Design of Br@Ch.25+732 - 1x18

CONTENTS
1) Design of Abutment
2) Design of Superstucture
3) Design of Deck Slab
4) Bearing loads and forces
Design of Substructure (Abutment)
Span : 18 m (c/c of Exp. Joint)
Bridge at Ch.26+732
SALIENT FEATURES OF THE BRIDGE :
Span c/c of brg. = 16.6 m
c/L of brg. c/L of exp. J = 0.7 m
Exp. Gap = 40 mm
Overall span = 18.0 m
Depth of super-structure = 1.52 m

Cross Grider below Girder soffite = 0 m
Wearing Coat thickness = 65 mm
Depth of Bearing + Pedestal (minimum) = 500 mm
Overall carriageway width = 8.5 m

Clear carriageway width = 7.5 m
Cross Camber = 2.50%
MATERIAL USED & THERE PROPERTIES :

CONCRETE
Grade of Concrete fck = M 35 Mpa
Mean value of concrete compressive strength fcm = 45 Mpa
Design Concrete compressive strength fcd = 0.447 *fck
= 15.633 MPa
Secant Modulus of Elasticity Ecm = 32308.2 MPa
Mean axial tensile strength fctm = 2.77 Mpa
REINFORCING STEEL
Grade of Reinforcement fyk = Fe 500 Mpa
Design yield strength of reinforcement fyd = 0.870 *fyk
= 434.8 Mpa
Modulus of Elasticity Es = 200000 Mpa
3
RCC Density = 2.5 t/m
ANALYSES ASSUMPTION
Enviromental parameters
Relative humidity = 80 %
Exposure condition = SEVERE
Modulus of Elasticity for Concrete

For short Term loading Ecm = 32308.2 Mpa
For long Term loading Ecm' = Ecm/ (1+f)
f = Creep coefficent
Creep coefficent for Foundation f = 1 ( As ho =  , For foundations)
Ecm' = 16154.1 Mpa

Creep for abutment shaft
Cross-sectional Area Ac = 10.20 m2
Perimeter in contact with atmosphere u = 8.50 m
Notational size ho 2Ac/u = 2400 mm
Age of concrete at the time of loading to = 90 days
t considered = 25550 days
f () = 1.24 (Refer Appendix B)
@ 1.11 *(Reduced by 10% on the conservative side)
2
Ecm' = 15294.2 N/mm
SERVICEABILITY LIMIT STATE :
Max permissible Stress in Concrete
Rare Combination = 0.48*fck = 16.8 Mpa
Quasi permanent Combination = 0.36*fck = 12.6 Mpa
Max permissible Stress in Steel = 0.8*fyk = 400 Mpa
Permissible crack width wk,max = 0.3 mm
Backfill Soil Parameter

o
f = Angle of internal friction, = 35
o
d = Angle of friction between soil and concrete = 22.5
o
dsubmerged= 1/2 d dry = 11.25
i = Surcharge angle = 0o
3
gdry = Dry density of earth = 2 t/m
3
gsat = Saturated density of earth = 2 t/m
3
gwater = water density = 1 t/m
3
gsub = Submerged density of earth = 1 t/m
m = coeff. Of friction b/w footing base & earth = 0.5
Live Load Surcharge :

Equivelent to 1.2 m Earth Fill
2
Live Load surcharge intensity q = 2.4 t/m
SEISMIC PARAMETER
Seismic Zone = V
Type of soil = medium
Zone factor Z = 0.36
Importance factor I = 1.2
Response Reduction Factor, Rlong. = 3
Response Reduction Factor, Rtrans. = 1
Response Reduction Factor, Rvert. = 1
LEVEL DETAILS :
Formation level = 239.000 m
Highest flood Level = 233.710 m
Lowest water level = 229.700 m
Ground Level = 232.210 m
Max Scour Level = 231.210 m
Founding Level = 229.700 m
2
Bearing capacity = 30.0 t/m */( Working State, Non-Seismic case)
2
= 40.5 t/m */( Working State, Seismic Case)
8.5
0.5 0 7.500 0.5
0.065 thick WC
FRL : 239.000
2.5%
1.52
A1 A2
0 (min) 236.831 236.831
0.5 Cap Top : 236.831
1.25 3 c/c of girder
Nos. of Girder = 3 Nos.
Sign Convention :
T
MTT
MLL L
Showing +ve Force & Moment Direction

ABUTMENT COMPONENT :-
Length of Abutment = 8.5 m
1.52
8.08 0.3 1.22
FRL : 239.000
1 0.5 2.169
19 Cap Top : 236.831
2 0.6
4 3 5
20 0
0.5 18a 4a
0.52 1 0 9.30 HFL : 233.710
17 18 4.631
LWL : 229.700
6
7 8
16 1.1
11 0 0.2 13
9 0.8
10 12 FDN: 229.700
8.6 1.2 2.1

11.9
o
a = Angle of wall face with horizontal = 90
T-T
0.55
0.5
L-L 7.95
8.5 14
15
0.55 0.6
8.6 1.2 2.1 RETURN WALL

11.9
FOOTING PLAN
FORCES DUE TO SELFWEIGHT OF SUB_STRUCTURE & FOUNDATION :
Forces @ Footing Base
eL = Cg. w.r.t. Toe Edge (along L-L axis)
eT = Cg. Form c/L of base ( along T-T axis)
eY = Cg. From Footing base
Calculating Selfweight of Sub-structure :

Element Area Factor B H L V W eY eL eT
3
m m m m Tonne m m m
Dirt Wall & Abutment Cap
1 1 0.3 2.169 8.5 5.53 13.83 8.22 -3.67 0
2 1 1.52 0.6 8.5 7.752 19.38 6.83 -3.06 0
3 1 1 0 8.5 0 0 6.53 -2.8 0
4 1 0.52 0 8.5 0.00 0.00 6.53 -3.47333 0
4(a 0.5 0.52 0.5 8.5 1.11 2.76 6.36 -3.47333 0
5 1 0 0 8.5 0.00 0.00 6.53 -2.300 0
Total 14.39 35.97 7.33 -3.33 0.00

*/ Increase Abutment cap weight by 15% on account of bearing, bearing pedestal, stopper etc.
Abutment Cap weight Considered 16.55 41.37 7.33 -3.33 0.00
Abutment Shaft
6 1 1 4.63 8.5 39.36 98.4 4.22 -2.8 0
7 0.5 0 4.13 8.5 0.00 0.0 3.28 -3.3 0
8 0.5 0.2 4.63 8.5 3.94 9.8 3.44 -2.233 0
Abutment shaft weight considered. 43.30 108.24 4.15 -2.75 0.00

Total Sub-structure self weight at base of shaft 59.84 149.61 5.02 -2.91 0.000
Calculating Selfweight Foundation:

Element Area Factor No.s B H L V W eY eL eT
3
m m m m Tonne m m m
Footing
9 1 1 1.2 1.9 8.5 19.38 48.45 0.95 -2.7 0
10 1 1 8.6 0.8 8.5 58.48 146.20 0.40 -7.6 0
11 0.5 1 8.6 1.1 8.5 40.21 100.51 1.17 -6.17 0
12 1 1 2.1 0.8 8.5 14.28 35.70 0.40 -1.05 0
13 0.5 1 2.1 1.1 8.5 9.82 24.54 1.17 -1.4 0
Total Footing weight 142.16 355.41 0.74 -5.44 0.00

Return wall
14 1 2 0.5 7.95 8.6 68.37 170.93 3.98 -7.6 0
15 0.5 2 0.1 7.95 8.6 6.84 17.09 2.65 -7.6 0
Total Footing weight 75.21 188.02 3.85 -7.60 0.00
Total Sub-structure + Footing 277.21 693.03 2.51 -5.48 0.00
Total Weight of sub-structure & foundation = 693.03 T

Lever arm about toe (along L-L axis) = -5.48 m
Moment MTT = -3797.64 Tm
Lever arm about c/L base (along T-T axis) = 0m

Moment MLL = 0 Tm
Calculating Weight of Backfill Dry Condition
3
m m m m Tonne m m m
Earth Fill Weight

