0.113 0.125 0.014 0.1620 0.000586
1 x 0.25 0.250 0.850 0.213 0.0564 0.020833
0.1 x 0.1 0.010 0.283 0.003 0.0109 0.000006
0.8 x 0.15 0.120 1.525 0.183 0.0048 0.000225
0.275 x 0.1 0.028 1.417 0.039 0.0002 0.000015
0.25 x 0.1 0.025 1.400 0.035 0.0001 0.000021
0.25 x 0.1 0.025 0.300 0.008 0.0263 0.000021
T O T A L 1.245 1.650 0.3620 0.024554
3 x 0.225 0.675 1.713 1.156 0.1013 0.002848
Extreme Fiber from bottom = 1.65 / 1.245
= m
M.I. (composite) = 0.0246 + 0.362
= m4
Section modulus (bottom of girder) Zgb = 0.387 / 1.325
= m3
Section modulus (top of slab) Zst = 0.387 / 0.5
= m3
Section modulus (bottom of slab) Zsb = 0.387 / 0.275
1.325
0.3866
0.292
0.773
= m3
First moment of Area of girder above N.A. = ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 )
= m3
First Moment of Area of composite secton above N.A.
= ( 0.12 x 0.2 ) + ( 0.028 x 0.092 ) + ( 0.025 x 0.075)
( 0.006 x 0.012 ) ( 0.675 x 0.387 )
= m3
0.29
1.407
0.028
PROPERTIES OF END CROSS-GIRDER
1450
400
1 225
2 0
0
0
1350.0 1350 1575
3
400
Area
Mrk A =Area
Y from
Bott AY MI h Ah2
Izz=Ixx +
Ah2
J=Ixx=T
orsional
moment
of Inertia
1 326250.00 1462.5 477140625 1376367188 490.909 7.862E+10 8E+10 2.8E+09
1 0.00 1350 0 0 378.409 0 0 0
2 0.00 1350 0 0 378.409 0 0
3 540000.00 675 364500000 8.2013E+10 296.591 4.75E+10 1.295E+11 2.9E+103 540000.00 675 364500000 8.2013E+10 296.591 4.75E+10 1.295E+11 2.9E+10
866250 mm2
841640625 Izz 2.095E+11 3.2E+10 mm4
Area of Girder 866250 mm2
= 0.8663 m2
CG from Bottom 971.590909 mm = 0.9716 m
CG from Top 603.409091 mm = 0.6034 m
Zbg = 215640296 mm3
= 0.2156 m3
Zts = 347217426 mm3
= 0.3472 m3
Ztg = 553671030 mm3
= 0.5537 m3
Izz = 2.0951E+11 mm4
= 0.2095 m4
J=Ixx=Torsional moment of Inertia 3.1553E+10 mm4
= 0.0316 m4
Iyy = 6.4362E+10 mm4
= 0.0644 m4
Weight of girder without deck (UDL) = 1.35 t/m
Weight of girder with deck (UDL) = 2.16575 t/m
DESIGN METHODOLOGY
The following salient features are considered in this design note.
The RCC girder bridge is checked for the following two conditions
• Ultimate strength check
• Serviceability check
o Ultimate compressive strain in the concrete (єcu3) has been considered as 0.0035
o Design yield strength of reinforcement for bending fyd = fyk/γs
4.0
o The bending moment for various loads were obtained from the floor analysis. And the same is
multiplied with the partial safety factor for obtaining the factored bending moment.
o Partial safety factor of 1.5 has been adopted for concrete and 1.15 has been adopted for steel as
per Cl: 6.4.2.8 & 6.3.5 of IRC: 112 respectively.
o For Ultimate strength check, Table 3.2 of IRC: 6 has been considered for the partial safety factor for
various loads.
o For Serviceability check, Table 3.3 of IRC: 6 has been considered for the partial safety factor for
various loads.
o Design yield strength of reinforcement for shear fywd = fyk/γs
DESIGN METHODOLOGY FOR SERVICEABILITY LIMIT STATE:
The following check are done as per IRC: 112 prescribed
o For stress Check
o For Crack width Check
o For Deflection check:
Based on the design methodology, The Ultimate limit state design of bridge has been done and
presented below.
Due to long term creep and shrinkage effect, the effective concrete modulus is reduced for sustained
load.
Maximum stress at outermost compression fibre and outermost tension fibre were limited to
permissible stresses mentioned in IRC:112.
The crack width in concrete has been checked in accordance with Cl:12.3.4 of IRC:112. Maximum
crack width is limited to 0.3mm as per table 12.1 of IRC:112.
For calculation of deflection due to sustain loads, the cracked moment of inertia has been considered
as 70% of the uncracked moment of inertia as per Cl:12.4.2 (1) of IRC:112.
Due to long term creep and shrinkage effect, the effective concrete modulus is reduced for sustained
load as per Cl:12.4.2 (2) of IRC :112.
o Area of tension reinforcement is calculated and made ensured that the strain in the reinforcement
is sufficient to cause yeilding.
LOADS:
The following loads and Load Combinations are considered in this design note.
• Dead Loads:
• Super imposed Dead Loads (SIDL)
o Wearing Coat:
o RCC Crash barrier:
• Live Loads:
The following loads specified in IRC were considered in the design:
o 70R - Wheeled Vehicle
o Class A Vehicle
• Live load Combination:
Self weight of the RCC girder & slab is calculated based on the unit weight of 25 KN/m3 in accordance
with Cl: 203 of IRC: 6-2010.
Thickness of Wearing coat on top of the deck slab for design is assumed as 65mm thick for future
overlay and the self weight is calculated based on the unit weight of 22 KN/m3.
For calculation of self weight of crash barrier, the cross sectional area of the crash barrier is taken as
0.4 m2.
All the possible load combination for 2-Lanes carriage way structure as per table-2 of IRC: 6 have been
done.
5.0 LOADS
The following loads and load combinations are considered in this design note
Dead load:
The dead load is applied as a UDL or floor load. The intensity of loads is as under:
SIDL except surfacing
Crash Barrier
Railing (assuming 50% perforation)
Kerb
Footpath
SIDL- surfacing
Wearing Coat (min 0.2 t/m2)
Outer girder
End section
Tapered section
Mid section
Density
(m2) (t/m
3) (t/m)
Type of
Load
UDL
UDL
UDL
Floor
Floor
Load
(t/m2)
0
2.5 1.00
2.5 0.175
2.5 0.375
0.4
0.07
0.15
Area
0.2
b
(m)
h
(m)
0.2 0.7
0.5 0.3
0
0.065
0
2.2
1.96
UDL 0.677 2.5 1.6925
UDL 0.784 2.5
1.425UDL 0.57 2.5
Outer girder-composite
End section
Tapered section
Mid section
Inner girder
End section
Tapered section
Mid section
Inner girder-composite
End section
Tapered section
Mid section
Live loads:
The live loads are applied as moving vehicular loads, as defined by IRC:6-2010.
UDL 1.4587 2.5 3.6468
3.3796
UDL 1.245 2.5 3.1125
UDL 1.3519 2.5
1.96
UDL 0.677 2.5 1.6925
UDL 0.784 2.5
1.425
UDL 1.4587 2.5 3.6468
UDL 0.57 2.5
3.3796
UDL 1.245 2.5 3.1125
UDL 1.3519 2.5
Footpath Live loads:
The footpath live loads are applied as per Clause:206.2 of IRC:6-2010.
Effective span(L) = m & Width of footway(W) = m
Therefore, The live load in kg/m2
= kg/m2
= t/m2
Distributing the above load on girders:
Footpath Live Loads
For outer girder
For inner girder
For outer girder
Weight of shuttering:
The intensity of weight of shuttering is assumed as 100 kg/m2.
Weight of shuttering
For outer girder
For inner girder
Note: Negative sign indicates load acting in positive y direction.
UDL
UDL
Load
(m) (m) (m2) (t/m
3) (t/m) (t/m
2)
UDL
17.2 1.5
456.89 0.457
Type of
Load
b h Area Density
UDL 1.2
UDL 1.2
bType of
Load
h Area Density Load
(m) (m2) (t/m
3)(m) (t/m) (t/m
2)
6.0 ANALYSIS RESULTS
G-1 G-2 G-3 O-design I-design G-1 G-2 G-3 O-design I-design
0 0.55 0.55 0.55 0.548 0.548 0 13.01 13.01 13.01 13.007 13.006
0 0 Deff 9.81 9.82 9.81 9.814 9.822
2.99 30.36 30.34 30.36 30.36 30.337 EOT 9.72 9.73 9.72 9.724 9.725
4.86 42.85 42.84 42.85 42.85 42.835 4.86 5.35 5.35 5.35 5.354 5.35
6.73 50.34 50.33 50.34 50.339 50.332 6.73 2.68 2.68 2.68 2.68 2.676
8.60 52.83 52.83 52.83 52.828 52.829 8.60 0.00 0.00 0.00 0 0
G-1 G-2 G-3 O-design I-design G-1 G-2 G-3 O-design I-design
0 0.20 0.09 0.20 0.203 0.091 0 2.58 2.28 2.54 2.579 2.283
0 0 Deff 2.21 1.91 2.21 2.21 1.906
2.99 6.59 6.16 6.59 6.589 6.164 EOT 2.13 1.90 2.13 2.125 1.898
4.86 9.33 8.67 9.33 9.332 8.667 4.86 1.37 1.20 1.37 1.365 1.197
6.73 10.97 10.16 10.97 10.973 10.161 6.73 0.85 0.67 0.85 0.852 0.671
8.6 11.52 10.65 11.52 11.518 10.648 8.6 0.26 0.15 0.26 0.262 0.145
G-1 G-2 G-3 O-design I-design G-1 G-2 G-3 O-design I-design
0 0.85 0.65 0.85 0.848 0.651 0 17.17 15.86 17.17 17.174 15.862
0 0 Deff 13.36 12.38 13.36 13.359 12.375
2.99 43.16 41.17 43.16 43.162 41.17 EOT 13.36 12.38 13.36 13.359 12.375
4.86 60.81 57.78 60.81 60.805 57.777 4.86 9.56 8.89 9.56 9.557 8.891
6.73 71.37 67.71 71.37 71.37 67.707 6.73 5.77 5.38 5.77 5.765 5.384
Girder Self-weight-Moment Girder Self-weight-Shear
Weight of shuttering-Moment
Green wt of deck slab-ShearGreen wt of deck slab-Moment
Weight of shuttering-Shear
6.73 71.37 67.71 71.37 71.37 67.707 6.73 5.77 5.38 5.77 5.765 5.384
8.6 74.88 70.96 74.88 74.884 70.963 8.6 1.98 1.86 1.98 1.98 1.856
G-1 G-2 G-3 O-design I-design G-1 G-2 G-3 O-design I-design
0 0.57 0.62 0.57 0.566 0.616 0 15.88 14.55 15.88 15.884 14.554
0 0 Deff 12.36 11.36 12.36 12.361 11.355
2.99 40.18 37.41 40.18 40.175 37.405 EOT 12.36 11.36 12.36 12.361 11.355
4.86 56.57 52.59 56.57 56.565 52.586 4.86 8.72 8.15 8.72 8.719 8.147
6.73 66.38 61.68 66.38 66.381 61.677 6.73 5.33 4.93 5.33 5.332 4.926
8.6 69.65 64.68 69.65 69.652 64.679 8.6 1.82 1.69 1.82 1.824 1.694
G-1 G-2 G-3 O-design I-design G-1 G-2 G-3 O-design I-design
0 0.19 3.90 3.26 3.262 3.9 0 11.67 2.97 10.60 11.672 2.967
0 0 Deff 9.52 2.02 9.52 9.522 2.018
2.99 27.65 2.81 24.57 27.645 2.813 EOT 9.52 2.02 8.39 9.522 2.018
4.86 39.81 6.37 35.71 39.81 6.374 4.86 6.83 1.08 5.74 6.834 1.077
6.73 47.07 6.63 42.36 47.072 6.633 6.73 4.16 0.36 3.22 4.163 0.355
8.6 49.48 6.48 44.66 49.481 6.475 8.6 1.50 0.23 1.63 1.628 0.233
G-1 G-2 G-3 O-design I-design G-1 G-2 G-3 O-design I-design
0 0.25 0.19 0.31 0.31 0.187 0 5.19 4.53 5.11 5.188 4.526
0 0 Deff 4.22 3.78 4.22 4.223 3.782
2.99 13.37 12.11 13.32 13.373 12.105 EOT 4.22 3.77 4.22 4.219 3.769
4.86 18.92 17.06 18.87 18.915 17.06 4.86 2.90 2.38 2.70 2.903 2.375
6.73 22.24 20.03 22.20 22.236 20.025 6.73 1.71 1.33 1.50 1.714 1.331
8.60 23.34 21.00 23.31 23.341 21 8.6 0.53 0.28 0.37 0.525 0.282
SIDL(surfacing) MOMENT
SIDL(except surfacing) SHEARSIDL(except surfacing) MOMENT
Deck Slab weight-ShearDeck slab weight-Moment
SIDL(surfacing) SHEAR
Footpath Live Load
G-1 G-2 G-3 O-design I-design G-1 G-2 G-3 O-design I-design
0 1.257 1.079 0.002 1.257 1.079 0 5.745 0.297 0.029 5.745 0.297
0 0 0 0 0 Deff 5.45 0.1 0.66 5.45 0.1
2.99 13.672 1.991 0.12 13.672 1.991 EOT 4.664 0.269 0.026 4.664 0.269
4.86 19.553 2.425 0.16 19.553 2.425 4.86 3.332 0.213 0.021 3.332 0.213
6.73 23.026 2.666 0.182 23.026 2.666 6.73 2.027 0.134 0.007 2.027 0.134
8.6 24.145 2.66 -0.189 24.145 2.66 8.6 0.736 0.046 0.007 0.736 0.046
Live Load
Case1: Governing LL
G-1 G-2 G-3 O-design I-design G-1 G-2 G-3 O-design I-design
0 8.282 30.103 21.652 21.652 30.103 0 8.89 49.326 39.9 39.9 49.326
0 0 0 0 0 Deff 0.88 24.6 40.15 40.15 24.6
2.99 27.009 107.16 91.67 91.67 107.16 EOT 7.761 41.998 36.7 36.7 41.998
4.86 37.445 145.02 125.24 125.24 145.02 4.86 6.12 30.153 28.1 28.1 30.153
6.73 43.224 168.49 145.34 145.34 168.49 6.73 4.241 23.707 20.4 20.4 23.707
8.6 44.505 176.42 153.23 153.23 176.42 8.6 3.237 18.034 11.211 11.211 18.034
Footpath LL MOMENT Footpath LL SHEAR
LL SHEARLL MOMENT
Number of lanes = 2
Reduction due to longitudinal effect = 0 %
Impact factor for class A Loading = 4.5/(6+L) = 0.194
Impact factor for class 70R Loading = 0.175
Moment summary:
For outer girder:
Case-1 Case-2 Case-3 Case-1 Case-2 Case-3 Case-1 Case-2 Case-3
0 21.652 0 0 21.65 0 0 25.44 0 0 25.44 1.257
2.99 91.67 0 0 91.67 0 0 107.71 0 0 107.71 13.672
4.86 125.24 0 0 125.24 0 0 147.16 0 0 147.16 19.553
6.73 145.34 0 0 145.34 0 0 170.77 0 0 170.77 23.026
8.6 153.23 0 0 153.23 0 0 180.05 0 0 180.05 24.145
For inner girder:
Case-1 Case-2 Case-3 Case-1 Case-2 Case-3 Case-1 Case-2 Case-3
0 30.103 0 0 30.1 0 0 35.37 0 0 35.37 1.079
2.99 107.16 0 0 107.16 0 0 125.91 0 0 125.91 1.991
4.86 145.02 0 0 145.02 0 0 170.4 0 0 170.4 2.425
6.73 168.49 0 0 168.49 0 0 197.98 0 0 197.98 2.666
Design
momentMax
moment
Max
moment
Footpath
LL mom
Footpath
LL mom
36.449
127.901
Moment
Moment
With reduction
With reduction With impact
With impact
26.697
172.825
200.646
121.382
166.713
193.796
204.195
Design
moment
6.73 168.49 0 0 168.49 0 0 197.98 0 0 197.98 2.666
8.6 176.42 0 0 176.42 0 0 207.29 0 0 207.29 2.66
Shear summary:
For outer girder:
Case-1 Case-2 Case-3 Case-1 Case-2 Case-3 Case-1 Case-2 Case-3
0 39.9 0 0 39.9 0 0 46.88 0 0 46.88 5.745
Deff 40.15 0 0 40.15 0 0 47.18 0 0 47.18 5.45
EOT 36.7 0 0 36.7 0 0 43.12 0 0 43.12 4.664
4.86 28.1 0 0 28.1 0 0 33.02 0 0 33.02 3.332
6.73 20.4 0 0 20.4 0 0 23.97 0 0 23.97 2.027
8.6 11.211 0 0 11.21 0 0 13.17 0 0 13.17 0.736
For inner girder:
Case-1 Case-2 Case-3 Case-1 Case-2 Case-3 Case-1 Case-2 Case-3
0 49.326 0 0 49.33 0 0 57.96 0 0 57.96 0.297
Deff 24.6 0 0 24.6 0 0 28.91 0 0 28.91 0.1
EOT 41.998 0 0 42 0 0 49.35 0 0 49.35 0.269
4.86 30.153 0 0 30.15 0 0 35.43 0 0 35.43 0.213
6.73 23.707 0 0 23.71 0 0 27.86 0 0 27.86 0.134
8.60 18.034 0 0 18.03 0 0 21.19 0 0 21.19 0.046
Max
Shear
Max
Shear
Footpath
LL shear
Footpath
LL shear
36.352
25.997
13.906
Design shear
29.01
49.619
35.643
27.994
21.236
209.95
Design shear
52.625
52.63
47.784
With impactWith reduction
With reduction
Shear
Shear With impact
200.646
58.257
7.0 DESIGN
Fy = MpaFck = MpaWidth of Beam = mDepth of Beam = mm Ru = (depends on grade of steel used)fctm =
Design of Outer Girder under ULS(Ultimate Limit State)
Dia Nos Dia Nos Dia Nos Dia Nos Dia Nos32 5 32 5 32 5 32 5 32 532 4 32 4 32 4 32 4 32 532 0 32 0 32 0 32 4 32 4
32 0
50040
3
450 250Width of web (mm)
157.572
250 250 250Effective width of
girder(mm) 3000 3000 3000 3000 3000
Layer 7Layer 8
1.35
1.50
1.351.35
47.072DL (t.m) 1.114 70.535 99.415 116.720
Load factorsDL
SIDL-except surfacing
LL
1.35
Layer 1Layer 2Layer 3
0.451825
cg frm bottomLayers of steel
0.133
SIDL-except surfacing (t.m)
7238.229Ast (mm2)
196 196 196Layer 4Layer 5Layer 6
196
Section0 2.99 4.86 6.73 8.6
cg frm bottom
cg frm bottom
cg frm bottom
cg frm bottom
132 132 13268
132
165.34866.799
306.293
TOTAL M (t.m) 46.50 338.02 471.12 550.73 579.29
DL (t.m) 1.504 95.22237.321
182.073
53.744
250.070
63.547
1.75
Unfactored moment122.480
166.713
39.810
CG frm bottom (mm)
1.351.35
SIDL-except surfacing (t.m)
LL (t.m)
4.404
40.046 290.694
134.210
121.382
27.645
204.195
49.481
10455.220
Factored moment
1.35
1.50
1.35
1.50
1.35
193.796LL (t.m)
3.262
26.697
1.35
1.501.50
SIDL- surfacing (t.m) 0.310 13.373 18.915 22.236 23.341
SIDL- surfacing 1.75 1.75 1.75 1.75
SIDL- surfacing (t.m) 0.543 23.403 33.101 38.913 40.847
68 68 68 68
127.07711259.468
127.4297238.229
96.444
196260
96.444
132
7238.22996.444
CHECK FOR EFFECTIVE DEPTH
* The area of steel, Ast is calculated according to the depth of Neutral Axis from top.If the depth of neutral axis is less than the thickness of slab,i.e. xu <= Df
If the depth of neutral axis is greater than the thickness of slab,i.e. xu > Df
**
Depth of NA(mm)Max depth of NA(mm)
Status795.138 781.043 780.882
Ok Ok Ok Ok Ok
113.377
Effective depth provided (mm)
Ok
Effective depth required (mm)
Status
105.278<= Df
OKStatus OK OK OK
Ok4768.72
1213.449 4547.499
619.649Ast (mm2)*
Ast provided (mm2) 7238.229
Ast (min) (mm2)**Ast (max) (mm2)**
4547.499 6366.361 7601.997
Ok
7238.229 10455.220
Total Moment (t.m)
1697.92
587.43
Ok Ok
46.50
72.885 72.885 72.885 105.278795.138 795.138
Check for NA depth
113.377<= Df <= Df
225.000 225.000 225.000 225.00072.885
<= Df72.885
Depth of slab (Df) (mm)
<= Df
225.000
Ok
Ok
602.46
Ok1728.56
Check for depth required
Moment of resistance,Mu=Rufckbd2 (t.m)
Status
1697.57
Depth of NA (mm)
For the minimum and maximum area of steel (Ast min and Ast max) respectively please refer clause 16.5.1.1 of IRC:112-2011
OK7238.229
Check for Moment
Ast, req (mm2) 6366.361 7601.99711259.468
4599.26
8005.995
1728.56 1728.56
Ok
1213.449 674.138 674.138 662.189 662.05236467.500 31125.000 31125.000 31125.000 31125.000
471.12 550.73
Ok4768.72 4768.72 4601.16
338.02
8005.995
170.69 460.21 543.31
579.29
72.885
Design of Outer Girder under ULS(Ultimate Limit State)
Dia Nos Dia Nos Dia Nos Dia Nos Dia Nos Dia Nos
32 5 32 5 32 5 32 5 32 5 32 5
32 4 32 4 32 4 32 4 32 4 32 5
32 0 32 0 32 0 32 0 32 0 32 4
0 0 0 0 0 0 0 0 0 0 32 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 260
Layer 1 68 68 68 68 68
Section
0 EOT 4.86 6.73 8.6Deff
132 132 132
68
Layer 4 0
Layers of steel
cg frm
bottom
cg frm
bottom
cg frm
bottom
cg frm
bottom
cg frm
bottom
cg frm
bottom
132
196
0
Layer 3 196 196 196 196 196
Layer 2 132 132
Layer 6 0 0 0 0 00
Layer 5 0 0 0 0 00
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
Layer 6 0 0 0 0 00
Layer 8 0 0 0 0 00
Layer 7 0 0 0 0 00
127.42996.444
22.175
1.35
1.824
Ast (mm2) 7238.229 7238.229 7238.229 7238.229 11259.4687238.229
1.35 1.35 1.351.35
13.906
1.628
CG frm bottom (mm) 96.444 96.444 96.444 96.444
9.522
47.784 36.352 25.997
SIDL-except surfacing (t) 11.672 9.522 6.834 4.163
SIDL-except surfacing 1.35 1.35 1.35 1.35
SIDL-surfacing (t) 5.188 4.223 4.219 2.903 1.714
LL 1.50 1.50 1.50 1.50 1.501.50
Check for Shear
Unfactored Shear
DL (t) 28.891 22.085 14.073 8.012
29.93625 2.4624
Factored Shear
DL (t) 39.00285 29.81475 18.99855 10.8162
0.525
SIDL-surfacing 1.75 1.75 1.75 1.75 1.75 1.75
1.35
Load factors
DL 1.35
1.35
52.63LL (t) 52.625
26.44
20.859
Width of web (mm) 450
9.2259 5.62005
K**
σcp
ρ1*+
Effective depth of
girder(mm)1728.56 1728.56 1728.56 1728.56 1697.571728.56
265.78
7238.23
1.34 1.34 1.34 1.34 1.341.34
0 0 0 0 0
0.0093 0.0167 0.0167 0.0167 0.020.0158
0
26.44
25.829 25.829 25.829 26.92126.962
129.13
Vrdc (t)*
38.325
250
Asl (mm2) 7238.23 7238.23 7238.23 7238.23 11259.47
29.93625
12.8547
78.945
129.13
2.4624
SIDL-except surfacing (t) 15.7572 12.8547
Total Shear (t)
DL (t) 39.00285 29.81475 18.99855 10.8162
Total Shear (t) 142.78 121.73 87.83 58.43
LL (t) 78.9375 71.676 54.528 38.9955
250 250 250
142.78 121.73 87.83 58.43
SIDL-surfacing (t) 9.079 7.39025 7.38325 5.08025 2.9995 0.91875
2.1978
1005.31 1005.31 1005.31 1005.31
Check for shear
reinforcement spacingOK OK OK OK OK OK
ρmin****
0.0009 0.0009 0.0009 0.0009 0.0009 0.0009
26.44129.13Total Shear (t) 142.78 121.73 87.83 58.43
Z+++
1555.70 1555.70 1555.70 1555.70 1527.81
Check for Shear
reinforcement
Shear Reinf
Required
Shear Reinf
Required
Shear Reinf
Required
Shear Reinf
Required
No Shear Reinf
required
1555.70
Shear Reinf
Required
αcw 1 1 1 1 1
ν1 0.6 0.6 0.6 0.6 0.60.6
1
0.3805 21.80 deg 0.3805 21.80 deg 0.380521.80 deg
cot θ ; tan θ 2.50 0.40 2.50 0.40
θ (degrees) 21.80 deg 0.3805 21.80 deg 0.380521.80 deg 0.3805
2.50 0.40
150
2.50 0.40 2.50 0.40 2.50 0.40
2 Leg 12 dia 2 Leg 12 dia 2 Leg
Asw (mm2)
++*226.195 226.195 226.195 226.195 226.195226.195
Max spacing for steel
provided++++ 558.51 945.62
spacing (mm) 100 100 120 150
Shear reinforcement 12 dia 2 Leg 12 dia 2 Leg 12 dia12 dia 2 Leg
100
Areqd (mm2)
++** 40.500 23.920 22.500 27.000 33.750 33.750
Check for min shear
reinforcementOK OK OK OK OK OK
reinforcement spacing
Vrd,max***
305.993
258.783 143.768 143.768 143.768 141.191152.843
Vrd,s (t)++
305.993 305.993 254.994 203.995 200.338
CHK FOR SHEAR OK OK OK OK OK
Vrd (t) 258.783 143.768 143.768 143.768 141.191152.843
OK
Total Shear (t) 142.780 121.730 87.830 58.430 26.440129.130
The design Shear resistance of the member without Shear reinforcement VRD.c is given by,
*(Eq. 10.1, cl: 10.3.2, IRC: 112-2011)
subject to minimum of
**(Eq. 10.2, cl: 10.3.2, IRC: 112-2011)
(Eq. 10.3, cl: 10.3.2, IRC: 112-2011)
*+
For members with vertical shear reinforcement, the shear resistance Vrd is smaller of,
++
***
****(Eq. 10.20, cl: 10.3.2, IRC: 112-2011)
++**
++++
αρ sinmin wreqd sbA =
swAs =
++++
++* Asw = Cross sectional area of shear reinforcement at a section pg-90
++** Areqd = Min area of reinforcement required
s = Spacing of shear reinforcement pg-91+++
z = lever arm to be taken as 0.9 for RC sect & calculated for PSC section pg-91
fywd = Design strength of web reinforcement used to resist shear (0.8fyk/γm) pg-86
1 = Strength reduction factor for concrete cracked in shear
= 0.6 for fck<=80Mpa
= 0.9-fck/250 > 0.5 for fck>80Mpa
αρ sinmin
max
w
sw
b
As =
Design of Inner Girder under ULS(Ultimate Limit State)
Dia Nos Dia Nos Dia Nos Dia Nos Dia Nos
32 5 32 5 32 5 32 5 32 5
32 4 32 4 32 4 32 4 32 5
32 4
LL (t.m) 36.449 127.901 172.825 200.646 209.950
SIDL- surfacing (t.m) 0.187 12.105 17.060 20.025 21.000
SIDL-except surfacing (t.m) 3.900 2.813 6.374 6.633 6.475
Unfactored moment
DL (t.m) 1.164 67.742 95.421 112.009 117.508
CG frm bottom (mm) 96.444 96.444 96.444 96.444 125.714
Ast (mm2) 7238.229 7238.229 7238.229 7238.229 11259.468
Layer 8
Layer 7
Layer 6
Layer 5
Layer 4
Layer 3 190
Layer 2 132 132 132 132 132
Layer 1 68 68 68 68 68
Layers of steel
cg frm
bottom
cg frm
bottom
cg frm
bottom
cg frm
bottom
cg frm
bottom
Section
0 2.99 4.86 6.73 8.6
<= Df <= Df <= Df <= Df <= Df
Depth of NA (mm) 72.885 72.885 72.885 72.885 113.377
Depth of slab (Df) (mm) 225.000 225.000 225.000 225.000 225.000
Effective width of
girder(mm) 3000 3000 3000 3000 3000
Width of web (mm) 450 250 250 250 250
TOTAL M (t.m) 61.84 308.28 426.52 496.18 519.05
LL (t.m) 54.674 191.852 259.238 300.969 314.925
SIDL- surfacing (t.m) 0.327 21.184 29.855 35.044 36.750
SIDL-except surfacing (t.m) 5.265 3.798 8.605 8.955 8.741
Factored moment
DL (t.m) 1.571 91.452 128.818 151.212 158.636
LL 1.50 1.50 1.50 1.50 1.50
SIDL- surfacing 1.75 1.75 1.75 1.75 1.75
1.35
SIDL-except surfacing 1.35 1.35 1.35 1.35 1.35
Load factors
DL 1.35 1.35 1.35 1.35
LL (t.m) 36.449 127.901 172.825 200.646 209.950
Ast, req (mm2) 1213.449 4143.315 5755.058 6710.659 7150.754
Ast (max) (mm2)** 36467.500 31125.000 31125.000 31125.000 31125.000
Ast (min) (mm2)** 1213.449 674.138 674.138 674.138 662.723
Ast (mm2)* 824.474 4143.315 5755.058 6710.659 7150.754
Status Ok Ok Ok Ok Ok
Moment of
resistance,Mu=Rufckbd2
(t.m) 4768.72 4768.72 4768.72 4768.72 4608.59
Check for Moment
Total Moment (t.m) 61.84 308.28 426.52 496.18 519.05
Status Ok Ok Ok Ok Ok
Max depth of NA(mm) 795.138 795.138 795.138 795.138 781.673
Check for NA depth
Depth of NA(mm) 72.885 72.885 72.885 72.885 113.377
Status Ok Ok Ok Ok Ok
Effective depth provided
(mm) 1728.56 1728.56 1728.56 1728.56 1699.29
Check for depth requiredEffective depth required
(mm) 196.84 439.5 516.96 557.57 570.28
CHECK FOR EFFECTIVE DEPTH
* The area of steel, Ast is calculated according to the depth of Neutral Axis from top.
