19R002-SDN-MJB-021-SUP-01.pdf

CONTRACTOR :
APPROVING AUTHORITY :
DESIGN CONSULTANT :
TITLE :
DSGN
CHKD
APPD
DOCUMENT NUMBER:
1 9 R 0 0 2 - S D N - M J B - 0 2 1 -S U P - 0 1
RELEASED FOR PRELIMINARY TENDER INFORMATION P APPROVAL CONSTRUCTION
0
NAME SIGN DATE
Design of PSC I-Girder of 35m Span
VD 07/02/2020
AL 07/02/2020
PJ 07/02/2020
REV.
JOB No. 19R002
TOTAL NO. OF PAGES 82
CLIENT :
PROJECT :
Construction of proposed Narnaul Bypass (design length 24.0km) & Ateli Mandi to Narnaul section of NH-11
from km 43.445 to km 56.900 (design length 14.0km) as a Economic corridor & Feeder route in the state of
Haryana on Hybrid Annuity Mode
Approved
07/02/2020 0 FOR APPROVAL VD AL PJ
DATE REV. NO. DESCRIPTION Designed Checked
National Highways Authority of India
(Mininstry of Road Transport & Highway)
(Govt. of India)
REVISIONS
HGIEL
A1, III Floor Sheel Mohar Plaza, Tilak Marg, C Scheme, Ashok Nagar, Jaipur,
Rajasthan 302005

Table of contents
i Cover 1
ii Table of contents 2
1 Introduction 4
1.1 General Arrangement 4
1.2 Construction methodology 5
1.3 References 5
1.4 Software used 5
2 Design inputs 6
2.1 Geometry 6
2.2 Material 7
2.3 Loading 8
3 Section properties 18
3.1 Internal girder - Mid span 18
3.2 Internal girder - End span 20
3.3 External girder - Mid span 22
3.4 External girder - End span 24
4 Prestressing details 26
4.1 Profile generation inputs 26
4.2 Cable profiles 27
4.3 Shortest distance matrix 28
4.4 Results of prestressing 31
5 Analysis results 33
5.1 Dead load (Girder + Diaphragms + Slab ) 33
5.2 SIDL (excluding wearing coat) 34
5.3 Wearing coat 35
5.4 Wind (downward) 36
5.5 Live load (Maxima including FPLL) 37
6 Stresses due to Differential temperature 38
6.1 Positive differential temperature 38
6.2 Negative differential temperature 40
7 Contruction stage stresses 42
7.1 Permissible stresses during construction 42
7.2 Stresses during construction 42
7.3 Lateral Instability of Slender Beam 46
8 Serviceability limit state design 47
8.1 Design philosophy 47
8.2 Stress limits 47
8.3 Rare serviceability checks 48
8.4 Frequent serviceability checks 51
19R002-SDN-MJB-021-SUP-01 Page 2

8.5 Quasi permanent serviceability checks 54
8.6 Check for Min. Reinforcement for Crack Control 55
8.7 Check for Surface Reinforcement 56
9 Ultimate limit state design 57
9.1 Bending design 57
9.2 Shear & torsion design 59
9.3 Interface shear 66
9.4 Sample calculation for Moment of resistance (MoR) 67
10 Design of End diaphragm 71
10.1 Design 72
10.2 Detailing of Deep Beam Reinforcement 73
11 Design of Intermediate diaphragm as deep beam 75
11.1 Design of top reinforcement 75
11.2 Design of bottom reinforcement 76
11.3 Detailing of Deep Beam Reinforcement 76
A-I Calculation of Spalling Reinforcement 78
A-II Cable force distribution at transfer (External Girder) 79
A-III Checks for Special Purpose Vehicle (SPV) 81

1 Introduction
1.1 General Arrangement
The Ministry of Road Transport & Highways is engaged in the “Construction of proposed Narnaul
Bypass (design length 24.0km) & Ateli Mandi to Narnaul section of NH-11 from km 43.445 to km
56.900 (design length 14.0km) as a Economic corridor & Feeder route in the state of Haryana on
Hybrid Annuity Mode". NHAI has awarded the project to HG Infra Engineering Limited. HG Infra
Engineering Limited has appointed Force Structural Engineers Pvt. Ltd., Mumbai as "Design
Consultant" to carry out the Detailed Engineering Design services for the structure of the project.
Elevation of superstructure
Typical cross section of superstructure at support
The deck width is 12.5m as per Tender stage GAD. The deck System comprises of 4 nos. of PSC I-girder
with 240mm thick deck slab which consist of 240mm thick cast in situ portion. The figure below shows
typical section of the superstructure.
This report presents super-structure design of 35.0m span on project highway. The structure is consist
of PSC Girder type super-structure, circular pier with Pile foundation.

1.2 Construction methodology
The analysis and design is done assuming the following construction methodology:
- The girders are cast in precasting yard or on site
- Girder is lifted from casting bed to stacking bed
- Second Stage of prestressing applied on 21st day
- Deck slab and diaphragms are cast on shuttering
- Crash barrier and wearing coat are cast after deck slab attains full strength
1.3 References
[1] IRC: 6 – Loads and Stresses for Road bridges
[2] IRC: 112 – Code of practice for concrete road bridges
[3] IS: 14268 - Uncoated stress relieved low relaxation seven-ply strand for prestressed concrete
[4] ‘Concrete bridge practice’ by Dr. V K Raina
[5] IRC SP 105 - Explanatory Handbook to IRC:112
1.4 Software used
- SOFiSTiK FEM for grillage analysis & shell analysis of deck slab
- In house MS Excel spreadsheets for design
- STAAD.Pro for the analysis of End Diaphragm
- Girders are lifted with the help of crane or launching girder, one by one, and placed over the
permanent bearings
Latest versions of following codes, standards and references, along with their amendments and errata
will be used in the design of structure
The following software's were used for analysis and design of superstructure
- First stage of prestressing applied after 7th
day or after concrete achieves a strength of 30MPa,
whichever is later

2 Design inputs
2.1 Geometry
Length of the bridge between expansion joints 35.000 m
Length of the bridge between bearings 33.500 m
Width of bridge deck 12.500 m
No. of girders 4
Cantilever overhang from center of end girders 1.750 m
C/C distance between girders 3.000 m
Thickness of slab 240 mm
Thickness of intermediate diaphragms 300 mm
No. of intermediate diaphragms 2
Alignment of intermediate diaphragms Orthogonal
Thickness of end diaphragms 400 mm
Length of end section (from bearing) 1.500 m
Length of variable section (transition) 2.500 m
Angle of skew 0.00 degrees
Spacing of transverse members for grillage analysis 0.95 m
This section presents the inputs required for the the analysis and design of PSC I girder bridge
superstructure. It includes contractual, codal and designer's requirements.
Isometric view of 3D Model of girder superstructure in SOFiSTiK
Plan view of grillage analysis line model

2.2 Material
2.2.1 Concrete
Grade of concrete for I girders fckg= M50
Modulus of elasticity for concrete for I girders Ecg = 35000 MPa
Mean tensile strength of concrete, fctm fctm = 3.5 MPa
Characterstic tensile strength of concrete at 5% fractile, fctk0.5 2.5 MPa
Grade of concrete for deck slab fckd= M35
Modulus of elasticity for concrete for deck slab Ecd = 32000 MPa
2.2.2 Reinforcing steel
Grade of reinforcing steel Fe500
Modulus of elasticity for steel Es= 200000 MPa
Exposure condition on site (as per Contract) Moderate
Clear cover to reinforcement in girders 35 mm
Clear cover to reinforcement in deck slab 40 mm
2.2.3 Prestressing steel and Sheathing duct
Jacking type
Prestressing systems used for cables: Dynamic
Material of sheathing duct
Friction Coefficient, μ 0.17
Wobble Coefficient, k 0.002 /m
1st Stage Prestress 7 day
Full Prestress 21 day
mm mm
2
No. mm
2
mm mm
1 19DP13 12.7 98.7 12 1184 84 98
2 19DP13 12.7 98.7 19 1875 84 98
3 19DP13 12.7 98.7 19 1875 84 98
4 19DP13 12.7 98.7 19 1875 84 98
5
6
7
8
One end prestress from right
Area of
cable
Internal
diameter
of duct
(ID)
Table 6.5 of
IRC 112
Prestressing steel will be conforming to IS 14268, class 2 Low Relaxation uncoated stress relieved
strands with the following characteristics:
Table 6.5 of
IRC 112
Corrugated HDPE
(as per table
7.1 of IRC
112)
Cable no. Cable
profile
Prestressi
ng
system
Strands
Nominal
dia.
Strands
Nominal
Area
No. of
Strands
stressed
It is
presented
in ch. 4:
"prestressi
ng details
of girder"
of this
document
External
diameter
of duct
(OD)

Strength Characteristic Stress, fpu 1860 MPa
Maximum jacking stress, 0.783 fpu 1456 MPa
Modulus of elasticity, Ep 195000 MPa
Relaxation Loss As per table 6.2 of IRC 112
Wedge Draw-In or slip for post-tensioning 6 mm
2.3 Loading
Following loads and characterstic values are used in the design of this bridge
2.3.1 Dead load
Unit weight of concrete ϒconc.= 25 kN/m
3
The dead load is calculated by the software based on the above unit weight & geometry
Thickness of precast concrete planks for deck casting (if used) 0 mm
Width of precast plank (girder spacing - top width of girder) 2.200 m
Thus, uniformly distributed line load on external girders 0.0 kN/m
Uniformly distributed line load on internal girders 0.0 kN/m
2.3.2 Superimposed dead load
Crash barrier
Area of crash barrier (from AutoCAD) 0.3500 m2
Weight of crash barrier per running m = density x area 8.75 kN/m
Width of crash barrier @ base 450 mm
Uniformly distributed area load of crash barrier 19.4 kN/m2
Wearing coat
Thickness of wearing coat 53 mm
Density of wearing coat ϒwc= 22 kN/m
3
Uniformly distrubuted area load due to wearing coat 1.17 kN/m2
Details of crash barrier for bridges with Footpath
The maximum jacking force as per clause 7.9.2 of IRC 112 is 90% of proof stress. Taking proof
stress as 0.87 fpu, the jacking stress will be 0.9 x 0.87 x fpu = 0.783 fpu
The table given in IRC 112 is input in SOFiSTiK and the software automatically calculates the
relaxation loss as per the stress in cable after immediate losses.
100 175 225
50
450
75
250
1175
175