16 0.5 1 8.6 1.1 7.4 35.00 70.00 1.53 -9.03333 0
17 1 1 8.6 4.631 7.4 294.69 589.39 4.22 -7.6 0
18 0.5 1 0 4.131 7.4 0.00 0.00 4.65 -3.3 0
18a 0.5 1 0.52 0.500 7.4 0.96 1.92 6.20 -3.64667 0
19 1 1 8.08 2.769 7.4 165.59 331.17 7.92 -7.86 0
20 0 1 0.52 0 7.4 0.00 0.00 6.53 -3.64667 0
Total Earth Fill 496.24 992.49 5.26 -7.78 0.00
Total Weight of backfill = 992.49 T


Moment MLL = 0 Tm
Calculation of Bouyancy
9.77
HFL 233.710
4.01
1.1
0.8 FDN 229.700
9.8 2.1

3
m m m m Tonne m m m
Earth Fill Weight

1 1 -1 9.77 4.01 8.5 -333.12 -333.12 2.01 -7.01 0
2 0.5 -1 0.03 4.01 8.5 -0.46 -0.46 2.67 -2.12 0
3 1 -1 2.1 0.8 8.5 -14.28 -14.28 0.40 -1.05 0
4 0.5 -1 2.1 1.1 8.5 -9.82 -9.82 1.17 1.40 0
Total Earth Fill -357.67 -357.67 1.92 -6.54 0.00
Total buoyant weight = -357.67 T

Moment MTT = 2338.52 Tm
Lever arm about c/L base (along T-T axis) = 0.00 m

Moment MLL = 0 Tm
DEAD LOAD CALCULATION OF SUPER-STRUCTURE :
Overall Span = 17.96 m
C/c of Bearing = 16.6 m
Total Deck Width = 8.5 m
Thickness of Deck width = 0.22 m
Total depth of super-structure = 1.52 m
Depth of girder = 1.3 m
c/c of Girders = 3 m
Density of RCC = 2.5 T/m
8.5
0.22
Nos of Girder = 3 1.3 1.52
1.25 3
Super-structure Cross-section
Girder Cross-Section :
0.75 0.75
1 0.2 1 0.2
2 0.1 2 0
3
3
0.325 1.3 1.3
4 0.2
5 0.25
0.75 0.75
Section at Mid span Section at support
0.6
0.38
0.75 0.325
0.68 1 1.3 6
8.3
Section Property of Girder At Mid Span
Elemen B D A cgy'
Factor Nos.
t No. m m m2
m
1 1 0.213 0.2 2 0.085 0.1
2 0.5 0.213 0.1 2 0.0213 0.23333
3 1 0.325 1.3 1 0.423 0.65
4 0.5 0.2125 0.2 2 0.043 0.98
5 1 0.2125 0.25 2 0.106 1.18
Total 0.678 0.671
Section Property of Girder At Support Section

Elemen B D A cgy'
Factor Nos.
t No. m m m2
m
1 1 0.000 0.2 2 0.000 0.1
2 0.5 0.000 0.00 2 0.0000 0.2
3 1 0.75 1.3 1 0.975 0.65
Total 0.975 0.650
Self weight of Precast Beam

2.44 t/m
1.69 t/m
c/L
0.68 1 1.3 6
8.3
Reaction due to self weight of each girder

Description wt/m Length weight cg. From top
T/m m T m
Weight of Support Section 2.44 1.68 4.095 0.650
Weight of Transition section 2.07 1.3 2.68531 0.661
Weight of mid span 1.69 6 10.1625 0.671
Total Reaction 16.9428 0.664
Total weight of one Girder = 33.89 Tonne
Total Nos. of girder = 3 Nos.
Total weight of all girders = 101.66 Tonne

Calculating weight of superstruture Cg. From Deck
Weight Top
Weight of all Girder = 101.66 T 0.88 m
Weigth of Concrete Deck = 83.96 T 0.11 m
Diaphragm = 10.67 T 1.01 m
Total Concrete Weight = 196.29 T

Increase Concrete weight by 10% = 215.92 T 0.56 m
Reaction Over Each End = 107.96 Tonne
Total Reaction at Each support = 108.0 Tone

Cg. From Deck Top = 0.6 m
Forces due to Super-Structure DL about base slab toe :

Vertical Load (Sup DL Reaction) = 107.96 Tonne

Moment MLL = 0 Tm
Cg. From base slab bottom = 8.67 m

Calculation of SIDL
8.5
0.5 0 7.5 0 0.5
0.065 thick WC

Crash barrier weight = 1 t/m
Cg. From crash barrier bottom = 0.4 m 0
Footpath weight = 0 t/m 0.35

Cg. Of Footpath above deck = 0.175 m
2
Wearing coat = 0.2 t/m
Forces & Moments @ Foundation base

Element Description wt/m L W eY eT
t/m m Tonne m m
SIDL (excluding surfacing)

1 Crash barrier Left 1 17.96 17.96 0.4 -4
2 Crash barrier Right 1 17.96 17.96 0.4 4
3 Footpath Left 0 17.96 0.00 0.175 -3.75
4 Footpath Right 0 17.96 0.00 0.175 3.75
Tootal Load 35.92 0.40 0.00
Reaction per support 17.96 0.40 0.00
Forces due to Super-Structure SIDL about base slab toe :

Vertical Load (Sup SIDL Reaction) = 17.96 Tonne

Moment MLL = 0.00 Tm
Cg. From base Slab bottom = 9.64 m

Selfweight of surfacing
2
Element Description wt/m B L W eY eT
2
t/m m m Tonne m m
Surfacing
1 Wearing coat 0.2 7.5 17.96 26.94 0.033 0
Total Load 26.94 0.033 0
Reaction per support 13.47 0.033 0
Forces due to Super-Structure Surfacing about base slab toe :

Vertical Load (Sup Surfacing Reaction) = 13.47 Tonne

Moment MLL = 0 Tm

FINDING LIVE LOAD REACTIONS OVER PIER
17.96
16.6
SPAN_1 0.68 16.6 0.68
CLASS A
TYPE 1 6.8 6.8 6.8 6.8 11.4 11.4 2.7 2.7
DIST 3 3 3 4.3 1.2 3.2 1.1
CLASS 70R Wheeled

TYPE 2 8 12 12 17 17 17 17
DIST 3.96 1.52 2.13 1.37 3.05 1.37
CLASS 70R Tracked

TYPE 3 7 14 14 14 14 7
DIST 0.95 0.95 0.95 0.95 0.95
Reactions R11 R12 Transverse Ecc

Tonne Tonne
Maximum Reaction Case :
Class A 34.8 15.2 2.45
Clas 70R wheeled 72.6 27.4 1.16
Clas 70R tracked 61.8 8.2 1.53
Class A 2Lane 69.7 30.3 0.7
Class A 3Lane 104.5 45.5 -1.05
Class A + 70R wheeled 107.5 42.5 0.04
Class A + 70R tracked 96.6 23.4 0.33
Governing Case 72.6 27.4 1.16
Forces due to LL about base slab toe : Max Reaction Min Reaction
Vertical Load (CW LL Reaction) = 72.63 Tonne 27.3723 Tonne
Lever arm about toe (along L-L axis) = -2.8 m -2.8 m
Moment MTT = -203.36 Tm -76.642 Tm
Lever arm about c/L base (along T-T axis) = 1.16 m 1.16 m
Moment MLL = 84.25 Tm 31.75 Tm
Calculation of Longitudinal Forces
Horizontal force at bearing level in the longitudinal direction at fixed bearing (other than elastomeric bearing)
i) Fh - m (Rg +Rq) Refer Clause 211.5 IRC: 6-2010
= Maximum of
ii) Fh / 2 + m (Rg + Rq)
Where
Fh = Applied Horizontal force
Rg = Reaction at free end due to dead load and SIDL
Rq = Reaction at free end due to live load load
m = Coefficent of Friction at movable bearing = 0.03 or 0.05 which ever govern
* Fh (breaking force) is considered 20 % of the first train load + 10 % of the load of the succeeding trains or part
thereof.
Reaction due to dead load and SIDL

DL SIDL Surfacing
Rg = 107.96 + 17.96 + 13.47
= 139.39 tonne
Rq max = 72.63 tonne
Corresponding Live load over Span = 100 tonne of Class 70 R

Breaking Force Fh = 100 x 0.2 + 0 x 0.05
= 20 tonne
FLongitudinal = Fh - m (Rg +Rq) = 20 - 0.03 x ( 72.6277 + 139.392 )

Max of
Fh / 2 + m (Rg + Rq) = 10 + 0.05 x ( 72.6277 + 139.392 )
= Max of ( 13.6394 , 20.601 )