If the depth of neutral axis is less than the thickness of slab,i.e. xu <= Df
If the depth of neutral axis is greater than the thickness of slab,i.e. xu > Df
** For the minimum and maximum area of steel (Ast min and Ast max) respectively please refer clause 16.5.1.1
of IRC:112-2011
Status OK OK OK OK OK
Ast provided (mm2) 7238.229 7238.229 7238.229 7238.229 11259.468
Ast, req (mm ) 1213.449 4143.315 5755.058 6710.659 7150.754
Design of Inner Girder under ULS(Ultimate Limit State)
Dia Nos Dia Nos Dia Nos Dia Nos Dia Nos Dia Nos
32 5 32 5 32 5 32 5 32 5 32 5
32 4 32 4 32 4 32 4 32 4 32 5
0 0 0 0 0 0 0 0 0 0 32 4
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
21.236
Load factors
DL 1.35 1.35 1.35 1.35 1.35 1.35
LL (t) 58.257 29.01 49.619 35.643 27.994
0.233
SIDL-surfacing (t) 4.526 3.782 3.769 2.375 1.331 0.282
SIDL-except surfacing (t) 2.967 2.018 2.018 1.077 0.355
125.714
Check for Shear
Unfactored Shear
DL (t) 27.56 21.177 21.08 13.497 7.602 1.694
CG frm bottom (mm) 96.444 96.444 96.444 96.444 96.444
0
Ast (mm2) 7238.229 7238.229 7238.229 7238.229 7238.229 11259.468
Layer 8 0 0 0 0 0
0
Layer 7 0 0 0 0 0 0
Layer 6 0 0 0 0 0
0
Layer 5 0 0 0 0 0 0
Layer 4 0 0 0 0 0
132
Layer 3 0 0 0 0 0 190
Layer 2 132 132 132 132 132
cg frm
bottom
Layer 1 68 68 68 68 68 68
Layers of steel
cg frm
bottom
cg frm
bottom
cg frm
bottom
cg frm
bottom
cg frm
bottom
Section
0 Deff EOT 4.86 6.73 8.6
cot θ ; tan θ 2.50 0.40 2.50 0.40 2.50 0.400.40 2.50 0.40 2.50 0.40 2.50
1
θ (degrees) 21.80 deg 0.3805 21.80 deg 0.3805 21.80 deg 0.3805 21.80 deg 0.3805
αcw 1 1 1 1 1
21.80 deg 0.3805 21.80 deg 0.3805
1529.36
ν1 0.6 0.6 0.6 0.6 0.6 0.6
Z+++
1555.70 1555.70 1555.70 1555.70 1555.70
Shear Reinf
Required
ρmin****
0.0009 0.0009 0.0009 0.0009 0.0009 0.0009
Check for Shear
reinforcement
Shear Reinf
Required
Shear Reinf
Required
Shear Reinf
Required
Shear Reinf
Required
Shear Reinf
Required
26.948
Total Shear (t) 136.52 81.45 112.21 77.3 55.06 34.95
Vrdc (t)*
38.325 26.962 25.829 25.829 25.829
0.02
σcp 0 0 0 0 0 0
ρ1*+
0.0093 0.0158 0.0167 0.0167 0.0167
250
K**
1.34 1.34 1.34 1.34 1.34 1.34
Width of web (mm) 450 265.78 250 250 250
1699.29
Asl (mm2) 7238.23 7238.23 7238.23 7238.23 7238.23 11259.47
Effective depth of
girder(mm) 1728.56 1728.56 1728.56 1728.56 1728.56
31.854
Total Shear (t) 136.52 81.45 112.21 77.3 55.06 34.95
LL (t) 87.3855 43.515 74.4285 53.4645 41.991
0.31455
SIDL-surfacing (t) 7.9205 6.6185 6.59575 4.15625 2.32925 0.4935
SIDL-except surfacing (t) 4.00545 2.7243 2.7243 1.45395 0.47925
1.50
Factored Shear
DL (t) 37.206 28.58895 28.458 18.22095 10.2627 2.2869
LL 1.50 1.50 1.50 1.50 1.50
1.35
SIDL-surfacing 1.75 1.75 1.75 1.75 1.75 1.75
SIDL-except surfacing 1.35 1.35 1.35 1.35 1.35
DL 1.35 1.35 1.35 1.35 1.35 1.35
The design Shear resistance of the member without Shear reinforcement VRD.c is given by,
*(Eq. 10.1, cl: 10.3.2, IRC: 112-2011)
subject to minimum of
**(Eq. 10.2, cl: 10.3.2, IRC: 112-2011)
(Eq. 10.3, cl: 10.3.2, IRC: 112-2011)
OKCHK FOR SHEAR OK OK OK OK OK
141.334
Total Shear (t) 136.520 81.450 112.210 77.300 55.060 34.950
Vrd (t) 258.783 152.843 143.768 143.768 143.768
200.541
Vrd,max***
258.783 152.843 143.768 143.768 143.768 141.334
Vrd,s (t)++
305.993 305.993 305.993 254.994 203.995
1005.31
Check for shear
reinforcement spacingOK OK OK OK OK OK
Max spacing for steel
provided++++ 558.51 945.62 1005.31 1005.31 1005.31
226.195
Check for min shear
reinforcementOK OK OK OK OK OK
Asw (mm2)
++*226.195 226.195 226.195 226.195 226.195
150
Areqd (mm2)
++** 40.500 23.920 22.500 27.000 33.750 33.750
12 dia 2 Leg 12 dia 2 Leg
spacing (mm) 100 100 100 120 150
Shear reinforcement 12 dia 2 Leg 12 dia 2 Leg 12 dia 2 Leg 12 dia 2 Leg
(Eq. 10.3, cl: 10.3.2, IRC: 112-2011)
*+
For members with vertical shear reinforcement, the shear resistance Vrd is smaller of,
++
***
****(Eq. 10.20, cl: 10.3.2, IRC: 112-2011)
++**
++++
++*Asw = Cross sectional area of shear reinforcement at a section pg-90
++**Areqd = Min area of reinforcement required
s = Spacing of shear reinforcement pg-91+++
z = lever arm to be taken as 0.9 for RC sect & calculated for PSC section pg-91
fywd = Design strength of web reinforcement used to resist shear (0.8fyk/γm) pg-86
1 = Strength reduction factor for concrete cracked in shear
= 0.6 for fck<=80Mpa
= 0.9-fck/250 > 0.5 for fck>80Mpa
αρ sinmin wreqd sbA =
αρ sinmin
max
w
sw
b
As =
8.0 STRESSES DUE TO DIFFERENTIAL SHRINKAGE FOR OUTER GIRDER
i) At 0.5 L
0.388
1.713
1.325
As per cl. 606.2, IRC:22-1986, composite action shall be considered to be effective only after the in-situ
concrete has attained atleast 75% of its cube strength.
cast-in slab
girder
Strain at 10 days in slab = 0.0003
Strain at 28 days in girder = 0.00019
Differential shrinkage strain ( e DS ) = -0.00011
C.G. of Composite Section (from bottom ) = 1.325 m
C.G. of in-situ section (from bottom ) = 1.713 m
Lever arm for differential shrinkage moment (e DS ) = 0.388 m
Area of composite section (A) = 1.245 m2
Area of concrete in slab (A slab ) = 0.675 m2
Perimeter of slab in contact with atmosphere (u is ) = 5.2 m
Notional size = 2A /u is = 478.85 mm
Atmospheric conditions depending on relative humidity =
Final creep co-efficient ( F ) = 4.6
Creep reduction factor ( a ) = 0.215
Modulus of elasticity of concrete (E c ) = 3366000 t/m2
Dry Conditions-50%
Restraining force , F DS = e DS .E c .A slab . a = -53.73 t
Moment M DS = F DS .e DS = -20.85 tm
Internal stresses:
Restraining Stresses = e DS .E c . a = -79.61 t/m2
Axial Release:
Axial Stress = Restraining Force/Area = 43.16 t/m2
Section moduli:
Section modulus of top of slab, Z tslab = 0.7734 m3
Section modulus of bottom of slab, Z bslab = 1.4065 m3
Section modulus of bottom of beam, Zbbeam = 0.2917 m3
Moment Release:
At top of slab M DS /Z tslab = 26.96 t/m2
At bottom of slab M DS /Z bslab = 14.82 t/m2
At bottom of beam M DS /Z bbeam = -71.48 t/m2
Top of slab 0 -79.61 43.16 26.96 -9.49
Bottom of slab 0.225 -79.61 43.16 14.82 -21.63
Bottom of beam 1.825 0 43.16 -71.48 -28.32
+ +
LocationShrinkage
StressesDepth
Restrained
stresses
Axial
Release
Moment
Release
-79.6
1
-79.6
1
0
Restrained Stress
43.1
6 43.1
6
43.1
6
Axial Release
26.96
14.82
-
71.48
0
Moment Release
=
0 671.48
0-9.49
-21.6357.98
-28.320
Shrinkage Stress
ii) At 0.391 L
0.388
1.713
1.325
Strain at 10 days in slab = 0.0003
Strain at 28 days in girder = 0.00019
As per cl. 606.2, IRC:22-1986, composite action shall be considered to be effective only after the in-situ
concrete has attained atleast 75% of its cube strength.
cast-in slab
girder
Differential shrinkage strain ( e DS ) = -0.00011
C.G. of Composite Section (from bottom ) = 1.325 m
C.G. of in-situ section (from bottom ) = 1.713 m
Lever arm for differential shrinkage moment (e DS ) = 0.388 m
Area of composite section (A) = 1.245 m2
Area of concrete in slab (A slab ) = 0.675 m2
Perimeter of slab in contact with atmosphere (u is ) = 5.2 m
Notional size = 2A slab /u is = 259.62 mm
Atmospheric conditions depending on relative humidity =
Final creep co-efficient ( F ) = 4.6
Creep reduction factor ( a ) = 0.215
Modulus of elasticity of concrete (E c ) = 3366000 t/m2
Dry Conditions
Restraining force , F DS = e DS .E c .A slab . a = -53.73 t
Moment M DS = F DS .e DS = -20.85 tm
Internal stresses:
Restraining Stresses = e DS .E c . a = -79.61 t/m2
Axial Release:
Axial Stress = Restraining Force/Area = 43.16 t/m2
Section moduli:
Section modulus of top of slab, Z tslab = 0.7734 m3
Section modulus of bottom of slab, Z bslab = 1.4065 m3
Section modulus of bottom of beam, Zbbeam = 0.2917 m3
Moment Release:
At top of slab M DS /Z tslab = 26.96 t/m2
At bottom of slab M DS /Z bslab = 14.82 t/m2
At bottom of beam M DS /Z bbeam = -71.48 t/m2
Top of slab 0 -79.61 43.16 26.96 -9.49
Bottom of slab 0.225 -79.61 43.16 14.82 -21.63
Bottom of beam 1.825 0 43.16 -71.48 -28.32
+ +
Location DepthRestrained
stresses
Axial
Release
Moment
Release
Shrinkage
Stresses
-
79.6
1
-79.6
1
0
Restrained Stress
43.1
6 43.1
6
43.1
6
Axial Release
26.96
14.82
-71.4
8
0
Moment Release
=
0 68
0-9.49
-21.6357.98
-28.320
Shrinkage Stress
iii) At 0.283 L
0.388
1.713
1.325
Strain at 10 days in slab = 0.0003
Strain at 28 days in girder = 0.00019
As per cl. 606.2, IRC:22-1986, composite action shall be considered to be effective only after the in-situ
concrete has attained atleast 75% of its cube strength.
cast-in slab
girder
Differential shrinkage strain ( e DS ) = -0.00011
C.G. of Composite Section (from bottom ) = 1.325 m
C.G. of in-situ section (from bottom ) = 1.713 m
Lever arm for differential shrinkage moment (e DS ) = 0.388 m
Area of composite section (A) = 1.245 m2
Area of concrete in slab (A slab ) = 0.675 m2
Perimeter of slab in contact with atmosphere (u is ) = 5.2 m
Notional size = 2A slab /u is = 259.62 mm
Atmospheric conditions depending on relative humidity =
Final creep co-efficient ( F ) = 4.6
Creep reduction factor ( a ) = 0.215
Modulus of elasticity of concrete (E c ) = 3366000 t/m2
Dry Conditions
Restraining force , F DS = e DS .E c .A slab . a = -53.73 t
Moment M DS = F DS .e DS = -20.85 tm
Internal stresses:
Restraining Stresses = e DS .E c . a = -79.61 t/m2
Axial Release:
Axial Stress = Restraining Force/Area = 43.16 t/m2
Section moduli:
Section modulus of top of slab, Z tslab = 0.7734 m3
Section modulus of bottom of slab, Z bslab = 1.4065 m3
Section modulus of bottom of beam, Zbbeam = 0.2917 m3
Moment Release:
At top of slab M DS /Z tslab = 26.96 t/m2
At bottom of slab M DS /Z bslab = 14.82 t/m2
At bottom of beam M DS /Z bbeam = -71.48 t/m2
Top of slab 0 -79.61 43.16 26.96 -9.49
Bottom of slab 0.225 -79.61 43.16 14.82 -21.63
Bottom of beam 1.825 0 43.16 -71.48 -28.32
+ +
Location DepthRestrained
stresses
Axial
Release
Moment
Release
Shrinkage
Stresses
-
79.6
1
-79.6
1
0
Restrained Stress
43.1
6 43.1
6
43.1
6
Axial Release
26.96
14.82
-
71.48
0
Moment Release
=
0 671.48
0-9.49
-21.6357.98
-28.320
Shrinkage Stress
iv) At 0.174 L
0.388
1.713
1.325
Strain at 10 days in slab = 0.0003
Strain at 28 days in girder = 0.00019
As per cl. 606.2, IRC:22-1986, composite action shall be considered to be effective only after the in-situ
concrete has attained atleast 75% of its cube strength.
cast-in slab
girder
Differential shrinkage strain ( e DS ) = -0.00011
C.G. of Composite Section (from bottom ) = 1.325 m
C.G. of in-situ section (from bottom ) = 1.713 m
Lever arm for differential shrinkage moment (e DS ) = 0.388 m
Area of composite section (A) = 1.245 m2
Area of concrete in slab (A slab ) = 0.675 m2
Perimeter of slab in contact with atmosphere (u is ) = 5.2 m
Notional size = 2A slab /u is = 259.62 mm
Atmospheric conditions depending on relative humidity =
Final creep co-efficient ( F ) = 4.6
Creep reduction factor ( a ) = 0.215
Modulus of elasticity of concrete (E c ) = 3366000 t/m2
Dry Conditions
Restraining force , F DS = e DS .E c .A slab . a = -53.73 t
Moment M DS = F DS .e DS = -20.85 tm
Internal stresses:
Restraining Stresses = e DS .E c . a = -79.61 t/m2
Axial Release:
Axial Stress = Restraining Force/Area = 43.16 t/m2
Section moduli:
Section modulus of top of slab, Z tslab = 0.7734 m3
Section modulus of bottom of slab, Z bslab = 1.4065 m3
Section modulus of bottom of beam, Zbbeam = 0.2917 m3
Moment Release:
At top of slab M DS /Z tslab = 26.96 t/m2
At bottom of slab M DS /Z bslab = 14.82 t/m2
At bottom of beam M DS /Z bbeam = -71.48 t/m2
Top of slab 0 -79.61 43.16 26.96 -9.49
Bottom of slab 0.225 -79.61 43.16 14.82 -21.63
Bottom of beam 1.825 0 43.16 -71.48 -28.32
+ +
Location DepthRestrained
stresses
Axial
Release
Moment
Release
Shrinkage
Stresses
-
79.6
1
-79.6
1
0
Restrained Stress
43.1
6 43.1
6
43.1
6
Axial Release
26.96
14.82
-
71.48
0
Moment Release
=
0 671.48
0-9.49
-21.6357.98
-28.320
Shrinkage Stress
v) At 0 L
0.46
1.713
1.253
Strain at 10 days in slab = 0.0003
Strain at 28 days in girder = 0.00019
As per cl. 606.2, IRC:22-1986, composite action shall be considered to be effective only after the in-situ
concrete has attained atleast 75% of its cube strength.
cast-in slab
girder
Differential shrinkage strain ( e DS ) = -0.00011
C.G. of Composite Section (from bottom ) = 1.253 m
C.G. of in-situ section (from bottom ) = 1.713 m
Lever arm for differential shrinkage moment (e DS ) = 0.46 m
Area of composite section (A) = 1.4587 m2
Area of concrete in slab (A slab ) = 0.675 m2
Perimeter of slab in contact with atmosphere (u is ) = 5.2 m
Notional size = 2A slab /u is = 259.62 mm
Atmospheric conditions depending on relative humidity =
Final creep co-efficient ( F ) = 4.6
Creep reduction factor ( a ) = 0.215
Modulus of elasticity of concrete (E c ) = 3366000 t/m2
Dry Conditions
Restraining force , F DS = e DS .E c .A slab . a = -53.73 t
Moment M DS = F DS .e DS = -24.72 tm
Internal stresses:
Restraining Stresses = e DS .E c . a = -79.61 t/m2
Axial Release:
Axial Stress = Restraining Force/Area = 36.83 t/m2
Section moduli:
Section modulus of top of slab, Z tslab = 0.7888 m3
Section modulus of bottom of slab, Z bslab = 1.3005 m3
Section modulus of bottom of beam, Zbbeam = 0.3599 m3
Moment Release:
At top of slab M DS /Z tslab = 31.34 t/m2
At bottom of slab M DS /Z bslab = 19.01 t/m2
At bottom of beam M DS /Z bbeam = -68.69 t/m2
Top of slab 0 -79.61 36.83 31.34 -11.44
Bottom of slab 0.225 -79.61 36.83 19.01 -23.77
Bottom of beam 1.825 0 36.83 -68.69 -31.86
+ +
Location DepthRestrained
stresses
Axial
Release
Moment
Release
Shrinkage
Stresses
-
79.6
1
-79.6
1
0
Restrained Stress
43.1
6 43.1
6
43.1
6
Axial Release
26.96
14.82
-
71.48
0
Moment Release
=
0 671.48
0-9.49
-21.6357.98
-28.320
Shrinkage Stress
Summary:
0.0L
0.174L
0.283L
0.391L
0.5L
-21.63
-21.63
-21.63
-21.63
Section
-31.86
-28.32
-28.32
-28.32
-11.44
-9.49
-9.49
-9.49
-9.49
Stress at top of slabStress at top of
girder
Stress at bottom of
girder
-28.32
-23.77
STRESSES DUE TO DIFFERENTIAL SHRINKAGE FOR INNER GIRDER
i) At 0.5 L
0.388
1.713
1.325
As per cl. 606.2, IRC:22-1986, composite action shall be considered to be effective only after the in-situ
concrete has attained atleast 75% of its cube strength.
cast-in slab
girder
Strain at 10 days in slab = 0.0003
Strain at 28 days in girder = 0.00019
Differential shrinkage strain ( e DS ) = -0.00011
C.G. of Composite Section (from bottom ) = 1.325 m
C.G. of in-situ section (from bottom ) = 1.713 m
Lever arm for differential shrinkage moment (e DS ) = 0.388 m
Area of composite section (A) = 1.245 m2
Area of concrete in slab (A slab ) = 0.675 m2
Perimeter of slab in contact with atmosphere (u is ) = 5.2 m
Notional size = 2A /u is = 478.85 mm
Atmospheric conditions depending on relative humidity =
Final creep co-efficient ( F ) = 4.6
Creep reduction factor ( a ) = 0.215
Modulus of elasticity of concrete (E c ) = 3366000 t/m2
Dry Conditions-50%
Restraining force , F DS = e DS .E c .A slab . a = -53.73 t
Moment M DS = F DS .e DS = -20.85 tm
Internal stresses:
Restraining Stresses = e DS .E c . a = -79.61 t/m2
Axial Release:
Axial Stress = Restraining Force/Area = 43.16 t/m2
Section moduli:
Section modulus of top of slab, Z tslab = 0.7734 m3
Section modulus of bottom of slab, Z bslab = 1.4065 m3
Section modulus of bottom of beam, Zbbeam = 0.2917 m3
Moment Release:
At top of slab M DS /Z tslab = 26.96 t/m2
At bottom of slab M DS /Z bslab = 14.82 t/m2
At bottom of beam M DS /Z bbeam = -71.48 t/m2
Top of slab 0 -79.61 43.16 26.96 -9.49
Bottom of slab 0.225 -79.61 43.16 14.82 -21.63
Bottom of beam 1.825 0 43.16 -71.48 -28.32
+ +
Shrinkage
StressesLocation Depth
Restrained
stresses
Axial
Release
Moment
Release
-79.6
1
-79.6
1
0
Restrained Stress
43.1
6 43.1
6
43.1
6
Axial Release
26.96
14.82
-
71.48
0
Moment Release
=
0 671.48
0-9.49
-21.6357.98
-28.320
Shrinkage Stress
ii) At 0.391 L
0.388
1.713
1.325
Strain at 10 days in slab = 0.0003
Strain at 28 days in girder = 0.00019
As per cl. 606.2, IRC:22-1986, composite action shall be considered to be effective only after the in-situ
concrete has attained atleast 75% of its cube strength.
cast-in slab
girder
Differential shrinkage strain ( e DS ) = -0.00011
C.G. of Composite Section (from bottom ) = 1.325 m
C.G. of in-situ section (from bottom ) = 1.713 m
Lever arm for differential shrinkage moment (e DS ) = 0.388 m
Area of composite section (A) = 1.245 m2
Area of concrete in slab (A slab ) = 0.675 m2
Perimeter of slab in contact with atmosphere (u is ) = 5.2 m
Notional size = 2A slab /u is = 259.62 mm
Atmospheric conditions depending on relative humidity =
Final creep co-efficient ( F ) = 4.6
Creep reduction factor ( a ) = 0.215
Modulus of elasticity of concrete (E c ) = 3366000 t/m2
Dry Conditions
Restraining force , F DS = e DS .E c .A slab . a = -53.73 t
Moment M DS = F DS .e DS = -20.85 tm
Internal stresses:
Restraining Stresses = e DS .E c . a = -79.61 t/m2
Axial Release:
Axial Stress = Restraining Force/Area = 43.16 t/m2
Section moduli:
Section modulus of top of slab, Z tslab = 0.7734 m3
Section modulus of bottom of slab, Z bslab = 1.4065 m3
Section modulus of bottom of beam, Zbbeam = 0.2917 m3
Moment Release:
At top of slab M DS /Z tslab = 26.96 t/m2
At bottom of slab M DS /Z bslab = 14.82 t/m2
At bottom of beam M DS /Z bbeam = -71.48 t/m2
Top of slab 0 -79.61 43.16 26.96 -9.49
Bottom of slab 0.225 -79.61 43.16 14.82 -21.63
Bottom of beam 1.825 0 43.16 -71.48 -28.32
+ +
Shrinkage
StressesLocation Depth
Restrained
stresses
Axial
Release
Moment
Release
-
79.6
1
-79.6
1
0
Restrained Stress
43.1
6 43.1
6
43.1
6
Axial Release
26.96
14.82
-
71.48
0
Moment Release
=
0 671.48
0-9.49
-21.6357.98
-28.320
Shrinkage Stress
iii) At 0.283 L
0.388
1.713
1.325
Strain at 10 days in slab = 0.0003
Strain at 28 days in girder = 0.00019
As per cl. 606.2, IRC:22-1986, composite action shall be considered to be effective only after the in-situ
concrete has attained atleast 75% of its cube strength.
cast-in slab
girder
Differential shrinkage strain ( e DS ) = -0.00011
C.G. of Composite Section (from bottom ) = 1.325 m
C.G. of in-situ section (from bottom ) = 1.713 m
Lever arm for differential shrinkage moment (e DS ) = 0.388 m
Area of composite section (A) = 1.245 m2
Area of concrete in slab (A slab ) = 0.675 m2
Perimeter of slab in contact with atmosphere (u is ) = 5.2 m
Notional size = 2A slab /u is = 259.62 mm
Atmospheric conditions depending on relative humidity =
Final creep co-efficient ( F ) = 4.6
Creep reduction factor ( a ) = 0.215
Modulus of elasticity of concrete (E c ) = 3366000 t/m2
Dry Conditions
Restraining force , F DS = e DS .E c .A slab . a = -53.73 t
Moment M DS = F DS .e DS = -20.85 tm
Internal stresses:
Restraining Stresses = e DS .E c . a = -79.61 t/m2
Axial Release:
Axial Stress = Restraining Force/Area = 43.16 t/m2
Section moduli:
Section modulus of top of slab, Z tslab = 0.7734 m3
Section modulus of bottom of slab, Z bslab = 1.4065 m3
Section modulus of bottom of beam, Zbbeam = 0.2917 m3
Moment Release:
At top of slab M DS /Z tslab = 26.96 t/m2
At bottom of slab M DS /Z bslab = 14.82 t/m2
At bottom of beam M DS /Z bbeam = -71.48 t/m2
Top of slab 0 -79.61 43.16 26.96 -9.49
Bottom of slab 0.225 -79.61 43.16 14.82 -21.63
Bottom of beam 1.825 0 43.16 -71.48 -28.32
+ +
Shrinkage
StressesLocation Depth
Restrained
stresses
Axial
Release
Moment
Release
-
79.6
1
-79.6
1
0
Restrained Stress
43.1
6 43.1
6
43.1
6
Axial Release
26.96
14.82
-
71.48
0
Moment Release
=
0 671.48
0-9.49
-21.6357.98
-28.320
Shrinkage Stress
iv) At 0.174 L
0.388
1.713
1.325
Strain at 10 days in slab = 0.0003
Strain at 28 days in girder = 0.00019
As per cl. 606.2, IRC:22-1986, composite action shall be considered to be effective only after the in-situ
concrete has attained atleast 75% of its cube strength.