S. no. Item Area Load Start End
kN/m
2
m m
1 Left kerb + Railing 19.4 -6.250 -5.750
2 Left footpath slab + Utility 0.0 -5.750 -4.250 Not applicable
3 Left crash barrier + Utility 0.0 -4.250 -3.800 Not applicable
4 Median 0 -0.500 0.500 Not applicable
5 Right crash barrier + Utility 0.0 3.800 4.250 Not applicable
6 Right footpath slab + Utility 0.00 4.250 5.750 Not applicable
7 Right kerb + railing 19.4 5.750 6.250
8 1.17 -5.750 5.750
9 0 0.000 0.000 (0 if only 1 carriageway)
*(0,0) corresponds to the center of superstructure.
Wearing coat-1st carriageway
Wearing coat-2nd carriageway
Superimposed dead load (except wearing coat) as applied in software

2.3.3 Live load
Vehicular load
No. of carriageways 1
Width of each carriageway 11500 mm
No. of lanes in each carriageway 3
Impact factor for class A vehicles 11.4%
Impact factor for class 70R wheeled vehicles 11.4%
Ref. Cl.
208.2, 208.3
of IRC: 6-
2016
Following types of vehicle are considered in the design of superstructure:
- 70R 'L' type wheeled vehicle
- Class A wheeled vehicle
These vehicles are moved on the superstructure independently in various lanes and appropriate
combination of simultaneous vehicles are made. The software is capable of maximizing the
forces for variable loads like live load. Thus, live load results are taken directly from the software.
Live load reduction as per section 205 of IRC 6 is applied based on no. of lanes loaded at a time.
Wearing coat load as applied in software

Live load combinations based on the IRC 6:2017- Table 6A
1 x Class A next to crash barrier
No. of lane - 1
No. of lane - 2
1 x 70R next to crash barrier 2 x Class A next to crash barrier
No. of lane - 3
3 x Class A next to crash barrier 1 x Class A next to crash barrier + 1 x 70R

4 x Class A next to crash barrier
2 x 70R next to crash barrier
2 x Class A next to crash barrier + 1 x 70R
No. of lane - 4
1 x 70R + 1 x Class A + 1 x 70R 1 x Class A next to crash barrier + 2 x 70R
No. of lane - 5
No. of lane - 6

Footpath load (Not Applicable)
Basic intensity of footpath loading 0 kg/m
2
Width of footpath 1.5 m NA
Modified intensity of footpath loading for span length 0.00 kN/m
2 Cl. 206.3 of
IRC 6
2.3.4 Wind load
Basic wind speed at bridge site Vb= 44.00 m/sec
Height of superstructure CG from retarding surface 10 m
Terrain type Plain
Footpath live load as modeled in the software (Not Applicable)
2 x Class A next to crash barrier + 2 x 70R 1 x 70R+2 X Class A+ 1 x 70R

Wind speed at deck level due to 33m/sec basic speed 27.8 m/sec
Wind pressure at deck level due to 33m/sec basic speed 464 N/m
2
Wind speed at deck level Vz = 37.1 m/sec
Wind pressure at deck level Pz = 824 N/m
2
Increase in wind pressure due to topography 1
Lift coefficient for I girder bridges CL= 0.75
Gust factor G= 2
Thus, resultant wind pressure in vertically Fv = Pz x G x CL 1.24 KN/m2
downward direction
2.3.5 Temperature
Temperature gradient across the depth of girder is considered as per section 215.3 of IRC 6.
For the design of girder superstructure, the vertical component of wind will be most critical
because it adds to the bending and shear due to permanent loads. Thus, only the vertical load is
considered in the design.
Since the bridge is simply supported and free to contract and expand on bearings, no forces are
expected due to seasonal temperature variations.
Wind downward lift force on deck as applied in software

Detail calculation for temperature gradient stresses are presented in chapter 6 of this document.
2.3.6 Concrete compressive strength with time
Type of cement Normal portland
Coefficient S S= 0.25
Age of concrete t1= 7 days
Age of concrete t2= 21 days
Coefficient beta for t1 days βcc= 0.778801
Coefficient beta for t2 days βcc= 0.962063
Mean compressive strength at age '28' days fcm= 60 MPa
Mean compressive strength at age '7' days fcm(t)= 47 MPa
Mean compressive strength at age '21' days fcm(t)= 58 MPa
Required compressive strength of concrete as per IRC 112 for application of prestressing = 30 MPa
Hence the first stage of prestressing is applied after 7th day of casting.
2.3.7 Shrinkage strains (Only Girder)
Grade of concrete of PSC I Girder M50
Autogenous shrinkage of concrete 0.000075
Notional size of the cross section (PSC I Girder) 311
Coefficient Kh 0.747
Relative humidity RH=50
Unrestrained drying shrinkage 0.00042
Long term value of drying shrinkage, Kh x cd 0.00031
Total shrinkage strain 0.00039
No. of days after which the shrinkage to be considered T= 7
Residual Autogenous shrinkage of concrete 0.000044
Day at which curing ends 3
Residual drying shrinkage of concrete 0.00031
Total residual shrinkage strain after T days (only Girder) 0.000352
2.3.8 Shrinkage strains (Only Deck Slab)
Grade of concrete of Deck Slab 35 Mpa
Nonlinear temperature gradients across superstructure depth (Ref. Fig. 10 (a) of IRC 6)
𝛽𝑐𝑐 𝑡 = 𝑒𝑥𝑝 𝑆 1 −
28
ൗ
𝑡
𝑡1
1/2

Autogenous shrinkage of concrete 0.000045
Notional size of the cross section (full deck width) 235
Coefficient Kh 0.815
Relative humidity RH=50
Unrestrained drying shrinkage 0.00049
Long term value of drying shrinkage, Kh x cd 0.00040
Total shrinkage strain 0.00044
No. of days after which the shrinkage to be considered T= 3
Residual Autogenous shrinkage of concrete 0.000032
Day at which curing ends 3
Residual drying shrinkage of concrete 0.00040
Total residual shrinkage strain after T days (only Deck Slab) 0.00043
2.3.9 Creep strains (Only Girder)
Notional size of the cross section (PSC I Girder) h0 = 311
Detail calculation for Creep Co-Efficient as per Annexure 2.5.
Creep Coefficient
Where, is ultimate creep coefficient
RH is the relative humidity of the ambient environment in percent
α1/2/3 are coefficients to consider the influence of the concrete strength
t0 is the age of concrete at loading in days = 7 day
Mean concrete compressive strength at age '28' days, fcm 60 MPa
α1= 0.817604
α2= 0.944088
α3= 0.866025
if f cm ≤ 45 Mpa
1.514
if f cm > 45 Mpa
2.424
0.635
is a factor to allow for the effect of relative humidity on the notional creep
coefficient
is a factor to allow for the effect of concrete strength on the notional creep
coefficient
is a factor to allow for the effect of concrete age at loading on the notional
creep coefficient
∅ 𝑡, 𝑡0 = ∅0𝛽𝑐(𝑡, 𝑡0)
∅0 = ∅𝑅𝐻.𝛽 𝑓
𝑐𝑚 .𝛽(𝑡0)
∅𝑅𝐻
∅𝑅𝐻 = 1 +
1 − 𝑅𝐻/100
0.1 3
ℎ0
∅𝑅𝐻 = (1 +
1 − 𝑅𝐻/100
0.1 3
ℎ0
𝛼1) 𝛼2
𝛽 𝑓
𝑐𝑚
𝛽 𝑡0
∅𝑅𝐻 =
𝛼1 =
45
𝑓
𝑐𝑚
0.7
𝛼2 =
45
𝑓
𝑐𝑚
0.2
𝛼3 =
45
𝑓
𝑐𝑚
0.5
𝛽 𝑓
𝑐𝑚 =
𝛽 𝑡0 =
1
0.1 + 𝑡0
0.20
𝛽 𝑡0 =
𝛽 𝑓
𝑐𝑚 =
18.78
√𝑓
𝑐𝑚

Ultimate creep coefficient 2.33
2.3.10 Creep strains (Only Deck Slab)
Notional size of the cross section (PSC I Girder) h0 = 235
Detail calculation for Creep Co-Efficient as per Annexure 2.5.
Age of concrete at loading in days T= 3 day
Mean concrete compressive strength at age '28' days, fcm 45 MPa
α1= 1.00
α2= 1.00
α3= 1.00
if f cm ≤ 45 Mpa
1.810
if f cm > 45 Mpa
2.800
0.743
Ultimate creep coefficient 3.76
∅0 =
∅𝑅𝐻 = 1 +
1 − 𝑅𝐻/100
0.1 3
ℎ0
∅𝑅𝐻 = (1 +
1 − 𝑅𝐻/100
0.1 3
ℎ0
𝛼1) 𝛼2
∅𝑅𝐻 =
𝛼1 =
45
𝑓
𝑐𝑚
0.7
𝛼2 =
45
𝑓
𝑐𝑚
0.2
𝛼3 =
45
𝑓
𝑐𝑚
0.5
𝛽 𝑓
𝑐𝑚 =
𝛽 𝑡0 =
1
0.1 + 𝑡0
0.20 𝛽 𝑡0 =
∅0 =
𝛽 𝑓
𝑐𝑚 =
18.78
√𝑓
𝑐𝑚

3 Section properties
3.1 Internal girder - Mid span
3.000
0.24
0.15
0.05 0.00
2
0.15
0.25
All dimensions are in m
Width of I girder on top 1 m
Width of I girder at bottom 0.8 m
Thickness of web 0.275 m
Depth of I girder alone 2 m
3.1.1 Effective width calculation for top slab
The effective width is calculated as per Clause 7.6.1.2 of IRC 112.
Width available for internal girder i.e. girder c/c b= 3.000 m
Net width available on right side b 1 = 1.36 m
Net width available on left side b 2 = 1.36 m
Span of the bridge between bearings 33.50 m
Effective width on right side b eff1 = 1.36 m
Effective width on left side b eff2 = 1.36 m
Width of web of I girder at top 0.275 m
Total effective width 3.000 m
Thus, entire available width over one girder is effective in analysis
0.800
1.000
0.275
𝑏𝑒𝑓𝑓 = ෍ 𝑏𝑒𝑓𝑓 ,𝑖 + 𝑏𝑤 ≤ 𝑏

3.1.2 Cross section properties
Girder only Composite
Moment of inertia (m4
)
about x axis 1.779 1.793
about y axis 0.029 0.569
Area of section (m
2
) 0.847 1.567
Centroid-X m 0.000 0.000
Centroid-Y m 1.27157 0.743
M.I. about centroid (m4
)
m 6.737 11.217
mm 252 279
Perimeter
Notional size 2Ac/u
Graphical representation of section in mid zone
-3
-2
-1
0
1
2
3
-2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50

3.2 Internal girder - End span
3.000
0.24
0.150
0.023 0.00
2.000
0.00
0.25
1.000
Graphical representation of section in end zone
0.8
0.8
-3
-2
-1
0
1
2
3
-2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50

)
Area of section (m
2
) 1.632 2.352
Centroid-Y m 1.222 0.885
)
m 5.959 10.439
mm 548 451
Perimeter
Notional size 2Ac/u