= 20.6 tonne
Forces due to LL Longitudinal Forces, about base slab toe :

Longitudinal Force = 20.6 Tonne
Lever arm from footing base = 7.715 m
Moment in about transverse axis MTT = 158.9 tm

FLUID PRESSURE CALCULATION UP TO FOUNDING LEVEL :
3
Fluid density = 0.48 t/m
Abutment Length L = 8.5 m
Footing Base width B = 11.9 m
FRL 239.000
9.3
1
Found.L 229.700
2
4.46 t/m
Fluid Pressure
Total Fluid Presure

Component Factor p h L F ey
T/m2 m m Tonne m
1 0.5 4.464 9.3 8.5 176.44 3.1
Total 176.44 3.100
Total fluid Pressure = 176.44 Tonne

Lever arm = 3.10
Net Moment MTT = 546.96 Tm
SUMMARY FLUID PRESSURE :

Description Fluid Pressure
Horizontal ( HL ) MTT (Dest)
Tonne Tm
1) LWL Condition 176.44 546.96
ACTIVE EARTH PRESSURE CALCULATION FOR OVER-TURNING & SLIDING:
A) Non-Seismic Case :
Coefficient of Active Earth Pressure
Active earth presure

o
f = 35 = 0.611 Radians
o
d = 22.5 = 0.393 Radians
o
dsubmerged = 11.25 = 0.196 Radians
o
i = 0 = 0 Radians
o
a = 90.00 = 1.571 Radians
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
2
LL surcharge intensity q = 2.4 t/m

Ka Dry = 0.244
Ka' Submerged = 0.251
1) LWL CONDITION
Ka = 0.244
Ka' = 0.251
3
gdry = 2 t/m
3
gsub = 1 t/m
o
d = 22.5
o
dsubmerged = 11.25
2
q = 2.4 t/m
L = 8.5 m
B = 11.9 m
FRL 239.000
9.3 4
1
2
LWL 229.700 0.5856 t/m
2
4.5384 t/m
0 2 5
3
FDN 229.700
2 2
Kagh = 4.5384 t/m Ka*q 0.6024 t/m
Earth Pressure Surcharge Pressure

Total Active Earth Presure
Component Factor p h L F d F*Cosd ey F*Sind ex
T/m2 m m Tonne deg Tonne m Tonne m
1 0.5 4.5384 9.3 8.5 179.38 22.5 165.73 3.906 68.65 -11.9
2 1 4.5384 0 8.5 0.00 11.25 0.00 0 0.00 -11.9
3 0.5 0 0 8.5 0.00 11.25 0.00 0.000 0.00 -11.9
Total 179.38 165.726 3.906 68.64585 -11.9
Total Active Earth Pressure = 179.38 Tonne

Horizontal Component = 165.73
Lever arm = 3.91
Vertical Component = 68.65

Lever arm = -11.90 m
Net Moment MTT = -169.56 Tm
Total Surcharge pressure

T/m2 m m Tonne m
4 1 0.5856 9.3 8.5 46.2917 4.65

5 1 0.6024 0 8.5 0 0
Total 46.2917 4.65
Total Surcharge Pressure = 46.29 Tonne

Lever arm above base = 4.65 m
2) HFL CONDITION
Ka = 0.244
Ka' = 0.251
3
gdry = 2 t/m
3
gsub = 1 t/m
o
d = 22.5
o
dsubmerged = 11.25
2
q = 2.4 t/m
L = 8.5 m
B = 11.9 m
FRL 239.000
5.29 4
1
2
HFL 233.710 0.5856 t/m
2
2.58152 t/m
4.01 2 5
3
FDN 229.700
2 2
Kagh = 3.58803 t/m Ka*q 0.6024 t/m
Total Active Earth Presure

2
T/m m m Tonne deg Tonne m Tonne m
1 0.5 2.58152 5.29 8.5 58.04 22.5 53.62 6.2318 22.21 -11.9
2 1 2.58152 4.01 8.5 87.99 11.25 86.30 2.005 17.17 -11.9
3 0.5 1.00651 4.01 8.5 17.15 11.25 16.82 1.337 3.35 -11.9
Total 163.184 156.745 3.379 42.72326 -11.9
Total Active Earth Pressure = 163.18 Tonne

Lever arm = 3.38


T/m2 m m Tonne m
4 1 0.5856 5.29 8.5 26.3315 6.655

5 1 0.6024 4.01 8.5 20.5328 2.005
Total 46.8643 4.61768

SUMMARY OF FORCES FOR OVERTURNING AND SLIDING
Ka Dry = 0.244
Ka' Submerged = 0.251

SUMMARY ACTIVE EARTH PRESSURE :
Description Earth Pressure
Horizontal ( HL ) MTT (Dest) Vertical ( V ) MTT (Steb)
Tonne Tm Tonne Tm
68.65 -816.9
2) HFL Condition 156.75 529.68

42.72 -508.4
SUMMARY SURCHARGE PRESSURE :

Description Surcharge Pressure
Tonne Tm

SEISMIC FORCE CALCULATION :
Time Period Calculation T = 2 D

1000 F
D = Approximate DL of super-structure & LL in Tonne (DL+20% LL)
= 107.962 + 14.5 t
= 122.487 Tonne
F = Horizontal force in Tonne required to be applied at center of mass of

super-structure for 1 mm deflection at the top of pier / abutment
along the considered direction of horizontal force.
F = 6EI for 1 mm deflection at x F

2
x *(3L-x) 1.08469
Top of abut. cap
2
E = 32308.2 N/mm
Column Cross-Section 1 mm deflection
B = 8.5 m 5.23063
D = 1.1 m (Average)
4
IL = 6.59954E+11 m
4
IT = 3.94064E+13 m
Force required in Long. Dir.FL = 34.1 tonne

Force required in Long. Dir. FT = 2035.7 tonne
Time Period -Longitudinal Seismic Case = 0.120

Time Period -Transverse Seismic Case = 0.02
Sa/g -Longitudinal Seismic Case = 2.5

Sa/g -Transverse Seismic Case = 2.5
Sa/g -Vertical Seismic Case = 2.5
Seismic Zone = V
Type of soil = medium
Zone factor Z = 0.36
Importance factor I = 1.2
Horizontal seismic coeff. -Long., AhL' = (Z/2)*(I)*(Sa/g)(Long.) = 0.54

Horizontal seismic coeff. -Trans., AhT' = (Z/2)*(I)*(Sa/g)(Trans.) = 0.54
Vertical seismic coeff. Av' =2/3 Ah = 0.36
Response Reduction Factor, Rlong. = 3

Response Reduction Factor, Rtrans. = 1
Response Reduction Factor, Rvert. = 1
Design Horizontal Longitudinal seismic coeff., AhL = Ah'/R(Long.) = 0.18

Design Horizontal Transverse seismic coeff., AhT = Ah'/R(Trans.) = 0.54
Design Vertical Seismic Coefficient - Av= Av'/R(vert.) = 0.36
DYNAMIC EARTH PRESSURE CALCULATION FOR OVER-TURNING & SLIDING :
Coefficient of Active Earth Pressure
Ka Dry = 0.244
Ka' Ssubmerged = 0.251

f = 35 o = 0.61087 Radians
o
d = 22.5 = 0.3927 Radians
o
i = 0o = 0 Radians
o
a = 90 = 1.5708 Radians
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
2

ah = 0.18
av = 0.36
l Formula used For +av -av +av -av
ldry = tan-1 ah 7.54 15.71 deg 0.13 0.27 Radians
1 ± av
-1
lsubmerged = tan gsat * ah 14.83 29.3578 deg 0.26 0.51 Radians
(gsat - 1) (1 ± av)
Seismic case (Coefficent of Earth Pressure)

For Seismic downward dry condition Ca 0.447
For Seismic downward submerged condition Ca' 0.592
For Seismic upward dry condition Ca- 0.296

For Seismic upward submerged condition Ca-' 0.562
1) LWL Seismic Downward
Ka = 0.244
Ka' = 0.251
Ca = 0.447
Ca' = 0.592
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
d = 22.5 deg
dsubmerged = 11.25 deg
2
q = 2.4 t/m
L = 8.5 m
B = 11.9 m
1.02 =3*(Ca'-Ka')
0.61 =3*(Ca-Ka)
FRL
Water Level
h'
FDN
Dynamic Earth Pressure Coeff. Variation
2.38 2.46
2.84 1.46
FRL 239.000
9.3 9.3
9.3
LWL 229.700
0 0
FDN 229.700
Dynamic Earth Dynamic Surcharge Pressure