cast-in slab
girder
Differential shrinkage strain ( e DS ) = -0.00011
C.G. of Composite Section (from bottom ) = 1.325 m
C.G. of in-situ section (from bottom ) = 1.713 m
Lever arm for differential shrinkage moment (e DS ) = 0.388 m
Area of composite section (A) = 1.245 m2
Area of concrete in slab (A slab ) = 0.675 m2
Perimeter of slab in contact with atmosphere (u is ) = 5.2 m
Notional size = 2A slab /u is = 259.62 mm
Atmospheric conditions depending on relative humidity =
Final creep co-efficient ( F ) = 4.6
Creep reduction factor ( a ) = 0.215
Modulus of elasticity of concrete (E c ) = 3366000 t/m2
Dry Conditions
Restraining force , F DS = e DS .E c .A slab . a = -53.73 t
Moment M DS = F DS .e DS = -20.85 tm
Internal stresses:
Restraining Stresses = e DS .E c . a = -79.61 t/m2
Axial Release:
Axial Stress = Restraining Force/Area = 43.16 t/m2
Section moduli:
Section modulus of top of slab, Z tslab = 0.7734 m3
Section modulus of bottom of slab, Z bslab = 1.4065 m3
Section modulus of bottom of beam, Zbbeam = 0.2917 m3
Moment Release:
At top of slab M DS /Z tslab = 26.96 t/m2
At bottom of slab M DS /Z bslab = 14.82 t/m2
At bottom of beam M DS /Z bbeam = -71.48 t/m2
Top of slab 0 -79.61 43.16 26.96 -9.49
Bottom of slab 0.225 -79.61 43.16 14.82 -21.63
Bottom of beam 1.825 0 43.16 -71.48 -28.32
+ +
Shrinkage
StressesLocation Depth
Restrained
stresses
Axial
Release
Moment
Release
-
79.6
1
-79.6
1
0
Restrained Stress
43.1
6 43.1
6
43.1
6
Axial Release
26.96
14.82
-
71.48
0
Moment Release
=
0 671.48
0-9.49
-21.6357.98
-28.320
Shrinkage Stress
v) At 0 L
0.46
1.713
1.253
Strain at 10 days in slab = 0.0003
Strain at 28 days in girder = 0.00019
As per cl. 606.2, IRC:22-1986, composite action shall be considered to be effective only after the in-situ
concrete has attained atleast 75% of its cube strength.
cast-in slab
girder
Differential shrinkage strain ( e DS ) = -0.00011
C.G. of Composite Section (from bottom ) = 1.253 m
C.G. of in-situ section (from bottom ) = 1.713 m
Lever arm for differential shrinkage moment (e DS ) = 0.46 m
Area of composite section (A) = 1.4587 m2
Area of concrete in slab (A slab ) = 0.675 m2
Perimeter of slab in contact with atmosphere (u is ) = 5.2 m
Notional size = 2A slab /u is = 259.62 mm
Atmospheric conditions depending on relative humidity =
Final creep co-efficient ( F ) = 4.6
Creep reduction factor ( a ) = 0.215
Modulus of elasticity of concrete (E c ) = 3366000 t/m2
Dry Conditions
Restraining force , F DS = e DS .E c .A slab . a = -53.73 t
Moment M DS = F DS .e DS = -24.72 tm
Internal stresses:
Restraining Stresses = e DS .E c . a = -79.61 t/m2
Axial Release:
Axial Stress = Restraining Force/Area = 36.83 t/m2
Section moduli:
Section modulus of top of slab, Z tslab = 0.7888 m3
Section modulus of bottom of slab, Z bslab = 1.3005 m3
Section modulus of bottom of beam, Zbbeam = 0.3599 m3
Moment Release:
At top of slab M DS /Z tslab = 31.34 t/m2
At bottom of slab M DS /Z bslab = 19.01 t/m2
At bottom of beam M DS /Z bbeam = -68.69 t/m2
Top of slab 0 -79.61 36.83 31.34 -11.44
Bottom of slab 0.225 -79.61 36.83 19.01 -23.77
Bottom of beam 1.825 0 36.83 -68.69 -31.86
+ +
Shrinkage
StressesLocation Depth
Restrained
stresses
Axial
Release
Moment
Release
-
79.6
1
-79.6
1
0
Restrained Stress
43.1
6 43.1
6
43.1
6
Axial Release
26.96
14.82
-
71.48
0
Moment Release
=
0 671.48
0-9.49
-21.6357.98
-28.320
Shrinkage Stress
Summary:
0.0L
0.174L
0.283L
0.391L
0.5L
Section Stress at top of slabStress at top of
girder
Stress at bottom of
girder
-11.44 -23.77 -31.86
-9.49 -21.63 -28.32
-9.49 -21.63 -28.32
-9.49 -21.63 -28.32
-9.49 -21.63 -28.32
Temperature Stresses
A) Sample Calculation for thermal stresses (temperature rise) at section 0.5L for outer girder
Temperature stress at fibre due to rise in temperature is,
- Σ F - Σ M * y + α t E
Where,
Σ F = Σ ( α tn E An ) = α E Σ ( An tn )
Σ M = Σ ( α tn E An yn ) = α E Σ ( An tn yn )
n = No. of zones
= Area of nth zone
= Mean temperature of nth zone
= C.G. of nth zone from N.A.
= Area of Cross-section
= Distance of considered section to N.A.
= Moment of Inertia about C.G. of the Section
= Temperature at considered section
Co-efficient of thermal expansion, α = peroC
For M GRADE, fck = N/mm2
Elastic Modulus, E = 5000 * SQRT(fck) = t/m2
oC
a
4oC
b
9.0
A I
Cl.218.4. IRC:6-2000
40 40
An
tn
yn
A
y
I
3 17.8
0.225 0.15
0.80.15
t
0.0000117
3366000
c
N A
X X
d
e
oC
1.825
1.275
0.1
0.1
0.25 0.15
2.1
0.45Positive
Temperature
Differenece
0.1 0.25
0.275
0.25
Fig.10. IRC:6-2000
Moment of Inertia @ X-X :
Description
Y = Σ AY = m Ycg from top = m
Σ A Ycg from bott = m
= Σ Icg + Σ AY2
- Σ Ah2
= m4
Considering following zones: Zone a - Deck Slab
Zone b - Top flange
Zone c -web above centroid
Zone d - web below centroid
Zone e - Bottom flange
No. b d A y from top Ay Ay x y Icg
Deck Slab 1 3.000 0.225 0.675 0.113 0.076 0.009 0.002848
0.000225
1 0.250 0.100 0.025 0.425 0.011
Top Flange 1 0.800 0.150 0.120 0.300
0.005 0.000021
Bottom Flange 1 0.250 0.100 0.025 1.525 0.038 0.058
0.036 0.011
0.000015
Web 1 0.250 1.000 0.250 0.975 0.244 0.238 0.020833
2 0.275 0.100 0.028 0.408 0.011 0.005
0.000021
2 0.100 0.100 0.010 1.542 0.015 0.024 0.000006
1 0.450 0.250 0.113 1.700 0.191 0.325 0.000586
0.673 0.024554
0.50 0.50
1.33
Ixx 0.386604
Total 1.245 0.622
At Aty
(oC) (m
2)
zone Bot.of zone
from top (m)
c.g of zone
from top (m)
t (for zone) Ac.g.of zone
from N.A.
y (m)
4.776 1.850
b 0.475 0.335 0.905 0.173 0.164 0.156 0.026
a 0.225 0.113 7.075 0.675 0.387
0.000 0.000
d 1.475 1.475 0.000 0.244 -0.975 0.000 0.000
c 0.500 0.487 0.000 0.006 0.012
0.000 0.000
total 1.245 4.932 1.876
e 1.825 1.660 0.000 0.148 -1.160
Σ F = α E Σ ( An tn ) = * * = t/m2
Σ M = α E Σ ( An tn yn ) = * * = tm
Σ F / A Σ M y / I
Temperature Stress and its Distribution (t/m2)
Stress @
section from
top (m)
Dist. From
N.A. y
(m)
t α t E Temp. Stress
1.17E-05 3366000 4.932 156.000
A 1.245
= (- Σ F / A - ΣMy/I + α t E)
t/m2
t/m2
(oC) t/m
2 (t/m
2)
1.17E-05 3366000 1.876 73.865
449.499 (Comp.)
0.225 156.000 0.275 52.516 2.450 96.486 -112.029 (Tensile)
0.000 156.000 0.500 95.504 17.800 701.003
-160.751 (Tensile)
0.500 156.000 0.000 0.000 0.000 0.000 -156.000 (Tensile)
0.475 156.000 0.025 4.751 0.000 0.000
449.499
-112.029
-160.751
-156.000
30.309
179.883
30.309 (Comp.)
1.825 156.000 -1.325 -253.180 2.100 82.703 179.883 (Comp.)
1.475 156.000 -0.975 -186.309 0.000 0.000
B) Sample Calculation for thermal stresses (temperature fall) at section 0.5L for outer girder
Temperature stress at fibre due to rise in temperature is,
- Σ F - Σ M * y + α t E
Where,
Σ F = Σ ( α tn E An ) = α E Σ ( An tn )
Σ M = Σ ( α tn E An yn ) = α E Σ ( An tn yn )
n = No. of zones
= Area of nth zone
= Mean temperature of nth zone
= C.G. of nth zone from N.A.
= Area of Cross-section
= Distance of considered section to N.A.
= Moment of Inertia about C.G. of the Section
= Temperature at considered section
Co-efficient of thermal expansion, α = peroC
For M 40 GRADE
fck = N/mm2
Elastic Modulus, E = 5000 * SQRT(fck) = t/m2
Considering following zones: Zone a - Deck Slab
A I
Cl.218.4. IRC:6-2000
40
3366000 Cl.10.2. IRC:18-2000
An
tn
yn
A
y
I
t
1.17E-05
Zone b - Top flange
Zone c -web above centroid
Zone d - web below centroid
Zone e - Bottom flange
oC
a
oC
b
c
d
eoC
oC
-0.7
0.1 0.25
0.275
0.25
1.825
3 -10.6
0.225 0.25
0.80.15
0.825
0.1
0.1 0.25
-0.8
0.25 0.25
-6.6
0.45Reverse
Temperature
Differenece
Fig.10. IRC:6-2000
Moment of Inertia @ X-X :
Description
Y = S AY = m Ycg from top = m
S A Ycg from bott = m
= S Icg + S AY2
- S Ah2
= m4
Centroid of zone a :
y from top = Σ = = m
Σ
Centroid of zone b :
y from top = Σ = = m
Σ
No. b d A y from top Ay Ay x y Icg
0.076 0.009 0.002848Deck Slab-a 1 3.000 0.225 0.675 0.113
0.011 0.000225
1 0.250 0.100 0.025 0.425 0.011 0.005 0.000021
Top Fl.-b 1 0.800 0.150 0.120 0.300 0.036
2 0.275 0.100 0.028 0.408 0.011 0.005 0.000015
0.244 0.238 0.020833
Bottom Fl.-e 1 0.250 0.100 0.025 1.525 0.038
web-c&d 1 0.250 1.000 0.250 0.975
0.058 0.000021
2 0.100 0.100 0.010 1.542 0.015 0.024 0.000006
Ixx 0.386604
0.325 0.000586
Total 1.245 0.622 0.673 0.024554
1 0.450 0.250 0.113 1.700 0.191
A 0.675
AY 0.058 0.335
A 0.173
0.4999 0.4999
1.3251
AY 0.076 0.113
Centroid of zone c :
for zone c:
y from top = Σ = = m
Σ
Centroid of zone d :
for zone d:
y from top = Σ = = m
Σ
Centroid of zone e :
y from top = Σ = = m
Σ
Σ F = α E Σ ( An tn ) = * * = t/m2
(m2)
1 0.250 0.025 0.006 0.487 0.003
No. b d A y from top Ay
(m) (m) (m2) (m)
AY 0.003 0.487
Total 0.006 0.003 A 0.006
Total 0.244 0.241 A
(m) (m2)
1 0.250 0.975 0.244 0.987 0.241
No. b d A y from top Ay
(m) (m) (m2)
0.244
AY 0.245 1.660
A 0.148
AY 0.241 0.987
At Aty
(oC) (m
2)
zone Bot.of zone
from top (m)
c.g of zone
from top (m)
t (for zone) Ac.g.of zone
from N.A.
y (m)
-4.148 -1.607
b 0.475 0.335 -0.239 0.173 0.164 -0.041 -0.007
a 0.225 0.113 -6.145 0.675 0.387
-0.004 0.000
d 1.475 0.987 0.000 0.244 -0.488 0.000 0.000
c 0.500 0.487 -0.665 0.006 0.012
-0.408 0.473
total 1.245 -4.601 -1.141
e 1.825 1.660 -2.763 0.148 -1.160
1.17E-05 3366000 -4.601 -145.533
A 1.245
Σ M = α E Σ ( An tn yn ) = * * = tm
Σ F / A Σ M y / IStress @
section from
top (m)
Dist. From
N.A. y
(m)
t α t E Temp. Stress
= (- Σ F / A - ΣMy/I + α t E)
t/m2
t/m2
(oC) t/m
2 (t/m
2)
1.17E-05 3366000 -1.141 -44.934
-213.821 (Tensile)
0.475 -145.533 0.025 -2.890 -0.630 -24.811 123.612 (Comp.)
0.000 -145.533 0.500 -58.098 -10.600 -417.451
0.225 -145.533 110.924-66.556-1.690-31.9470.275 (Comp.)
117.980 (Comp.)
1.475 -145.533 -0.975 113.337 -0.320 -12.602 19.594 (Comp.)
0.500 -145.533 0.000 0.000 -0.700 -27.553
-213.821
123.612
117.980
19.594
-268.406 (Tensile)1.825 -145.533 -1.325 154.016 -6.600 -259.923
Temperature Stress and its Distribution (t/m2)
-268.406
0.000
C) Sample Calculation for thermal stresses (temperature rise) at section 0.5L for inner girder
Temperature stress at fibre due to rise in temperature is,
- Σ F - Σ M * y + α t E
Where,
Σ F = Σ ( α tn E An ) = α E Σ ( An tn )
Σ M = Σ ( α tn E An yn ) = α E Σ ( An tn yn )
n = No. of zones
= Area of nth zone
= Mean temperature of nth zone
= C.G. of nth zone from N.A.
= Area of Cross-section
= Distance of considered section to N.A.
= Moment of Inertia about C.G. of the Section
= Temperature at considered section
Co-efficient of thermal expansion, α = peroC
For M GRADE, fck = N/mm2
Elastic Modulus, E = 5000 * SQRT(fck) = t/m2
oC
a
4oC
0.225 0.15
0.8
A I
Cl.218.4. IRC:6-2000
40 40
3 17.8
t
0.0000117
3366000
An
tn
yn
A
y
I
4 C
b
c
N A
X X
d
e
oC
0.80.15
0.1
0.1
0.25 0.15
2.1
0.45Positive
Temperature
Differenece
0.1 0.25
0.275
0.25
1.275
1.825
Fig.10. IRC:6-2000
Moment of Inertia @ X-X :
Description
Y = Σ AY = m Ycg from top = m
Σ A Ycg from bott = m
= Σ Icg + Σ AY2
- Σ Ah2
= m4
Considering following zones: Zone a - Deck Slab
Zone b - Top flange
Zone c -web above centroid
Zone d - web below centroid
Zone e - Bottom flange
No. b d A y from top Ay Ay x y Icg
Deck Slab 1 3.000 0.225 0.675 0.113 0.076 0.009 0.002848
0.000225
1 0.250 0.100 0.025 0.425 0.011
Top Flange 1 0.800 0.150 0.120 0.300
0.005 0.000021
Bottom Flange 1 0.250 0.100 0.025 1.525 0.038 0.058
0.036 0.011
0.000015
Web 1 0.250 1.000 0.250 0.975 0.244 0.238 0.020833
2 0.275 0.100 0.028 0.408 0.011 0.005
0.000021
2 0.100 0.100 0.010 1.542 0.015 0.024 0.000006
1 0.450 0.250 0.113 1.700 0.191 0.325 0.000586
0.673 0.024554
0.50 0.50
1.33
Ixx 0.386604
Total 1.245 0.622
At Aty
(oC) (m
2)
zone Bot.of zone
from top (m)
c.g of zone
from top (m)
t (for zone) Ac.g.of zone
from N.A.
y (m)
4.776 1.850
b 0.475 0.335 0.905 0.173 0.164 0.156 0.026
a 0.225 0.113 7.075 0.675 0.387
0.000 0.000c 0.500 0.487 0.000 0.006 0.012
Σ F = α E Σ ( An tn ) = * * = t/m2
Σ M = α E Σ ( An tn yn ) = * * = tm
Σ F / A Σ M y / I
Temperature Stress and its Distribution (t/m2)
d 1.475 1.475 0.000 0.244 -0.975 0.000 0.000
0.000 0.000
total 1.245 4.932 1.876
e 1.825 1.660 0.000 0.148 -1.160
Stress @
section from
top (m)
Dist. From N.A.
y (m)t α t E Temp. Stress
1.17E-05 3366000 4.932 156.000
A 1.245
= (- Σ F / A - ΣMy/I + α t E)
t/m2
t/m2
(oC) t/m
2 (t/m
2)
1.17E-05 3366000 1.876 73.865
449.499 (Comp.)
0.225 156.000 0.275 52.516 2.450 96.486 -112.029 (Tensile)
0.000 156.000 0.500 95.504 17.800 701.003
-160.751 (Tensile)
0.500 156.000 0.000 0.000 0.000 0.000 -156.000 (Tensile)
0.475 156.000 0.025 4.751 0.000 0.000
449.499
-112.029
-160.751
-156.000
30.309
179.883
30.309 (Comp.)
1.825 156.000 -1.325 -253.180 2.100 82.703 179.883 (Comp.)
1.475 156.000 -0.975 -186.309 0.000 0.000
D) Sample Calculation for thermal stresses (temperature fall) at section 0.5L for inner girder
Temperature stress at fibre due to rise in temperature is,
- Σ F - Σ M * y + α t E
Where,
Σ F = Σ ( α tn E An ) = α E Σ ( An tn )
Σ M = Σ ( α tn E An yn ) = α E Σ ( An tn yn )
n = No. of zones
= Area of nth zone
= Mean temperature of nth zone
= C.G. of nth zone from N.A.
= Area of Cross-section
= Distance of considered section to N.A.
= Moment of Inertia about C.G. of the Section
= Temperature at considered section
Co-efficient of thermal expansion, α = peroC
For M 40 GRADE
fck = N/mm2
Elastic Modulus, E = 5000 * SQRT(fck) = N/mm2
= t/m2
A I
An
tn
yn
A
y
I
t
40
31622.78
1.17E-05 Cl.218.4. IRC:6-2000
3366000 Cl.10.2. IRC:18-2000
Considering following zones: Zone a - Deck Slab
Zone b - Top flange
Zone c -web above centroid
Zone d - web below centroid
Zone e - Bottom flange
oC
a
oC
b
c
d
eoC
oC
0.225 0.25
0.80.15
-0.7
0.1 0.25
-0.8
Fig.10. IRC:6-2000
3 -10.6
0.25 0.25
-6.6
0.45Reverse
Temperature
Differenece
0.275
0.25
1.825
0.825
0.1
0.1 0.25
Moment of Inertia @ X-X :
Description
Y = S AY = m Ycg from top = m
S A Ycg from bott = m
= S Icg + S AY2
- S Ah2
= m4
Centroid of zone a :
y from top = Σ = = m
Σ
Centroid of zone b :
y from top = Σ = = m
0.036 0.011 0.000225
0.005 0.000021
0.000015
0.020833
0.000021
0.673 0.024554
No. b d A y from top Ay Ay x y Icg
Deck Slab-a 1 3.000 0.225 0.675 0.113 0.076 0.009 0.002848
1 0.250 0.100 0.025 0.425 0.011
Top Fl.-b 1 0.800 0.150 0.120 0.300
2 0.275 0.100 0.028 0.408 0.011 0.005
Bottom Fl.-e 1 0.250 0.100 0.025 1.525
web-c&d 1 0.250 1.000 0.250 0.975 0.244 0.238
0.038 0.058
2 0.100 0.100 0.010 1.542 0.015 0.024 0.000006
1 0.450 0.250 0.113 1.700 0.191 0.325 0.000586
0.4999 0.4999
1.3251
Ixx 0.386604
Total 1.245 0.622
AY 0.076 0.113
A 0.675
AY 0.058 0.335
Σ
Centroid of zone c :
for zone c:
y from top = Σ = = m
Σ
Centroid of zone d :
for zone d:
y from top = Σ = = m
Σ
Centroid of zone e :
y from top = Σ = = m
Σ
Ay
(m2)
No. b d A y from top
(m) (m) (m2) (m)
A 0.173
AY 0.003 0.487
Total 0.006 0.003 A
1 0.250 0.025 0.006 0.487 0.003
0.006
Total 0.244 0.241 A
(m) (m2)
1 0.250 0.975 0.244 0.987 0.241
No. b d A y from top Ay
(m) (m) (m2)
0.244
AY 0.245 1.660
A 0.148
AY 0.241 0.987
At Aty
(oC) (m
2)
zone Bot.of zone
from top (m)
c.g of zone
from top (m)
t (for zone) Ac.g.of zone
from N.A.
y (m)
-4.148 -1.607
b 0.475 0.335 -0.239 0.173 0.164 -0.041 -0.007
a 0.225 0.113 -6.145 0.675 0.387
-0.004 0.000
d 1.475 0.987 0.000 0.244 -0.488 0.000 0.000
c 0.500 0.487 -0.665 0.006 0.012
-0.408 0.473
total 1.245 -4.601 -1.141
e 1.825 1.660 -2.763 0.148 -1.160
Σ F = α E Σ ( An tn ) = * * = t/m2
Σ M = α E Σ ( An tn yn ) = * * = tm
Σ F / A Σ M y / I
110.924-66.556-1.690-31.9470.275 (Comp.)
1.825 -145.533 -1.325 154.016 -6.600 -259.923 -268.406
123.612
117.980
-213.821
t/m2
t/m2
(oC) t/m
2 (t/m
2)
0.000 -145.533 0.500 -58.098 -10.600 -417.451 -213.821 (Tensile)
1.17E-05 3366000 -4.601 -145.533
A 1.245
1.17E-05
0.475 -145.533 0.025 -2.890 -0.630 -24.811
3366000 -1.141
123.612
-44.934
Stress @
section from
top (m)
Dist. From
N.A. y
(m)
t α t E Temp. Stress
= (- Σ F / A - ΣMy/I + α t E)
(Comp.)
0.225 -145.533
0.500 -145.533 0.000 0.000 -0.700 -27.553 117.980 (Comp.)
1.475 -145.533 -0.975 113.337 -0.320 -12.602 19.594 (Comp.)
(Tensile)
Temperature Stress and its Distribution (t/m2)
-268.406
0.000
19.594
Summary of temperature stresses:
Depth of girder + slab = m
Outer Girder-temperature rise
Outer Girder-temperature fall
1 0.5L 449.5 -112.03 150.82
Stress at top of slab (t/m2)SectionS.No.
2 0.391L 449.5 -112.03 150.82
3 0.283L 449.5 -112.03 150.82
4 0.74L 449.5 -112.03 150.82
5 0.0L 457.19 -104.3 152.35
S.No. Section Stress at top of slab (t/m2) Stress at top of girder (t/m
2)
Stress at level of extreme
reinforcement (t/m2)
1 0.5L -213.82 110.92 -212.45
1.757
Depth of extreme
layer of steel (m)
1.757
Depth of extreme
layer of steel (m)
1.825
1.757
1.757
1.757
1.757
Stress at top of girder (t/m2)
Stress at level of extreme
reinforcement (t/m2)
Inner Girder-temperature rise
Inner Girder-temperature fall
1 0.5L -213.82 110.92 -212.45
2 0.391L -213.82 110.92 -212.45
3 0.283L -213.82 110.92 -212.45
4 0.74L -213.82 110.92 -212.45
5 0.0L -221.21 101.31 -214.51
S.No. Section Stress at top of slab (t/m2) Stress at top of girder (t/m
2)
Stress at level of extreme
reinforcement (t/m2)
1 0.5L 449.5 -112.03 150.82
2 0.391L 449.5 -112.03 150.82
3 0.283L 449.5 -112.03 150.82
4 0.74L 449.5 -112.03 150.82
5 0.0L 457.19 -104.3 152.35
S.No. Section Stress at top of slab (t/m2) Stress at top of girder (t/m
2)
Stress at level of extreme
reinforcement (t/m2)
1 0.5L -213.82 110.92 -212.45
2 0.391L -213.82 110.92 -212.45
3 0.283L -213.82 110.92 -212.45
4 0.74L -213.82 110.92 -212.45
5 0.0L -221.21 101.31 -214.51
1.757
1.757
1.757
1.757
1.757
1.757
Depth of extreme
layer of steel (m)
1.757
1.757
1.757
1.757
1.757
Depth of extreme
layer of steel (m)
1.757
1.757
1.757
1.757
Serviceability Limit State
Design Methodology:
The following check are done as per IRC:112-2011
о For stress check:
-
-
о For crack width check:
-
о For deflection check:
-
10.0
Due to long term creep and shrinkage effect, the effective concrete modulus is reduced for sustained
load.
Maximum stress at outermost compression fibre and outermost tension fibre were limited to
permissible stresses mentioned in IRC:112-2011
The crack width in concrete has been checked in accordance with Cl:12.3.4 of IRC:112-2011.
Maximum crack width is limited to 0.3mm as per table 12.1 of IRC:112-2011.
For calculation of deflection due to sustained loads, the cracked moment of inertia has been
considered as 70% of the uncracked moment of inertia as per Cl:12.4.2(1) of IRC:112
-
The load factors for serviceablity limit state for rare combination are:
Dead Load = 1
Super-imposed dead load = 1
Live load = 1
Based on the design methodology, Serviceability Limit State checks have been done and presented below.
considered as 70% of the uncracked moment of inertia as per Cl:12.4.2(1) of IRC:112
Due to long term creep and shrinkage effect, the effective concrete modulus is reduced for sustained
load as per Cl:12.4.2(2) of IRC:112-2011.