3.3 External girder - Mid span
3.250
0.24
0.15
0.05 0.00
2
0.15
0.25
Width available on top of external girder b 1 = 3.250 m
Net width available on right side b 2 = 1.36 m
Net width available on cantilever side 1.61 m
Span of the bridge between bearings b eff1 = 33.50 m
Effective width on right side b eff2 = 1.36 m
Effective width on cantilever side 1.61 m
Width of web of I girder at top 0.275 m
Thus, entire available width over one girder is effective in analysis
0.275
1
0.800
𝑏𝑒𝑓𝑓 = ෍ 𝑏𝑒𝑓𝑓 ,𝑖 + 𝑏𝑤 ≤ 𝑏

)
Area of section (m
2
) 0.847 1.627
)
m 6.737 11.717
mm 252 278
Perimeter
Notional size 2Ac/u
Graphical representation of section in mid zone
-3
-2
-1
0
1
2
3
-2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50

3.4 External girder - End span
3.250
0.24
0.150
0.02 0.00
2.000
0.00
0.25
Width available for internal girder i.e. girder c/c 3.250 m
Net width available on right side 1.00 m
Net width available on left side 1.25 m
Span of the bridge between bearings 33.50 m
Effective width on right side 1.00 m
Effective width on left side 1.25 m
Width of I girder at top 1 m
1.000
0.8
0.8

)
Area of section (m
2
) 1.632 2.412
)
m 5.959 10.939
mm 548 441
Perimeter
Notional size 2Ac/u
Graphical representation of section in end zone
-3
-2
-1
0
1
2
3
-2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50

4 Prestressing details
This section defines the cable profiles for post tensioned I girder. The general cable profile is symmetric about the mid span and is as follows:
4.1 Profile generation inputs
X Y Z Angle X Start X End X Start X End X Y Z
mm mm mm (°) mm mm mm mm mm mm mm No. mm2
mm mm2
1 -330 0 750 9 670 670 12500 14000 14000 0 1915 19DP13 12 98.7 12.7 1184
2 -330 0 1100 9 670 670 12500 14000 14000 0 2115 19DP13 19 98.7 12.7 1875
3 -330 165 1450 9 670 670 5000 3000 6000 200 2115 19DP13 19 98.7 12.7 1875
4 -330 -165 1450 9 670 670 5000 3000 6000 -200 2115 19DP13 19 98.7 12.7 1875
5 0
6
7
8
Note: X = 0 corresponds to bearing center (Y,Z) = (0,0) at top center of girder with slab
Anchor --> Straight at specified angle --> Cubic curve in elevation + Cubic curve in Plan --> Straight upto mid span
Final
Coordinates
Strands
Nominal
dia.
Strands
Nominal
Area
Prestres
sing
system
Cable no. No. of
Strands
stressed
Area of
cable
Straight
curve
Elevation curve Plan curve
Anchor location
Minimum center to center distance between cables (=2 x duct dia) 2X DUCT DIA.
Cable 1 2 3 4 5 6 7 8
1 - 200 283 283 196 mm
2 - 200 200 196 mm
3 - 330 196 mm
4 - 196 mm
5 -
6 -
7 -
8 -

4.2 Cable profiles
X Y Z Y Z Y Z Y Z Y Z Y Z Y Z Y Z
mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm
-330 0 750 0 1100 165 1450 -165 1450
600 0 897 0 1247 165 1597 -165 1597
1000 0 960 0 1310 165 1661 -165 1661
1500 0 1036 0 1384 165 1743 -165 1743
2000 0 1110 0 1454 165 1824 -165 1824
2500 0 1180 0 1521 165 1900 -165 1900
3000 0 1248 0 1583 165 1969 -165 1969
3500 0 1313 0 1641 168 2029 -168 2029
4000 0 1375 0 1696 174 2075 -174 2075
4500 0 1434 0 1747 183 2104 -183 2104
5000 0 1490 0 1794 191 2115 -191 2115
5500 0 1543 0 1838 197 2115 -197 2115
6000 0 1592 0 1878 200 2115 -200 2115
6500 0 1638 0 1915 200 2115 -200 2115
7000 0 1681 0 1948 200 2115 -200 2115
7500 0 1721 0 1979 200 2115 -200 2115
8000 0 1757 0 2005 200 2115 -200 2115
8500 0 1789 0 2029 200 2115 -200 2115
9000 0 1818 0 2050 200 2115 -200 2115
9500 0 1844 0 2068 200 2115 -200 2115
10000 0 1865 0 2082 200 2115 -200 2115
10500 0 1883 0 2094 200 2115 -200 2115
11000 0 1897 0 2103 200 2115 -200 2115
Cable 1 Cable 2 Cable 3 Cable 4 Cable 5 Cable 6 Cable 7 Cable 8
Cable 1 2 3 4 5 6 7 8
1 - 200 283 283 196 mm
2 - 200 200 196 mm
3 - 330 196 mm
4 - 196 mm
5 -
6 -
7 -
8 -

11500 0 1907 0 2110 200 2115 -200 2115
12000 0 1913 0 2114 200 2115 -200 2115
12500 0 1915 0 2115 200 2115 -200 2115
13000 0 1915 0 2115 200 2115 -200 2115
13250 0 1915 0 2115 200 2115 -200 2115
13500 0 1915 0 2115 200 2115 -200 2115
13750 0 1915 0 2115 200 2115 -200 2115
14000 0 1915 0 2115 200 2115 -200 2115
14250 0 1915 0 2115 200 2115 -200 2115
14500 0 1915 0 2115 200 2115 -200 2115
14750 0 1915 0 2115 200 2115 -200 2115
15000 0 1915 0 2115 200 2115 -200 2115
15250 0 1915 0 2115 200 2115 -200 2115
15500 0 1915 0 2115 200 2115 -200 2115
15750 0 1915 0 2115 200 2115 -200 2115
16000 0 1915 0 2115 200 2115 -200 2115
16750 0 1915 0 2115 200 2115 -200 2115
4.3 Shortest distance matrix
Minimum center to center distance between cables (=2 x duct dia) 2X DUCT DIA.
Cable 1 2 3 4 5 6 7 8
1 - 200 283 283 196 mm
2 - 200 200 196 mm
3 - 330 196 mm
4 - 196 mm
5 -
6 -
7 -
8 -

2X DUCT DIA. 196 196 196 196
mm mm mm mm
Elevation showing cable profiles
Plan showing cable profiles
0
500
1000
1500
2000
2500
-1000 1000 3000 5000 7000 9000 11000 13000 15000 17000 19000
-250
-200
-150
-100
-50
0
50
100
150
200
250
-1000 1000 3000 5000 7000 9000 11000 13000 15000 17000 19000

No. of cables to be stressed in stage 1 to ensure that ample compression is generated in the section for lifting 2 Nos.
Section showing cables at anchor location Section showing cables at mid span
-3
-2
-1
0
1
2
3
-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00
-3
-2
-1
0
1
2
3
-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00

4.4 Results of prestressing
Axial Force due to prestressing alone after long term losses due to creep, shrinkage & relaxation (in kN-m)

Max. stress in cable at active end at transfer 1360 MPa = 0.73 UTS < 0.740 UTS (0.75UTS or 85% of 0.87UTS whichever is less)
% loss calculation at mid span
Stress
% of UTS
Loss
MPa MPa
1456 78.3% -
1360 73.1% 96
1082 58.2% 374
Condition
Theoretical stress in cables without any losses i.e. jacking stress
Stress in cables at transfer i.e. after friction, wobble & elastic shortening losses
Stress in cables at T = 100 years i.e. after long term losses of creep, shrinkage & relaxation
Minimum Stresses in prestressing cables after long term losses of creep, shrinkage and relaxation (in MPa)
Maximum stresses in prestressing cables at transfer to concrete i.e. before long term losses (in MPa)

5 Analysis results
5.1 Dead load (Girder + Diaphragms + Slab )
Shear force diagram for dead load
Bending moment diagram for dead load

5.2 SIDL (excluding wearing coat)
Bending moment diagram for SIDL (excluding wearing coat)
Shear force diagram for SIDL (excluding wearing coat)

5.3 Wearing coat
Bending moment diagram for wearing coat
Shear force diagram for wearing coat

5.4 Wind (downward)
Bending moment diagram for wind downward
Shear force diagram for wind downward

5.5 Live load (Maxima including FPLL)
Maxima of bending moment due to live load (including FPLL)
Maximma of shear force due to live loads (including FPLL)

6 Stresses due to Differential temperature
6.1 Positive differential temperature
17.8
150 Zone I
4
2240 250 Zone II
1690
Zone III
150 2.10
3000
240
1000
150
50
1.00
275 2000
150
250
800
* All dimensions are in mm
The strain distribution due to prescribed temperature variation is not linear. If the fibers were free of
each other (i.e. unrestrained) then they could accept this non linear thermal strain ofαT. But since their
deformations must follow a linear law (Plane sections remain plane), the difference between final linear
and induced non linear strain will cause eigenstresses. Since the bridge is free to expand/contract in
longitudinal direction axial eigen stresses are relieved and there will be no axial force due to them.
Since the bridge is simply supported the flexural eigen stresses are redistributed such that total
This section reports the calculation of stresses generated within the main girders + slab due to
difference in temperature at top and bottom surface of the bridge. The variation in temperature is
taken as given in IRC 6

Calculating the forces and moments generated by induced non linear strain distribution
Coefficient of thermal expansion for concrete 1.20E-05
Modulus of elasticity of concrete (Ecm for temp loading) 35000 MPa
Distance of CG of gross section from top 743 mm
Overall depth of the cross section 2240 mm
Gross area of cross section 1.57 m
2
Moment of inertia of cross section 0.93 m4
(mm2
) degree (Mpa) (kN) (mm) (mm) (kNm)
I 450000 10.9 1.31E-04 4.58 2060 59 683 1408
II 426365 2.56 3.07E-05 1.07 458 211 532 244
III 120000 1.05 1.26E-05 0.44 53 2190 -1447 -77
Σforce = 2571 Σmoment 1575
Uniform Axial stress in section due to axial force (P/A) 1.64 MPa
Distance of top most fiber from CG of section 743 mm
Stress at top most fiber due to bending moment (My/I) 1.26 MPa
Distance of bottom most fiber from CG of section -1497 mm
Stress at bottom most fiber due to bending moment (My/I) -2.54 MPa
Distance of girder slab junction from CG of section 503 mm
Stress at girder slab junction due to bending moment (My/I) 0.85 MPa
Temperature at top most fiber 17.8
o
C
Theoretical stress at top fiber due to non linear temp (αTE) 7.48 MPa
Temperature at bottom most fiber 2.10
o
C
Theoretical stress at bottom fiber due to non linear temp (αTE) 0.88 MPa
Temperature at girder slab junction 2.56
o
C
Theoretical stress at girder slab jn due to non linear temp (αTE) 1.08 MPa
Resultant stress at top after release due to redistribution 4.58 MPa
Resultant stress at bottom after release due to redistribution 1.78 MPa
-1.42 MPa
each other (i.e. unrestrained) then they could accept this non linear thermal strain ofαT. But since their
moment due to them is zero.
Zone Area Strain Stress Axial
Force
Dist. Of
force
from top
Dist. Of
force
from CG
Moment
Temp. @
CG
Resultant stress at girder slab junction after release due to
redistribution

6.2 Negative differential temperature
-10.6
250 Zone I
-0.7
2240 250 Zone II
1240
-0.8
250 Zone IV
-6.60
3000
240
1000
150
1
50
275 2000
150
250
800
* All dimensions are in mm
250 Zone III
each other (i.e. unrestrained) then they could accept this non linear thermal strain of αT. But since their
moment due to them is zero.