Pressure
Dyanmic Earth Pressure Calculation
Parabola above Water Level Parabola below Water Level
2
p_mid_height = 2.84 t/m p_mid_height = 2.38 t/m2
h = 9.3 m h = 9.3 m
y = 4.65 m y = -4.65 m
L = 8.5 m L = 8.5 m
Dyanmic Earth Pressure Pa d Pa*Cosd ey Pa*Sind ex

T deg. T m T m
Parabola above Water Level 149.4 22.5 138.0 4.7 57.2 -11.9
Parabola below Water Level 0.0 11.25 0.0 0.0 0.0 -11.9
Total Dynamic Earth Pressure 149.4 138.0 4.7 57.2 -11.9
Total Dynamic Earth Pressure = 149.42 Tonne

Lever arm = 4.65

Dyanmic Surcharge Pressure Calculation

Pressure Distribution above water level Pressure Distribution below water level
2 2
Intensity at top = 1.46 t/m Intensity at water Level = 0.00 t/m
2 2
Intensity at water Level = 0.000 t/m Intensity at base = 0 t/m
h-h' = 9.3 m h = 0m
L = 8.5 m L = 8.5 m
Dyanmic Surcharge Pressure Pa Lever arm above Base

T/m m
Trapozial Portion above water Level 57.84 6.20
Traingular Portion below water Level 0.00 0.00
Total Dynamic Surcharge Pressure 57.84 6.20

Levera arm above base = 6.20 m
2) LWL Seismic Upward
Ka = 0.244
Ka' = 0.251
Ca- = 0.296
Ca-' = 0.562
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
d = 22.5 deg
2
q = 2.4 t/m
L = 8.5 m
B = 11.9 m
0.93 =3*(Ca'-Ka')
0.16 =3*(Ca-Ka)
FRL
Water Level
h'
FDN
2.17 2.24
0.73 0.38
FRL 239.000
9.3 9.3
9.3
LWL 229.700
0 0
FDN 229.700

Pressure
2
h = 9.3 m h = 9.3 m
y = 4.65 m y = -4.65 m
L = 8.5 m L = 8.5 m

T deg. T m T m

Lever arm = 4.65


2 2
2 2
h-h' = 9.3 m h = 0m
L = 8.5 m L = 8.5 m

T/m m

3) HFL Seismic Downward
Ka = 0.244
Ka' = 0.251
Ca = 0.447
Ca' = 0.592
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
d = 22.5 deg
2
q = 2.4 t/m
L = 8.5 m
B = 11.9 m
1.02 =3*(Ca'-Ka')
0.61 =3*(Ca-Ka)
FRL
Water Level
h'
FDN
2.38 2.46
2.84 1.46
FRL 239.000
5.29 9.3
9.3
HFL 233.710
4.01 4.01
FDN 229.700

Pressure
2
h = 9.3 m h = 9.3 m
y = 0.64 m y = -0.64 m
L = 8.5 m L = 8.5 m

T deg. T m T m

Lever arm = 4.75


2 2
2 2
h-h' = 5.29 m h = 4.01 m
L = 8.5 m L = 8.5 m

T/m m

4) HFL Seismic Upward
Ka = 0.244
Ka' = 0.251
Ca- = 0.296
Ca-' = 0.562
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
d = 22.5 deg
2
q = 2.4 t/m
L = 8.5 m
B = 11.9 m
0.93 =3*(Ca'-Ka')
0.16 =3*(Ca-Ka)
FRL
Water Level
h'
FDN
2.17 2.24
0.73 0.38
FRL 239.000
5.29 9.3
9.3
HFL 233.710
4.01 4.01
FDN 229.700

Pressure
2
h = 9.3 m h = 9.3 m
y = 0.64 m y = -0.64 m
L = 8.5 m L = 8.5 m

T deg. T m T m

Lever arm = 3.67


2 2
2 2
h-h' = 5.29 m h = 4.01 m
L = 8.5 m L = 8.5 m

T/m m

SUMMARY DYNAMIC EARTH PRESSURE :
Description Dynamic Earth Pressure
Horizontal (HL ) MTT (Dest) Vertical (V ) MTT (Steb)
Tonne Tm Tonne Tm
Horizontal Component 138.05 641.91
Vertical Component 57.18 -680.45



SUMMERY DYNAMIC SURCHARGE PRESSURE :

Description Dynamic Surcharge Pressure
Horizontal (HL ) MTT (Dest)
Tonne Tm
1) LWL Seismic Downward 57.84 358.61
2) LWL Seismic Upward 14.83 91.93
3) HFL Seismic Downward 65.13 378.11
4) HFL Seismic Upward 28.51 128.51
SEISMIC COMPONENT OF SUPER-STRUCTURE DL & SIDL :
Longitudinal Horizontal seismic coefficent AhL = 0.18
Transverse Horizontal seismic coefficent AhT = 0.54
Vertical seismic coefficent AV = 0.36
Loads & Their Lever arm from base slab bottom

Description W ey
Tonne m
Total Super-Structure DL = 215.9 8.67
Total Super-Structure SIDL = 35.9 9.64
Total Surfacing weight = 26.9 9.27
Total 278.8 8.9

W = Weight of super-structure
ey = Cg. above base slab in vertical direction
Distance From base slab bottom to bearing top = 7.715 m

Distance form toe tip to c/L of brg = -2.8 m
SEISMIC LONGITUDINAL :
Longitudinal seismic coefficent AhL = 0.18
Total weight of sup DL, SIDL & surfacing = 278.8 Tonne
Forces at fixed end

Seismic Component = 50.2 Tonne
Lever arm above base slab = 7.7 m
Moment about T-T axis MTT = 387.1 Tm
Forces at free end

SEISMIC TRANSVERSE :
Horizontal seismic coefficent AhT = 0.54
Forces at fixed end

Moment about LL axis MLL = 666.6 Tm
Forces at free end

SEISMIC VERTICAL :
Horizontal seismic coefficent Av = 0.36
Forces at fixed end

Lever arm from toe = -2.8 m
Moment about T-T axis MTT = -140.5 Tm
Forces at free end

Summary of Permanent Load (DL+SIDL+SURFACING) seismic Component :

At Fixed End, Force about V HL HT ey eL MLL MTT
toe T T T m m Tm Tm
Seismic Longitudinal 50.2 7.7 387.1
Seismic Transverse 75.3 8.9 666.6
Seismic Vertical 50.2 -2.8 -140.5

SEISMIC COMPONENT OF LIVE LOAD :

Loads & Their Lever arm from base slab bottom

Description W ey
Tonne m
Maximum Live Load = 72.6 10.5
Minimum Live Load 27.4 10.5
W = Live Load Reaction

Distance From base slab bottom to bearing top = 7.78 m

Distance form toe tip to c/L of brg. = -2.8 m
SEISMIC LONGITUDINAL :
No Live Load seismic component is considered in longitudinal direction
Max Live Load Reaction Case :

Maximum Live Load reaction = 72.63 Tonne
Min Live Load Reaction Case :

Minimum Live Load reaction = 27.37 Tonne
SEISMIC VERTICAL :
Vertical seismic coefficent AhT = 0.36

Maximum Live Load reaction = 72.63 Tonne
Moment about LL axis MLL = -73.21 Tm

Minimum Live Load reaction = 27.37 Tonne
Moment about LL axis MLL = -27.59 Tm
Summary of LL seismic component transferred from super-structure :

At Fixed/ Free End V HL HT ey eL MLL MTT
T T T m m Tm Tm

T T T m m Tm Tm

SEISMIC COMPONENT OF SUB-STRUCTURE & BACKFILL :

Sub-structure Vertical load

Description W ey ex
Tonne m m
Sub-structure = 149.6 5.0 -2.9
Return wall = 188.0 3.9 -7.6
Total 337.6 4.4 -5.5

W = Weight of super-structure
Backfill Vertical load

Description W ey ex
Tonne m m
Backfill Weight = 992.5 5.3 -7.8
Total 992.5 5.3 -7.8
SEISMIC LONGITUDINAL : Sub-Structure

Total weight of Sub-structure = 337.6 Tonne


SEISMIC VERTICAL :

Summery of Sub-structure seismic component :