Stress Check at 0.5L for outer girder
Grade of concrete = M 40
Span of girder (m) =
Width of beam bw =
Depth of girder =
Depth of girder+slab =
Depth of extreme layer of steel =
Modular ratio, m = 6.06 (for live load)
Modular ratio, m = 12.12 (for DL+SIDL)
fc1
in tmt *+
267
11.0
1.473 0.15 12.12 0.25 0.6811 -4373.50 267.49
Stress
in m2
in m in m in m in m in m Fbg**+ Ftg*++
b* d ds**
m
bw n
Fts***
17.200 m
0.250 m
1.600 m
1.825 m
S.No. Description
Mom Ast
1 Gider Self weight 52.828 0.0113
1.757 m
0.80 267
58
379
0
0
-2.3
-58
66
333
166
* For girder alone property, b = width of top flange, and for composite property, b = effective width of slab
** For girder alone property, ds = tck of top flange, and for composite property, ds = tck of slab
-212.45 110.92 -213.82
12 Temp Rise 150.82 -112.03 449.50
11 Differential Shrinkage -28.32 -21.63 -9.49
13 Temp Fall
0.2578 -6124.40 21.17 166.26
0.2578 -12248.84 42.35 332.55
1.698 0.225
6.06 0.259 Live Load 204.195 0.0113 3 1.698 0.225
6.06 0.25
12.12 0.258 SIDL 49.481 0.0113 3 1.698 0.225
12.12 0.25 0.6813 953.60 -45.50 -58.34
0.3756 -3064.30 26.27 65.52
1.473
7 De-shuttering -11.518 0.0113 0.80 1.473 0.15
0.15 12.12 0.25 0.6778 38.09 -2.316
Loss in wt of Deck slab due to
drying -0.46072 0.0113 0.80 1.473
0.8 0.00 0.005 Construction Live load 0 0.0113 0.80 1.473 0.15 12.12 0.25
0.25 0.8 0.00 0.004 Weight of cross-girder 0.15 12.12
12.123 Green weight of deck slab 74.884 0.0113 0.80 1.473 0.15
0.15 12.12 0.25 0.6813 -953.60 58.342 Weight of shuttering 11.518 0.0113 0.80
1.473 0.15 12.12 0.25
1.473
0.6811 -4373.50 267.49
0.25 0.6811 -6199.42 379.15
1 Gider Self weight 52.828 0.0113 0.80
0 0.0113 0.80
10 50% Live Load 102.0975 0.0113 3
b
fc1
ds C1
fc2
n c2
d bw
fst T
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm2
Stress at the bottom of the slab= fc2 = fc1 x (n-ds)/n
Stress at the c.g of steel = fst = m x fc1 x (d - n)/n
Total Compression, C = C1 + C2
Where, C1 = fc1 x b x ds x (2n-ds)/2n
C2 =( fc1 x bw x (n-ds)^2)/2n
C = fc1 x ( b x ds x (2n-ds)/2n + bw x (n-ds)^2/2n )
Total tension, T = m x fc1 x Ast(d - n)/n
By equating the internal forces
Moment of resistance = m x fc1 x Ast(d - n)/n x (d-n/3)
*+ fc1 =
m x Ast(d - n)/n x (d-n/3)
Stress at CG of steel = fst = m x fc1 x (d - n)/n
**+ Stress in the extreme layer of steel = Fbg = (fst *(d-n)+cg form bottom)/(d-n)
*++ Stress in Concrete at top of girder = Ftg = fc1 x (n - ds) / n
*** Stress in Concrete at deck top = Fts = (fst / m) x (n / (d - n ))
Moment
Summary of Stress check at section
As per clause:12.2.2 of IRC:112-2011:
Permissible stresses
In concrete = 0.48fck = 19.2 Mpa = 1958 t/m2
In steel = 0.8fyk = 400 Mpa = 40800 t/m2
TFtg Fts
Top of
Girder
Ftg
0.00
4 Weight of cross-girder 0.00 -11526.51 0.00 704.98 0.00 0.00
3 Green weight of deck slab -6199.42 -11526.51 379.15 704.98 0.00
2 Weight of shuttering -953.60 -5327.09 58.34 325.83 0.00 0.00
1 Gider Self weight -4373.50 -4373.50 267.49 267.49
TFts
0.00 0.00
Cumulative
Top of Girder
Top of
SlabCumulative Top
of SlabSr No Description
Bottom of
GirderCumulative
Bottom of Girder
Fbg TFbg
-9.49
12 Temp Rise 150.82 -31849.87 -112.03 613.31 449.50
10 50 % Live Load -6124.40 -31972.37 21.17 746.97 166.26
-213.82 732.1813 Temp Fall -212.45 -32062.32 110.92 724.23
946.00
11 Differential Shrinkage -28.32 -32000.69 -21.63 725.34
332.55 339.73
505.99
9 Live Load -12248.84 -25847.97 42.35 725.80
496.50
-58.34
8 SIDL -3064.30 -13599.13 26.27 683.45 65.52 7.18
7
Loss wt of Deck slab due to
drying 953.60 -10534.83 -45.50 657.18 -58.34
0.00
6 De-shuttering 38.09 -11488.42 -2.31 702.67 0.00 0.00
5 Construction Live Load 0.00 -11526.51 0.00 704.98 0.00
4 Weight of cross-girder 0.00 -11526.51 0.00 704.98 0.00 0.00
Combination 1+2+3+4+5+6+7+8+9
(Service Condition with Live load)
Combination 1+2+3+4+5+6+7+8
(Service Condition without Live load)
Combination 1+ 2+ 3+ 4+5
( Girder Alone property)
Combination 1+2+3+4+5+6+7+8+9+11
(Service Condition with Live load and
shrinkage)
Combination 1+2+3+4+5+6+7+8+10+11+12
Combinations
339.73 OK
-40800.00 -25876.29 1958.40 704.17 1958.40 330.24 OK
-40800.00 -25847.97 1958.40 725.80 1958.40
Status
-40800.00 -11526.51 1958.40 704.98 1958.40 0.00 OK
1958.40 7.18 OK
Permissible stress
in steel
Actual stress in
steel
Permissible
stress in
concrete
Actual stress
in concrete
Permissible
stress in
concrete
Actual stress in
concrete
-40800.00 -13599.13 1958.40 683.45
Note: Negative value indicates tension. Positive value indicates compression.
1958.40 815.09 1958.40
Combination 1+2+3+4+5+6+7+8+10+11+12
(50% Live Load+ Temp Rise)
-40800.00 -26088.74 OK
Combination 1+2+3+4+5+6+7+8+10+11+13
(50% Live Load+ Temp fall)
-40800.00 -25725.47 1958.40 592.14 1958.40 779.74 OK
116.42
Stress Check at 0.391L for outer girder
Grade of concrete = M 40
Span of girder (m) =
Width of beam bw =
Depth of girder =
Depth of girder+slab =
Depth of extreme layer of steel =
Modular ratio, m = 6.06 (for live load)
Modular ratio, m = 12.12 (for DL+SIDL)
fc1
in tmt *+
268
58
380
0
0
0 0.0072 0.80 1.504
0.8 0.00 0.005 Construction Live load 0 0.0072 0.80 1.504 0.15 12.12 0.25
0.25 0.8 0.00 0.004 Weight of cross-girder 0.15 12.12
12.123 Green weight of deck slab 71.37 0.0072 0.80 1.504 0.15
0.15 12.12 0.25 0.5715 -1274.02 58.412 Weight of shuttering 10.973 0.0072 0.80 1.504
0.5714 -5844.44 267.91
0.25 0.5714 -8286.14 379.82
1 Gider Self weight 50.339 0.0072 0.80 1.504 0.15 12.12 0.25
in m2
in m in m in m in m in m Fbg**+ Ftg*++
b* d ds**
m
bw n
Fts***
17.200 m
0.250 m
1.600 m
1.825 m
S.No. Description
Mom Ast Stress
1.757 m
0
-2.3
-58
68
371
185
* For girder alone property, b = width of top flange, and for composite property, b = effective width of slab
** For girder alone property, ds = tck of top flange, and for composite property, ds = tck of slab
13 Temp Fall -212.45 110.92 -213.82
12 Temp Rise 150.82 -112.03 449.50
11 Differential Shrinkage -28.32 -21.63 -9.49
185.32
0.2111 -17172.61 -24.45 370.60
-4260.24 16.69 68.47
10 50% Live Load 96.898 0.0072 3.00 1.729 0.225
6.06 0.259 Live Load 193.796 0.0072 3.00 1.729 0.225
6.06 0.25 0.2111 -8586.33 -12.21
0.80 1.504
12.12 0.258 SIDL 47.072 0.0072 3.00 1.729 0.225
12.12 0.25 0.5715 1274.02 -43.08 -58.41
0.2975
7 De-shuttering -10.973 0.0072 0.80 1.504 0.15
0.15 12.12 0.25 0.5668 50.88 -2.306
Loss in wt of Deck slab due
to drying -0.43892 0.0072
0.8 0.00 0.005 Construction Live load 0 0.0072 0.80 1.504 0.15 12.12 0.25
b
fc1
ds C1
fc2
n c2
d bw
fst T
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm2
Stress at the bottom of the slab= fc2 = fc1 x (n-ds)/n
Stress at the c.g of steel = fst = m x fc1 x (d - n)/n
Total Compression, C = C1 + C2
Where, C1 = fc1 x b x ds x (2n-ds)/2n
C2 =( fc1 x bw x (n-ds)^2)/2n
C = fc1 x ( b x ds x (2n-ds)/2n + bw x (n-ds)^2/2n )
Total tension, T = m x fc1 x Ast(d - n)/n
By equating the internal forces
Moment of resistance = m x fc1 x Ast(d - n)/n x (d-n/3)
*+ fc1 =
m x Ast(d - n)/n x (d-n/3)
Stress at CG of steel = fst = m x fc1 x (d - n)/n
**+ Stress in the extreme layer of steel = Fbg = (fst *(d-n)+cg form bottom)/(d-n)
*++ Stress in Concrete at top of girder = Ftg = fc1 x (n - ds) / n
*** Stress in Concrete at deck top = Fts = (fst / m) x (n / (d - n ))
Moment
Summary of Stress check at section
As per clause:12.2.2 of IRC:112-2011:
Permissible stresses
In concrete = 0.48fck = 19.2 Mpa = 1958 t/m2
In steel = 0.8fyk = 400 Mpa = 40800 t/m2
370.60 380.669 Live Load -17172.61 -35512.55 -24.45 653.00
-58.41 -58.41
8 SIDL -4260.24 -18339.94 16.69 677.45 68.47 10.06
7
Loss wt of Deck slab due to
drying 1274.02 -14079.70 -43.08 660.76
0.00 0.00
6 De-shuttering 50.88 -15353.72 -2.30 703.84 0.00 0.00
5 Construction Live Load 0.00 -15404.60 0.00 706.14
0.00 0.00
4 Weight of cross-girder 0.00 -15404.60 0.00 706.14 0.00 0.00
3 Green weight of deck slab -8286.14 -15404.60 379.82 706.14
TFts
0.00 0.00
2 Weight of shuttering -1274.02 -7118.46 58.41 326.32 0.00 0.00
1 Gider Self weight -5844.44 -5844.44 267.91 267.91
Sr No DescriptionBottom of
GirderCumulative
Bottom of Girder
Top of
GirderCumulative
Top of Girder
Top of
SlabCumulative Top
of Slab
Fbg TFbg Ftg TFtg Fts
-213.82 792.1713 Temp Fall -212.45 -44188.83 110.92 618.04
-9.49 556.49
12 Temp Rise 150.82 -43976.38 -112.03 507.12 449.50 1005.99
11 Differential Shrinkage -28.32 -44127.20 -21.63 619.15
370.60 380.66
10 50 % Live Load -8586.33 -44098.88 -12.21 640.78 185.32 565.98
9 Live Load -17172.61 -35512.55 -24.45 653.00
157.35 OK
Combination
1+2+3+4+5+6+7+8+10+11+13
(50% Live Load+ Temp fall) -40800.00 -35753.32 1958.40 742.29 1958.40
371.17 OK
Combination
1+2+3+4+5+6+7+8+10+11+12
(50% Live Load+ Temp Rise) -40800.00 -35390.05 1958.40 519.34 1958.40 820.67 OK
Combination 1+2+3+4+5+6+7+8+9+11
(Service Condition with Live load and
shrinkage) -40800.00 -35540.87 1958.40 631.37 1958.40
10.06 OK
Combination 1+2+3+4+5+6+7+8+9
(Service Condition with Live load)-40800.00 -35512.55 1958.40 653.00 1958.40 380.66 OK
Combination 1+2+3+4+5+6+7+8
(Service Condition without Live load)-40800.00 -18339.94 1958.40 677.45 1958.40
Status
Combination 1+ 2+ 3+ 4+5
( Girder Alone property) -40800.00 -15404.60 1958.40 706.14 1958.40 0.00 OK
CombinationsPermissible
stress in steel
Actual stress in
steel
Permissible
stress in
concrete
Actual stress
in concrete
Permissible
stress in
concrete
Actual stress in
concrete
Note: Negative value indicates tension. Positive value indicates compression.
Stress Check at 0.283L for outer girder
Grade of concrete = M 40
Span of girder (m) =
Width of beam bw =
Depth of girder =
Depth of girder+slab =
Depth of extreme layer of steel =
Modular ratio, m = 6.06 (for live load)
Modular ratio, m = 12.12 (for DL+SIDL)
fc1
in tmt *+
228
500.15 12.12 0.25 0.5715 -1083.48 49.672 Weight of shuttering 9.332 0.0072 0.80 1.504
0.5714 -4974.84 228.001 Gider Self weight 42.85 0.0072 0.80 1.504 0.15 12.12 0.25
in m2
in m in m in m in m in m Fbg**+ Ftg*++
b* d ds**
m
bw n
Fts***
17.200 m
0.250 m
1.600 m
1.825 m
S.No. Description
Mom Ast Stress
1.757 m
50
324
0
0
-2
-50
58
319
159
* For girder alone property, b = width of top flange, and for composite property, b = effective width of slab
** For girder alone property, ds = tck of top flange, and for composite property, ds = tck of slab
13 Temp Fall -212.45 110.92 -213.82
12 Temp Rise 150.82 -112.03 449.50
11 Differential Shrinkage -28.32 -21.63 -9.49
159.42
0.2111 -14772.75 -21.03 318.82
-3602.97 14.11 57.90
10 50% Live Load 83.3565 0.0072 3 1.729 0.225
6.06 0.259 Live Load 166.713 0.0072 3 1.729 0.225
6.06 0.25 0.2111 -7386.39 -10.51
0.80 1.504
12.12 0.258 SIDL 39.81 0.0072 3 1.729 0.225
12.12 0.25 0.5715 1083.48 -36.63 -49.67
0.2975
0 0.0072 0.80 1.504
7 De-shuttering -9.332 0.0072 0.80 1.504 0.15
0.15 12.12 0.25 0.567 43.27 -1.966
Loss in wt of Deck slab due
to drying -0.37328 0.0072
0.8 0.00 0.005 Construction Live load 0 0.0072 0.80 1.504 0.15 12.12 0.25
0.25 0.8 0.00 0.004 Weight of cross-girder 0.15 12.12
12.123 Green weight of deck slab 60.805 0.0072 0.80 1.504 0.15
0.15 12.12 0.25 0.5715 -1083.48 49.672 Weight of shuttering 9.332 0.0072 0.80 1.504
0.25 0.5715 -7059.62 323.63
b
fc1
ds C1
fc2
n c2
d bw
fst T
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm2
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm
Stress at the bottom of the slab= fc2 = fc1 x (n-ds)/n
Stress at the c.g of steel = fst = m x fc1 x (d - n)/n
Total Compression, C = C1 + C2
Where, C1 = fc1 x b x ds x (2n-ds)/2n
C2 =( fc1 x bw x (n-ds)^2)/2n
C = fc1 x ( b x ds x (2n-ds)/2n + bw x (n-ds)^2/2n )
Total tension, T = m x fc1 x Ast(d - n)/n
By equating the internal forces
Moment of resistance = m x fc1 x Ast(d - n)/n x (d-n/3)
*+ fc1 =
m x Ast(d - n)/n x (d-n/3)
Stress at CG of steel = fst = m x fc1 x (d - n)/n
**+ Stress in the extreme layer of steel = Fbg = (fst *(d-n)+cg form bottom)/(d-n)
*++ Stress in Concrete at top of girder = Ftg = fc1 x (n - ds) / n
*** Stress in Concrete at deck top = Fts = (fst / m) x (n / (d - n ))
Moment
Summary of Stress check at section
As per clause:12.2.2 of IRC:112-2011:
Permissible stresses
In concrete = 0.48fck = 19.2 Mpa = 1958 t/m2
In steel = 0.8fyk = 400 Mpa = 40800 t/m2
0.00 0.005 Construction Live Load 0.00 -13117.93 0.00 601.31
0.00 0.00
4 Weight of cross-girder 0.00 -13117.93 0.00 601.31 0.00 0.00
3 Green weight of deck slab -7059.62 -13117.93 323.63 601.31
TFts
0.00 0.00
2 Weight of shuttering -1083.48 -6058.31 49.67 277.67 0.00 0.00
1 Gider Self weight -4974.84 -4974.84 228.00 228.00
Sr No DescriptionBottom of
GirderCumulative
Bottom of Girder
Top of
Girder
Cumulative
Top of
Girder
Top of
SlabCumulative Top
of Slab
Fbg TFbg Ftg TFtg Fts
-213.82 712.6613 Temp Fall -212.45 -37843.24 110.92 522.54
-9.49 476.98
12 Temp Rise 150.82 -37630.79 -112.03 411.62 449.50 926.48
11 Differential Shrinkage -28.32 -37781.61 -21.63 523.65
318.82 327.05
10 50 % Live Load -7386.39 -37753.29 -10.51 545.28 159.42 486.47
9 Live Load -14772.75 -30366.91 -21.03 555.79
-49.67 -49.67
8 SIDL -3602.97 -15594.15 14.11 576.82 57.90 8.23
7
Loss wt of Deck slab due to
drying 1083.48 -11991.18 -36.63 562.71
0.00 0.00
6 De-shuttering 43.27 -13074.66 -1.96 599.35 0.00 0.00
5 Construction Live Load 0.00 -13117.93 0.00 601.31
317.56 OK
Combination
1+2+3+4+5+6+7+8+10+11+12
(50% Live Load+ Temp Rise) -40800.00 -30244.41 1958.40 422.13 1958.40 767.06 OK
Combination 1+2+3+4+5+6+7+8+9+11
(Service Condition with Live load and
shrinkage) -40800.00 -30395.23 1958.40 534.16 1958.40
8.23 OK
Combination 1+2+3+4+5+6+7+8+9
(Service Condition with Live load)-40800.00 -30366.91 1958.40 555.79 1958.40 327.05 OK
Combination 1+2+3+4+5+6+7+8
(Service Condition without Live load)-40800.00 -15594.15 1958.40 576.82 1958.40
Status
Combination 1+ 2+ 3+ 4+5
( Girder Alone property) -40800.00 -13117.93 1958.40 601.31 1958.40 0.00 OK
CombinationsPermissible
stress in steel
Actual stress in
steel
Permissible
stress in
concrete
Actual stress
in concrete
Permissible
stress in
concrete
Actual stress in
concrete
Note: Negative value indicates tension. Positive value indicates compression.
103.74 OK
Combination
1+2+3+4+5+6+7+8+10+11+13
(50% Live Load+ Temp fall) -40800.00 -30607.68 1958.40 645.08 1958.40
(50% Live Load+ Temp Rise) -40800.00 -30244.41 1958.40 422.13 1958.40 767.06 OK
Stress Check at 0.174L for outer girder
Grade of concrete = M 40
Span of girder (m) =
Width of beam bw =
Depth of girder =
Depth of girder+slab =
Depth of extreme layer of steel =
Modular ratio, m = 6.06 (for live load)
Modular ratio, m = 12.12 (for DL+SIDL)
fc1
in tmt *+
162
350.15 12.12 0.25 0.5717 -765.05 35.092 Weight of shuttering 6.589 0.0072 0.80 1.504
0.5714 -3524.79 161.551 Gider Self weight 30.36 0.0072 0.80 1.504 0.15 12.12 0.25
in m2
in m in m in m in m in m Fbg**+ Ftg*++
b* d ds**
m
bw n
Fts***
17.200 m
0.250 m
1.600 m
1.825 m
S.No. Description
Mom Ast Stress
1.757 m
35
230
0
0
-1.4
-35
40
232
116
* For girder alone property, b = width of top flange, and for composite property, b = effective width of slab
** For girder alone property, ds = tck of top flange, and for composite property, ds = tck of slab
13 Temp Fall -212.45 110.92 -213.82
12 Temp Rise 150.82 -112.03 449.50
11 Differential Shrinkage -28.32 -21.63 -9.49
116.06
0.2111 -10755.89 -15.31 232.13
-2502.01 9.80 40.21
10 50% Live Load 60.691 0.0072 3 1.729 0.225
6.06 0.259 Live Load 121.382 0.0072 3 1.729 0.225
6.06 0.25 0.2111 -5377.94 -7.66
0.80 1.504
12.12 0.258 SIDL 27.645 0.0072 3 1.729 0.225
12.12 0.25 0.5717 765.05 -25.88 -35.09
0.2975
0 0.0072 0.80 1.504
7 De-shuttering -6.589 0.0072 0.80 1.504 0.15
0.15 12.12 0.25 0.572 30.61 -1.416
Loss in wt of Deck slab due
to drying -0.26356 0.0072
0.8 0.00 0.005 Construction Live load 0 0.0072 0.80 1.504 0.15 12.12 0.25
0.25 0.8 0.00 0.004 Weight of cross-girder 0.15 12.12
12.123 Green weight of deck slab 43.162 0.0072 0.80 1.504 0.15
0.15 12.12 0.25 0.5717 -765.05 35.092 Weight of shuttering 6.589 0.0072 0.80 1.504
0.25 0.5714 -5011.16 229.71
b
fc1
ds C1
fc2
n c2
d bw
fst T
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm2
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm
Stress at the bottom of the slab= fc2 = fc1 x (n-ds)/n
Stress at the c.g of steel = fst = m x fc1 x (d - n)/n
Total Compression, C = C1 + C2
Where, C1 = fc1 x b x ds x (2n-ds)/2n
C2 =( fc1 x bw x (n-ds)^2)/2n
C = fc1 x ( b x ds x (2n-ds)/2n + bw x (n-ds)^2/2n )
Total tension, T = m x fc1 x Ast(d - n)/n
By equating the internal forces
Moment of resistance = m x fc1 x Ast(d - n)/n x (d-n/3)
*+ fc1 =
m x Ast(d - n)/n x (d-n/3)
Stress at CG of steel = fst = m x fc1 x (d - n)/n
**+ Stress in the extreme layer of steel = Fbg = (fst *(d-n)+cg form bottom)/(d-n)
*++ Stress in Concrete at top of girder = Ftg = fc1 x (n - ds) / n
*** Stress in Concrete at deck top = Fts = (fst / m) x (n / (d - n ))
Moment
Summary of Stress check at section
As per clause:12.2.2 of IRC:112-2011:
Permissible stresses
In concrete = 0.48fck = 19.2 Mpa = 1958 t/m2
In steel = 0.8fyk = 400 Mpa = 40800 t/m2
0.00 0.005 Construction Live Load 0.00 -9301.00 0.00 426.35
0.00 0.00
4 Weight of cross-girder 0.00 -9301.00 0.00 426.35 0.00 0.00
3 Green weight of deck slab -5011.16 -9301.00 229.71 426.35
TFts
0.00 0.00
2 Weight of shuttering -765.05 -4289.84 35.09 196.65 0.00 0.00
1 Gider Self weight -3524.79 -3524.79 161.55 161.55
Sr No DescriptionBottom of
GirderCumulative
Bottom of Girder
Top of
Girder
Cumulative
Top of
Girder
Top of
SlabCumulative Top
of Slab
Fbg TFbg Ftg TFtg Fts
-213.82 579.5113 Temp Fall -212.45 -27231.13 110.92 363.16
-9.49 343.83
12 Temp Rise 150.82 -27018.68 -112.03 252.24 449.50 793.33
11 Differential Shrinkage -28.32 -27169.50 -21.63 364.27
232.13 237.25
10 50 % Live Load -5377.94 -27141.18 -7.66 385.90 116.06 353.32
9 Live Load -10755.89 -21763.24 -15.31 393.56
-35.09 -35.09
8 SIDL -2502.01 -11007.35 9.80 408.87 40.21 5.12
7
Loss wt of Deck slab due to
drying 765.05 -8505.34 -25.88 399.06
0.00 0.00
6 De-shuttering 30.61 -9270.40 -1.41 424.95 0.00 0.00
5 Construction Live Load 0.00 -9301.00 0.00 426.35
227.76 OK
Combination
1+2+3+4+5+6+7+8+10+11+12
(50% Live Load+ Temp Rise) -40800.00 -21640.74 1958.40 259.90 1958.40 677.26 OK
Combination 1+2+3+4+5+6+7+8+9+11
(Service Condition with Live load and
shrinkage) -40800.00 -21791.56 1958.40 371.93 1958.40
5.12 OK
Combination 1+2+3+4+5+6+7+8+9
(Service Condition with Live load)-40800.00 -21763.24 1958.40 393.56 1958.40 237.25 OK
Combination 1+2+3+4+5+6+7+8
(Service Condition without Live load)-40800.00 -11007.35 1958.40 408.87 1958.40
Status
Combination 1+ 2+ 3+ 4+5
( Girder Alone property) -40800.00 -9301.00 1958.40 426.35 1958.40 0.00 OK
CombinationsPermissible
stress in steel
Actual stress in
steel
Permissible
stress in
concrete
Actual stress
in concrete
Permissible
stress in
concrete
Actual stress in
concrete
Note: Negative value indicates tension. Positive value indicates compression.
13.94 OK
Combination
1+2+3+4+5+6+7+8+10+11+13
(50% Live Load+ Temp fall) -40800.00 -22004.01 1958.40 482.85 1958.40
(50% Live Load+ Temp Rise) -40800.00 -21640.74 1958.40 259.90 1958.40 677.26 OK
Stress Check at 0.0L for outer girder
Grade of concrete = M 40
Span of girder (m) =
Width of beam bw =
Depth of girder =
Depth of girder+slab =
Depth of extreme layer of steel =
Modular ratio, m = 6.06 (for live load)
Modular ratio, m = 12.12 (for DL+SIDL)
fc1
in tmt *+
2.5
0.90.15 12.12 0.45 0.5228 -23.17 0.932 Weight of shuttering 0.203 0.0072 0.80 1.504
0.525 -62.60 2.521 Gider Self weight 0.548 0.0072 0.80 1.504 0.15 12.12 0.45
in m2
in m in m in m in m in m Fbg**+ Ftg*++
b* d ds**
m
bw n
Fts***
17.200 m
0.450 m
1.600 m
1.825 m
S.No. Description
Mom Ast Stress
1.757 m
0.9
3.9
0
0
-0.1
-0.9
4.7
51
26
* For girder alone property, b = width of top flange, and for composite property, b = effective width of slab
** For girder alone property, ds = tck of top flange, and for composite property, ds = tck of slab
13 Temp Fall -214.51 101.31 -221.21
12 Temp Rise 152.35 -104.30 457.19
11 Differential Shrinkage -31.86 -23.77 -11.44
25.52
0.2111 -2365.67 -3.37 51.05
-295.18 1.15 4.73
10 50% Live Load 13.3485 0.0072 3 1.729 0.225
6.06 0.459 Live Load 26.697 0.0072 3 1.729 0.225
6.06 0.45 0.211 -1182.82 -1.69
0.80 1.504
12.12 0.458 SIDL 3.262 0.0072 3 1.729 0.225
12.12 0.45 0.5228 23.17 -0.66 -0.93
0.297
0 0.0072 0.80 1.504
7 De-shuttering -0.203 0.0072 0.80 1.504 0.15
0.15 12.12 0.45 0.672 0.98 -0.066
Loss in wt of Deck slab due
to drying -0.00812 0.0072
0.8 0.00 0.005 Construction Live load 0 0.0072 0.80 1.504 0.15 12.12 0.45
0.45 0.8 0.00 0.004 Weight of cross-girder 0.15 12.12
12.123 Green weight of deck slab 0.848 0.0072 0.80 1.504 0.15
0.15 12.12 0.45 0.5228 -23.17 0.932 Weight of shuttering 0.203 0.0072 0.80 1.504
0.45 0.5249 -96.87 3.90
b
fc1
ds C1
fc2
n c2
d bw
fst T
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm2
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm
Stress at the bottom of the slab= fc2 = fc1 x (n-ds)/n
Stress at the c.g of steel = fst = m x fc1 x (d - n)/n
Total Compression, C = C1 + C2
Where, C1 = fc1 x b x ds x (2n-ds)/2n
C2 =( fc1 x bw x (n-ds)^2)/2n
C = fc1 x ( b x ds x (2n-ds)/2n + bw x (n-ds)^2/2n )
Total tension, T = m x fc1 x Ast(d - n)/n
By equating the internal forces
Moment of resistance = m x fc1 x Ast(d - n)/n x (d-n/3)
*+ fc1 =
m x Ast(d - n)/n x (d-n/3)
Stress at CG of steel = fst = m x fc1 x (d - n)/n
**+ Stress in the extreme layer of steel = Fbg = (fst *(d-n)+cg form bottom)/(d-n)
*++ Stress in Concrete at top of girder = Ftg = fc1 x (n - ds) / n
*** Stress in Concrete at deck top = Fts = (fst / m) x (n / (d - n ))
Moment
Summary of Stress check at section
As per clause:12.2.2 of IRC:112-2011:
Permissible stresses
In concrete = 0.48fck = 19.2 Mpa = 1958 t/m2
In steel = 0.8fyk = 400 Mpa = 40800 t/m2
0.00 0.005 Construction Live Load 0.00 -182.65 0.00 7.35
0.00 0.00
4 Weight of cross-girder 0.00 -182.65 0.00 7.35 0.00 0.00
3 Green weight of deck slab -96.87 -182.65 3.90 7.35
TFts
0.00 0.00
2 Weight of shuttering -23.17 -85.77 0.93 3.45 0.00 0.00
1 Gider Self weight -62.60 -62.60 2.52 2.52
Sr No DescriptionBottom of
GirderCumulative
Bottom of Girder
Top of
Girder
Cumulative
Top of
Girder
Top of
SlabCumulative Top
of Slab
Fbg TFbg Ftg TFtg Fts
-221.21 304.9213 Temp Fall -214.51 -4096.18 101.31 -24.04
-11.44 68.94
12 Temp Rise 152.35 -3881.67 -104.30 -125.35 457.19 526.13
11 Differential Shrinkage -31.86 -4034.02 -23.77 -21.05
51.05 54.86
10 50 % Live Load -1182.82 -4002.16 -1.69 2.72 25.52 80.38
9 Live Load -2365.67 -2819.35 -3.37 4.41
-0.93 -0.93
8 SIDL -295.18 -453.68 1.15 7.78 4.73 3.81
7
Loss wt of Deck slab due to
drying 23.17 -158.49 -0.66 6.63
0.00 0.00
6 De-shuttering 0.98 -181.67 -0.06 7.29 0.00 0.00
5 Construction Live Load 0.00 -182.65 0.00 7.35
43.42 OK
Combination
1+2+3+4+5+6+7+8+10+11+12
(50% Live Load+ Temp Rise) -40800.00 -2698.86 1958.40 -123.66 1958.40 500.61 OK
Combination 1+2+3+4+5+6+7+8+9+11
(Service Condition with Live load and
shrinkage) -40800.00 -2851.21 1958.40 -19.36 1958.40
3.81 OK
Combination 1+2+3+4+5+6+7+8+9
(Service Condition with Live load)-40800.00 -2819.35 1958.40 4.41 1958.40 54.86 OK
Combination 1+2+3+4+5+6+7+8
(Service Condition without Live load)-40800.00 -453.68 1958.40 7.78 1958.40
Status
Combination 1+ 2+ 3+ 4+5
( Girder Alone property) -40800.00 -182.65 1958.40 7.35 1958.40 0.00 OK
CombinationsPermissible
stress in steel
Actual stress in
steel
Permissible
stress in
concrete
Actual stress
in concrete
Permissible
stress in
concrete
Actual stress in
concrete
Note: Negative value indicates tension. Positive value indicates compression.