Calculating the forces and moments generated by induced non linear strain distribution
Coefficient of thermal expansion for concrete 1.20E-05
Modulus of elasticity of concrete (Ecm for temp loading) 35000 MPa
Distance of CG of gross section from top 743 mm
Overall depth of the cross section 2240 mm
Gross area of cross section 1.57 m2
Moment of inertia of cross section 0.93 m4
Zone Area
Temp. @
CG
Strain Stress Force
Dist. Of
force
from top
Dist. Of
force
from CG
Moment
(mm2
) degree (Mpa) (kN) (mm) (mm) (kNm)
I 730000 -5.78 -6.94E-05 -2.43 -1772 88 655 -1160
II 188325 -0.42 -5.09E-06 -0.18 -34 323 419 -14
III 108125 -0.49 -5.85E-06 -0.20 -22 1925 -1183 26
IV 200000 -3.70 -4.44E-05 -1.55 -311 2147 -1405 437
Σforce = -2139 Σmoment -712
Uniform Axial stress due to axial force -1.36 MPa
Distance of top most fiber from CG of section 743 mm
Stress at top most fiber due to bending moment (My/I) -0.57 MPa
Distance of bottom most fiber from CG of section -1497 mm
Stress at bottom most fiber due to bending moment (My/I) 1.15 MPa
Distance of girder slab junction from CG of section 503 mm
Stress at girder slab junction due to bending moment (My/I) -0.39 MPa
Temperature at top most fiber -10.6
o
C
Theoretical stress at top fiber due to non linear temp (αTE) -4.45 MPa
Temperature at bottom most fiber -6.60
o
C
Theoretical stress at bottom fiber due to non linear temp (αTE) -2.77 MPa
Temperature at girder slab junction -1.096
o
C
Theoretical stress at girder slab jn due to non linear temp (αTE) -0.46 MPa
Resultant stress at top after release due to redistribution -2.52 MPa
Resultant stress at bottom after release due to redistribution -2.56 MPa
1.29 MPa
Resultant stress at girder slab junction after release due to
redistribution

7 Contruction stage stresses
7.1 Permissible stresses during construction
Allowable compressive stress in concrete during Full Prestress = 0.48fck 22.907 MPa
Allowable compressive stress in concrete during 1st Stage = 0.48fck 17.63 MPa
Allowable tensile stress in concrete during construction = fctd -3.50 MPa
STOP - Stresspoint at deck slab top (susceptible to max. compressive stresses)
GTOP - Stresspoint at girder slab junction (Susceptible to max. compressive stresses)
BOT - Stresspoint at girder bottom (Susceptible to max. tensile stresses)
7.2 Stresses during construction
7.2.1 Stage 1: Girder + 1st stage prestressing (after 7 days)
Diagram showing critical stress points in the section for stress check
This section presents stresses at critical points during erection of bridge. Load factor for all loads
during construction is taken as 1. The stresses are kept within permissible limits to ensure safety of
the structure during construction
3D model of superstructure for construction stage 1 with girders only
-2000. -1000. 0. 1000. 2000. 3000.
1550
3125
S
M
STOP
GTOP
BOT

7.2.2 Stage 2: Creep+Shrinkage losses before 2nd stage prestressing (after 21 days)
7.2.3 Stage 3: Full prestressing (after 21 days)
Stresses in construction stage 1 at stresspoints (a) GTOP (b) BOT

7.2.4 Stage 4: Green concrete of slab on girders
3D model of superstructure after activation of deck slab portion in composite girder

7.2.5 Stage 5: Laying of SIDL
7.2.6 Stage 6: After long term creep, shrinkage & relaxation
In Software results, -ve values mean compression and +ve values mean tension.
Stresses in construction stage 6 at stresspoints (a) STOP (b) GTOP (c) BOT
Stresses in construction stage 5 at stresspoints (a) STOP (b) GTOP (c) BOT

7.3 Lateral Instability of Slender Beam
In transient situations:
Where,
Iot is the distance between torsional restraints 33.50
h is the total depth of beam in central part of Iot 2
b is the effective width of compression flange 0.8
(bottom flange during prestressing) h/b 2.50 OK
70/(h/b)
1/3
51.58
I0t/b 41.88 OK
7.3.1 Slenderness limits for beams
48
80.0
Clear distance between lateral restraints 33.5 OK
To ensure lateral stability, a simply supported or continuous beam should be so proportioned that
the clear distance between lateral restraints does not exceed the following values, whichever is
lesser as per IRC:112, Cl. 11.4.2
PSC I girder shall be cast, launched and erected without any persistent lateral support. After
casting of deck and diaphragm it will attain continuous lateral support.
Lateral instability of slender beams shall be taken into account where necessary viz. for precast
beams during transport and erection and for beam without sufficient lateral bracing in the
construction stage and in the completed structure.
𝐼0𝑡
𝑏
≤
70
ℎ
𝑏
1/3 and
ℎ
𝑏
≤3.5 (IRC:112, Cl. 11.4.1)
60b and
250 *
𝑏2
ℎ

8 Serviceability limit state design
1) Rare combination - For checking the stress limits in concrete and steel
2) Freqent combination - For checking the deflection and crack width
3) Quasi permanent combination- For checking the permanent stresses in concrete
8.1 Design philosophy
- Crack width check is not required as the bridge is in compression in frequent combination
STOP - Stresspoint at deck slab top (susceptible to max. compressive stresses)
GTOP - Stresspoint at girder slab junction (Susceptible to max. compressive stresses)
BOT - Stresspoint at girder bottom (Susceptible to max. tensile stresses)
This section presents the design checks for serviceability limit state combinations as per IRC 6. For
prestressed concrete structures, SLS is classified into three categories:
- Maximum tensile stress in concrete in rare combination is limited to fctm. Linear stresses are valid till
tensile stress in concrete are less than fctm
- Stresses due to differential temperature are calculated separately and added linearly to software
results in relevant combinations
- Deflection is checked for vehicular + pedestrian load and limited to permissible deflections. Since the
bridge is in compression, full moment of inertia is taken for calculating deflections
- No tension is allowed in the bottom fiber in frequent and quasi permanent combinations to avoid
fatigue check as per note b) of Cl. 5.3.2.5 of IRC 112.
Diagram showing critical stress points in the section for stress check
-2000. -1000. 0. 1000. 2000. 3000.
1550
3125
S
M
STOP
GTOP
BOT

8.2 Stress limits
Max. compressive stress in concrete in rare comb. = 0.48fck 24 MPa
Max. compressive stress in concrete in quasi permanent comb. = 0.36fck 18 MPa
Max. tensile stress in concrete frequent comb. for tension face 0.00 MPa
8.3 Rare serviceability checks
8.3.1 Load combinations
Nomenclature
G Dead load
Gsd Superimposed dead loadd (SIDL) excluding wearing coat
Gwc Wearing coat
P Prestressing
Qml Maximum bending effects of live loads
Qv Maximum shear force effects of live loads
Wdh Lift force due to Wind (in downward direction)
Ftg Effects of temperature gradient (positive & negative)
Title
Leading
load
SLS-R-L1
SLS-R-L2
SLS-R-T1 Temp
SLS-R-W1 Wind
Note: Symbol 'G' in the above table includes (G+Gs+Gsd) because these load cases have same load factor
8.3.2 Stresses
Combination
G + 1.2Gwc + 0.9P + Qml + 0.6Wdh
Live
G + 1.2Gwc + 0.9P + Qml + 0.6Ftg
G + 1.2Gwc + 0.9P + 0.75Qml + Ftg
G + 1.2Gwc + 0.9P + 0.75Qml + Wdh
IRC 112 recommends superior & inferior factors of 1.1 and 0.9 for prestressing in serviceability
combinations. In this section, only the inferior factor of 0.9 is presented because it is more critical
for stresses in top as well as bottom for simply supported beams.

Stresses in rare serviceability comb. SLS-R-L1 a) STOP b) GTOP c) BOT
Stresses in rare serviceability comb. SLS-R-L2 a) STOP b) GTOP c) BOT

8.3.3 Stresses due to differential temperature
STOP GTOP BOT
4.58 -1.42 1.78
-2.52 1.29 -2.56
The above values are added to linear stress result from SOFiSTiK after multiplying with partial load
factors in relevant load combination. Please see table below for resultant stresses with temp.
Stresses in rare serviceability comb. SLS-R-T1 a) STOP b) GTOP c) BOT
Stresses in rare serviceability comb. SLS-R-W1 a) STOP b) GTOP c) BOT
Positive gradient
Negative gradient
Case/ Stress point-->

8.3.4 Summary of stresses
Without temperature gradient stresses
GTOP STOP
LC Max Min Max Max
MPa MPa MPa MPa
SLS-R-L1 9.29 0.59 10.23 4.43
SLS-R-L2 9.49 1.05 10.06 4.21
SLS-R-T1 9.80 2.46 9.55 3.53
SLS-R-W1 9.46 1.64 9.85 3.93
NOTE: In Software results, -ve values mean compression and +ve values mean tension.
In summary of stresses table, -ve values mean tension and +ve values mean compression
With temperature gradient stresses
GTOP STOP
LC Max Min Max Max
MPa MPa MPa MPa
SLS-R-L1 9.29 0.59 10.23 4.43
SLS-R-L2 10.56 -0.48 10.83 6.96
SLS-R-T1 11.58 -0.10 10.84 8.11
SLS-R-W1 9.46 1.64 9.85 3.93
Observed maximum compression in Rare serviceability comb. 11.58 MPa OK
Allowable compressive stress in concrete in rare comb. 24.00 MPa
8.4 Frequent serviceability checks
Title
Leading
load
SLS-F-L1
SLS-F-L2
SLS-F-T1 Temp
SLS-F-W1 Wind
Note: Symbol 'G' in the above table includes (G+Gs+Gsd) because these load cases have same load factor
BOT
BOT
G + 1.2Gwc + 0.9P + 0.75Qml + 0.5Ftg
G + 1.2Gwc + 0.9P + 0.2Qml + 0.6Ftg
Combination
G + 1.2Gwc + 0.9P + 0.2Qml + 0.6Wdh
Live
G + 1.2Gwc + 0.9P + 0.75Qml + 0.5Wdh
Tensile stresses are observed at bottom fiber but limited to fctm for section to remain uncracked.
Minimum reinforcement for crack control is checked in Section 8.6