At Fixed End V HL HT MLL MTT
T T T Tm Tm
Seismic Longitudinal 60.8 265.8
Seismic Transverse 182.3 797.3
Seismic Vertical 121.5 -671.1
SEISMIC COMPONENT OF BACK FILL :

SEISMIC LONGITUDINAL : Earth Fill


SEISMIC VERTICAL :

Summery of Earthfill seismic component :

At Fixed End V HL HT MLL MTT
T T T Tm Tm
Seismic Longitudinal 178.6 940.5
Seismic Vertical 357.3 -2779.8

-----
VERIFICATION of EQUILIBRIUM (OVERTURNING & SLIDING)
LOAD COMBINATION (TABLE 3.1)
LC-1 NS, LWL, Min LL Lead Forces about toe LC-1

S.N. Description V HL HT MTT MLL
Tonne Tonne Tonne Tm Tm
1) Sub-structure & Foundation 693.0 -3798 0.0 0.95
2) Backfill 992.5 -7721.7 0.0 0.95
3) Super-structure DL 108.0 -302.3 0.0 0.95
4) SIDL (excluding surfacing) 18.0 -50.3 0.0 0.95
5) Surfacing 13.5 -37.7 0.0 1
6.2) Live Load Vertical Load Min Reaction 27.4 -76.6 31.8 1.5
7) Live Load Horizontal Forces 20.6 158.9 1.5
9.1) Earth Pressure LWL 1.5
Horizontal Component 165.7 647.3 1.5
Vertical Component 68.6 -816.9 1.5
10.1) Surcharge Pressure LWL 46.3 215.3 1.2
S.N. Description Forces about toe

V HL HT MTT(Dest) MTT(Steb) MLL(Dest)
Tonne Tonne Tonne Tm Tm Tm
LC-1 NS, LWL, Min LL Lead 1878.37 335.04 0 1467.7 -12656
LC-2 NS, HFL, Min LL Lead Forces about toe LC-2

2) Backfill 992.5 -7721.7 0.0 0.95
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 1
9.2) Earth Pressure HFL 1.5
10.2) Surcharge Pressure HFL 46.9 216.4 1.2

LC-2 NS, HFL, Min LL Lead 1481.81 322.257 0 3631.12 -12194

LC-3 SIS,LWL,Min LL Acc,Seismic Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-3
2) Backfill 992.5 -7721.7 0.0 0.95
5) Surfacing 13.5 -37.7 0.0 1
9.1) Earth Pressure LWL 1
Horizontal Component 165.7 647.3 1
Vertical Component 68.6 -816.9 1
Seismic Longitudinal 1.5
11) Sub-structure Component 60.8 265.8 1.5
12) Earth fill 178.6 940.5 1.5
12) Super-Structure DL, SIDL, & Surfacing Component 50.2 387.1 1.5
13) Dynamic Earth Pressure 1.5
Seismic Transveres 0.45
18.2) Live Load Component (Min. Reaction) 14.8 155.2 0.09
Seismic Vertical Downward 0.45
19) Sub-structure Component 121.5 -671.1 0.45
20) Earthfill component 357.3 -2779.8 0.45
21) Super-Structure DL, SIDL, & Surfacing Component
50.2 -140.5 0.45
22.2) Live Load Component (Min. Reaction) 9.9 -27.6 0.09

LC-3 SIS,LWL,Min LL Acc,Seismic Sx=1,Sz=0.3,Sy=0.3

2133.18 811.316 117.246 4032.12 -14788
LC-4 SIS, LWL,Min LL Acc,Seismic Sx=1,Sz=0.3,Sy=-0.3 Forces about toe LC-4
2) Backfill 992.5 -7721.7 0.0 0.95
5) Surfacing 13.5 -37.7 0.0 1
12) Earth fill 178.6 940.5 1.5
19) Sub-structure Component 121.5 -671.1 -0.45
50.2 -140.5 -0.45
22.2) Live Load Component (Min. Reaction) 9.9 -27.6 -0.09

LC-4 SIS, LWL,Min LL Acc,Seismic Sx=1,Sz=0.3,Sy=-0.3

1752.28 657.329 117.246 3683.76 -12410
LC-5 SIS, HFL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-5
2) Backfill 992.5 -7721.7 0.0 0.95
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 1
9.2) Earth Pressure HFL 1
12) Earth fill 178.6 940.5 1.5
50.2 -140.5 0.45

LC-5 SIS, HFL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=0.3

1730.08 793.353 117.246 6230.18 -14247
LC-6 SIS, HFL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=-0.3 Forces about toe LC-6
2) Backfill 992.5 -7721.7 0.0 0.95
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 1
12) Earth fill 178.6 940.5 1.5
50.2 -140.5 -0.45

LC-6 SIS, HFL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=-0.3

1373.23 694.033 117.246 6020.6 -12156
LC-7 NS, -ve long LL, LWL, Min LL Lead Forces about toe LC-7
2) Backfill 992.5 -7721.7 0.0 0.95
5) Surfacing 13.5 -37.7 0.0 1
7) Live Load Horizontal Forces 20.6 158.9 -1.5

LC-7 NS, -ve long LL, LWL, Min LL Lead 1878.37 273.237 0 1229.29 -12895
LC-8 NS, -ve long LL, HFL, Min LL Lead Forces about toe LC-8
2) Backfill 992.5 -7721.7 0.0 0.95
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 1

LC-8 NS, -ve long LL, HFL, Min LL Lead 1481.81 260.454 0 3392.72 -12432
LC-9 SIS -ve long LL,LWL, Min LL Acc,Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-9
2) Backfill 992.5 -7721.7 0.0 0.95
5) Surfacing 13.5 -37.7 0.0 1
Seismic Longitudinal -1.5
11) Sub-structure Component 60.8 265.8 -1.5
50.2 -140.5 0.45

LC-9 SIS -ve long LL,LWL, Min LL Acc,Sx=1,Sz=0.3,Sy=0.3

2047.41 145.718 117.246 1228.04 -14197
LC-10 SIS,-ve long LL,HFL, Min LL Acc,Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-10
2) Backfill 992.5 -7721.7 0.0 0.95
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 1
Seismic Longitudinal -1.5
11) Sub-structure Component 60.8 265.8 -1.5
50.2 -140.5 0.45

LC-10 SIS,-ve long LL,HFL, Min LL Acc,Sx=1,Sz=0.3,Sy=0.3

1663.81 136.737 117.246 3448.91 -13889
VERIFICATION of EQUILIBRIUM (OVERTURNING & SLIDING) :
FOS|sliding = (m*SV + SHrestoring ) ≥ 1 NS

SHsliding 1 Seismic
m = 0.50
FOS|overturning = SMrestoring / SMoverturning ≥ 1 NS

1 Seismic
SUMMERY OF FORCES :
S.N. Description Forces about toe Along Long. Dirn About Trans. Dirn
V HL HT MTT(Dest) MTT(Steb) MLL(Dest) MLL(Steb) FOS FOS
Check Check
Tonne Tonne Tonne Tm Tm Tm Tm |sliding |overturning
LC-1 NS, LWL, Min LL Lead 1878.37 335.04 0 1467.7 -12656.4 47.6278 0 2.80 OK 8.62 OK
LC-2 NS, HFL, Min LL Lead 1481.81 322.257 0 3631.12 -12193.7 47.6278 0 2.30 OK 3.36 OK
LC-3 SIS,LWL,Min LL Acc,Seismic Sx=1,Sz=0.3,Sy=0.3
2133.18 811.316 117.246 4032.12 -14787.6 679.079 0 1.31 OK 3.67 OK
LC-4 SIS, LWL,Min LL Acc,Seismic Sx=1,Sz=0.3,Sy=-0.3
1752.28 657.329 117.246 3683.76 -12409.9 679.079 0 1.33 OK 3.37 OK
LC-5 SIS, HFL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=0.3
1730.08 793.353 117.246 6230.18 -14247 679.079 0 1.09 OK 2.29 OK
LC-6 SIS, HFL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=-0.3
1373.23 694.033 117.246 6020.6 -12155.5 679.079 0 1.01 OK 2.02 OK
LC-7 NS, -ve long LL, LWL, Min LL Lead 1878.37 273.237 0 1229.29 -12894.8 47.6278 0 3.44 OK 10.49 OK
LC-8 NS, -ve long LL, HFL, Min LL Lead 1481.81 260.454 0 3392.72 -12432.1 47.6278 0 2.84 OK 3.66 OK
2047.41 145.718 117.246 1228.04 -14197.3 679.079 0 7.03 OK 11.56 OK
1663.81 136.737 117.246 3448.91 -13888.9 679.079 0 6.08 OK 4.03 OK
EARTH PRESSURE AT REST FOR FOUNDATION DESIGN & BASE PRESSURE:
Coefficient of Earth Pressure at rest
Earth at rest

o
f = 35 = 0.611 Radians
o
d = 22.5 = 0.393 Radians
o
o
i = 0 = 0 Radians
o
a = 90.00 = 1.571 Radians
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
2