-177.79 OK
Combination
1+2+3+4+5+6+7+8+10+11+13
(50% Live Load+ Temp fall) -40800.00 -3065.72 1958.40 81.95 1958.40
(50% Live Load+ Temp Rise) -40800.00 -2698.86 1958.40 -123.66 1958.40 500.61 OK
Stress Check at 0.5L for inner girder
Grade of concrete = M 40
Span of girder (m) =
Width of beam bw =
Depth of girder =
Depth of girder+slab =
Depth of extreme layer of steel =
Modular ratio, m = 6.06 (for live load)
Modular ratio, m = 12.12 (for DL+SIDL)
fc1
in tmt *+
267
540.15 12.12 0.25 0.6819 -878.70 53.852 Weight of shuttering 10.648 0.0113 0.80 1.474
0.6817 -4359.24 267.011 Gider Self weight 52.829 0.0113 0.80 1.474 0.15 12.12 0.25
in m2
in m in m in m in m in m Fbg**+ Ftg*++
b* d ds**
m
bw n
Fts***
17.200 m
0.250 m
1.600 m
1.825 m
S.No. Description
Mom Ast Stress
1.757 m
54
359
0
0
-2.1
-54
8.6
341
171
* For girder alone property, b = width of top flange, and for composite property, b = effective width of slab
** For girder alone property, ds = tck of top flange, and for composite property, ds = tck of slab
13 Temp Fall -212.45 110.92 -213.82
12 Temp Rise 150.82 -112.03 449.50
11 Differential Shrinkage -28.32 -21.63 -9.49
170.71
0.258 -12566.24 43.67 341.41
-400.04 3.43 8.56
10 50% Live Load 104.975 0.0113 3 1.699 0.225
6.06 0.259 Live Load 209.95 0.0113 3 1.699 0.225
6.06 0.25 0.258 -6283.12 21.83
0.80 1.474
12.12 0.258 SIDL 6.475 0.0113 3 1.699 0.225
12.12 0.25 0.6819 878.70 -42.00 -53.85
0.3757
0 0.0113 0.80 1.474
7 De-shuttering -10.648 0.0113 0.80 1.474 0.15
0.15 12.12 0.25 0.6801 35.12 -2.146
Loss in wt of Deck slab due
to drying -0.42592 0.0113
0.8 0.00 0.005 Construction Live load 0 0.0113 0.80 1.474 0.15 12.12 0.25
0.25 0.8 0.00 0.004 Weight of cross-girder 0.15 12.12
12.123 Green weight of deck slab 70.963 0.0113 0.80 1.474 0.15
0.15 12.12 0.25 0.6819 -878.70 53.852 Weight of shuttering 10.648 0.0113 0.80 1.474
0.25 0.6818 -5855.70 358.72
b
fc1
ds C1
fc2
n c2
d bw
fst T
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm2
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm
Stress at the bottom of the slab= fc2 = fc1 x (n-ds)/n
Stress at the c.g of steel = fst = m x fc1 x (d - n)/n
Total Compression, C = C1 + C2
Where, C1 = fc1 x b x ds x (2n-ds)/2n
C2 =( fc1 x bw x (n-ds)^2)/2n
C = fc1 x ( b x ds x (2n-ds)/2n + bw x (n-ds)^2/2n )
Total tension, T = m x fc1 x Ast(d - n)/n
By equating the internal forces
Moment of resistance = m x fc1 x Ast(d - n)/n x (d-n/3)
*+ fc1 =
m x Ast(d - n)/n x (d-n/3)
Stress at CG of steel = fst = m x fc1 x (d - n)/n
**+ Stress in the extreme layer of steel = Fbg = (fst *(d-n)+cg form bottom)/(d-n)
*++ Stress in Concrete at top of girder = Ftg = fc1 x (n - ds) / n
*** Stress in Concrete at deck top = Fts = (fst / m) x (n / (d - n ))
Moment
Summary of Stress check at section
As per clause:12.2.2 of IRC:112-2011:
Permissible stresses
In concrete = 0.48fck = 19.2 Mpa = 1958 t/m2
In steel = 0.8fyk = 400 Mpa = 40800 t/m2
0.00 0.005 Construction Live Load 0.00 -11093.65 0.00 679.58
0.00 0.00
4 Weight of cross-girder 0.00 -11093.65 0.00 679.58 0.00 0.00
3 Green weight of deck slab -5855.70 -11093.65 358.72 679.58
TFts
0.00 0.00
2 Weight of shuttering -878.70 -5237.94 53.85 320.86 0.00 0.00
1 Gider Self weight -4359.24 -4359.24 267.01 267.01
Sr No DescriptionBottom of
GirderCumulative
Bottom of Girder
Top of
Girder
Cumulative
Top of
Girder
Top of
SlabCumulative Top
of Slab
Fbg TFbg Ftg TFtg Fts
-213.82 693.0213 Temp Fall -212.45 -29519.18 110.92 681.63
-9.49 457.34
12 Temp Rise 150.82 -29306.73 -112.03 570.71 449.50 906.84
11 Differential Shrinkage -28.32 -29457.55 -21.63 682.74
341.41 296.12
10 50 % Live Load -6283.12 -29429.23 21.83 704.37 170.71 466.83
9 Live Load -12566.24 -23146.11 43.67 682.53
-53.85 -53.85
8 SIDL -400.04 -10579.87 3.43 638.86 8.56 -45.29
7
Loss wt of Deck slab due to
drying 878.70 -10179.83 -42.00 635.43
0.00 0.00
6 De-shuttering 35.12 -11058.53 -2.14 677.43 0.00 0.00
5 Construction Live Load 0.00 -11093.65 0.00 679.58
286.63 OK
Combination
1+2+3+4+5+6+7+8+10+11+12
(50% Live Load+ Temp Rise) -40800.00 -23023.61 1958.40 548.87 1958.40 736.13 OK
Combination 1+2+3+4+5+6+7+8+9+11
(Service Condition with Live load and
shrinkage) -40800.00 -23174.43 1958.40 660.90 1958.40
-45.29 OK
Combination 1+2+3+4+5+6+7+8+9
(Service Condition with Live load)-40800.00 -23146.11 1958.40 682.53 1958.40 296.12 OK
Combination 1+2+3+4+5+6+7+8
(Service Condition without Live load)-40800.00 -10579.87 1958.40 638.86 1958.40
Status
Combination 1+ 2+ 3+ 4+5
( Girder Alone property) -40800.00 -11093.65 1958.40 679.58 1958.40 0.00 OK
CombinationsPermissible
stress in steel
Actual stress in
steel
Permissible
stress in
concrete
Actual stress
in concrete
Permissible
stress in
concrete
Actual stress in
concrete
Note: Negative value indicates tension. Positive value indicates compression.
72.81 OK
Combination
1+2+3+4+5+6+7+8+10+11+13
(50% Live Load+ Temp fall) -40800.00 -23386.88 1958.40 771.82 1958.40
(50% Live Load+ Temp Rise) -40800.00 -23023.61 1958.40 548.87 1958.40 736.13 OK
Stress Check at 0.391L for inner girder
Grade of concrete = M 40
Span of girder (m) =
Width of beam bw =
Depth of girder =
Depth of girder+slab =
Depth of extreme layer of steel =
Modular ratio, m = 6.06 (for live load)
Modular ratio, m = 12.12 (for DL+SIDL)
fc1
in tmt *+
268
540.15 12.12 0.25 0.5715 -1179.72 54.082 Weight of shuttering 10.161 0.0072 0.80 1.504
0.5714 -5843.58 267.851 Gider Self weight 50.332 0.0072 0.80 1.504 0.15 12.12 0.25
in m2
in m in m in m in m in m Fbg**+ Ftg*++
b* d ds**
m
bw n
Fts***
17.200 m
0.250 m
1.600 m
1.825 m
S.No. Description
Mom Ast Stress
1.757 m
54
360
0
0
-2.2
-54
9.6
384
192
* For girder alone property, b = width of top flange, and for composite property, b = effective width of slab
** For girder alone property, ds = tck of top flange, and for composite property, ds = tck of slab
13 Temp Fall -212.45 110.92 -213.82
12 Temp Rise 150.82 -112.03 449.50
11 Differential Shrinkage -28.32 -21.63 -9.49
191.86
0.2111 -17779.61 -25.31 383.71
-600.30 2.35 9.64
10 50% Live Load 100.323 0.0072 3 1.729 0.225
6.06 0.259 Live Load 200.646 0.0072 3 1.729 0.225
6.06 0.25 0.2111 -8889.81 -12.66
0.80 1.504
12.12 0.258 SIDL 6.633 0.0072 3 1.729 0.225
12.12 0.25 0.5715 1179.72 -39.89 -54.08
0.2974
0 0.0072 0.80 1.504
7 De-shuttering -10.161 0.0072 0.80 1.504 0.15
0.15 12.12 0.25 0.57 47.16 -2.156
Loss in wt of Deck slab due
to drying -0.40644 0.0072
0.8 0.00 0.005 Construction Live load 0 0.0072 0.80 1.504 0.15 12.12 0.25
0.25 0.8 0.00 0.004 Weight of cross-girder 0.15 12.12
12.123 Green weight of deck slab 67.707 0.0072 0.80 1.504 0.15
0.15 12.12 0.25 0.5715 -1179.72 54.082 Weight of shuttering 10.161 0.0072 0.80 1.504
0.25 0.5714 -7860.84 360.32
b
fc1
ds C1
fc2
n c2
d bw
fst T
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm2
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm
Stress at the bottom of the slab= fc2 = fc1 x (n-ds)/n
Stress at the c.g of steel = fst = m x fc1 x (d - n)/n
Total Compression, C = C1 + C2
Where, C1 = fc1 x b x ds x (2n-ds)/2n
C2 =( fc1 x bw x (n-ds)^2)/2n
C = fc1 x ( b x ds x (2n-ds)/2n + bw x (n-ds)^2/2n )
Total tension, T = m x fc1 x Ast(d - n)/n
By equating the internal forces
Moment of resistance = m x fc1 x Ast(d - n)/n x (d-n/3)
*+ fc1 =
m x Ast(d - n)/n x (d-n/3)
Stress at CG of steel = fst = m x fc1 x (d - n)/n
**+ Stress in the extreme layer of steel = Fbg = (fst *(d-n)+cg form bottom)/(d-n)
*++ Stress in Concrete at top of girder = Ftg = fc1 x (n - ds) / n
*** Stress in Concrete at deck top = Fts = (fst / m) x (n / (d - n ))
Moment
Summary of Stress check at section
As per clause:12.2.2 of IRC:112-2011:
Permissible stresses
In concrete = 0.48fck = 19.2 Mpa = 1958 t/m2
In steel = 0.8fyk = 400 Mpa = 40800 t/m2
0.00 0.005 Construction Live Load 0.00 -14884.15 0.00 682.26
0.00 0.00
4 Weight of cross-girder 0.00 -14884.15 0.00 682.26 0.00 0.00
3 Green weight of deck slab -7860.84 -14884.15 360.32 682.26
TFts
0.00 0.00
2 Weight of shuttering -1179.72 -7023.31 54.08 321.94 0.00 0.00
1 Gider Self weight -5843.58 -5843.58 267.85 267.85
Sr No DescriptionBottom of
GirderCumulative
Bottom of Girder
Top of
Girder
Cumulative
Top of
Girder
Top of
SlabCumulative Top
of Slab
Fbg TFbg Ftg TFtg Fts
-213.82 757.3213 Temp Fall -212.45 -41016.92 110.92 581.85
-9.49 521.64
12 Temp Rise 150.82 -40804.47 -112.03 470.93 449.50 971.14
11 Differential Shrinkage -28.32 -40955.29 -21.63 582.96
383.71 339.27
10 50 % Live Load -8889.81 -40926.97 -12.66 604.59 191.86 531.13
9 Live Load -17779.61 -32037.16 -25.31 617.25
-54.08 -54.08
8 SIDL -600.30 -14257.55 2.35 642.56 9.64 -44.44
7
Loss wt of Deck slab due to
drying 1179.72 -13657.26 -39.89 640.22
0.00 0.00
6 De-shuttering 47.16 -14836.98 -2.15 680.10 0.00 0.00
5 Construction Live Load 0.00 -14884.15 0.00 682.26
329.78 OK
Combination
1+2+3+4+5+6+7+8+10+11+12
(50% Live Load+ Temp Rise) -40800.00 -31914.66 1958.40 483.59 1958.40 779.28 OK
Combination 1+2+3+4+5+6+7+8+9+11
(Service Condition with Live load and
shrinkage) -40800.00 -32065.48 1958.40 595.62 1958.40
-44.44 OK
Combination 1+2+3+4+5+6+7+8+9
(Service Condition with Live load)-40800.00 -32037.16 1958.40 617.25 1958.40 339.27 OK
Combination 1+2+3+4+5+6+7+8
(Service Condition without Live load)-40800.00 -14257.55 1958.40 642.56 1958.40
Not OK
Combination 1+ 2+ 3+ 4+5
( Girder Alone property) -40800.00 -14884.15 1958.40 682.26 1958.40 0.00 OK
CombinationsPermissible
stress in steel
Actual stress in
steel
Permissible
stress in
concrete
Actual stress
in concrete
Permissible
stress in
concrete
Actual stress in
concrete
Note: Negative value indicates tension. Positive value indicates compression.
115.96 OK
Combination
1+2+3+4+5+6+7+8+10+11+13
(50% Live Load+ Temp fall) -40800.00 -32277.93 1958.40 706.54 1958.40
(50% Live Load+ Temp Rise) -40800.00 -31914.66 1958.40 483.59 1958.40 779.28 OK
Stress Check at 0.283L for inner girder
Grade of concrete = M 40
Span of girder (m) =
Width of beam bw =
Depth of girder =
Depth of girder+slab =
Depth of extreme layer of steel =
Modular ratio, m = 6.06 (for live load)
Modular ratio, m = 12.12 (for DL+SIDL)
fc1
in tmt *+
228
460.15 12.12 0.25 0.5714 -1006.25 46.122 Weight of shuttering 8.667 0.0072 0.80 1.504
0.5714 -4973.17 227.951 Gider Self weight 42.835 0.0072 0.80 1.504 0.15 12.12 0.25
in m2
in m in m in m in m in m Fbg**+ Ftg*++
b* d ds**
m
bw n
Fts***
17.200 m
0.250 m
1.600 m
1.825 m
S.No. Description
Mom Ast Stress
1.757 m
46
307
0
0
-1.8
-46
9.3
331
165
* For girder alone property, b = width of top flange, and for composite property, b = effective width of slab
** For girder alone property, ds = tck of top flange, and for composite property, ds = tck of slab
13 Temp Fall -212.45 110.92 -213.82
12 Temp Rise 150.82 -112.03 449.50
11 Differential Shrinkage -28.32 -21.63 -9.49
165.26
0.2111 -15314.34 -21.80 330.50
-576.84 2.25 9.26
10 50% Live Load 86.4125 0.0072 3 1.729 0.225
6.06 0.259 Live Load 172.825 0.0072 3 1.729 0.225
6.06 0.25 0.2111 -7657.17 -10.90
0.80 1.504
12.12 0.258 SIDL 6.374 0.0072 3 1.729 0.225
12.12 0.25 0.5714 1006.25 -34.02 -46.12
0.2973
0 0.0072 0.80 1.504
7 De-shuttering -8.667 0.0072 0.80 1.504 0.15
0.15 12.12 0.25 0.566 40.17 -1.816
Loss in wt of Deck slab due
to drying -0.34668 0.0072
0.8 0.00 0.005 Construction Live load 0 0.0072 0.80 1.504 0.15 12.12 0.25
0.25 0.8 0.00 0.004 Weight of cross-girder 0.15 12.12
12.123 Green weight of deck slab 57.777 0.0072 0.80 1.504 0.15
0.15 12.12 0.25 0.5714 -1006.25 46.122 Weight of shuttering 8.667 0.0072 0.80 1.504
0.25 0.5714 -6708.00 307.49
b
fc1
ds C1
fc2
n c2
d bw
fst T
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm2
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm
Stress at the bottom of the slab= fc2 = fc1 x (n-ds)/n
Stress at the c.g of steel = fst = m x fc1 x (d - n)/n
Total Compression, C = C1 + C2
Where, C1 = fc1 x b x ds x (2n-ds)/2n
C2 =( fc1 x bw x (n-ds)^2)/2n
C = fc1 x ( b x ds x (2n-ds)/2n + bw x (n-ds)^2/2n )
Total tension, T = m x fc1 x Ast(d - n)/n
By equating the internal forces
Moment of resistance = m x fc1 x Ast(d - n)/n x (d-n/3)
*+ fc1 =
m x Ast(d - n)/n x (d-n/3)
Stress at CG of steel = fst = m x fc1 x (d - n)/n
**+ Stress in the extreme layer of steel = Fbg = (fst *(d-n)+cg form bottom)/(d-n)
*++ Stress in Concrete at top of girder = Ftg = fc1 x (n - ds) / n
*** Stress in Concrete at deck top = Fts = (fst / m) x (n / (d - n ))
Moment
Summary of Stress check at section
As per clause:12.2.2 of IRC:112-2011:
Permissible stresses
In concrete = 0.48fck = 19.2 Mpa = 1958 t/m2
In steel = 0.8fyk = 400 Mpa = 40800 t/m2
0.00 0.005 Construction Live Load 0.00 -12687.41 0.00 581.57
0.00 0.00
4 Weight of cross-girder 0.00 -12687.41 0.00 581.57 0.00 0.00
3 Green weight of deck slab -6708.00 -12687.41 307.49 581.57
TFts
0.00 0.00
2 Weight of shuttering -1006.25 -5979.41 46.12 274.08 0.00 0.00
1 Gider Self weight -4973.17 -4973.17 227.95 227.95
Sr No DescriptionBottom of
GirderCumulative
Bottom of Girder
Top of
Girder
Cumulative
Top of
Girder
Top of
SlabCumulative Top
of Slab
Fbg TFbg Ftg TFtg Fts
-213.82 685.0913 Temp Fall -212.45 -35279.30 110.92 492.55
-9.49 449.41
12 Temp Rise 150.82 -35066.85 -112.03 381.63 449.50 898.91
11 Differential Shrinkage -28.32 -35217.67 -21.63 493.66
330.50 293.64
10 50 % Live Load -7657.17 -35189.35 -10.90 515.29 165.26 458.90
9 Live Load -15314.34 -27532.18 -21.80 526.19
-46.12 -46.12
8 SIDL -576.84 -12217.84 2.25 547.99 9.26 -36.86
7
Loss wt of Deck slab due to
drying 1006.25 -11641.00 -34.02 545.74
0.00 0.00
6 De-shuttering 40.17 -12647.24 -1.81 579.75 0.00 0.00
5 Construction Live Load 0.00 -12687.41 0.00 581.57
284.15 OK
Combination
1+2+3+4+5+6+7+8+10+11+12
(50% Live Load+ Temp Rise) -40800.00 -27409.68 1958.40 392.53 1958.40 733.65 OK
Combination 1+2+3+4+5+6+7+8+9+11
(Service Condition with Live load and
shrinkage) -40800.00 -27560.50 1958.40 504.56 1958.40
-36.86 OK
Combination 1+2+3+4+5+6+7+8+9
(Service Condition with Live load)-40800.00 -27532.18 1958.40 526.19 1958.40 293.64 OK
Combination 1+2+3+4+5+6+7+8
(Service Condition without Live load)-40800.00 -12217.84 1958.40 547.99 1958.40
Not OK
Combination 1+ 2+ 3+ 4+5
( Girder Alone property) -40800.00 -12687.41 1958.40 581.57 1958.40 0.00 OK
CombinationsPermissible
stress in steel
Actual stress in
steel
Permissible
stress in
concrete
Actual stress
in concrete
Permissible
stress in
concrete
Actual stress in
concrete
Note: Negative value indicates tension. Positive value indicates compression.
70.33 OK
Combination
1+2+3+4+5+6+7+8+10+11+13
(50% Live Load+ Temp fall) -40800.00 -27772.95 1958.40 615.48 1958.40
(50% Live Load+ Temp Rise) -40800.00 -27409.68 1958.40 392.53 1958.40 733.65 OK
Stress Check at 0.174L for inner girder
Grade of concrete = M 40
Span of girder (m) =
Width of beam bw =
Depth of girder =
Depth of girder+slab =
Depth of extreme layer of steel =
Modular ratio, m = 6.06 (for live load)
Modular ratio, m = 12.12 (for DL+SIDL)
fc1
in tmt *+
161
330.15 12.12 0.25 0.571 -715.54 32.762 Weight of shuttering 6.164 0.0072 0.80 1.504
0.5714 -3522.11 161.431 Gider Self weight 30.337 0.0072 0.80 1.504 0.15 12.12 0.25
in m2
in m in m in m in m in m Fbg**+ Ftg*++
b* d ds**
m
bw n
Fts***
17.200 m
0.250 m
1.600 m
1.825 m
S.No. Description
Mom Ast Stress
1.757 m
33
219
0
0
-1.3
-33
4.1
245
122
* For girder alone property, b = width of top flange, and for composite property, b = effective width of slab
** For girder alone property, ds = tck of top flange, and for composite property, ds = tck of slab
13 Temp Fall -212.45 110.92 -213.82
12 Temp Rise 150.82 -112.03 449.50
11 Differential Shrinkage -28.32 -21.63 -9.49
122.30
0.2111 -11333.54 -16.14 244.60
-254.61 1.00 4.10
10 50% Live Load 63.9505 0.0072 3 1.729 0.225
6.06 0.259 Live Load 127.901 0.0072 3 1.729 0.225
6.06 0.25 0.2111 -5666.77 -8.07
0.80 1.504
12.12 0.258 SIDL 2.813 0.0072 3 1.729 0.225
12.12 0.25 0.571 715.54 -24.16 -32.76
0.2978
0 0.0072 0.80 1.504
7 De-shuttering -6.164 0.0072 0.80 1.504 0.15
0.15 12.12 0.25 0.5773 28.69 -1.346
Loss in wt of Deck slab due
to drying -0.24656 0.0072
0.8 0.00 0.005 Construction Live load 0 0.0072 0.80 1.504 0.15 12.12 0.25
0.25 0.8 0.00 0.004 Weight of cross-girder 0.15 12.12
12.123 Green weight of deck slab 41.17 0.0072 0.80 1.504 0.15
0.15 12.12 0.25 0.571 -715.54 32.762 Weight of shuttering 6.164 0.0072 0.80 1.504
0.25 0.5714 -4779.83 219.08
b
fc1
ds C1
fc2
n c2
d bw
fst T
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm2
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm
Stress at the bottom of the slab= fc2 = fc1 x (n-ds)/n
Stress at the c.g of steel = fst = m x fc1 x (d - n)/n
Total Compression, C = C1 + C2
Where, C1 = fc1 x b x ds x (2n-ds)/2n
C2 =( fc1 x bw x (n-ds)^2)/2n
C = fc1 x ( b x ds x (2n-ds)/2n + bw x (n-ds)^2/2n )
Total tension, T = m x fc1 x Ast(d - n)/n
By equating the internal forces
Moment of resistance = m x fc1 x Ast(d - n)/n x (d-n/3)
*+ fc1 =
m x Ast(d - n)/n x (d-n/3)
Stress at CG of steel = fst = m x fc1 x (d - n)/n
**+ Stress in the extreme layer of steel = Fbg = (fst *(d-n)+cg form bottom)/(d-n)
*++ Stress in Concrete at top of girder = Ftg = fc1 x (n - ds) / n
*** Stress in Concrete at deck top = Fts = (fst / m) x (n / (d - n ))
Moment
Summary of Stress check at section
As per clause:12.2.2 of IRC:112-2011:
Permissible stresses
In concrete = 0.48fck = 19.2 Mpa = 1958 t/m2
In steel = 0.8fyk = 400 Mpa = 40800 t/m2
0.00 0.005 Construction Live Load 0.00 -9017.48 0.00 413.27
0.00 0.00
4 Weight of cross-girder 0.00 -9017.48 0.00 413.27 0.00 0.00
3 Green weight of deck slab -4779.83 -9017.48 219.08 413.27
TFts
0.00 0.00
2 Weight of shuttering -715.54 -4237.65 32.76 194.19 0.00 0.00
1 Gider Self weight -3522.11 -3522.11 161.43 161.43
Sr No DescriptionBottom of
GirderCumulative
Bottom of Girder
Top of
Girder
Cumulative
Top of
Girder
Top of
SlabCumulative Top
of Slab
Fbg TFbg Ftg TFtg Fts
-213.82 564.4213 Temp Fall -212.45 -25618.13 110.92 341.84
-9.49 328.74
12 Temp Rise 150.82 -25405.68 -112.03 230.92 449.50 778.24
11 Differential Shrinkage -28.32 -25556.50 -21.63 342.95
244.60 215.93
10 50 % Live Load -5666.77 -25528.18 -8.07 364.58 122.30 338.23
9 Live Load -11333.54 -19861.40 -16.14 372.65
-32.76 -32.76
8 SIDL -254.61 -8527.86 1.00 388.78 4.10 -28.67
7
Loss wt of Deck slab due to
drying 715.54 -8273.25 -24.16 387.78
0.00 0.00
6 De-shuttering 28.69 -8988.80 -1.34 411.94 0.00 0.00
5 Construction Live Load 0.00 -9017.48 0.00 413.27
206.44 OK
Combination
1+2+3+4+5+6+7+8+10+11+12
(50% Live Load+ Temp Rise) -40800.00 -19738.90 1958.40 238.99 1958.40 655.94 OK
Combination 1+2+3+4+5+6+7+8+9+11
(Service Condition with Live load and
shrinkage) -40800.00 -19889.72 1958.40 351.02 1958.40
-28.67 OK
Combination 1+2+3+4+5+6+7+8+9
(Service Condition with Live load)-40800.00 -19861.40 1958.40 372.65 1958.40 215.93 OK
Combination 1+2+3+4+5+6+7+8
(Service Condition without Live load)-40800.00 -8527.86 1958.40 388.78 1958.40
Not OK
Combination 1+ 2+ 3+ 4+5
( Girder Alone property) -40800.00 -9017.48 1958.40 413.27 1958.40 0.00 OK
CombinationsPermissible
stress in steel
Actual stress in
steel
Permissible
stress in
concrete
Actual stress
in concrete
Permissible
stress in
concrete
Actual stress in
concrete
Note: Negative value indicates tension. Positive value indicates compression.