8.4.2 Stresses
Stresses in frequent serviceability comb. SLS-F-L2 a) STOP b) GTOP c) BOT
Stresses in frequent serviceability comb. SLS-F-L1 a) STOP b) GTOP c) BOT

Stresses in frequent serviceability comb. SLS-F-T1 a) STOP b) GTOP c) BOT
Stresses in frequent serviceability comb. SLS-F-W1 a) STOP b) GTOP c) BOT

8.4.3 Summary of maximum stresses
GTOP STOP
LC Max Min Max Max
MPa MPa MPa MPa
SLS-F-L1 9.64 2.07 9.69 3.72
SLS-F-L2 9.80 2.46 9.55 3.53
SLS-F-T1 10.58 5.19 8.43 2.05
SLS-F-W1 10.37 5.06 8.61 2.28
With temperature gradient stresses
GTOP STOP
LC Max Min Max Max
MPa MPa MPa MPa
SLS-F-L1 9.64 2.07 9.69 3.72
SLS-F-L2 10.44 1.18 10.19 5.82
SLS-F-T1 11.35 3.66 9.20 4.80
SLS-F-W1 10.37 5.06 8.61 2.28
Observed min. compression in girder bottom in frequent comb. 1.18 MPa OK
Allowable min. compression in girder bottom in frequent comb. 0.00 MPa
Stresses in tension face i.e. BOT are compressive as required to avoid fatigue check.
8.4.4 Deflection
Span of girder between bearings 33.500 m
Allowable deflection under vehicular + pedestrain loading = Span/1000 33.50 mm
Maximum deflection 13.32 mm
OK
BOT
Maximum deflection of girders under vehicular & pedestrian loading
BOT

8.5 Quasi permanent serviceability checks
Title Remarks
SLS-Q-T1
No live
load
8.5.1 Stresses
8.5.3 Summary of stresses
LC STOP GTOP BOT
MPa MPa MPa
SLS-R-L1 1.51 8.02 10.88
Allowable 18.00
Status OK
Compressive Stress Maximum comp.
stress with temp.
gradient
MPa
11.77
Max
Stresses in quasi permanent serviceability comb. SLS-Q-T1 a) STOP b) GTOP c) BOT
Combination
G + 1.2Gwc + 0.9P + 0.5Ftg

8.6 Check for Min. Reinforcement for Crack Control
Minimum reinforcement shall be checked as per cl. 12.3.3 of IRC 112-2011.
where Xu = fctm * d / (0.36*fck + fctm)
Characteristic compressive strength of concrete fck= M50 MPa
Depth of concrete in tension Xu= 365 mm
Area of concrete within Tensile zone Act= 291721 mm2
Provided Reinforcement 12 dia @ 150 mm
Maximum stress permitted in the reinforcement σs= 240 MPa Table 12.2, IRC 112
Axial force (Prestress after all losses = 0.5fpu*Ap) NED= 6334 kN
Mean stress on concrete σc= 4.04 MPa
Factored height of cross section h*= 1000 mm cl. 12.3.3, IRC 112
Coefficient for effect of axial force on stress distribution k1= 1.50
Coefficient for non-uniform self equilibrium stresses k= 0.65 cl. 12.3.3, IRC 112
Mean Tensile strength of concrete effective at first crack fct.eff= 3.5 MPa cl. 12.3.3, IRC 112
Coefficient for stress distribution within section kc= 0.246 Eq. 12.2, IRC 112
Minimum area of reinforcing steel within the tensile zone
As,min= kc*k*fct,eff*Act/σs Eq. 12.1, IRC 112
As,min= 680 mm2
Provided area of reinforcing steel As,given= 754 mm2
Check: OK
Provided reinforcement is sufficient
0.36*fck
fctm
Compression Zone
Tension Zone Xu
d

8.7 Check for Surface Reinforcement
Surface reinforcement shall be checked as per cl. 16.5.4 of IRC 112.
Clear Cover to main reinforcement 35 mm
Surface Reinforcement to control cracking in webs Depth = 2 m Required
if beams >1m deep Surface Reinforcement is necessary
Minimum Surface Reinforcement As,sur =
Calculating for 1 m surface length 0.01*cover*1000
350 mm2
Diameter of bar provided 12 mm
Spacing Required 323 mm
Spacing Provided 200 mm SAFE
Maximum Spacing shall be less than 200 mm
As per IRC : 112-
2011 cl. No.
16.5.4
0.01*Act.ext

9 Ultimate limit state design
9.1 Bending design
Title
Leading
load
ULS-B-L1 Live
ULS-B-W1 Wind
These combinations with load factors are made in SOFiSTiK and results are presented below
Combination Remarks
1.35G + 1.75Gwc + P + 1.5Qml + 0.9Wdh Unfavorable DL & SIDL
This section presents the ultimate limit state design of PSC superstructure. It includes flexure, shear and
torsion checks.
1.35G + 1.75Gwc + P + 1.15Qml + 1.5Wdh Unfavorable DL & SIDL
Bending moment diagram for ultimate limit state combination ULS-B-L1
Bending moment diagram for ultimate limit state combination ULS-B-L1

9.1.2 External girders
9.1.2.1 Ultimate moments (in kN-m)
X (in mm) 0 750 1500 2750 4000 7187 10375 13562 16750
LC
ULS-B-L1 20 1493 2962 5224 7257 11603 14883 16700 17368
ULS-B-W1 -28 977 1937 3382 4694 7432 9338 10565 10991
Max 20 1493 2962 5224 7257 11603 14883 16700 17368
9.1.2.2 Axial force (in kN)
X (in mm) 0 750 1500 2750 4000 7187 10375 13562 16750
Axial force 7466 7472 7416 7351 7278 7503 7588 7680 7734
9.1.2.3 Prestressing details
X (in mm) 0 750 1500 2750 4000 7187 10375 13562 16750
Cable CG 1240 1359 1477 1659 1805 1971 2050 2065 2065
9.1.2.4 Summary of MoR (in kN-m)
X (in mm) 0 750 1500 2750 4000 7187 10375 13562 16750
MoR 13824 14964 16136 17803 19237 20847 21626 21626 21641
ULS
moment
20 1493 2962 5224 7257 11603 14883 16700 17368
Check Safe Safe Safe Safe Safe Safe Safe Safe Safe
9.1.3 Internal girders
9.1.3.1 Ultimate moments (in kN-m)
X (in mm) 0 750 1500 2750 4000 7187 10375 13562 16750
LC
ULS-B-L1 -11 1447 2845 4983 6883 10765 13466 15285 15945
ULS-B-L2 -19 919 1824 3202 4471 7228 9353 10439 10751
Max -11 1447 2845 4983 6883 10765 13466 15285 15945
9.1.3.2 Axial force (in kN)
X (in mm) 0 750 1500 2750 4000 7187 10375 13562 16750
Axial force 7455 7436 7366 7276 7195 7425 7537 7619 7660
Moment of resistance is calculated at different X because of variable cable profile. Sample calculation for
mid span i.e. maximum bending moment location is presented in section 9.4 of this document. Same process
is repeated for other locations and summary of MoR is reported below.

9.1.3.3 Prestressing details
X (in mm) 0 750 1500 2750 4000 7187 10375 13562 16750
Cable CG 1240 1359 1477 1659 1805 1971 2050 2065 2065
9.1.3.4 Summary of MoR (in kN-m)
X (in mm) 0 750 1500 2750 4000 7187 10375 13562 16750
MoR 14222 15361 16551 18188 19632 21238 21932 22104 22118
ULS
moment
-11 1447 2845 4983 6883 10765 13466 15285 15945
Check Safe Safe Safe Safe Safe Safe Safe Safe Safe
9.2 Shear & torsion design
Title Leading
ULS-B-L1 Live
9.2.2 External girders
9.2.2.1 Shear force
X (in mm) 0 750 1500 2750 4000 7187 10375 13562 16750
ULS-B-L1 2169 2067 1929 1782 1624 1319 975 683 333
9.2.2.2 Torsional moment
X (in mm) 0 750 1500 2750 4000 7187 10375 13562 16750
ULS-B-L1 232 236 233 226 207 161 106 55 29
9.2.3 Internal girders
9.2.3.1 Shear force
X (in mm) 0 750 1500 2750 4000 7187 10375 13562 16750
ULS-B-L1 2071 1969 1833 1685 1504 1203 914 613 265
9.2.3.2 Torsional moment
X (in mm) 0 750 1500 2750 4000 7187 10375 13562 16750
ULS-B-L1 217 364 346 315 213 145 100 61 29
Moment of resistance is calculated at different X because of variable cable profile. Sample calculation for
mid span i.e. maximum bending moment location is presented in section 9.4 of this document. Same process
is repeated for other locations and summary of MoR is reported below.
Combination Remarks
1.35G + 1.75Gwc + P + 1.5Qv + 0.9Wdh Unfavorable DL & SIDL

9.2.4 Design methodology
The calculations at different location of span are presented in subsequent pages.
Shear force diagram in ultimate limit state in ULS-B-L1
Step 1: Calculate the shear resistance of concrete without shear reinforcement, VRdc , using equation 10.1 or
10.4 whichever is applicable depending on the status of section (Cracked or Uncracked)
Step 2: Calculate torsion in web. Check the maximum resistance of concrete struts subjected to torsion and
shear using equation 10.47 (TED/TRdmax +VED/VRdmax <= 1.0) based on chosen strut angle. Revise the section if
equation is not satisfied.
Step 3: Calculate the shear force due to torsion using equation 10.46 and add it to the shear force in web. If
the combined shear force is less than VRdc , no shear reinforcement is required, else the shear reinforcement
is calculated using equation. 10.7, subject to a minimum reinforcement as per equation 10.20.