Earth pressure action from toe B = 3.3 m
Ko Dry = 0.426
1) LWL CONDITION
Ka = 0.426
3
gdry = 2 t/m
3
gsub = 1 t/m
o
d = 22.5
o
dsubmerged = 11.25
2
q = 2.4 t/m
L = 8.5 m
B = 3.3 m
FRL 239.000
9.3 4
1
LWL 229.700 1.02 t/m2
2
7.9 t/m
0 2 5
3
FDN 229.700
2
Kagh = 7.93 t/m Ka*q 1.02 t/m2

Total Earth Presure at rest
1 0.5 7.93148 9.3 8.5 313.49 22.5 289.63 3.906 119.97 -3.3
2 1 7.93148 0 8.5 0.00 11.25 0.00 0 0.00 -3.3
3 0.5 0 0 8.5 0.00 11.25 0.00 0.000 0.00 -3.3
Total 313.492 289.629 3.906 119.9681 -3.3
Total Earth Pressure at rest = 313.49 Tonne

Lever arm = 3.91

Lever arm = -3.30 m

T/m2 m m Tonne m
4 1 1.02342 9.3 8.5 80.9011 4.65

5 1 1.02342 0 8.5 0 0
Total 80.9011 4.65

2) HFL CONDITION
Ka = 0.42642
3
gdry = 2 t/m
3
gsub = 1 t/m
o
d = 22.5
o
dsubmerged = 11.25
2
q = 2.4 t/m
L = 8.5 m
B = 3.3 m
FRL 239.000
5.29 4
1
2
HFL 233.710 1.02342 t/m
2
4.51156 t/m
4.01 2 5
3
FDN 229.700
2 2
Kagh = 6.22152 t/m Ka*q 1.02342 t/m
Total Earth Presure at rst

2
1 0.5 4.51156 5.29 8.5 101.43 22.5 93.71 6.2318 38.82 -3.3
2 1 4.51156 4.01 8.5 153.78 11.25 150.82 2.005 30.00 -3.3
3 0.5 1.70996 4.01 8.5 29.14 11.25 28.58 1.337 5.69 -3.3
Total 284.35 273.114 3.385 74.50167 -3.3

Lever arm = 3.39

Lever arm = -3.30 m

T/m2 m m Tonne m
4 1 1.02342 5.29 8.5 46.0179 6.655

5 1 1.02342 4.01 8.5 34.8832 2.005
Total 80.9011 4.65

SUMMARY OF EARTH PRESSURE FOR BASE PRESSURE AND STRUTURAL DESIGN
Tonne Tm Tonne Tm
1) LWL Condition 289.63 1131.29
119.97 -395.9

74.50 -245.9
SUMMARY SURCHARGE PRESSURE :

Tonne Tm

DYNAMIC EARTH PRESSURE CALCULATION FOR FOUNDATION DESIGN & BASE PRESSURE :
Coefficient of Earth Pressure
Ka Dry = 0.426
Ka' Ssubmerged = 0.426

f = 35 o = 0.611 Radians
o
d = 22.5 = 0.3927 Radians
o
i = 0o = 0 Radians
o
a = 90 = 1.5708 Radians
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
2

Earth pressure action from toe B = 3.3 m
ah = 0.18
av = 0.36
1 ± av
-1
(gsat - 1) (1 ± av)


Ka = 0.426
Ca = 0.447
Ca' = 0.592
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
d = 22.5 deg
2
q = 2.4 t/m
L = 8.5 m
B = 3.3 m
0.50 =3*(Ca'-Ka')
0.06 =3*(Ca-Ka)
FRL
Water Level
h'
FDN
1.16 1.19
0.29 0.15
FRL 239.000
9.3 9.3
9.3
LWL 229.700
0 0
FDN 229.700

Pressure
2
h = 9.3 m h = 9.3 m
y = 4.65 m y = -4.65 m
L = 8.5 m L = 8.5 m

T deg. T m T m

Lever arm = 4.65

Lever arm = -3.30 m

2 2
2 2
h-h' = 9.3 m h = 0m
L = 8.5 m L = 8.5 m

T/m m

Ka = 0.42642
Ca- = 0.296
Ca-' = 0.562
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
d = 22.5 deg
2
q = 2.4 t/m
L = 8.5 m
B = 3.3 m
0.41 =3*(Ca'-Ka')
0.00 =3*(Ca-Ka)
FRL
Water Level
h'
FDN
0.94 0.97
0.00 0.00
FRL 239.000
9.3 9.3
9.3
LWL 229.700
0 0
FDN 229.700

Pressure
2
h = 9.3 m h = 9.3 m
y = 4.65 m y = -4.65 m
L = 8.5 m L = 8.5 m

T deg. T m T m
Total Dynamic Earth Pressure 0.0 0.0 0.0 0.0 0.0

Lever arm = 0.00

Lever arm = 0.00 m
Moment MTT = 0 Tm

2 2
2 2
h-h' = 9.3 m h = 0m
L = 8.5 m L = 8.5 m

T/m m

Ka = 0.42642
Ca = 0.447
Ca' = 0.592
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
d = 22.5 deg
2
q = 2.4 t/m
L = 8.5 m
B = 3.3 m
0.50 =3*(Ca'-Ka')
0.06 =3*(Ca-Ka)
FRL
Water Level
h'
FDN
1.16 1.19
0.29 0.15
FRL 239.000
5.29 9.3
9.3
HFL 233.710
4.01 4.01
FDN 229.700

Pressure
2
h = 9.3 m h = 9.3 m
y = 0.64 m y = -0.64 m
L = 8.5 m L = 8.5 m

T deg. T m T m

Lever arm = 3.46

Lever arm = -3.30 m

2 2
2 2
h-h' = 5.29 m h = 4.01 m
L = 8.5 m L = 8.5 m

T/m m

Ka = 0.42642
Ca- = 0.296
Ca-' = 0.562
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
d = 22.5 deg
2
q = 2.4 t/m
L = 8.5 m
B = 3.3 m
0.41 =3*(Ca'-Ka')
0.00 =3*(Ca-Ka)
FRL
Water Level
h'
FDN
0.94 0.97
0.00 0.00
FRL 239.000
5.29 9.3
9.3
HFL 233.710
4.01 4.01
FDN 229.700

Pressure
2
h = 9.3 m h = 9.3 m
y = 0.64 m y = -0.64 m
L = 8.5 m L = 8.5 m

T deg. T m T m

Lever arm = 2.54

Lever arm = -3.30 m

2 2
2 2
h-h' = 5.29 m h = 4.01 m
L = 8.5 m L = 8.5 m

T/m m
Trapozial Portion above water Level 0.00 0

SUMMARY DYNAMIC EARTH PRESSURE :
Tonne Tm Tonne Tm

Vertical Component 0.00 0.00



Tonne Tm
'------
BASE PRESSURE
LOAD COMBINATION(FOR BASE PRESSURE)
LC-1 NS, LWL, Min LL Forces about toe LC-1

1) Sub-structure & Foundation 693.0 -3798 0.0 1
2) Backfill 992.5 -7721.74 0.0 1
3) Super-structure DL 108.0 -302.3 0.0 1
4) SIDL (excluding surfacing) 18.0 -50.3 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
6.2) Live Load Vertical Load Min Reaction 27.4 -76.6 31.8 1
7) Live Load Horizontal Forces 20.6 158.9 1
10.1) Surcharge Pressure LWL 80.9 376.2 1

V HL HT MTT MLL
LC-1 NS, LWL, Min LL 1972.25 391.13 0 -10715.8 31.7519
LC-2 NS, HFL, Min LL Forces about toe LC-2

2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 1
10.2) Surcharge Pressure HFL 80.9 376.2 1