-7.38 OK
Combination
1+2+3+4+5+6+7+8+10+11+13
(50% Live Load+ Temp fall) -40800.00 -20102.17 1958.40 461.94 1958.40
(50% Live Load+ Temp Rise) -40800.00 -19738.90 1958.40 238.99 1958.40 655.94 OK
Stress Check at 0.0L for inner girder
Grade of concrete = M 40
Span of girder (m) =
Width of beam bw =
Depth of girder =
Depth of girder+slab =
Depth of extreme layer of steel =
Modular ratio, m = 6.06 (for live load)
Modular ratio, m = 12.12 (for DL+SIDL)
fc1
in tmt *+
2.5
0.40.15 12.12 0.45 0.5209 -10.38 0.412 Weight of shuttering 0.091 0.0072 0.80 1.504
0.5234 -62.57 2.511 Gider Self weight 0.548 0.0072 0.80 1.504 0.15 12.12 0.45
in m2
in m in m in m in m in m Fbg**+ Ftg*++
b* d ds**
m
bw n
Fts***
17.200 m
0.450 m
1.600 m
1.825 m
S.No. Description
Mom Ast Stress
1.757 m
0.4
3
0
0
-0
-0.4
5.6
70
35
* For girder alone property, b = width of top flange, and for composite property, b = effective width of slab
** For girder alone property, ds = tck of top flange, and for composite property, ds = tck of slab
13 Temp Fall -214.51 101.31 -221.21
12 Temp Rise 152.35 -104.30 457.19
11 Differential Shrinkage -31.86 -23.77 -11.44
34.84
0.2111 -3229.80 -4.61 69.70
-352.87 1.36 5.65
10 50% Live Load 18.2245 0.0072 3 1.729 0.225
6.06 0.459 Live Load 36.449 0.0072 3 1.729 0.225
6.06 0.45 0.211 -1614.89 -2.31
0.80 1.504
12.12 0.458 SIDL 3.9 0.0072 3 1.729 0.225
12.12 0.45 0.5209 10.38 -0.29 -0.41
0.2964
0 0.0072 0.80 1.504
7 De-shuttering -0.091 0.0072 0.80 1.504 0.15
0.15 12.12 0.45 0.544 0.42 -0.026
Loss in wt of Deck slab due
to drying -0.00364 0.0072
0.8 0.00 0.005 Construction Live load 0 0.0072 0.80 1.504 0.15 12.12 0.45
0.45 0.8 0.00 0.004 Weight of cross-girder 0.15 12.12
12.123 Green weight of deck slab 0.651 0.0072 0.80 1.504 0.15
0.15 12.12 0.45 0.5209 -10.38 0.412 Weight of shuttering 0.091 0.0072 0.80 1.504
0.45 0.5255 -74.38 3.00
b
fc1
ds C1
fc2
n c2
d bw
fst T
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm2
Stress in the extreme compression fibre (i.e at the top of the deck slab) = fc1 N/mm
Stress at the bottom of the slab= fc2 = fc1 x (n-ds)/n
Stress at the c.g of steel = fst = m x fc1 x (d - n)/n
Total Compression, C = C1 + C2
Where, C1 = fc1 x b x ds x (2n-ds)/2n
C2 =( fc1 x bw x (n-ds)^2)/2n
C = fc1 x ( b x ds x (2n-ds)/2n + bw x (n-ds)^2/2n )
Total tension, T = m x fc1 x Ast(d - n)/n
By equating the internal forces
Moment of resistance = m x fc1 x Ast(d - n)/n x (d-n/3)
*+ fc1 =
m x Ast(d - n)/n x (d-n/3)
Stress at CG of steel = fst = m x fc1 x (d - n)/n
**+ Stress in the extreme layer of steel = Fbg = (fst *(d-n)+cg form bottom)/(d-n)
*++ Stress in Concrete at top of girder = Ftg = fc1 x (n - ds) / n
*** Stress in Concrete at deck top = Fts = (fst / m) x (n / (d - n ))
Moment
Summary of Stress check at section
As per clause:12.2.2 of IRC:112-2011:
Permissible stresses
In concrete = 0.48fck = 19.2 Mpa = 1958 t/m2
In steel = 0.8fyk = 400 Mpa = 40800 t/m2
0.00 0.005 Construction Live Load 0.00 -147.33 0.00 5.92
0.00 0.00
4 Weight of cross-girder 0.00 -147.33 0.00 5.92 0.00 0.00
3 Green weight of deck slab -74.38 -147.33 3.00 5.92
TFts
0.00 0.00
2 Weight of shuttering -10.38 -72.95 0.41 2.92 0.00 0.00
1 Gider Self weight -62.57 -62.57 2.51 2.51
Sr No DescriptionBottom of
GirderCumulative
Bottom of Girder
Top of
Girder
Cumulative
Top of
Girder
Top of
SlabCumulative Top
of Slab
Fbg TFbg Ftg TFtg Fts
-221.21 334.3113 Temp Fall -214.51 -5428.11 101.31 -26.70
-11.44 98.33
12 Temp Rise 152.35 -5213.60 -104.30 -128.01 457.19 555.52
11 Differential Shrinkage -31.86 -5365.95 -23.77 -23.71
69.70 74.93
10 50 % Live Load -1614.89 -5334.09 -2.31 0.06 34.84 109.77
9 Live Load -3229.80 -3719.20 -4.61 2.37
-0.41 -0.41
8 SIDL -352.87 -489.40 1.36 6.97 5.65 5.23
7
Loss wt of Deck slab due to
drying 10.38 -136.53 -0.29 5.61
0.00 0.00
6 De-shuttering 0.42 -146.91 -0.02 5.91 0.00 0.00
5 Construction Live Load 0.00 -147.33 0.00 5.92
63.49 OK
Combination
1+2+3+4+5+6+7+8+10+11+12
(50% Live Load+ Temp Rise) -40800.00 -3598.71 1958.40 -125.70 1958.40 520.68 OK
Combination 1+2+3+4+5+6+7+8+9+11
(Service Condition with Live load and
shrinkage) -40800.00 -3751.06 1958.40 -21.40 1958.40
5.23 OK
Combination 1+2+3+4+5+6+7+8+9
(Service Condition with Live load)-40800.00 -3719.20 1958.40 2.37 1958.40 74.93 OK
Combination 1+2+3+4+5+6+7+8
(Service Condition without Live load)-40800.00 -489.40 1958.40 6.97 1958.40
Not OK
Combination 1+ 2+ 3+ 4+5
( Girder Alone property) -40800.00 -147.33 1958.40 5.92 1958.40 0.00 OK
CombinationsPermissible
stress in steel
Actual stress in
steel
Permissible
stress in
concrete
Actual stress
in concrete
Permissible
stress in
concrete
Actual stress in
concrete
Note: Negative value indicates tension. Positive value indicates compression.
-157.72 OK
Combination
1+2+3+4+5+6+7+8+10+11+13
(50% Live Load+ Temp fall) -40800.00 -3965.57 1958.40 79.91 1958.40
(50% Live Load+ Temp Rise) -40800.00 -3598.71 1958.40 -125.70 1958.40 520.68 OK
CRACK WIDTH CHECK for outer girder
Sample calculation at 0.5 L
Crack width checking during SLS condition under Quasi-permanent Load combination
(As per Cl:12.03.4 (1) of IRC:112-2011)
Maximum Crack width is limited to Wkmax = mm Table 12.1
Chararcteristic Strength of Concrete, fck = N/mm2
Table 6.5
Yield Strength of Steel, fy = N/mm2
Table 18.1
Modulus of elasticity of reinf. of steel Es = N/mm2
12.0
0.3
40
500
2E+05
Modulus of elasticity of concrete=22*(fcm/12.5)0.3
Ecm = N/mm2
Creep Coefficient φ = Table 6.9
Effictive Modulus of elasticity Eceff =
Effective Modular ratio αe = (Es/Eceff) αe =
Clear Cover C = mm
Width of Structure Bw = mm
1
16673Cl. 12.4.2 (2) of
IRC:112
12
40
450
33346
Details of reinforcement bars provided:
Total area of reinforcement As = mm2
Centroid of reinforcing bars from bottom = mm
Equivalent diameter Φ eq = SniΦi2
= mm
SniΦi
Depth of neutral axis X = mm
Stress in Steel at CG, σsc = Mpa
Σ =
Overall Depth, D or h h = mm
Tensile Strength of Concrete, fctm = Mpa
32 5 132 78.50 160 5120
11259.47
32 5 68 78.50 160 5120 128
Dia Nos.CG from
bottom
c/c
spacingniΦi niΦi
2
0 0 0 0.00 0 0
32
32 0 260 0.00 0 0
32 4 196 104.67 128 4096
113.38
0 0 0 0.00 0 0
0 0 0 0.00 0 0
133.32
448 14336
1825
3
0 0 0 0.00 0 0
Tensile Strength of Concrete, fctm = Mpa
Effective Cover = mm
Effective Depth d = mm
Spacing of bonded reinforcement with in tension zone < 5*(C+φ/2)
Effective spacing = = 88 < mm
Hence the maximum crack width is Sr,max , shall be calculated
Crack Spacing
Coefficent based on bond properties k1 = for Deformed bars
Coefficent based on distribution of strain k2 = for bending
3
56
Eq.12.8 of IRC:112-
2011
0.8
0.5
1697
Cl. 12.3.4 (3) of
IRC:112105445.7 280
1203.68 OK
eff
r
kkcS
ρρ
φ*2*1*425.0*4.3
max+=
Calculation of effective area of concrete in tension (Ac.eff):
Depth hceff is the lesser of
1. One third of the tension zone depth of the cracked section, (h-x)/3, with x negative
when whole section is in tension = mm
2. half of section depth,h/2, or = mm
3. 2.5*(h-d) = mm
hceff = mm
Aceff = mm2
ρρeff = As/Aceff ρρeff =
From fig. 12.2 of
IRC:112-2011
570.5
912.5
320
320
Effective area of of Concrete in tension
surrounding the reinforcement
144000
0.078ρρeff = As/Aceff ρρeff =
Crack Spacing Srmax = mm
= =
Crack Width = Wk = mm
< 0.3mm hence Safe
Eq.12.8 of IRC:112-
2011
≥5E-04
Eq. 12.6 of IRC:112-
2011
0.099Eq. 12.5 of IRC:112-
2011
0.078
205.6eff
kkcSr
ρρ
φ*2*1*425.0*4.3max +=
Summary of crack width at various sections:
c/c
spacingDia Nos.
CG from
bottom
c/c
spacingDia Nos.
Section
0 2.99 4.86 6.73 8.6
5 68 78.50
CG from
bottom
c/c
spacing
Layers of steel
Layer 1 32 5 68 78.50 32 5
Dia Nos.CG from
bottom
c/c
spacingDia Nos.
CG from
bottom
c/c
spacingDia Nos.
CG from
bottom
32 4 132 104.67 32
68 78.50
Layer 2 32 4 132 104.67 32 4 132
32 5 68 78.50 32 568 78.50 32
104.6732 0 196 0.00 32 0
78.50
Layer 3 32 0 196 0.00 32 0 196 0.00
4 132 104.67 32 5 132104.67
0 0 0.00 0
196 0.00 32 4 196
0 260 0.00
Layer 5 0 0 0 0.00 0 0
0.00 0 0 0 0.00 320 0 0.00 0 0 0Layer 4 0
0 0.00
Layer 6 0 0 0 0.00 0 0 0
0
0
0 0 0.00 0 00 0.00 0 0 0 0.00
0 0 0.00
0.00
Layer 7 0 0 0 0.00 0 0 0 0.00
0 0 0.00 0 0 00.00 0 0 0 0.00
0 0.00 0 0 0 0.000 0 0 0.00 0 0
Total area of 7238.23 7238.23 7238.23 7238.23 11259.47
0.00 0 0 0 0.00 00 0 0.00 0 0 0Layer 8 0 0 0 0.00 0
Total area of
reinforcement7238.23 7238.23 7238.23 7238.23 11259.47
SniΦi 288 288 288 288 448
Centroid of reinforcing
bars from bottom96.44 96.44 96.44 96.44 127.43
Φ eq 32 32 32 32 32
SniΦi2
9216 9216 9216 9216 14336
Shear rf at section 12 12 12 12 12
bw 450 450 450 450 450
Stress in steel at
CG (N/mm2)4.45 107.92 152.88 179.8 133.32
Depth of neutral
axis, x72.88 72.88 72.88 72.88 113.38
Tensile strength of
concrete, fctm3 3 3 3 3
Overall depth, D or
h1825 1825 1825 1825 1825
Effective depth, d 1729 1729 1729 1729 1698
Effective cover 56 56 56 56 56
5*(C+φ/2) 280 280 280 280 280
Spacing of bonded rf
in tension zone92.01 92.01 92.01 92.01 87.6
(i) (h-x)/3 584.04 584.04 584.04 584.04 570.54
Check OK OK OK OK OK
(iii) 2.5*(h-d) 240 240 240 240 317.5
(ii) h/2 912.5 912.5 912.5 912.5 912.5
Ac eff 108000 108000 108000 108000 142875
Depth hc eff (lesser of
I,ii &iii)240 240 240 240 317.5
Sr max 217.19 217.19 217.19 217.19 204.86
ρρ eff 0.067 0.067 0.067 0.067 0.079
Wk 0 0.065 0.13 0.152 0.102
εsm-εcm 0 0.0003 0.0006 0.0007 0.0005
Check OK OK OK OK OK
Limiting crack
width0.3 0.3 0.3 0.3 0.3
CRACK WIDTH CHECK for inner girder
Sample calculation at 0.5 L
Crack width checking during SLS condition under Quasi-permanent Load combination
(As per Cl:12.03.4 (1) of IRC:112-2011)
Maximum Crack width is limited to Wkmax = mm Table 12.1
Chararcteristic Strength of Concrete, fck = N/mm2
Table 6.5
Yield Strength of Steel, fy = N/mm2
Table 18.1
Modulus of elasticity of reinf. of steel Es = N/mm2
12.0
0.3
40
500
2E+05
Modulus of elasticity of concrete=22*(fcm/12.5)0.3
Ecm = N/mm2
Creep Coefficient φ = Table 6.9
Effictive Modulus of elasticity Eceff =
Effective Modular ratio αe = (Es/Eceff) αe =
Clear Cover C = mm
Width of Structure Bw = mm
1
16673Cl. 12.4.2 (2) of
IRC:112
12
40
450
33346
Details of reinforcement bars provided:
Total area of reinforcement As = mm2
Centroid of reinforcing bars from bottom = mm
Equivalent diameter Φ eq = SniΦi2
= mm
SniΦi
Depth of neutral axis X = mm
Stress in Steel at CG, σsc = Mpa
Σ =
Overall Depth, D or h h = mm
Tensile Strength of Concrete, fctm = Mpa
32 5 132 78.50 160 5120
11259.47
32 5 68 78.50 160 5120 126
Dia Nos.CG from
bottom
c/c
spacingniΦi niΦi
2
0 0 0 0.00 0 0
32
0 0 0 0.00 0 0
32 4 190 104.67 128 4096
113.38
0 0 0 0.00 0 0
0 0 0 0.00 0 0
103.72
448 14336
1825
3
0 0 0 0.00 0 0
Tensile Strength of Concrete, fctm = Mpa
Effective Cover = mm
Effective Depth d = mm
Spacing of bonded reinforcement with in tension zone < 5*(C+φ/2)
Effective spacing = = 88 < mm
Hence the maximum crack width is Sr,max , shall be calculated
Crack Spacing
Coefficent based on bond properties k1 = for Deformed bars
Coefficent based on distribution of strain k2 = for bending
3
56
Eq.12.8 of IRC:112-
2011
0.8
0.5
1699
Cl. 12.3.4 (3) of
IRC:112105445.7 280
1203.68 OK
eff
r
kkcS
ρρ
φ*2*1*425.0*4.3
max+=
Calculation of effective area of concrete in tension (Ac.eff):
Depth hceff is the lesser of
1. One third of the tension zone depth of the cracked section, (h-x)/3, with x negative
when whole section is in tension = mm
2. half of section depth,h/2, or = mm
3. 2.5*(h-d) = mm
hceff = mm
Aceff = mm2
ρρeff = As/Aceff ρρeff =
From fig. 12.2 of
IRC:112-2011
570.5
912.5
315
315
Effective area of of Concrete in tension
surrounding the reinforcement
141750
0.079ρρeff = As/Aceff ρρeff =
Crack Spacing Srmax = mm
= =
Crack Width = Wk = mm
< 0.3mm hence Safe
Eq.12.8 of IRC:112-
2011
≥3E-04
Eq. 12.6 of IRC:112-
2011
0.068Eq. 12.5 of IRC:112-
2011
0.079
204.5eff
kkcSr
ρρ
φ*2*1*425.0*4.3max +=
Summary of crack width at various sections:
c/c
spacingDia Nos.
CG from
bottom
c/c
spacingDia Nos.
Section
0 2.99 4.86 6.73 8.6
5 68 78.5
CG from
bottom
c/c
spacing
Layers of steel
Layer 1 32 5 68 78.5 32 5
Dia Nos.CG from
bottom
c/c
spacingDia Nos.
CG from
bottom
c/c
spacingDia Nos.
CG from
bottom
32 4 132 104.7 32
68 78.5
Layer 2 32 4 132 104.7 32 4 132
32 5 68 78.5 32 568 78.5 32
104.70 0 0 0 0 0
78.5
Layer 3 0 0 0 0 0 0 0 0
4 132 104.7 32 5 132104.7
0 0 0 0
0 0 32 4 190
0 0 0
Layer 5 0 0 0 0 0 0
0 0 0 0 0 00 0 0 0 0 0Layer 4 0
0 0
Layer 6 0 0 0 0 0 0 0
0
0
0 0 0 0 00 0 0 0 0 0
0 0 0
0
Layer 7 0 0 0 0 0 0 0 0
0 0 0 0 0 00 0 0 0 0
0 0 0 0 0 00 0 0 0 0 0
Total area of 7238.23 7238.23 7238.23 7238.23 11259.47
0 0 0 0 0 00 0 0 0 0 0Layer 8 0 0 0 0 0
Total area of
reinforcement7238.23 7238.23 7238.23 7238.23 11259.47
SniΦi 288 288 288 288 448
Centroid of reinforcing
bars from bottom96.44 96.44 96.44 96.44 125.71
Φ eq 32 32 32 32 32
SniΦi2
9216 9216 9216 9216 14336
Shear rf at section 12 12 12 12 12
bw 450 450 450 450 450
Stress in steel at
CG (N/mm2)4.8 83.61 119.78 139.78 103.72
Depth of neutral
axis, x72.88 72.88 72.88 72.88 113.38
Tensile strength of
concrete, fctm3 3 3 3 3
Overall depth, D or
h1825 1825 1825 1825 1825
Effective depth, d 1729 1729 1729 1729 1700
Effective cover 56 56 56 56 56
5*(C+φ/2) 280 280 280 280 280
Spacing of bonded rf
in tension zone92.01 92.01 92.01 92.01 87.6
(i) (h-x)/3 584.04 584.04 584.04 584.04 570.54
Check OK OK OK OK OK
(iii) 2.5*(h-d) 240 240 240 240 312.5
(ii) h/2 912.5 912.5 912.5 912.5 912.5
Ac eff 108000 108000 108000 108000 140625
Depth hc eff (lesser of
I,ii &iii)240 240 240 240 312.5
Sr max 217.19 217.19 217.19 217.19 204
ρρ eff 0.067 0.067 0.067 0.067 0.08
Wk 0 0.065 0.087 0.109 0.061
εsm-εcm 0 0.0003 0.0004 0.0005 0.0003
Check OK OK OK OK OK
Limiting crack
width0.3 0.3 0.3 0.3 0.3
CALCULATION OF DEFLECTION for outer girder
Deflection, for simply supported member = 5ML2/48EI
I, Moment of Inertia of section = mm4
Ec, Modulus of Elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
ho =2Ac / u = mm
Φ, creep coefficient =
Ec,eff,effective modulus of elasticity = Ec/(1+φ) = N/mm2
Moment due to girder selfweight = tm
Moment due to slab selfweight = tm
Moment due to SIDL = tm
Total moment due to sustained loading = tm (Permanent loads)
Moment due to vehicular loading = tm (Live loads)
A) Deflection due to vehicular loading
M, moment = tm
L, length = m
E, Modulus of elasticity = N/mm2
3.87E+11
33000
2.71E+11
373.42
13.0
204.195
153.1463
17.2
33000
1.35
14048.85
52.828
69.652
49.481
171.96
E, Modulus of elasticity = N/mm
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
Permissible deflection due to vehicular traffic = L/800 (12.4.1.(2) IRC:112-2011)
= mm
Hence the deflection is Within permissible limit
B) Deflection due to sustained loading
i) For short term deflection,
M, moment = tm
L, length = m
E, Modulus of elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
ii) Deflection due to creep,
acc(perm) = aicc(perm) - ai(perm)
33000
2.71E+11
5.285
21.5
171.96
17.2
33000
2.71E+11
5.934
For aicc(perm)
M, moment = t/m
L, length = m
Ec,eff ,Effective modulus of elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
For ai(perm)
M, moment = t/m
L, length = m
Ec,eff ,Effective modulus of elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
acc(perm) = -
= mm
iii) Deflection due to shrinkage,
acs = k3 * Ψcs * L2
Where, k3 is a constant representing effect of support conditions
k3 =
171.96
17.2
14048.85
2.71E+11
13.938
171.96
8.004
0.125 for simply supported members
17.2
33000
2.71E+11
5.934
13.938 5.934
k3 =
Ψcs = 1/ rcs As per Cl: 12.4.2, shrinkage curvature
1 = εcs * αe * S/I
rcs
As per Cl: 6.4.2.6, total shrinkage strain is given by
εcs = εcd + εca
εca = x 10-6
(table 6.6, page 45)
εcd = kh * εcd'
kh = (table 6.7, page 45)
εcd' = for relative humidity 50 %
εcd = x 10-6
Therefore, εcs =
αe =
S = mm3
I = mm4
Ψcs =
acs = mm
Total Deflection = Short term deflection+ Deflection due to creep + Deflection due to Shrinkage
Total Deflection = mm
0.125 for simply supported members
55
0.732
466
5.16
19.10
341.1
4E-04
14.24
9.56E+06
3.87E+11
1.39E-07
CALCULATION OF DEFLECTION for inner girder
Deflection, for simply supported member = 5ML2/48EI
I, Moment of Inertia of section = mm4
Ec, Modulus of Elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
ho =2Ac / u = mm
Φ, creep coefficient =
Ec,eff,effective modulus of elasticity = Ec/(1+φ) = N/mm2
Moment due to girder selfweight = tm
Moment due to slab selfweight = tm
Moment due to SIDL = tm
Total moment due to sustained loading = tm (Permanent loads)
Moment due to vehicular loading = tm (Live loads)
A) Deflection due to vehicular loading
M, moment = tm
L, length = m
E, Modulus of elasticity = N/mm2
157.4625
17.2
33000
123.98
209.95
373.42
1.35
52.829
64.679
6.475
3.87E+11
33000
2.71E+11
14048.85
E, Modulus of elasticity = N/mm
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
Permissible deflection due to vehicular traffic = L/800 (12.4.1.(2) IRC:112-2011)
= mm
Hence the deflection is Within permissible limit
B) Deflection due to sustained loading
i) For short term deflection,
M, moment = tm
L, length = m
E, Modulus of elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
ii) Deflection due to creep,
acc(perm) = aicc(perm) - ai(perm)
33000
2.71E+11
5.434
123.98
17.2
33000
2.71E+11
4.278
21.5
For aicc(perm)
M, moment = t/m
L, length = m
Ec,eff ,Effective modulus of elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
For ai(perm)
M, moment = t/m
L, length = m
Ec,eff ,Effective modulus of elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
acc(perm) = -
= mm
iii) Deflection due to shrinkage,
acs = k3 * Ψcs * L2
Where, k3 is a constant representing effect of support conditions
k3 = 0.125
10.049 4.278
5.771
for simply supported members
123.98
4.278
17.2
14048.85
2.71E+11
123.98
33000
2.71E+11
10.049
17.2
k3 =
Ψcs = 1/ rcs As per Cl: 12.4.2, shrinkage curvature
1 = εcs * αe * S/I
rcs
As per Cl: 6.4.2.6, total shrinkage strain is given by
εcs = εcd + εca
εca = x 10-6
(table 6.6, page 45)
εcd = kh * εcd'
kh = (table 6.7, page 45)
εcd' = for relative humidity 50 %
εcd = x 10-6
Therefore, εcs =
αe =
S = mm3
I = mm4
Ψcs =
acs = mm
Total Deflection = Short term deflection+ Deflection due to creep + Deflection due to Shrinkage
Total Deflection = mm
0.125 for simply supported members
5.16
15.21
55
4E-04
14.24
466
341.1
9.57E+06
0.732
1.4E-07
3.87E+11
CHECK FOR INTERFACE SHEAR for outer girder (10.3.4 IRC:112-2011)
Sample Calculation for section @ 0.0L
VDS, the shear due to Dead load of slab = x = t
VSIDL-1,the shear due to SIDL except surfacing = x = t
VSIDL-2, the shear due to surfacing = x = t
VLL, the shear due to live load = x = t
VED, the transverse shear force (factored) = t
Vgrdr ,factored shear due to dead weight of girder = x = t
Effective length considered = mm
μ, Coefficient of friction =
z, lever arm = mm
b1, width of interface = mm
ds, depth of slab = mm
β, ratio of longitudinal force in new concrete
to total longitudinal force
14.0
225.00
0.706
5.188 1.75 9.08
52.625 1.5 78.94
15.884 1.35 21.44
11.672 1.35 15.76
125.22
0.7
1555.70
800.00
13.007 1.35 17.56
VSIDL+VLL
VSIDL+VLL+Vgrdr+VDS
1000.00
= = Page 20 IRC:22-
1986
VEDi ,interface shear stress = β VED = N/mm2
z b1
Provided shear reinforcement: @ mm c/c spacing
As, area of shear reinforcement already provided = mm2
Additional reinforcement: @ mm c/c spacing
Ai, area of interface reinforcement = mm2
Asteel, total area of reinforcement crossing the joint = mm2
Aj, interface area of the joint = mm2
Amin, area of minimum reinforcement required = mm2
ρmin , mimimum reinforcement ratio =
ρ = /Aj =
α,angle of reinforcement to the interface = ˚
σn, minimum coexisting normal stress = < 0.6fcd = N/mm2
2261.95
800000
0.0057
90
6.96
0.71
VED/(b1.ds)
Cl:10.3.4 IRC:112-
2011
12 dia 2 Leg 100
12 dia 2 Leg 100
2261.95
4523.9
Asteel
1200
OK
0.0015
OK
ν, reduction factor for concrete cracked in shear = 0.6(1-fck/310) =
VRdi ,resisting capacity at section = μσn+ρfyd[μsinα+cosα] ≤ 0.5νfcd
= N/mm2 ≤ N/mm
2
= N/mm2
Interface Shear stress, VEDi = N/mm2
Resisting capacity at section, VRdi = N/mm2
Summary of interface shear at various sections:
Deff EOT 0.283L 0.391L 0.5L
0.71
4.645
OK
Section
0L
13.007 9.814
8.719
6.834
VDL (t)
VSIDL-1 (t)
VSIDL-2 (t)
VLL (t)
VED (t)
μ
Vgrdr (t)
15.884
11.672
5.188
52.625
125.2171
0.7
12.361
9.522
4.223
52.63
115.8773
0.7
12.361
9.522
4.219
47.784
108.6013
0.7
9.724 5.354 2.68
2.903
36.352
80.6048
0.7
0.525
13.906
26.43795
0.7
5.332
4.163
1.714
25.997
54.81325
0.7
0
4.645
0.52
6.607
4.645
1.824
1.628
eq 10.6 IRC:112-
2011
eq 10.21 IRC:112-
2011
90 ˚ 90 ˚ 90 ˚ 90 ˚ 90 ˚ 90 ˚
VRdi (t/m2) o
o
800.00
0.706
72.452
0.75
71.227
150
12 dia 2 Leg 12 dia 2 Leg
100 100 100 120 150
12 dia 2 Leg 12 dia 2 Leg 12 dia 2 Leg 12 dia 2 Leg
65.508
μ
z (mm)
b1 (mm)
β
α (deg;rad)
σn
VEDi (t/m2)
Status
VEDi (t/m2)
Shear r/f
spacing
As (mm2)
Aj (mm2)
ρ
VRdi (t/m2)
Additional rf
Ai (mm2)
Amin (mm2)
ρmin
Status
Asteel (mm2)
Status
0.7
1555.70
800
1555.70
0.7
35.89450.603
0.7
1555.70
800.00
0.736
0.7 0.7
1555.70
800.00
0.766
0.7
0.799
OK
473.824
2261.95 2261.95 1884.96 1507.96
800000 800000 800000 800000
0.0057
709.56
673.64
72.452
2261.95
800000
1.571 1.571 1.571 1.571
71.227 65.508 50.603 35.894
OK OK OK OK OK
0.0057 0.0052 0.0047 0.0038 0.0038
19.813
656.64 615.41 456.76 310.61 149.82
636.596 592.213 465.636 335.392 222.839
335.392 222.839
473.824
473.824 473.824 473.824 465.636
1.571 1.571
1527.81
800.00
0.898
19.813
1507.96
800000
1555.70
800.00
473.824 473.824 473.824 473.824
2 Leg 12 dia 2 Leg
spacing 100 100 120 120 150 150
12 dia 2 Leg 12 dia 2 Leg 12 dia 2 Leg 12 dia 2 Leg 12 dia
2261.95 2261.95 1884.96 1884.96 1507.96 1507.96
4523.9 4523.9 4146.91 3769.92 3015.92 3015.92
0.0015 0.0015 0.0015 0.0015 0.0015
1200 1200 1200 1200 1200 1200
OK OK OK OK OK OK
OK OK OK OK OK OK
0.0015
CHECK FOR INTERFACE SHEAR for inner girder (10.3.4 IRC:112-2011)
Sample Calculation for section @ 0.0L
VDS, the shear due to Dead load of slab = x = t
VSIDL-1,the shear due to SIDL except surfacing = x = t
VSIDL-2, the shear due to surfacing = x = t
VLL, the shear due to live load = x = t
VED, the transverse shear force (factored) = t
Vgrdr ,factored shear due to dead weight of girder = x = t
Effective length considered = mm
μ, Coefficient of friction =
z, lever arm = mm
b1, width of interface = mm
ds, depth of slab = mm
β, ratio of longitudinal force in new concrete
to total longitudinal forcePage 20 IRC:22-
1986VSIDL+VLL+Vgrdr+VDS
1555.70
800.00
225.00
=VSIDL+VLL
= 0.705
118.97
13.006 1.35 17.56
1000.00
0.7
4.526 1.75 7.92
58.257 1.5 87.39
14.0
14.554 1.35 19.65
2.967 1.35 4.01
VEDi ,interface shear stress = β VED = N/mm2
z b1
Provided shear reinforcement: @ mm c/c spacing
As, area of shear reinforcement already provided = mm2
Additional reinforcement: @ mm c/c spacing
Ai, area of interface reinforcement = mm2
Asteel, total area of reinforcement crossing the joint = mm2
Aj, interface area of the joint = mm2
Amin, area of minimum reinforcement required = mm2
ρmin , mimimum reinforcement ratio =
ρ = /Aj =
α,angle of reinforcement to the interface = ˚
σn, minimum coexisting normal stress = < 0.6fcd = N/mm2
OK
90
VED/(b1.ds) 6.61
800000
1200
OK
0.0015
Asteel 0.0057
2261.95
12 dia 2 Leg 100
2261.95
4523.9
0.67Cl:10.3.4 IRC:112-
2011
12 dia 2 Leg 100
ν, reduction factor for concrete cracked in shear = 0.6(1-fck/310) =
VRdi ,resisting capacity at section = μσn+ρfyd[μsinα+cosα] ≤ 0.5νfcd
= N/mm2 ≤ N/mm
2
= N/mm2
Interface Shear stress, VEDi = N/mm2
Resisting capacity at section, VRdi = N/mm2
Summary of interface shear at various sections:
0.7μ 0.7 0.7 0.7 0.7 0.7
34.94895
Vgrdr (t) 13.006 9.822 9.725 5.35 2.676 0
VED (t) 118.95935 68.18705 99.0778 70.07315 51.4496
0.282
VLL (t) 58.257 29.01 49.619 35.643 27.994 21.236
VSIDL-2 (t) 4.526 3.782 3.769 2.375 1.331
1.694
VSIDL-1 (t) 2.967 2.018 2.018 1.077 0.355 0.233
VDL (t) 14.554 11.355 11.355 8.147 4.926
OK
Section
0L Deff EOT 0.283L 0.391L 0.5L
eq 10.21 IRC:112-
20116.362 4.645
4.645
0.67
4.645
0.52 eq 10.6 IRC:112-
2011
90 ˚ 90 ˚ 90 ˚ 90 ˚ 90 ˚ 90 ˚
VRdi (t/m2) o
o
OKStatus OK OK OK OK OK
256.593
VEDi (t/m2) 68.734 34.76 58.789 42.67 33.564 27.038
VRdi (t/m2) 473.824 447.421 473.824 423.86 322.05
473.824 473.824 473.824 473.824 473.824 473.824
648.818 447.421 554.434 423.86 322.05 256.593
1.571
σn 674.1 386.39 561.44 397.08 291.55 198.04
α (deg;rad) 1.571 1.571 1.571 1.571 1.571
0.0038
Status OK OK OK OK OK OK
ρ 0.0057 0.0057 0.0052 0.0047 0.0038
OK
ρmin 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015
Status OK OK OK OK OK
800000
Amin (mm2) 1200 1200 1200 1200 1200 1200
Aj (mm2) 800000 800000 800000 800000 800000
1507.96
Asteel (mm2) 4523.9 4523.9 4146.91 3769.92 3015.92 3015.92
Ai (mm2) 2261.95 2261.95 1884.96 1884.96 1507.96
2 Leg
spacing 100 100 120 120 150 150
2 Leg 12 dia 2 Leg 12 dia 2 Leg 12 diaAdditional rf 12 dia 2 Leg 12 dia 2 Leg 12 dia
150
As (mm2) 2261.95 2261.95 2261.95 1884.96 1507.96 1507.96
12 dia 2 Leg 12 dia 2 Leg
spacing 100 100 100 120 150
27.038
Shear r/f 12 dia 2 Leg 12 dia 2 Leg 12 dia 2 Leg 12 dia 2 Leg
VEDi (t/m2) 68.734 34.76 58.789 42.67 33.564
800.00
β 0.705 0.622 0.724 0.743 0.796 0.928
b1 (mm) 800.00 800 800.00 800.00 800.00
0.7
z (mm) 1555.70 1555.70 1555.70 1555.70 1555.70 1529.36
μ 0.7 0.7 0.7 0.7 0.7
DESIGN OF DIAPHRAGMS
A) Jacking Condition
3.0 3.0 3.0
0.75 1.5 0.75 0.75 1.5 0.75 0.75 1.5 0.75
Total length of cross-girder = m
Distance between supports (jacks) = m
Centre to centre distance between main girders = m
Overall depth of girder = m
Width of girder = m
15.0
9
1.5
3
1.575
0.4
Reactions on main girders due to various loading. (These reactions would be the loads for cross-
girder)
t/m for m length
33.038
26.037
(Loads in t)
Self wt of cross-girder
LL (symmetric)
LL (eccentric)
SIDL
Dead Load
1.575
0
0 0
0
0
Reaction on G1 Reaction on G2 Reaction on G3
30.077 33.038
11.046 26.037
0
9.0
Cross-diaphragm is analysed as continous beam on STAAD and BM and Shear Forces are tabulated
below.