9.2.5 Max. shear force + coexisting torsion condition
1 2 3 4 5 6 7 8 9
mm 0 750 1500 2750 4000 7187 10375 13562 16750
From
Bearing
-
Transition
start
-
Transition
end
- - - Mid span
mm 800 800 800 538 275 275 275 275 275
mm 702 702 702 440 177 177 177 177 177
mm 2240 2240 2240 2240 2240 2240 2240 2240 2240
Max. shear force in ULS combination kN 2169 2067 1929 1782 1624 1319 975 683 333
kN -1169 -1174 -1161 -1342 -664 -221 -85 9 1
kN 1000 893 768 440 960 1098 890 692 334
kN 7455 7436 7366 7276 7195 7425 7537 7619 7660
MPa 5.80 5.39 5.07 6.19 7.70 4.14 -2.35 -4.35 -4.44
MPa 0.17 0.59 0.93 1.69 2.43 3.87 4.89 5.25 4.95
MPa -1.67 -1.67 -1.67 -1.67 -1.67 -1.67 -1.67 -1.67 -1.67
Uncracked Uncracked Uncracked Uncracked Uncracked Uncracked Cracked Cracked Cracked
mm
2
2352277 2352277 2352277 1959864 1567450 1567450 1567450 1567450 1567450
mm2
1267934 1267934 1267934 1126487 985040 985040 985040 985040 985040
mm 305 305 305 252 199 199 199 199 199
mm 885 885 885 814 743 743 743 743 743
mm 580 580 580 562 544 544 544 544 544
mm
3
7.35E+08 7.35E+08 7.3E+08 6.3E+08 5.4E+08 5.36E+08 5.36E+08 5.36E+08 5.4E+08
MPa 3.17 3.16 3.13 3.71 4.46 4.46 4.46 4.46 4.46
1 1 1 1 1 1 1 1 1
mm4
1.17E+12 1.17E+12 1.17E+12 1.05E+12 9.28E+11 9.28E+11 9.28E+11 9.28E+11 9.3E+11
kN 3173 3171 3161 2183 981 981 981 981 981
mm 0 750 1500 2750 4000 7187 10375 13562 16750
mm 2205 2205 2205 2205 2205 2205 2205 2205 2205
1.301 1.301 1.301 1.301 1.301 1.301 1.301 1.301 1.301
MPa 0.325 0.325 0.325 0.325 0.325 0.325 0.325 0.325 0.325
kN 1239 1238 1231 855 388 388 388 388 388
4 4 4 4 4 4 4 4 4
mm
2
1703 1703 1703 1703 1703 1703 1703 1703 1703
mm2
6810 6810 6810 6810 6810 6810 6810 6810 6810
0.004 0.004 0.004 0.007 0.017 0.017 0.017 0.017 0.017
kN 1359 1357 1350 995 508 508 508 508 508
kN 1359 1357 1350 995 508 508 508 508 508
kN 3173 3171 3161 2183 981 981 508 508 508
Area of 1 cable
Total area of prestressing cables, Asl
Ratio of reinforcement, ρ1 = Asl/(bwd)
Shear resistance VRd.c for cracked sect.
without shear reinf.
(ref. Equation 10.1 of IRC 112)
Shear resistance VRd.c for sect. without
shear reinf.
X -->
Location
Web thickness
Design tensile strength of concrete, fctd
Calculations for shear capacity of cracked section without shear reinforcement
Lever arm of Aca from centroidal axis
Reduced web thk for presence of ducts, bwc
Total depth of section, D
Design shear force in ULS comb., VED
Axial force in the section, P
Stress at Bottom (From SOFiSTiK), σbot
Section status :
σbot < fctd -> Uncracked
σbot > fctd -> Cracked
First moment of area = A x yCG
Comp. stress @ centroid, σcp = P/A <0.2fcd
Coefficient, k1 (=1 for post tension)
Moment of Inertia, Iz
Shear resistance VRd.c for uncracked sect.
without shear reinf.
Vertical component of prestress
Stress at Top (From SOFiSTiK), σtop
Calculations for shear capacity of uncracked section without shear reinforcement
Area of gross section, A
Area of section above centroidal axis, Aca
(from AutoCAD)
Centorid of Aca (From AutoCAD)
Centroid of gross section from top fibre
Effective depth of section, d = D-cover
Coefficient K (as per Eq. 10.2)
νmin = 0.031K3/2
fck1/2
Min Shear resistance VRd.cmin for cracked
sect. without shear reinf.
No. of prestressing cables
Shear resistance VRd.c for cracked sect.
without shear reinf. = Max(VRd.c , VRd.cmin)
X -->

Calculations for max. shear capacity with shear reinforcement
1.14 1.14 1.14 1.17 1.20 1.20 1.20 1.20 1.20
mm 1060 1178 1301 1480 1630 1791 1869 1872 1871
mm
2
0.281 0.281 0.281 0.281 0.281 0.281 0.281 0.281 0.281
mm
2
0.983 0.983 0.983 0.615 0.248 0.248 0.248 0.248 0.248
kN 1470 1379 1307 1611 2013 1155 -456 -952 -981
kN 2620 2670 2717 2276 1190 990 404 231 179
YES YES YES YES YES YES NO NO NO
1800 1800 1800 1800 1800 1800 1869 1872 1871
0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
degree 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0
kN 6713 6711 6703 4293 1778 1778 1846 1849 1849
Check for torsional capacity as per section 10.5 of IRC 112
mm 0 750 1500 2750 4000 7187 10375 13562 16750
kN-m 232 364 346 315 213 161 106 61 29
mm 2000 2000 2000 2000 2000 2000 2000 2000 2000
mm 800 800 800 538 275 275 275 275 275
2.50 2.50 2.50 3.72 7.27 7.27 7.27 7.27 7.27
0.249 0.249 0.249 0.276 0.303 0.303 0.303 0.303 0.303
mm4
2.55E+11 2.55E+11 2.55E+11 8.57E+10 1.26E+10 1.26E+10 1.26E+10 1.26E+10 1.26E+10
mm 3000 3000 3000 3000 3000 3000 3000 3000 3000
mm 240 240 240 240 240 240 240 240 240
12.50 12.50 12.50 12.50 12.50 12.50 12.50 12.50 12.50
0.312 0.312 0.312 0.312 0.312 0.312 0.312 0.312 0.312
mm
4
1.29E+10 1.29E+10 1.29E+10 1.29E+10 1.29E+10 1.29E+10 1.29E+10 1.29E+10 1.29E+10
mm
4
2.68E+11 2.68E+11 2.68E+11 9.87E+10 2.55E+10 2.55E+10 2.55E+10 2.55E+10 2.55E+10
0.95 0.95 0.95 0.87 0.49 0.49 0.49 0.49 0.49
kN-m 221 346 329 274 105 79 52 30 14
Effective thickness of web = Aw/uw mm 286 286 286 212 121 121 121 121 121
Twice the effecitve cover to rebar mm 100 100 100 100 100 100 100 100 100
Thus effective thickness of web, tef mm 286 286 286 212 121 121 121 121 121
mm 5600 5600 5600 5075 4550 4550 4550 4550 4550
MPa 22.3 22.3 22.3 22.3 22.3 22.3 22.3 22.3 22.3
1.14 1.14 1.14 1.17 1.20 1.20 1.20 1.20 1.20
0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
mm2
881633 881633 881633 582369 289612 289612 289612 289612 289612
degree 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0
kN-m 2677 2676 2673 1339 391 391 391 391 391
0.23 0.26 0.24 0.31 0.81 0.82 0.62 0.45 0.22
Calculation of stirrup reinforcement
mm 0 750 1500 2750 4000 7187 10375 13562 16750
400 400 400 400 400 400 400 400 400
kN 429 674 640 840 682 516 339 195 93
kN 1429 1567 1408 1280 1642 1614 1229 887 427
NO NO NO NO YES YES YES YES NO
mm
2
/mm 0.000 0.000 0.000 0.000 1.213 1.192 0.875 0.630 0.000
X -->
X -->
Reinf. requirement from shear & torsion,
Ast/s = (VED/+VTED)/(Zfydcotϴ)
Ratio of height/thickness
Thus coefficient β for web
Component of torsion in web
Torsional moment in web
Area enclosed by the centerlines, Ak
Coefficient, αcw
Height of web, a
Thickness of web, b
Strength reduction factor, v = 0.6(1-fck/310)
Area of less compressive chord (Area of bulb)
Area of web
Force in less compression chord
Force in web
Is Force in less comp. chord > (ΔFtd-1/3
Comp. forcce in web)
Lever arm of tendons, Z (For design)
VED + VTED =
Design torsional shear force, VTED =
Torsional inertia of web, Jw = βab3
Torsional inertia of slab, Jw = βab
3
Effective width of deck slab, a
Thickness of slab, b
Ratio of height/thickness
Shear reinforcement reqd?
YES if VED + VTED> VRd.c
Thus coefficient β for deck slab
Design compressive strength of concrete,
Coefficient, αcw
Design torsional resistance moment,
Unity check TED/TRd.max + VED/VRd.max <1
Design strength of steel in shear = 0.8fyk
Perimeter of enclosed area, uk
Total torsional inertia
Angle of compression strut
Lever arm of tendons, Z (From bending)
Strength reduction factor, v = 0.6(1-fck/310)
Selected angle of compression strut
Thus, Shear resistance of section with
Design torsional moment, TED

mm
2
/mm 0.815 0.815 0.815 0.547 0.280 0.280 0.280 0.280 0.280
mm
2
/mm 0.350 0.350 0.350 0.350 0.350 0.350 0.350 0.350 0.350
mm
2
/mm 0.815 0.815 0.815 0.547 1.213 1.192 0.875 0.630 0.350
mm 12 12 12 12 16 16 16 12 12
mm 140 140 140 140 140 140 200 200 200
2 2 2 2 2 2 2 2 2
mm
2
/mm 1.616 1.616 1.616 1.616 2.872 2.872 2.011 1.131 1.131
OK OK OK OK OK OK OK OK OK
mm 0 750 1500 2750 4000 7187 10375 13562 16750
kN -940 -840 -722 -414 -903 -1033 -837 -651 -314
MPa -138 -123 -106 -61 -133 -152 -123 -96 -46
mm 5600 5600 5600 5075 4550 4550 4550 4550 4550
kN -1319 -2069 -1967 -2243 -1553 -1174 -773 -445 -211
MPa -194 -304 -289 -329 -228 -172 -113 -65 -31
MPa -332 -427 -395 -390 -361 -324 -236 -161 -77
MPa -1095 -1092 -1082 -1068 -1056 -1090 -1107 -1119 -1125
MPa 524 526 537 550 562 528 511 499 493
Safe Safe Safe Safe Safe Safe Safe Safe Safe
Minimum shear reinf. in web,
Asw/s = 0.072bwside fck
0.5
/fyk
Provided area of shear reinforcement
No. of stirrup legs
Is provided reinf. > reqd. reinf
Check for additional longitudinal reinforcement due to shear & torsion
Requirement of surface reinforcement
(refer section 8.7 of this doc.)
X -->
Provided bar diameter for stirrups
Provided spacing of stirrups
Reserve strength in cables till failure =
0.87*1860-existing stress
Is provided prestressing adequate to resist
Total additional stress in prestressing
Additional tensile force due to shear, ΔFtd
Additional stress in cables to due this
Perimeter of enclosed area
Additional tensile force due to torsion (ref.
Eq. 10.49 of IRC 112)
Additional stress in cables to due this
Existing average stress in cable = P/Asl
Shear and torsion generate additional forces in longitudinal direction. The reserve strength in prestressing cables is checked against this additional
effect. If prestressing cable is insufficient then additional reinforcement is provided
Total reinf. Requirement