V HL HT MTT MLL
LC-2 NS, HFL, Min LL 1569.11 374.62 0 -8433.94 31.7519

LC-3 SIS, LWL, Min LL, Seismic Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-3
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
Seismic Longitudinal 1
11) Sub-structure Component 82.0 358.8 1
12) Super-Structure DL, SIDL, & Surfacing Component 67.7 522.6 1
13) Dynamic Earth Pressure 1
14.1) LWL Seismic Downward 8.0 49.6 0.2
67.7 -189.7 0.3

V HL HT MTT MLL
LC-3 SIS, LWL, Min LL, Seismic Sx=1,Sz=0.3,Sy=0.3

2028.61 480.41 105.521 -10459.5 611.806
LC-4 SIS, LWL, Min LL, Seismic Sx=1,Sz=0.3,Sy=-0.3 Forces about toe LC-4
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
Vertical Component 0.0 0.0 1
14.2) LWL Seismic Upward 0.0 0.0 0.2
67.7 -189.7 -0.3

V HL HT MTT MLL
LC-4 SIS, LWL, Min LL, Seismic Sx=1,Sz=0.3,Sy=-0.3

1880.01 459.72 105.521 -9870.23 611.806
LC-5 SIS, HFL, Min LL, Seismic Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-5
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 1
14.3) HFL Seismic Downward 18.3 77.3 0.2
67.7 -189.7 0.3

V HL HT MTT MLL
LC-5 SIS, HFL, Min LL, Seismic Sx=1,Sz=0.3,Sy=0.3

1628.7 490.42 105.521 -8120.64 611.806
LC-6 SIS, HFL, Min LL, Seismic Sx=1,Sz=0.3,Sy=-0.3 Forces about toe LC-6
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 1
14.4) HFL Seismic Upward 9.7 25.8 0.2
67.7 -189.7 -0.3

V HL HT MTT MLL
LC-6 SIS, HFL, Min LL, Seismic Sx=1,Sz=0.3,Sy=-0.3

1482.07 471.30 105.521 -7533.96 611.806
LC-7 NS, -ve long LL, LWL, Min LL Lead Forces about toe LC-7
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
7) Live Load Horizontal Forces 20.6 158.9 -1

V HL HT MTT MLL
LC-7 NS, -ve long LL, LWL, Min LL Lead 1972.25 349.93 0 -11033.7 31.7519
LC-8 NS, -ve long LL, HFL, Min LL Lead Forces about toe LC-8
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 1
10.2) Surcharge Pressure HFL 80.9 376.2 1

V HL HT MTT MLL
LC-8 NS, -ve long LL, HFL, Min LL Lead 1569.11 333.41 0 -8751.82 31.7519
LC-9 SIS -ve long LL,LWL, Min LL Acc,Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-9
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
67.7 -189.7 0.3

V HL HT MTT MLL

2020.7 451.48 105.521 -10595.6 611.806
LC-10 SIS,-ve long LL,HFL, Min LL Acc,Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-10
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 1
67.7 -189.7 0.3

V HL HT MTT MLL

1617.56 434.96 105.521 -8313.78 611.806
CHECK FOR MAXIMUM BASE PRESSRE
LOAD COMBINATION FOR MAXIMUM BASE PRESSURE
T-T
B C Coordinates of basecorner Properties of Base
2
eL Edges x (m) z (m) Area 11.9x8.5 = 101.15 m
4
A -5.950 -4.250 ITT 8.5x11.9^3/12 = 1193.65 m
4
8.5 B -5.950 4.250 ILL 11.9x8.5^3/12 = 609.007 m
L-L eT C 5.950 4.250
D 5.950 -4.250
Maximum Base Pressure Heel side Toe Side Bearing Capacity Check
Non-Seismic case LWL Condition 16.2 14.2 24.8 22.8 30.0 OK
A D HFL Condition 12.8 10.8 20.2 18.2 30.0 OK
11.9
Seismic Case LWL Condition 17.1 7.8 32.4 20.9 40.5 OK
HFL Condition 13.7 4.0 28.2 16.8 40.5 OK

SUMMERY OF FORCES : Eccentricity of Eccentricity of Moment and Base Pressure = P/ A ± M TT *x /
Vertical load Vertical load wrt forces at cg of
I TT ± M LL *z / I LL
from toe point cg of base base
S.N. Description Forces about toe eL1 eT1 eL eT MTT MLL base pressure at footing corners
V HL HT MTT MLL MTT/ V MLL/ V B/2-eL1 eT1 V*eL V*eT A B C D
Tonne Tonne Tonne Tm Tm m m m m Tm Tm T/m2 T/m2 T/m2 T/m2

LC-1 NS, LWL, Min LL 1972.25 391.131 0 -10715.8 31.7519 -5.43 0.02 0.52 0.02 1019.1 31.8 14.2 14.6 24.8 24.4
LC-2 NS, HFL, Min LL 1569.11 374.616 0 -8433.94 31.7519 -5.37 0.02 0.58 0.02 902.3 31.8 10.8 11.2 20.2 19.8
2028.61 480.409 105.521 -10459.5 611.806 -5.16 0.30 0.79 0.30 1610.8 611.8 7.8 16.3 32.4 23.8
1880.01 459.716 105.521 -9870.23 611.806 -5.25 0.33 0.70 0.33 1315.8 611.8 7.8 16.3 29.4 20.9
1628.7 490.425 105.521 -8120.64 611.806 -4.99 0.38 0.96 0.38 1570.1 611.8 4.0 12.5 28.2 19.7
1482.07 471.304 105.521 -7533.96 611.806 -5.08 0.41 0.87 0.41 1284.4 611.8 4.0 12.5 25.3 16.8
LC-7 NS, -ve long LL, LWL, Min LL Lead 1972.25 349.929 0 -11033.7 31.7519 -5.59 0.02 0.36 0.02 701.2 31.8 15.8 16.2 23.2 22.8
LC-8 NS, -ve long LL, HFL, Min LL Lead 1569.11 333.414 0 -8751.82 31.7519 -5.58 0.02 0.37 0.02 584.4 31.8 12.4 12.8 18.6 18.2
2020.7 451.476 105.521 -10595.6 611.806 -5.24 0.30 0.71 0.30 1427.5 611.8 8.6 17.1 31.4 22.8
1617.56 434.962 105.521 -8313.78 611.806 -5.14 0.38 0.81 0.38 1310.7 611.8 5.2 13.7 26.8 18.3
'----
DESIGN OF FOUNDATION
ULS LOAD COMBINATION
LC-1 NS(1), LWL, Min LL Acc, EP Lead Forces about toe LC-1
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75

V HL HT MTT MLL
LC-1 NS(1), LWL, Min LL Acc, EP Lead 2680.45 555.215 0 -14444 36.5146
LC-2 NS(1), LWL, Min LL Lead, EP Acc Forces about toe LC-2
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75

V HL HT MTT MLL
LC-2 NS(1), LWL, Min LL Lead, EP Acc 2630.04 417.611 0 -14782.9 47.6278
LC-3 NS(1), HFL, Min LL Acc, EP Lead Forces about toe LC-3
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
8) Buoyancy -357.7 2338.5 0.0 0.15

V HL HT MTT MLL
LC-3 NS(1), HFL, Min LL Acc, EP Lead 2558.6 530.443 0 -14178.2 36.5146
LC-4 NS(1), HFL, Min LL Lead, EP Acc Forces about toe LC-4
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
8) Buoyancy -357.7 2338.5 0.0 0.15

V HL HT MTT MLL
LC-4 NS(1), HFL, Min LL Lead, EP Acc 2530.93 401.097 0 -14488.8 47.6278
LC-5 NS(1), -ve long. LL, LWL, Min LL Lead, EP Acc Forces about toe LC-5
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75

V HL HT MTT MLL
LC-5 NS(1), -ve long. LL, LWL, Min LL Lead, EP

2630.04
Acc 355.808 0 -15259.7 47.6278
LC-6 NS(1), -ve long. LL, HFL, Min LL Lead, EP Acc Forces about toe LC-6
S.N. Description V H L HT MTT MLL
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
8) Buoyancy -357.7 2338.5 0.0 0.15

V HL HT MTT MLL
LC-6 NS(1), -ve long. LL, HFL, Min LL Lead, EP

2530.93
Acc 339.294 0 -14965.6 47.6278
LC-7 NS(2), LWL, Min LL Acc, EP Lead Forces about toe LC-7
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1

V HL HT MTT MLL
LC-7 NS(2), LWL, Min LL Acc, EP Lead 2008.24 478.019 0 -10495.2 31.7519
LC-8 NS(2), LWL, Min LL Lead, EP Acc Forces about toe LC-8
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1