i) Hogging Moment
Σ = 68.22235 44.749
Dead Load 25.221
19.528
0
1.35
1.75
1.5
Moment (t
m)
Factored Moment (t m)Loading
1 1
0Live Load
SIDL
1
1
Factors
0 0
ULS Rare Quasi perm ULS Rare Quasi perm
34.04835 25.221 25.221
34.174 19.528 19.528
1
44.749
0
ii) Sagging Moment
Σ =
Effective span of girder, L = mm
Dia of jacks = mm
Clear length of girder, Lclear = mm
Overall Depth of girder, D = mm
Ratio of effective span to overall depth = L/D =
Support conditions =
As the beam is a Continuous beam and the ratio l/D < it is a deep beam
Lever arm, z = = mm
Design Moment = tm
0 0
29.62 18.68 18.68
1500
1200
1575
0
7.67 7.67
SIDL 11.01 1.75 1 1 19.27 11.01 11.01
Dead Load 7.668 1.35 1 1 10.35
LoadingMoment (t
m)
Factors Factored Moment (t m)
ULS Rare Quasi perm ULS Rare Quasi perm
0.952
Continuous
2.5
0.5l 750
29.62
Live Load 0 1.5 1 0
300
Design Moment = tm
Grade of steel = Fe 500
29.62
Grade of concrete =
Width of section, b = mm
Overall depth of section = mm
Clear cover to any reinforcement = mm
Positive reinforcement requirement: 29.3.1 IS456:2000
Area of steel required, Ast = Mu/0.87fyz = mm2
Depth of tensile zone for reinforcement = 0.25D-0.05l = mm
Reinforcement details : = 16 mm Φ x 4 bars
16 mm Φ x 2 bars
16 mm Φ x 0 bars
Area of steel required <= Area of steel provided ----OK
907.89
318.75
= 1206.37
M 40
400
1575
40
mm2
16 mm Φ 0 bars
16 mm Φ 2 bars
16 mm Φ 4 bars
Negative reinforcement requirement: 29.3.2 IS456:2000
Area of steel required, Ast = Mu/0.87fyz = mm2
Ratio of clear span to overall depth = Lclear/D =
2091.11
0.76
Zone 1:
Depth of zone = = mm
Required Area of steel in zone = = mm2
Reinforcement details : = 20 mm Φ x 8 bars
0 mm Φ x 0 bars
Area of steel required <= Area of steel provided ----OK
Zone 2:
Depth of zone = 0 D =
Required Area of steel in zone = = mm2
Reinforcement details : = 12 mm Φ x 2 bars
12 mm Φ x 2 bars
Area of steel required <= Area of steel provided ----OK
1260.00
Entire area of steel 2091.11
= 2513.27 mm2
0
Ast - Ast in Zone 1 0.00
= 452.39 mm2
According to Cl: 29.3.2a)1) of IS456:2000, not more than half the negative reinforcement may be curtailed
after extending a distance of 0.5D from the face of support
0.8D
So all the negative reinforcement needs to be extended at least upto mm
from face of support
20mm dia 8bars
0mm dia 0bars 1260mm
787.50
Side face reinforcement requirement:
Vertical shear reinforcement:
Area of steel required = = mm2/m
Area of steel required on each face = mm2/m
Maximum diameter of bar = mm
Spacing of vertical bars, sv <= mm
Vertical reinforcement details on each face : = 12 mm Φ bars at
mm c/c spacing
Area of steel required <= Area of steel provided ----OK
Bar dia provided <= Maximum bar dia ----OK
Spacing provided <= Maximum Spacing ----OK
Horizontal reinforcement:
Area of steel required = = mm2/m
Area of steel required on each face = mm2/m
Maximum diameter of bar = mm
Spacing of horizintal bars, s <= mm
16
s < 450mm and s < 3b 450.00
0.12% of Gross area 480.00
240.00
16
sv < 450mm and sv < 3b 450.00
= 753.98 mm2/m
150
0.20% of Gross area 800.00
400.00
Spacing of horizintal bars, sh <= mm
Horizontal reinforcement details on face 1: = 12 mm Φ bars at
mm c/c spacing
Area of steel required <= Area of steel provided ----OK
Bar dia provided <= Maximum bar dia ----OK
Spacing provided <= Maximum Spacing ----OK
Horizontal reinforcement details on face 2: = 12 mm Φ bars at
mm c/c spacing
Area of steel required <= Area of steel provided ----OK
Bar dia provided <= Maximum bar dia ----OK
Spacing provided <= Maximum Spacing ----OK
Check for Shear at support location:
Σ =
Effective depth of girder = mm
Area of steel provided = mm2
Width of web = mm
=
=
sh < 450mm and sh < 3b 450.00
= 452.39 mm2/m
250
= 452.39 mm2/m
250
LoadingShear (t)
Factors Factored Moment (t m)
ULS Rare Quasi perm ULS Rare Quasi perm
Dead Load 34.31 1.35 1 1 46.32 34.31 34.31
SIDL 26.037 1.75 1 1 45.56 26.04 26.04
Live Load 0 1.5 1 0 0 0 0
91.88 60.35 60.35
1525.00
1206.37
400.00
1.36
0.31
=
NED, the applied longitudinal force =
=
The design Shear resistance of the member without Shear reinforcement VRD.c is given by,
subject to minimum of
= t
Total shear = t
Check for shear reinforcement requirement : Shear reinforcement required
0.002
0
18.91
91.88
0
=
z = lever arm to be taken as 0.9 for RC sect & calculated for PSC section = mm
1 = Strength reduction factor for concrete cracked in shear =
= for fck<=80Mpa
= 0.9-fck/250 > 0.5 for fck>80Mpa
αcw =
θ = ˚ = radians
cot θ =
tan θ =
Shear reinforcement : mm dia legged stirrups at mm c/c spacing.
Min area of reinforcement required, = mm2
Cross sectional area of shear reinforcement at a section, Asw = mm2
Min shear reinforcement required <= Shear reinforcement provided ----OK
Maximum spacing for steel provided, = mm
0.0009
1372.5
0.6
0.6
1
21.8 0.3805
628.32
2.5
0.4
54
12 2 150
226.195
αρ sinmin wreqd sbA =
max
swAs =Maximum spacing for steel provided, = mm
Spacing provided, s = mm
Maximum spacing for steel Spacing provided, s ----OK
For members with vertical shear reinforcement, the shear resistance Vrd is smaller of,
= t
= t
Vrd = t
Total factored shear, V = t
Check for shear ----OK
628.32
150
>
179.97
202.94
179.97
91.88
αρ sinmin
max
wbs =
B) Service Condition
3.0 3.0 3.0
Total length of cross-girder = m
Distance between supports (bearings) = m
Centre to centre distance between main girders = m
9.0
3.0
3.0
Overall depth of girder = m
Width of girder = m
Reactions on main girders due to various loading. (These reactions would be the loads for cross-
girder)
t/m for m length
Cross-diaphragm is analysed as continous beam on STAAD and BM and Shear Forces are tabulated
below.
i) Hogging Moment
Σ =
1.575
0.4
(Loads in t) Reaction on G1 Reaction on G2 Reaction on G3
LL (eccentric) 0 0 0
LL (symmetric) 0 0 0
Dead Load 33.038 30.077 33.038
SIDL 26.037 11.046 26.037
Self wt of cross-girder 1.575 9
LoadingMoment (t
m)
Factors Factored Moment (t m)
ULS Rare Quasi perm ULS Rare Quasi perm
Dead Load 2.946 1.35 1 1 3.9771 2.946 2.946
SIDL 4.615 1.75 1 1 8.07625 4.615 4.615
8.129 0
24.24685 15.69 7.561
Live Load 8.129 1.5 1 0 12.1935
ii) Sagging Moment
Σ =
Effective span of girder, L = mm
Width of bearing = mm
Clear length of girder, Lclear = mm
Overall Depth of girder, D = mm
LoadingMoment (t
m)
Factors Factored Moment (t m)
ULS Rare Quasi perm ULS Rare Quasi perm
Dead Load 1.572 1.35 1 1 2.12 1.57 1.57
1.67 1.67
Live Load 8.177 1.5 1 0 12.27 8.18 0
SIDL 1.67 1.75 1 1 2.92
1575
17.31 11.42 3.24
3000
400
2600
Overall Depth of girder, D = mm
Ratio of effective span to overall depth = L/D =
Support conditions =
As the beam is a Continuous beam and the ratio l/D < it is a deep beam
Lever arm, z = = mm
Design Moment = tm
Grade of steel =
Grade of concrete =
Width of section, b = mm
Overall depth of section = mm
Clear cover to any reinforcement = mm
1575
1.905
Continuous
2.5
0.2(l+1.5D) 1072.5
17.31
Fe 500
M 40
400
1575
40
Positive reinforcement requirement: 29.3.1 IS456:2000
Area of steel required, Ast = Mu/0.87fyz = mm2
Depth of tensile zone for reinforcement = 0.25D-0.05l = mm
Reinforcement details : = 16 mm Φ x 4 bars
16 mm Φ x 2 bars
16 mm Φ x 0 bars
Area of steel required <= Area of steel provided ----OK
16 mm Φ 0 bars
371.03
243.75
= 1206.37 mm2
16 mm Φ 0 bars
16 mm Φ 2 bars
16 mm Φ 4 bars
Negative reinforcement requirement: 29.3.2 IS456:2000
Area of steel required, Ast = Mu/0.87fyz = mm2
Ratio of clear span to overall depth = Lclear/D =
Zone 1:
Depth of zone = = mm
Required Area of steel in zone = = mm2
Reinforcement details : = 20 mm Φ x 8 bars
0 mm Φ x 0 bars
Area of steel required <= Area of steel provided ----OK
519.72
mm2
1.65
0.2D 315.00
Ast*(0.5*(L/D-0.5)) 299.10
= 2513.27
Zone 2:
Depth of zone = 0.3D on either side of mid-depth =
Required Area of steel in zone = = mm2
Reinforcement details : = 12 mm Φ x 2 bars
12 mm Φ x 2 bars
Area of steel required <= Area of steel provided ----OK
So all the negative reinforcement needs to be extended at least upto mm
from face of support
472.5
mm on either side of
mid-depth
Ast - Ast in Zone 1 220.62
= 452.39 mm2
According to Cl: 29.3.2a)1) of IS456:2000, not more than half the negative reinforcement may be curtailed
after extending a distance of 0.5D from the face of support
787.50
315mm
20mm dia 8bars
0mm dia 0bars 472.5mm
472.5mm
12mm dia 2bar
12mm dia 2bar
Side face reinforcement requirement:
Vertical shear reinforcement:
Area of steel required = = mm2/m
Area of steel required on each face = mm2/m
0.12% of Gross area 480.00
240.00
Maximum diameter of bar = mm
Spacing of vertical bars, sv <= mm
Vertical reinforcement details on each face : = 12 mm Φ bars at
mm c/c spacing
Area of steel required <= Area of steel provided ----OK
Bar dia provided <= Maximum bar dia ----OK
Spacing provided <= Maximum Spacing ----OK
Horizontal reinforcement:
Area of steel required = = mm2/m
Area of steel required on each face = mm2/m
Maximum diameter of bar = mm
Spacing of horizintal bars, s <= mm
sv < 450mm and sv < 3b 450.00
= 753.98 mm2/m
150
16
0.20% of Gross area 800.00
400.00
16
s < 450mm and s < 3b 450.00Spacing of horizintal bars, sh <= mm
Horizontal reinforcement details on face 1: = 12 mm Φ bars at
mm c/c spacing
Area of steel required <= Area of steel provided ----OK
Bar dia provided <= Maximum bar dia ----OK
Spacing provided <= Maximum Spacing ----OK
Horizontal reinforcement details on face 2: = 12 mm Φ bars at
mm c/c spacing
Area of steel required <= Area of steel provided ----OK
Bar dia provided <= Maximum bar dia ----OK
Spacing provided <= Maximum Spacing ----OK
Check for Shear at support location:
Σ =
= 452.39 mm2/m
250
= 452.39 mm2/m
250
sh < 450mm and sh < 3b 450.00
LoadingShear (t)
Factors Factored Moment (t m)
ULS Rare Quasi perm ULS Rare Quasi perm
3.5 3.5
SIDL 1.282 1.75 1 1 2.24 1.28 1.28
Dead Load 3.498 1.35 1 1 4.72
11.56 0
24.29 16.34 4.78
Live Load 11.556 1.5 1 0 17.33
Effective depth of girder = mm
Area of steel provided = mm2
Width of web = mm
=
=
=
NED, the applied longitudinal force =
=
The design Shear resistance of the member without Shear reinforcement VRD.c is given by,
subject to minimum of
1525.00
1206.37
400.00
1.36
0.31
0.002
0
0
subject to minimum of
= t
Total shear = t
Check for shear reinforcement requirement : Shear reinforcement required
=
z = lever arm to be taken as 0.9 for RC sect & calculated for PSC section = mm
1 = Strength reduction factor for concrete cracked in shear =
= for fck<=80Mpa
= 0.9-fck/250 > 0.5 for fck>80Mpa
αcw =
θ = ˚ = radians
cot θ =
tan θ =
Shear reinforcement : mm dia legged stirrups at mm c/c spacing.
18.91
24.29
0.0009
1372.5
0.6
0.6
1
21.8 0.3805
2.5
0.4
12 2 150
αρ sinsbA =
Min area of reinforcement required, = mm2
Cross sectional area of shear reinforcement at a section, Asw = mm2
Min shear reinforcement required <= Shear reinforcement provided ----OK
Maximum spacing for steel provided, = mm
Spacing provided, s = mm
Maximum spacing for steel Spacing provided, s ----OK
For members with vertical shear reinforcement, the shear resistance Vrd is smaller of,
= t
= t
V = t
54
226.195
628.32
150
>
179.97
202.94
179.97
αρ sinmin wreqd sbA =
αρ sinmin
max
w
sw
b
As =
Vrd = t
Total factored shear, V = t
Check for shear ----OK
179.97
24.29
DECK SLAB
Input Data
Span of Long. Girder (C/c of support) = m
No.of Cross Girder =
Width of Deck (Centre to centre of cross girder) = m
Type of Deck slab =
Overall Length of Deck = m
Dist.from Deck End to face of kerb(incl. footway if any)on LHS = m
Carriageway Width = m
Dist.from Deck End to face of kerb(incl. footway if any)on RHS = m
No. of Long. Girders =
Spacing between Long.Girders (Effective Span of Deck) = m
Top Flange Width of Girders = m
Thickness of Deck Between Long.Girders = m
Wearing Coat = m
Cantiliver Span of Deck on LHS = m
Dist.from centre of web to face of support of Cantilever. On LHS = m
Thickness of Deck at Free End of Cantilever.On LHS = m
Thickness of Deck at Face of Support of Cantilever.On LHS = m
Cantiliver Span of Deck on RHS = m
Dist.from centre of web to face of support of Cantilever. On RHS = m
Thickness of Deck at Free End of Cantilever.On RHS = m
Thickness of Deck at Face of Support of Cantilever.On RHS = m
Simple supp
1.500
0.225
2.500
0.500
0.065
0.800
0.225
0.225
0.225
9.000
3.000
4
1.500
12.000
2
17.200
17.200
0.225
0.225
0.225
On LHS
Area of Crash barrier/End Railing = m x m = m2
Footway = m x m
kerb (wheel guard) /Crash barrier = m x m = m2
On RHS
Area of Crash barrier/End Railing = m x m = m2
Footway = m x m
kerb (wheel guard) /Crash barrier = m x m = m2
Number of Lane for design purpose =
Designing slab for width = m
Material Properties:
Density of Wearing Coat = t/m3
Density of Concrete = t/m3
Chararcteristic Strength of Concrete, fck = N/mm2
Yield Strength of Steel, fy = N/mm2
1.0
0.450
0.000
500
2.2
1.500 0.300
40
2.5
2
0.000
0.000 0.900 0.000
0.450
Length Depth
Length Depth
0.500 0.900
0.500 0.900
0.500 0.4500.900
Dead Load & SIDL Calculations
Uniformly Distributed Load :
Deck (bet.long.girders)
wearing coat (carriageway)
Left Cant.Deck(sup.)
Left Cant.Deck(free end)
Right Cant.Deck(sup.)
Right Cant.Deck(free end)
Left Footway slab
Right Footway slab
Concentrated Load:
On LHS
Crash Barrier
Kerb
On RHS
Crash Barrier
Kerb
Description No.
2.500 1.125
1.1251 - - 0.450
1
1 - - 0.450 1.000
Length
0.450 1.000 2.500 1.125
Total Load
tt/m3
2.500
1 1.000
m m m2
0.225 0.225
1.000 0.225
0.300
Depth Area
1 1.000
1 1.000 0.000
0.300
1 1.000 0.065 0.065 -
1 1.000 0.225 0.225
t/m
1 1.000 0.225 0.225 -
t/m3
m
Length
0.563
0.200
0.563
0.5632.500
Width Density
Description No. Width Depth Area
m
Density
2.500
1
1 1.000 0.225
0.563
2.500
- 2.5000.225
Total Load
-
m
2.200
2.500-
m2
0.225 -
-
0.000 -
2.500
0.000
0.563
- -
0.000
2.500 0.750
m
2.500
1.000
1.0000.0001 - -
Footway Live Load Calculations
(i) For effective span of 7.5 m or less, footway live load P = 500 kg/m2
(ii) For effective span of over 7.5 m but not exceeding 30 m, the intensity of load,
P = P' - 40L - 300 where, P' = kg/m2
L = Effective span of main girder in m
(iii) For effective span of over 30 m, the intensity of load,
P = P' - + * - W where, W = Width of Footway in m
L
So, Footway live load on LHS = kg/m2
= t/m2
So, Footway live load on RHS = kg/m2
= t/m2
0.00
500
9
260
0.00
IRC:6-2000,Cl.209.4
456.89 0.45
4800
15
16.5
Live Load Calculation
70R Tracked
20t boggie
(For Tyre)
Class A
Where,
Vw = Outer to outer dist.of wheels of axles across the direction of motion
B = Ground Contact Area of Wheels in the direction of Motion
W = Ground Contact Area of Wheels Across the direction of Motion
f = Minimum Clearance of Outer edge of wheel from kerb, f
g =
For 20t boggie
Tyre contact area over road surface =
= x
= cm2
1.50
IRC:6-2000, cl.207.1.3
Min.Dist.bet.s
uccessive
axles (m)
-
0.263
1.2 1.22
Minimum Clearance between the Outer edges passing or crossing vehicles on
multi-lane bridges, g
1.500
1000
1.2
5.273
948.23
0.36
5
1.2
0.86
0.5 0.1511.4 0.25
Vehicle
Impact
Factor
(internal
Span)
1.25
1.25
4.57
-
0.84 1.270
20
Axle
Load (t)
2.9
1.2
1.2
f (m)Vw (m) B (m) W (m)
Impact
Factor
(Canti.