9.3 Interface shear
mm 0 750 1500 2750 4000 7187 10375 13562 16750
kN 2169 2067 1929 1782 1624 1319 975 683 333
kN 0 0 0 0 0 0 0 0 0
Max. shear force for interface design kN 2169 2067 1929 1782 1624 1319 975 683 333
mm 1000 1000 1000 1000 1000 1000 1000 1000 1000
1 1 1 1 1 1 1 1 1
mm 1800 1800 1800 1800 1800 1800 1869 1872 1871
Mpa 1.205 1.148 1.072 0.990 0.902 0.733 0.522 0.365 0.178
mm 12 12 12 12 16 16 16 12 12
mm 140 140 140 140 140 140 200 200 200
2 2 2 2 2 2 2 2 2
mm2
1616 1616 1616 1616 2872 2872 2011 1131 1131
0.0016 0.0016 0.0016 0.0016 0.0029 0.0029 0.0020 0.0011 0.0011
0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7
MPa 0.45 0.45 0.45 0.45 0.80 0.80 0.56 0.32 0.32
NO NO NO NO NO YES YES NO YES
YES YES YES YES YES NO NO YES NO
mm 16 16 16 16 12 12 12 12 12
mm 140 140 140 140 140 140 200 200 200
2 2 2 2 2 2 2 2 2
mm2
2872 2872 2872 2872 1616 1616 1131 1131 1131
0.0045 0.0045 0.0045 0.0045 0.0045 0.0045 0.0031 0.0023 0.0023
Mpa 1.26 1.26 1.26 1.26 1.26 1.26 0.88 0.63 0.63
0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015
OK OK OK OK OK OK OK OK OK
X-->
Interface shear stress, VEdi
Provided dia of stirrup for shear
Shear force due to 1.35 x dead load
Max shear force in ULS, VED
Min ratio of intersecting reinf. to interface
Status
Is additional reinf. Required?
Diameter of additional bar
Spacing of additional bar
No. of legs
Additional area at interface, As1
Is VRDi > VEDi ?
Friction coeff. at interface, μ
Resisting capacity, VRdi
The shear stress that arises between the interfaces of concrete placed at different times is refered to as interface shear. This bridge has precast beam
Provided spacing of stirrup
Ratio of intersecting reinf. to interface
New Resisting capacity, Vrdi
No. of legs
Area of reinforcement per m, As
Ratio of intersecting reinf. to interface
Width of interface, bi
Ratio of longitudinal force in new concrete
Lever arm

9.4 Sample calculation for Moment of resistance (MoR)
9.4.1 Sample calculation for mid span
3250
240
1000
150 897
1
50
dNA
275 2000
Prestressing
150 cable
250
800
Centroid of the section from top 743 mm
9.4.1.1 Concrete
Grade of concrete (min of girder & slab) M35
Design value of concrete compressive strength (=0.446fck) 15.61 MPa
Parabolic rectangular stress strain block as given in Fig. 6.5 of IRC 112-2011 is used for design.
Bending + Axial strain limit for linear relation εcu2 0.0035
Pure compression strain limit for linear relation εc2 0.002
This section presents the calculation of ultimate moment of resistance for prestressed girder for given
axial force. The concrete is assumed to reach it's maximum strain and steel is allowed to yield. The
moment of resistance is calculated from this strain distribution.
The girder is designed as a cracked section. Concrete takes only compressive stresses and no tensile
stresses. The tensile force is entirely taken by prestressing steel.
Equation representing the stress strain relation
(0,0)

Exponent coefficient η 2
9.4.1.2 Reinforcement
Prestressing cables
No. of cables in the section 4 nos
Total area of cables 6810 mm2
CG of prestressing cables from top surface 2065 mm
Deck slab top reinforcement (distribution)
Dia. of bars 10 mm
Spacing of bars 180 mm
Area of bars in effective width of slab 1418 mm2
Clear cover to reinforcement bars 40 mm
CG depth of reinforcement bars from top surface 57 mm
Deck slab bottom reinforcement (distribution)
Dia. Of bars 10 mm
Spacing of bars 180 mm
Area of bars in effective width of slab 1418 mm2
CG depth from top 183 mm
Grade of reinforcing steel 500 MPa
Modulus of elasticity for steel 200000 MPa
Yield strain of reinforcing steel @ 0.87fy 0.002175
Modular ratio 6.25
Grade of prestressing steel 1860 MPa
Modulus of elasticity for prestressing steel 195000 MPa
Yield strain of prestressing steel @ 0.87fpk/1.15 0.007216
Modular ratio 6.09
Axial force in the section due to prestressing 7734 kN
Existing strain in prestressing cables due to post tensioning -0.00582
9.4.1.3 Depth of neutral axis
Assumed depth of neutral axis from top surface 897 mm
0.0035 15.61
Strain and stress diagrams at failure corresponding to Ultimate Limit State
Since the process of finding stresses is iterative, a depth of neutral axis is assumed first and
calculations are done as per assumed neutral axis depth. The net internal force in concrete and steel
should be same as externally applied force on the section. The neutral axis depth is varied in and the
correct depth is achieved by equilibrium of external and internal force.

Calculation of internal forces
Area of uncracked concrete 1077423 mm2
Compressive force in concrete (after integration) 16083 kN
Point of application of force from top 194 mm
Depth
from top
Strain (due
to bending)
Prestrain
Total
strain
Stress Area Force
57 0.0033 0.0000 0.0033 435 1418 617
183 0.0028 0.0000 0.0028 435 1418 617
2065 -0.0046 -0.0058 -0.0104 -1407 6810 -9583
Net internal force due to steel & concrete 7734 kN
Externally applied force 7734 kN
external force - Internal force 0 OK
9.4.1.4 Calculation of moment of resistance
CG of gross concrete section 720 mm (from deck top)
Force
Point of
appllicati
on
Lever arm
(From CG)
Moment
16083 194 526 8457
617 57 663 409
617 183 537 331
-9583 2065 -1345 12893
22089
Thus, ultimate moment of resistance for this section 22089 kN-m
Calculating lever arm of prestressing tendons for shear design:
Point of application of compressive force due to uncracked conc 194 mm
CG of prestressing cables 2065 mm
Thus lever arm 1871 mm
Deck slab top reinf
Material
Since the material law for concrete in non linear and the section width also varies along the depth,
compressive force due to concrete is calculated by discrete integration i.e. breaking the section into
very small strips and then adding together. Detailed calculation is presented in table in section 9.4.1.5.
Item
Uncracked Concrete
Deck slab top reinf
Deck slab bottom reinf
Prestressing cables
Deck slab bottom reinf
Prestressing cables

9.4.1.5 Detailed calculation of properties of uncracked concrete
Divinding uncracked concrete in 40 parts
mm mm mm mm2
mm MPa kN kN-m
0.0 3250 3.50E-03 15.6
22.4 3250 22.4 72894 11.2 3.41E-03 15.6 1138 12.76
44.9 3250 22.4 72894 33.6 3.33E-03 15.6 1138 38.28
67.3 3250 22.4 72894 56.1 3.24E-03 15.6 1138 63.80
89.7 3250 22.4 72894 78.5 3.15E-03 15.6 1138 89.32
112.1 3250 22.4 72894 100.9 3.06E-03 15.6 1138 114.85
134.6 3250 22.4 72894 123.4 2.98E-03 15.6 1138 140.37
157.0 3250 22.4 72894 145.8 2.89E-03 15.6 1138 165.89
179.4 3250 22.4 72894 168.2 2.80E-03 15.6 1138 191.41
201.9 3250 22.4 72894 190.6 2.71E-03 15.6 1138 216.93
224.3 3250 22.4 72894 213.1 2.63E-03 15.6 1138 242.45
246.7 1000 22.4 47661 237.5 2.54E-03 15.6 744 176.68
269.1 1000 22.4 22429 257.9 2.45E-03 15.6 350 90.31
291.6 1000 22.4 22429 280.4 2.36E-03 15.6 350 98.16
314.0 1000 22.4 22429 302.8 2.28E-03 15.6 350 106.01
336.4 1000 22.4 22429 325.2 2.19E-03 15.6 350 113.86
358.9 1000 22.4 22429 347.6 2.10E-03 15.6 350 121.72
381.3 1000 22.4 22429 370.1 2.01E-03 15.6 350 129.57
403.7 800 22.4 20182 392.9 1.93E-03 15.6 315 123.70
426.1 475.3023 22.4 14298 415.9 1.84E-03 15.5 222 92.45
448.6 275 22.4 8414 438.4 1.75E-03 15.4 130 56.94
471.0 275 22.4 6168 459.8 1.66E-03 15.2 94 43.29
493.4 275 22.4 6168 482.2 1.58E-03 14.9 93 44.72
515.9 275 22.4 6168 504.6 1.49E-03 14.6 91 45.90
538.3 275 22.4 6168 527.1 1.40E-03 14.2 89 46.80
560.7 275 22.4 6168 549.5 1.31E-03 13.8 86 47.40
583.1 275 22.4 6168 571.9 1.23E-03 13.3 83 47.68
605.6 275 22.4 6168 594.4 1.14E-03 12.7 80 47.61
628.0 275 22.4 6168 616.8 1.05E-03 12.1 76 47.16
650.4 275 22.4 6168 639.2 9.62E-04 11.4 72 46.32
672.9 275 22.4 6168 661.7 8.75E-04 10.7 68 45.05
695.3 275 22.4 6168 684.1 7.87E-04 9.9 63 43.34
717.7 275 22.4 6168 706.5 7.00E-04 9.0 58 41.15
740.2 275 22.4 6168 728.9 6.12E-04 8.1 53 38.47
762.6 275 22.4 6168 751.4 5.25E-04 7.1 47 35.26
785.0 275 22.4 6168 773.8 4.37E-04 6.1 41 31.50
807.4 275 22.4 6168 796.2 3.50E-04 5.0 34 27.18
829.9 275 22.4 6168 818.7 2.62E-04 3.8 27 22.25
852.3 275 22.4 6168 841.1 1.75E-04 2.6 20 16.71
874.7 275 22.4 6168 863.5 8.75E-05 1.3 12 10.51
897.2 275 22.4 6168 885.9 0.00E+00 0.0 4 3.65
Σarea CGeff ΣF ΣM
1077423 219 16083 3117
Point of application of force = ΣM/ΣF 194 mm
Strain Stress Force Moment
(about top)
Depth Width Strip
height
Strip area Strip CG
(from
top)

10 Design of End diaphragm
3.00
End diaphragm
B1 B2 B3 B4 B5 B6
844.2 860.4 860.4 844.2
144.9 14.0 14.0 144.9
59.3 58.1 58.1 59.3
WC Load
The end diaphragm is designed for bearing replacement condition when the superstructure is lifted on
jacks. At this time, the loads from PSC girders is transferred to jacks through bending of diaphragm.
During bearing replacement condition, the bearing reaction due to Dead load, SIDL and Wearing Coat will
be applied through the web to the diaphragm. The diaphragm will be supported at the jacking location.
The bending moment is calculated using STAAD beam model.
Bearing reactions from SOFiSTiK grillage model due to a) Dead load b) SIDL c) Wearing coat
Load Case
Bearing Reaction (KN)
Dead Load
SIDL Load
Center line
3.75 m
0.750

The above reactions are extracted from SOFiSTiK model.
The static loads due to Dead Weight are applied in STAAD as follows:
10.1 Design
Beam type of diaphragm Continuous
Depth of diaphragm, D = 1.990 m
Width of diaphragm, b = 0.4 m
Effective span, l = 3.000 m
Span/Depth, l / D = 1.51 < 2.50
Hence, Diaphragm is designed as a deep beam Ref. Clause 29.1(a) of IS 456
Following load combinations are provided for ULS & SLS load combination as per IRC 6:
ULS-B 1.35G + 1.75Gwc
The load combination is made in STAAD and bending moment diagram for ULS case is provided below.
Bending moment diagram for ULS combination
Design moment and shear force in ULS-B 1.35G + 1.75Gwc
Bending Moment top bending, hog 1090.0 KN-m
Bending Moment bottom bending, sag 444.1 KN-m
The deep beam is designed as per clause 29 of IS 456 (Limit state method). Design is carried out for
Ultimate Limit States. The beam is not needed to be designed for shear as per clause 29.1 of IS 456.
Application of Dead loads in STAAD model

Grade of concrete, fck = 35 Mpa
Ultimate flexure capacity of section, Mu = 0.15 fck b (D)^2 = 8316.2 kN-m
Applied maximum ultimate moment (hog and sag) = 1090.0 kN-m < 8316.2
OK
Top reinforcement
Maximum Ultimate hogging moment = 1090.0 kNm
Area of main long. reinforcement, As = M / (0.87 fy z)
here, fy = 500 Mpa
lever arm ,z = 0.2 l + 0.3 D = 1.197 m
Hence, As required= 2093.4 mm2
Bottom reinforcement
Maximum Ultimate sagging moment = 444.1 kNm
Area of main long. Reinforcement, As = M / (0.87 fy z)
here, fy = 500 Mpa
lever arm ,z = 0.2 l + 0.3 D = 1.197 m
Hence, As required= 852.8 mm
2
10.2 Detailing of Deep Beam Reinforcement
Positive Reinforcement as per Cl. 29.3.1 of IS 456
Distribution
Tensile reinforcement to be placed within a zone Depth of 0.25*D-0.05*l = 348 mm
Area of tensile reinforcement required (bottom) = 853 mm2 i.e.
i.e. 16 dia 4.2 nos.
provide 16 dia 7 nos.
Negative Reinforcement as per Cl. 29.3.2 (b) of IS 456
Distribution
l/D = 1.5
Type of Distribution a)
Zone 1 Depth = 0.2 D = 398 mm
Proportion of area of tensile reinforcement in zone 1 0.5*(l/D-0.5)
Ast1 = 1055 mm2
Provide 16 dia 8 nos.
Zone 2 Depth = 0.3 D on either side of mid depth 0.6 D = 1194 mm
a) When ratio of Clear Span to Overall Depth is in the range 1.0 to 2.5 tensile reinforcement over a support
of deep beam is divided in 2 zones
b) When span to Depth ratios is less than unity, the steel shall be evenly distributed over a depth of 0.8D
measured from the tension face
Distribution Type a)

Area of tensile reinforcement in zone 2 Ast2 = 1039 mm2
Type of Distribution b)
Depth = 0.8 D= N.A. mm
Area of tensile reinforcement distributed evenly Ast = N.A. mm2
Provide 12 dia N.A.
Minimum vertical and horizontal reinforcement as per cl. 32.4 of IS:456
Area of Minimum Vertical Reinforcement (Stirrups) Ast;min/m length 480 mm2
/m
Provide on each face 240.0 mm2
/m
Dia of bar (Provide <16mm) 12 mm
Spacing 471 mm
Adopt 12 dia 200 mm O.K.
Area of Minimum Horizontal Reinforcement (Stirrups) Ast;min/m length 800 mm
2
/m
Provide on each face 400.0 mm
2
/m
Spacing 283 mm
400 mm
Zone 1 398 16 dia 8 nos.
mm
12 dia @
200 mm
Zone 2 1194
mm 12 dia 10 nos.
1990 mm
348 16 dia 7 nos.
mm 40 mm cover
160 mm

11 Design of Intermediate diaphragm as deep beam
3.000 m 3.000 m 3.000 m
Intermediate diaphragm
Design moment taken from Sofistik, ULS-B
Bending Moment top bending 551.2 KN-m (Hogging)
Bending Moment bottom bending 438.7 KN-m (Sagging)
The deep beam design is done as per recommendations of IS 456 :2000, Limit state method.
11.1 Design of top reinforcement
Depth of beam, h = 1.99 m
Width of beam, b = 0.3 m
Active depth, D = 1.99 m
Span/Depth, l / D = 1.51
Hence, Diaphragm is designed as a deep beam Ref. Clause 29.1(a) of IS 456 : 2000
Hence, fcu = 28 MPa
Ultimate flexure capacity of section, Mu = 0.12 fcu b (D)^2 = 3991.8 kN-m
Applied ultimate moment = 551.2 kN-m OK
here, fy = 500 Mpa
lever arm ,z = 0.2 l + 0.3 D = 1.197 m
Hence, As required= 1058.6 mm2 i.e. 12 dia 9.4 nos.
As = 1131.0 mm2 OK
For deep beams, design is carried out for Ultimate Limit states. The beam is not needed to be designed for
shear as per IS 456 : 2000 Section 4.
Center line

11.2 Design of bottom reinforcement
Depth of beam, h = 1.99 m
Width of beam, b = 0.3 m
Active depth, D = 1.99 m
Span/Depth, l / D = 1.51
Hence, Diaphragm is designed as a deep beam Ref. Clause 29.1(a) of IS 456 : 2000
Hence, fcu = 28 MPa
Ultimate flexure capacity of section, Mu = 0.12 fcu b (D)^2 = 3991.8 kN-m
Hence, applied ultimate moment = 438.7 kN-m OK
here, fy = 500 Mpa
lever arm ,z = 0.2 l + 0.3 D = 1.197 m
Hence, As required= 842.5 mm2 i.e. 16 dia 4.2 nos.
As = 1206.4 mm2 OK
11.3 Detailing of Deep Beam Reinforcement
Positive Reinforcement as per Cl. 29.3.1
Tensile reinforcement should be placed within a zone Depth of 0.25*D-0.05*l
= 348 mm
Area of tension reinforcement (bottom) = 843 mm2
Negative Reinforcement as per Cl. 29.3.2 (b)
Distribution
Distribution
l/D = 1.5 Type a)
Zone 1 Depth = 0.2 D = 398 mm
Area of tensile reinforcement in zone 1 0.5*(l/D-0.5)
Ast1 = 533 mm
2
As per IS:456 cl.29 & SP:24 - Section 4 Special Requirements for Structural Member and Systems cl 27
(Deep Beam)
a) When ratio of Clear Span to Overall Depth is in the range 1.0 to 2.5 tensile reinforcement over a support
of deep beam is divided in 2 zones
b) When span to Depth ratios less than unity, the steel shall be evenly distributed over a depth of 0.8D
measured from the tension face

Zone 2 Depth = 0.3 D on either side of mid depth 0.6 D = 1194 mm
Area of tensile reinforcement in zone 2 Ast2 = 525 mm2
Type of Distribution b)
Depth = 0.8 D= N.A. mm
Area of tensile reinforcement distributed evenly Ast = N.A. mm2
Provide 12 dia N.A.
As per IS:456 cl. 32.4
Area of Minimum Vertical Reinforcement (Stirrups) Ast;min/m length 716 mm2
/m
/m
Spacing 316 mm
Area of Minimum Horizontal Reinforcement (Stirrups) Ast;min/m length 1194 mm
2
/m
/m
Spacing 189 mm
300 mm 300 mm
Zone 1 398 12 dia 6 nos.
mm
12 dia @
200 mm 12 dia N.A.
Zone 2 1194
mm 12 dia 5 nos.
N.A.
1990 mm mm 300 mm
348 16 dia 6 nos.
mm 40 mm cover 40 mm cover
220 mm
Type of Distribution a) Type of Distribution b)
Applicable Not Applicable

A-I Calculation of Spalling Reinforcement
Reference to be made to Annex J of Eurocode EC2-2
Area of such reinforcement shall not be less than
in each direction
1.2
As,req. = 393.3 mm
2
Provide 2 nos. 16 mm dia in each direction As,prov. = 402 mm2
This reinforcement needs to be distributed in each direction over the length of the rectangular prism.
Strictly, a check of crack width would be necessary. To avoid such checks, stress in reinforcement can
be restricted to 250 MPa
𝐴𝑠 = 0.03
𝑃𝑚𝑎𝑥
𝑓𝑦𝑑
𝛾𝑝,𝑢𝑛𝑓𝑎𝑣
𝛾𝑝,𝑢𝑛𝑓𝑎𝑣

A-II Cable force distribution at transfer (External Girder)
p
Cable forces & stresses after immediate losses (at transfer) are reported in this appendix.
Cable 1
Cable 2
Cable 3

Cable 4
Cable 5

A-III Checks for Special Purpose Vehicle (SPV)
This appendix provides additional checks for special purpose vehicle (SPV)
SPV Load at 500m eccentricity from CL of bridge as applied in SOFiSTiK
Bending moment diagram due to SPV
Bending moment diagram due to standard live loading i.e. Class A & 70R vehicles

Maximum bending moment due to SPV 3358 kN-m
Factored bending moment due to SPV in ULS with factor =1.15 3861.7 kN-m
Maximum bending moment due to live load 3754 kN-m
Factored bending moment due to live load in ULS with factor =1.5 5631 kN-m
Effects of SPV is less than standard live load. Thus OK
GTOP STOP
LC Max Min Max Max
MPa MPa MPa MPa
SPV 8.72 -0.19 10.57 4.9
Tensile stresses are observed at bottom fiber but limited to fctm for section to remain uncracked.
Minimum reinforcement for crack control is checked in Section 8.6
Stresses in rare serviceability comb. With SPV a) STOP b) GTOP c) BOT
BOT

19R002-SDN-MJB-021-SUP-01.pdf

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