Span)
1.25
1.25
g (m)
Actual max. tyre load
Max. tyre pressure
2.79
2.3
= cm
Tyre width across the dir.of motion = - = mm
Tyre width along dir.of motion = * = mm
Dispersion of load across span (Simply Supported):
Effective width for a single concentrated load,
b ef = a a 1 - a + b1
lo
where, lo = Effective span = m
a = distance of c.g. of concentrated load from nearer support
b1 = width of concentration area of load = tyre width B + 2 x
b = width of slab = m
b/lo =
a = a constant depending upon the ratio of b/lo =
Dispersion of load across span (Cantilever) :
Effective width for a single concentrated load,
b ef = * a + b1
where,
a = distance of c.g. of concentrated load from face of cantilever support
b1 = width of concentration area of load = tyre width B + 2 x
Dispersion of load along span:
= + 2 x ( + deck thk. )
0.333
263.40
W (m) 0.065
0.065
410
948.23
50
IRC:21-2000,Cl.305.16.3
0.065
1.2
IRC:21-2000,Cl.305.16.2
3.000
1.00
1.267
IRC:21-2000,Cl.305.16.2
360
360.00
948.23 100
Dispersion calculation for 2-Lane Class-A Live Load on Deck Slab As per IRC21-2000, Clause 305.16
1Class A Tow Lane
1 2 3 4
0.9 1.8 1.7 1.8 1.7
1.200 0.10 3.100 1.30 2.801.2 4.700 -1.700
0.600 -1.200 1.80 0.1 1.3002.900 -0.100 -1.301.300
1.500 3.00 3.00 1.500
Dispersion along the span = = 0.5 x 2 x ( 0.225 + 0.065 )
1.08 mt
b1= = 0.25 + 0.065 x 2
0.38 mt
Beffective for Load (1) = 1.2 x a +b1
1.2 x 0.600 + 0.38
1.1 mt
Combined eff width = 1.1 mt
Beffective for Load (1) = 1.2 x a +b1
= 1.2 x 0.000 + 0
= 0 mt
Combined eff width = 0 mtCombined eff width = 0 mt
Beffective for Load (2) = α a (l-a/l0) +b1
2.60 x 1.200 x( 1 - 1.200 / 3.0 ) + 0.38
2.252 mt
Combined eff width = 1.726 mtBeffective for Load (3) = α a (l-a/l0) +b1
2.60 x 0.100 x( 1 - 0.100 / 3.0 ) + 0.380.6313 mt
Combined eff width = 0.6313 mtBeffective for Load (4) = α a (l-a/l0) +b1 0.6313
2.60 x 1.300 x( 1 - 1.300 / 3.0 ) + 0.382.2953 mt
Combined eff width = 1.7477 mt
UDL of
Tyre 1 = 5.70 x 1.5 /( 1.08 x 1.1 ) = 7.20 t/m2
Tyre 2 = 5.70 x 1.5 /( 1.08 x 1.726 ) = 4.59 t/m2
Tyre 3 = 5.70 x 1.5 /( 1.08 x 0.6313 ) = 12.54 t/m2
Tyre 4 = 5.70 x 1.5 /( 1.08 x 1.7477 ) = 4.53 t/m2
Dispersion calculation for 20T Boggie Axle Live Load on Deck Slab As per IRC21-2000, Clause 305.16
2 20 T Boggie axle ( Eccentrically placed)
1 2
2.130 1.93
0.630 0.440
-0.63 2.37 -0.440 3.4402.560
1.500 3.00 3.00 1.500
Dispersion along the span = = 0.81 + 2 x ( 0.225 + 0.065 )
1.39 mt
b1= = 0.263 + 0.065 x 2
0.393 mt
Beffective for Load (1) = 1.2 x a +b1
= 1.2 x 0.000 + 0
= 0 mt
Combined eff width = 0 mtor
Beffective for Load (1) = α a (l-a/l0) +b1
2.60 x 0.630 x( 1 - 0.630 / 3.0 ) + 0.393
1.687 mt
Combined eff width = 1.4435 mtCombined eff width = 1.4435 mt
Beffective for Load (2) = α a (l-a/l0) +b1
2.60 x 0.440 x( 1 - 0.440 / 3.0 ) + 0.39
1.3692 mt
Combined eff width = 1.2846 mt
UDL of
Tyre 1 = 12.5 /( 1.39 x 1.44351 ) = 6.23 t/m2
Tyre 2 = 12.5 /( 1.39 x 1.28461 ) = 7.00 t/m2
Dispersion calculation for 20T Boggie Axle Live Load on Deck Slab As per IRC21-2000, Clause 305.16
3 20 T Boggie axle ( Centrally placed)
1 2
1.93
0.535 0.535
2.4652.465
1.500 3.00 3.00 1.500
Dispersion along the span = = 0.81 x 2 x ( 0.225 + 0.065 )
1.39 mt
b1= = 0.263 + 0.065 x 2
0.393 mt
Beffective for Load (1) = α a (l-a/l0) +b1
2.60 x 0.535 x( 1 - 0.535 / 3.0 ) + 0.39
1.5359 mt
Combined eff width = 1.368 mt
Beffective for Load (3) = α a (l-a/l0) +b1
2.60 x 0.535 x( 1 - 0.535 / 3.0 ) + 0.39
1.5359 mt
Combined eff width = 1.368 mt
UDL of
Tyre 1 = 12.5 /( 1.39 x 1.37 ) = 6.57 t/m2
Tyre 2 = 12.5 /( 1.39 x 1.37 ) = 6.57 t/m2
Dispersion calculation for 20T Boggie Axle Live Load on Deck Slab As per IRC21-2000, Clause 305.16
4 20 T Boggie axle ( Centrally placed) on interior span
1 2
1.93
0.535 0.535
2.4652.465
4.500 3.00 1.50 1.500
Dispersion along the span = = 0.81 x 2 x ( 0.225 + 0.065 )
1.39 mt
b1= = 0.263 + 0.065 x 2
0.393 mt
Beffective for Load (1) = α a (l-a/l0) +b1
2.60 x 0.535 x( 1 - 0.535 / 3.0 ) + 0.39
1.5359 mt
Combined eff width = 1.368 mt
Beffective for Load (3) = α a (l-a/l0) +b1
2.60 x 0.535 x( 1 - 0.535 / 3.0 ) + 0.39
1.5359 mt
Combined eff width = 1.368 mt
UDL of
Tyre 1 = 12.5 /( 1.39 x 1.37 ) = 6.57 t/m2
Tyre 2 = 12.5 /( 1.39 x 1.37 ) = 6.57 t/m2
Dispersion calculation for 20T Boggie Axle Live Load on Deck Slab As per IRC21-2000, Clause 305.16
5 20 T Boggie axle ( Centrally placed) on interior support
1 2
1.93
0.965 0.965
2.0352.035
1.500 3.00 3.00 1.500
Dispersion along the span = = 0.81 x 2 x ( 0.225 + 0.065 )
1.39 mt
b1= = 0.263 + 0.065 x 2
0.393 mt
Beffective for Load (1) = α a (l-a/l0) +b1
2.60 x 0.965 x( 1 - 0.965 / 3.0 ) + 0.39
2.0949 mt
Combined eff width = 1.6475 mt
Beffective for Load (3) = α a (l-a/l0) +b1
2.60 x 0.965 x( 1 - 0.965 / 3.0 ) + 0.39
2.0949 mt
Combined eff width = 1.6475 mt
UDL of Tyre 1 = 12.5 /( 1.39 x 1.65 ) = 5.46 t/m2
Tyre 2 = 12.5 /( 1.39 x 1.65 ) = 5.46 t/m2
Dispersion calculation for 20T Boggie Axle Live Load on Deck Slab As per IRC21-2000, Clause 305.16
6 20 T Boggie axle ( Centrally placed) on central support
1 2
1.93
0.965 0.965
2.0352.035
4.500 3.00 3.00 1.500
Dispersion along the span = = 0.81 x 2 x ( 0.225 + 0.065 )
1.39 mt
b1= = 0.263 + 0.065 x 2
0.393 mt
Beffective for Load (1) = α a (l-a/l0) +b1
2.60 x 0.965 x( 1 - 0.965 / 3.0 ) + 0.39
2.0949 mt
Combined eff width = 1.6475 mt
Beffective for Load (3) = α a (l-a/l0) +b1
2.60 x 0.965 x( 1 - 0.965 / 3.0 ) + 0.39
2.0949 mt
Combined eff width = 1.6475 mt
UDL of Tyre 1 = 12.5 /( 1.39 x 1.65 ) = 5.46 t/m2
Tyre 2 = 12.5 /( 1.39 x 1.65 ) = 5.46 t/m2
Design of Solid RCC Slab
Material Properties:
Table 6.5 Chararcteristic Strength of Concrete, fck = N/mm2
Table 18.1 Yield Strength of Steel, fyk = N/mm2
Partial material safety factor for concrete = basic & seismic
Partial material safety factor for Steel = basic & seismic
Modulus of elasticity of reinforcement of steel Es = N/mm2
Anx A-2 & Tb:6.5 Tensile Strength of Concrete = 0.259*(fck)0.67
fctm = N/mm2
Design yield strength of shear reinforcement = fywd = N/mm2
fywd = 0.8*fyk/γs
Ultimate compressive strain in the concrete єcu3 =
Modulus of elasticity of concrete=22*(fcm/12.5)0.3 Ecm = N/mm
2
Modular ratio αe = (Es/Ecm) =
Ultimate tensile strain in the steel (εs) = =
[{fy/(γsEs)}+0.002]
Coefficient to consider the influence of concrete strength =
Factor (λ) =
Factor (η) =
fcd = (α*fck/gm) = = N/mm2
Creep Coefficient (taking long term of creep) =
for Balance section Limiting Neutral Axis Depth {εcu3/(εcu3+εs)}*d Xulim =
Limiting value of R = Q
0.456 d
η 1
fcd 0.447fck 17.867
Φ 1.2472
εs 0.0042
α 0.67
λ 0.8
200000
3.03
347.83
0.0035
33346
αe 5.9978
40
500
γm 1.5
γs 1.15
for Balance section Limiting value of R = Qlim =
0.36*fck*(Xulim/d)*{1-0.42*(Xulim/d)}
IRC:6-2010 Factors for Limit State Design:
Factored moment in ULS from STAAD (support) = tm
Factored moment in ULS from STAAD (span) = tm
Factored moment in rare combination (SLS) from STAAD (support) = tm
Factored moment in rare combination (SLS) from STAAD (span) = tm
Factored moment in Quasi-permanent (SLS) from STAAD (support) = tm
Factored moment in Quasi-permanent (SLS) from STAAD (span) = tm
5.31
ULSType of Load
Dead Load
SIDL-except
surfacing
SIDL-surfacing
Live load-Leading
Live load-
Accompanying
1.35 1.00
1.00 1.00
1.50 1.00 0.00
0.522
Frequent
1.00
1.00
1.00
0.75
0.20
SLS
1.15 0.75 0.00
Rare Quasi-perm
9.93
6.8
2.139
6.52
4.4
1.00
1.35 1.00 1.00
1.75
Design for Flexure
Sagging Moment:
Depth of member = mm
Width of Member = mm
Clear Cover, = mm
Dia.of Bar = mm
Effective Depth of Slab, d = mm
Bending Moment due to Applied Loads, Muls = kNm
SLS Moment (Rare Combination) = kNm
SLS Moment (Quasi-permanent Combination) = kNm
Required effective depth of slab = Sqrt(M/(Q*B)) = mm
SQRT(63.91*10^6/ (5.31*1000))
Area of Main Reinforcement:
Ast required = = mm2
Cl 16.5.1.1 IRC:112 Ast minimum = 0.26(fctm/fyk)*b*d or 0.0013*b*d = mm2
Hence, Ast required, = mm2
So, providing mm diameter bars @ mm spacing
Hence, Ast provided, = mm2/m
Percentage steel provided = %
Check for Area of steel reqd. A provided >= A required OK
12 110
1028.2
0.6
63.91
42.94
5.12
109.7
875
282.0
225
1000
179.0
40
12
874.6
−−=
2**
*6.411
**5.0
dbfck
Mu
fyk
dbfckAst
Check for Area of steel reqd. A st provided >= A st required OK
Spacing provided, Sprov = mm
Cl 16.6.1.1 (4) IRC:112 Maximum spacing, Smax = lesser of 2h and 250mm = mm
Check for Spacing S max >= S prov OK
Stress Check :-
Dist. of Netural Axis from Top = Xu = mm
[-αe*Ast-sqrt{(αe*Ast)^2-4*(0.5*b)*(-αe*Ast)}]/b
Compr. Stress for other load=M/(Area of comp.*LA) = < Mpa
Tensile Stress for other load=M/(Area of Tension*LA) = < Mpa
Hogging Moment:
Depth of member = mm
Width of Member = mm
Clear Cover, = mm
Dia.of Bar = mm
Effective Depth of Slab, d = mm
Bending Moment due to Applied Loads, Muls = kNm
SLS Moment (Rare Combination) = kNm
SLS Moment (Quasi-permanent Combination) = kNm
Required effective depth of slab = Sqrt(M/(Q*B)) = mm
SQRT(97.34*10^6/ (12.6065623877732*1000))
250
41.222
12.6 19.2
252.7 400
110
225
1000
40
16
177.0
97.34
66.73
20.98
135.4
Area of Main Reinforcement:
Ast required = = mm2
Cl 16.5.1.1 IRC:112 Ast minimum = 0.26(fctm/fyk)*b*d or 0.0013*b*d = mm2
Hence, Ast required, = mm2
So, providing mm diameter bars @ mm spacing
and mm diameter bars @ mm spacing
Hence, Ast provided, = mm2/m
Percentage steel provided = %
Check for Area of steel reqd. A st provided >= A st required OK
Spacing provided, Sprov = mm
Cl 16.6.1.1 (4) IRC:112 Maximum spacing, Smax = lesser of 2h and 250mm = mm
Check for Spacing S max >= S prov OK
Stress Check :-
Dist. of Netural Axis from Top = Xu = mm
[-αe*Ast-sqrt{(αe*Ast)^2-4*(0.5*b)*(-αe*Ast)}]/b
Compr. Stress for other load=M/(Area of comp.*LA) = < Mpa
Tensile Stress for other load=M/(Area of Tension*LA) = < Mpa
a) At Bottom
Area of the main reinforcement (Ast) = mm2
1028.2
1404
278.9
16 110
1827.8
1.0
110
250
52.291
16.0 19.2
228.8 400
1404.1
0 110
−−=
2**
*6.411
**5.0
dbfck
Mu
fyk
dbfckAst
Area of the main reinforcement (Ast) = mm
Cl 16.6.1.1(3) IRC 112 Area of transverse reinforcement required (0.2 Ast) = mm2
Cl 16.5.4(4) IRC 112 Min area of surface reinforcement (0.01Act.ext) = mm2
Min area of reinforcement at bottom face (0.12% of b.d) = mm2
Area of distribution steel required (max of above 3) = mm2
Dia of bars to be used for distribution reinforcement = mm
Spacing of bars to be used for distribution reinforcement = mm
Area of steel provided = = mm2
Check for Area of steel reqd. A st provided >= A st required OK
Spacing provided, Sprov = mm
Cl 16.6.1.1 (4) IRC:112 Maximum spacing, Smax = lesser of 3h and 400mm = mm
Check for Spacing S max >= S prov OK
Hence provide 10mm dia bars @ 150mm c/c spacing at bottom of slab
150
150
400
400
270
400
10
150
78.54 x 1000 523.6
1028.2
205.63
b) At Top
Area of the main reinforcement (Ast) = mm2
Cl 16.6.1.1(3) IRC 112 Area of transverse reinforcement required (0.2 Ast) = mm2
Cl 16.5.4(4) IRC 112 Min area of surface reinforcement (0.01Act.ext) = mm2
Min area of reinforcement at bottom face (0.12% of b.d) = mm2
Area of distribution steel required (max of above 3) = mm2
Dia of bars to be used for distribution reinforcement = mm
Spacing of bars to be used for distribution reinforcement = mm
Area of steel provided = = mm2
Check for Area of steel reqd. A st provided >= A st required OK
Spacing provided, Sprov = mm
Cl 16.6.1.1 (4) IRC:112 Maximum spacing, Smax = lesser of 3h and 400mm = mm
Check for Spacing S max >= S prov OK
Hence provide 10mm dia bars @ 150mm c/c spacing at top of slab
Cl 12.3.4 IRC 112 CALCULATION OF CRACK WIDTH
For bottom
Crack width ,
εsm-εcm =
≥
150
1827.8
365.57
400
270
400
10
150
78.54 x 1000 523.6
150
400
σsc = N/mm2
Kt =
fct,eff = N/mm2
ρp,eff = As/Ac,eff =
αe = Es/Ecm =
εsm-εcm =
For the case of deformed bars associated with pure bending, as per Eq. 12.11 of IRC:112-2011
Φ eq = = mm
=
= mm < 0.3 mm As per Cl.12.3 Table 12.1
30.1
0.5
3.03
3.2171
5.9978
0.0001
12.0
136.63
0.01
∑∑
ii
ii
n
n
φ
φ2
`
For top
Crack width ,
εsm-εcm =
≥
σsc = N/mm2
Kt =
fct,eff = N/mm2
ρp,eff = As/Ac,eff =
αe = Es/Ecm =
εsm-εcm =
For the case of deformed bars associated with pure bending, as per Eq. 12.11 of IRC:112-2011
Φ eq = = mm
=
= mm < 0.3 mm As per Cl.12.3 Table 12.1
Cl 12.4 IRC 112 CALCULATION OF DEFLECTION
Deflection, for simply supported member = 5ML2/48EI
I, Moment of Inertia of section = mm4
Ec, Modulus of Elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
ho = 2Ac / u = mm
7E+08
220.86
9E+08
33346
136.47
0.04
71.9
0.5
3.03
5.7861
5.9978
0.0003
16.0
∑∑
ii
ii
n
n
φ
φ2
`
ho = 2Ac / u = mm
Φ, creep coefficient =
Ec,eff,effective modulus of elasticity = Ec/(1+φ) = N/mm2
Moment due to slab selfweight = tm
Moment due to SIDL (surfacing) = tm
Moment due to SIDL (except surfacing) = tm
Total moment due to sustained loading = tm (Permanent loads)
Moment due to vehicular loading = tm (Live loads)
A) Deflection due to vehicular loading
Table3.3 IRC:6-2010 M, moment (including factor of 0.75 for freq combi) = tm
L, length = m
E, Modulus of elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
12.4.1.(2) IRC:112-2011 Permissible deflection due to vehicular traffic =
= mm
Hence the deflection is Within permissible limit
3.00
33346
7E+08
1.481
L/800
3.75
1.46
2.26
4.67
3.4995
220.86
1.25
14839
0.63
0.16
B) Deflection due to sustained loading
i) For short term deflection,
Table3.3 IRC:6-2010 M, moment (including factors for freq combi) = tm
L, length = m
E, Modulus of elasticity = N/mm2
Ir, Moment of Inertia of section = mm4
Deflection (δ) = mm
ii) Deflection due to creep,
acc(perm) = aicc(perm) - ai(perm)
For aicc(perm)
M, moment = t/m
L, length = m
Ec,eff ,Effective modulus of elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
For ai(perm)
M, moment = t/m
L, length = m
Ec,eff ,Effective modulus of elasticity = N/mm2
33346
3.00
14839
7E+08
2.15
2.26
3.00
2.26
3.00
33346
9E+08
0.668
2.26
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
acc(perm) = -
= mm
7E+08
0.95
2.15 0.95
1.20
iii) Deflection due to shrinkage,
acs = k3 * Ψcs * L2
Where, k3 is a constant representing effect of support conditions
k3 =
Ψcs= 1/ rcs As per Cl: 12.4.2, shrinkage curvature
1 = εcs * αe * S/I
rcs
As per Cl: 6.4.2.6, total shrinkage strain is given by
= +
= x 10-6
table 6.6, page 45 = kh * εcd'
table 6.7, page 45 =
= for relative humidity %
= x 10-6
Therefore,
=
=
= mm3
= mm4
=
S 23648
I 9E+08
Ψcs 1E-07
εcd 386.31
εcs 0.0004
αe 13.48
εcd
kh 0.829
εcd' 466 50
0.063 for continuous members
εcs εcd εca
εca 55
= mm
Total Deflection = Short term deflection+ Deflection due to creep + Deflection due to Shrinkage
Total Deflection = mm
acs 0.08
1.95
Design of Deck Slab Beyond Diaphragm
12 Wearing Coat
Depth m
Cantilever Span m
Wearing coat thickness = mTotal load/Axle = = tDistance between two wheel = mDistance between two Axle = mMin. dist. Between face of kerb and outer edge of wheel = m
Ground Contact Area of Tyre W = Width = m
Ground Contact Area of Tyre B = Breath = m
Cantilever slab projection beyond diaphragm has been checked for 40t boggie load,for the wheel placing as shown in above fig.
b1 = m(0.5-2*0.05)+2*(0.065)
a = m0.55-(0.25/2)
Effective width at support = m1.2*0.425+0.53 >1.2m over lap
Net Effective Width = = m1.04*0.5+0.5*0.5
Moment due to DL = tm0.35*2.5*0.55*0.55/2
Moment due to SIDL = tm0.065*2.2*0.55*0.55/2
Moment due to LL = tm11.4*1.5*0.425/0.77
Total Moment at support = tm9.438+0.132+0.022
1.8
0.55
0.5
0.25
1.04
0.425
1.2
0.35
11.40.065
9.592
9.438
0.022
0.132
0.770
0.53
0.250
0.5
0.15
Class A
65
IRC:6-2010 Factors for Limit State Design:
ULS factored moment due to DL = tm
ULS factored moment due to SIDL = tm
ULS factored moment due to LL = tm
Total ULS factored Moment = tm
Rare Combination factored moment due to DL = tm
Rare Combination factored moment due to SIDL = tm
Rare Combination factored moment due to LL = tm
Total Rare Combination factored Moment = tm
Quasi-permanent Combination factored moment due to DL = tm
Quasi-permanent Combination factored moment due to SIDL = tm
Quasi-permanent Combination factored moment due to LL = tm
Total Quasi-permanent Combination factored Moment = tm
Design for Flexure
Depth of member = mm
Width of Member = mm
Clear Cover, = mm
Dia.of Bar = mm
Effective Depth of Slab, d = mm
Bending Moment due to Applied Loads, Muls = kNm
SLS Moment (Rare Combination) = kNm
SLS Moment (Quasi-permanent Combination) = kNm
Required effective depth of slab = Sqrt(M/(Q*B)) = mm
SQRT(140.96*10^6/ (*1000))
SLS
Rare Quasi-perm FrequentType of Load ULS
Dead Load 1.35 1.00 1.00 1.00
SIDL-except
surfacing1.35 1.00 1.00 1.00
SIDL-surfacing 1.75 1.00 1.00 1.00
Live load-
Accompanying1.15 0.75 0.00
1.00 0.00 0.75
0.20
0.039
0.178
16
140.96
94.07
0.132
14.16
350
1000
40
302.0
1.51
162.9
0.022
0
0.154
14.37
0.132
0.022
9.438
9.592
Live load-Leading 1.50
Area of Main Reinforcement:
Ast required = = mm2
Cl 16.5.1.1 IRC:112 Ast minimum = 0.26(fctm/fyk)*b*d or 0.0013*b*d = mm2
Hence, Ast required, = mm2
So, providing mm diameter bars @ mm spacing
Hence, Ast provided, = mm2/m
Percentage steel provided = %
Check for Area of steel reqd. A st provided >= A st required OK
Spacing provided, Sprov = mm
Cl 16.6.1.1 (4) IRC:112 Maximum spacing, Smax = lesser of 2h and 250mm = mm
Check for Spacing S max >= S prov OK
Stress Check :-
Dist. of Netural Axis from Top = Xu = mm[-αe*Ast-sqrt{(αe*Ast)^2-4*(0.5*b)*(-αe*Ast)}]/b
Compr. Stress for other load=M/(Area of comp.*LA) = < Mpa
Tensile Stress for other load=M/(Area of Tension*LA) = < Mpa
Distribution Reinforcement
a) At Top
Area of the main reinforcement (Ast) = mm2
Cl 16.6.1.1(3) IRC 112 Area of transverse reinforcement required (0.2 Ast) = mm2
Cl 16.5.4(4) IRC 112 Min area of surface reinforcement (0.01Act.ext) = mm2
Min area of reinforcement at bottom face (0.12% of b.d) = mm2
Area of distribution steel required (max of above 3) = mm2
Dia of bars to be used for distribution reinforcement = mm
Spacing of bars to be used for distribution reinforcement = mm
Area of steel provided = = mm2
Check for Area of steel reqd. A st provided >= A st required OK
Spacing provided, Sprov = mm
Cl 16.6.1.1 (4) IRC:112 Maximum spacing, Smax = lesser of 3h and 400mm = mm
Check for Spacing S max >= S prov OK
Hence provide 10mm dia bars @ 150mm c/c spacing at bottom of slab
−−=
2**
*6.411
**5.0
dbfck
Mu
fyk
dbfckAst
b) At Bottom
Cl 16.5.4(4) IRC 112 Min area of surface reinforcement (0.01Act.ext) = mm2
Area of the distribution reinforcement required = mm2
Dia of bars to be used for distribution reinforcement = mm
Spacing of bars to be used for distribution reinforcement = mm
Area of steel provided = = mm2
Check for Area of steel reqd. A st provided >= A st required OK
Spacing provided, Sprov = mm
Cl 16.6.1.1 (4) IRC:112 Maximum spacing, Smax = lesser of 3h and 400mm = mm
Check for Spacing S max >= S prov OK
Hence provide 10mm dia bars @ 150mm c/c spacing at top of slab
Cl 12.3.4 IRC 112 CALCULATION OF CRACK WIDTH
Crack width ,
εsm-εcm =
≥
σsc = N/mm2
Kt =
fct,eff = N/mm2
ρp,eff = As/Ac,eff =
αe = Es/Ecm =
εsm-εcm =
For the case of deformed bars associated with pure bending, as per Eq. 12.11 of IRC:112-2011
Φ eq = = mm
=
= mm < 0.3 mm As per Cl.12.3 Table 12.1
Cl 12.4 IRC 112 CALCULATION OF DEFLECTION
Deflection, for simply supported member = 5ML2/48EI
I, Moment of Inertia of section = mm4
Ec, Modulus of Elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
ho = 2Ac / u = mm
Φ, creep coefficient =
Ec,eff,effective modulus of elasticity = Ec/(1+φ) = N/mm2
Moment due to slab selfweight = tm
Moment due to SIDL = tm
Total moment due to sustained loading = tm (Permanent loads)
Moment due to vehicular loading = tm (Live loads)
1E-05
16.0
136.6
4.0
0.5
150
10
150
400
400
1.25
14839
9.438
78.54 x 1000 523.6
0.00
150
400
0.13
0.02
0.15
4E+09
33346
3E+09
220.9
3.03
4.288
5.998
∑∑
ii
ii
n
n
φ
φ2
`
A) Deflection due to vehicular loading
Table3.3 IRC:6-2010 M, moment (including factor of 0.75 for freq combi) = tm
L, length = m
E, Modulus of elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
12.4.1.(2) IRC:112-2011Permissible deflection due to vehicular traffic =
= mm
Hence the deflection is Within permissible limit
B) Deflection due to sustained loading
i) For short term deflection,
Table3.3 IRC:6-2010 M, moment (including factors for freq combi) = tm
L, length = m
E, Modulus of elasticity = N/mm2
Ir, Moment of Inertia of section = mm4
Deflection (δ) = mm
ii) Deflection due to creep,
acc(perm) = aicc(perm) - ai(perm)
For aicc(perm)
M, moment = t/m
L, length = m
Ec,eff ,Effective modulus of elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
For ai(perm)
M, moment = t/m
L, length = m
Ec,eff ,Effective modulus of elasticity = N/mm2
Ir, Moment of Inertia of cracked section = mm4
Deflection (δ) = mm
acc(perm) = -
= mm
0.15
0.550
33346
0.550
14839
3E+09
7.079
0.550
33346
0.000
0.001
0.15
0.550
33346
3E+09
0.15
4E+09
0.001
0.001
0.001
0.000
0.027
0.688
3E+09
L/800
iii) Deflection due to shrinkage,
acs = k3 * Ψcs * L2
Where, k3 is a constant representing effect of support conditions
k3 =
Ψcs= 1/ rcs As per Cl: 12.4.2, shrinkage curvature
1 = εcs * αe * S/I
rcs
As per Cl: 6.4.2.6, total shrinkage strain is given by
= +
= x 10-6
table 6.6, page 45 = kh * εcd'
table 6.7, page 45 =
= for relative humidity %
= x 10-6
Therefore,
=
=
= mm3
= mm4
=
= mm
Total Deflection = Short term deflection+ Deflection due to creep + Deflection due to Shrinkage
Total Deflection = mm
εcd
kh 0.829
0.5 for cantilevers
Ψcs 5E-08
acs 0.0081
0.009
εcs εcd εca
55
50
εcd 386.3
I 4E+09
αe 13.48
S 32170
εcd' 466
εcs 4E-04
εca