V HL HT MTT MLL
LC-8 NS(2), LWL, Min LL Lead, EP Acc 1962.47 353.867 0 -10801.4 41.2774
LC-9 NS(2), HFL, Min LL Acc, EP Lead Forces about toe LC-9
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 0.15

V HL HT MTT MLL
LC-9 NS(2), HFL, Min LL Acc, EP Lead 1895.48 456.55 0 -10218.1 31.7519
LC-10 NS(2), HFL, Min LL Lead, EP Acc Forces about toe LC-10
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 0.15

V HL HT MTT MLL
LC-10 NS(2), HFL, Min LL Lead, EP Acc 1870.17 339.829 0 -10498.8 41.2774
LC-11 NS(2)-ve long. LL, LWL, Min LL Lead, EP Acc Forces about toe LC-11
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1

V HL HT MTT MLL
LC-11 NS(2)-ve long. LL, LWL, Min LL Lead, EP1962.47

Acc 300.304 0 -11214.7 41.2774
LC-12 NS(2)-ve long. LL, HFL, Min LL Lead, EP Acc Forces about toe LC-12
S.N. Description V H L HT MTT MLL
2) Backfill 992.5 -7721.74 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 0.15

V HL HT MTT MLL
LC-12 NS(2)-ve long. LL, HFL, Min LL Lead, EP1870.17

Acc 286.267 0 -10912 41.2774
LC-13 SIS(3), LWL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-13
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
67.7 -189.7 0.45

V HL HT MTT MLL
LC-13 SIS(3), LWL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=0.3

2711.84 565.649 158.282 -14331.4 914.534
LC-14 SIS(3), LWL, Min LL Lead, Seismic Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-14
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
67.7 -189.7 0.45

V HL HT MTT MLL
LC-14 SIS(3), LWL, Min LL Lead, Seismic Sx=1,Sz=0.3,Sy=0.3

2730.19 576.98 163.22 -14295.3 983.854
LC-15 SIS(3), LWL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=-0.3 Forces about toe LC-15
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
Vertical Component 0.0 0.0 1.5
67.7 -189.7 -0.45

V HL HT MTT MLL
LC-15 SIS(3), LWL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=-0.3

2488.94 534.61 158.282 -13447.5 914.534
LC-16 SIS(3), LWL, Min LL Lead, Seismic Sx=1,Sz=0.3,Sy=-0.3 Forces about toe LC-16
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
Vertical Component 0.0 0.0 1.5
67.7 -189.7 -0.45

V HL HT MTT MLL
LC-16 SIS(3), LWL, Min LL Lead, Seismic Sx=1,Sz=0.3,Sy=-0.3

2500.7 545.941 163.22 -13393 983.854
LC-17 SIS(3), HFL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-17
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
8) Buoyancy -357.7 2338.5 0.0 0.15
67.7 -189.7 0.45

V HL HT MTT MLL
LC-17 SIS(3), HFL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=0.3

2617.57 588.93 158.282 -13951.8 914.534
LC-18 SIS(3), HFL, Min LL Lead, Seismic Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-18
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
8) Buoyancy -357.7 2338.5 0.0 0.15
67.7 -189.7 0.45

V HL HT MTT MLL
LC-18 SIS(3), HFL, Min LL Lead, Seismic Sx=1,Sz=0.3,Sy=0.3

2635.92 600.261 163.22 -13915.8 983.854
LC-19 SIS(3), HFL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=-0.3 Forces about toe LC-19
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
8) Buoyancy -357.7 2338.5 0.0 0.15
67.7 -189.7 -0.45

V HL HT MTT MLL
LC-19 SIS(3), HFL, Min LL Acc, Seismic Sx=1,Sz=0.3,Sy=-0.3

2397.63 560.249 158.282 -13071.8 914.534
LC-20 SIS(3), HFL, Min LL Lead, Seismic Sx=1,Sz=0.3,Sy=-0.3 Forces about toe LC-20
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
8) Buoyancy -357.7 2338.5 0.0 0.15
67.7 -189.7 -0.45

V HL HT MTT MLL
LC-20 SIS(3), HFL, Min LL Lead, Seismic Sx=1,Sz=0.3,Sy=-0.3

2409.39 571.58 163.22 -13017.3 983.854
LC-21 SIS(3)-ve long. LL, LWL, Min LL Lead, Seismic Sx=1,Sz=0.3,Sy=0.3
Forces about toe LC-21
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
67.7 -189.7 0.45

V HL HT MTT MLL
LC-21 SIS(3)-ve long. LL, LWL, Min LL Lead, Seismic

2718.33
Sx=1,Sz=0.3,Sy=0.3
515.039 163.22 -14642.6 983.854
LC-22 SIS(3)-ve long. LL, HFL, Min LL Lead, Seismic Sx=1,Sz=0.3,Sy=0.3
Forces about toe LC-22
2) Backfill 992.5 -7721.74 0.0 1.35
5) Surfacing 13.5 -37.7 0.0 1.75
8) Buoyancy -357.7 2338.5 0.0 0.15
67.7 -189.7 0.45

V HL HT MTT MLL
LC-22 SIS(3)-ve long. LL, HFL, Min LL Lead, Seismic

2619.21
Sx=1,Sz=0.3,Sy=0.3
498.525 163.22 -14348.5 983.854
BASE PRESSRE CALCULATION
ULS LOAD COMBINATIONS
T-T Coordinates of basecorner Properties of Base

2
Edges x (m) z (m) Area 11.9x8.5 = 101.15 m
4
B B1 C1 C A -5.950 -4.250 ITT 8.5x11.9^3/12 = 1193.65 m
4
eL D 5.950 -4.250 ILL 11.9x8.5^3/12 = 609.007 m
B -5.950 4.250
8.5 C 5.950 4.250
L-L eT
A A1 D1 D
8.6 1.2 2.1
11.9
SUMMERY OF FORCES : Eccentricity of Eccentricity of Moment and Gross Base Pressure = P/ A ± M TT
*x / I TT ± M LL *z / I LL
V HL HT MTT MLL MTT/ V MLL/ V B/2-eL1 eT1 V*eL V*eT A D B C
Tonne Tonne Tonne Tm Tm m m m m Tm Tm T/m2 T/m2 T/m2 T/m2

LC-1 NS(1), LWL, Min LL Acc, EP Lead 2680.45 555.215 0 -14444 36.5146 -5.39 0.01 0.56 0.01 1504.7 36.5 18.7 33.7 19.3 34.3
LC-2 NS(1), LWL, Min LL Lead, EP Acc 2630.04 417.611 0 -14783 47.6278 -5.62 0.02 0.33 0.02 865.9 47.6 21.4 30.0 22.0 30.6
LC-3 NS(1), HFL, Min LL Acc, EP Lead 2558.6 530.443 0 -14178 36.5146 -5.54 0.01 0.41 0.01 1045.4 36.5 19.8 30.3 20.3 30.8
LC-4 NS(1), HFL, Min LL Lead, EP Acc 2530.93 401.097 0 -14489 47.6278 -5.72 0.02 0.23 0.02 570.2 47.6 21.8 27.5 22.5 28.2
LC-5 NS(1), -ve long. LL, LWL, Min LL Lead, EP

2630.04
Acc 355.808 0 -15260 47.6278 -5.80 0.02 0.15 0.02 389.1 47.6 23.7 27.6 24.4 28.3
LC-6 NS(1), -ve long. LL, HFL, Min LL Lead, EP
2530.93
Acc 339.294 0 -14966 47.6278 -5.91 0.02 0.04 0.02 93.4 47.6 24.2 25.2 24.9 25.8
LC-7 NS(2), LWL, Min LL Acc, EP Lead 2008.24 478.019 0 -10495 31.7519 -5.23 0.02 0.72 0.02 1453.9 31.8 12.4 26.9 12.8 27.3
LC-8 NS(2), LWL, Min LL Lead, EP Acc 1962.47 353.867 0 -10801 41.2774 -5.50 0.02 0.45 0.02 875.3 41.3 14.8 23.5 15.3 24.1
LC-9 NS(2), HFL, Min LL Acc, EP Lead 1895.48 456.55 0 -10218 31.7519 -5.39 0.02 0.56 0.02 1060.1 31.8 13.2 23.8 13.7 24.2
LC-10 NS(2), HFL, Min LL Lead, EP Acc 1870.17 339.829 0 -10499 41.2774 -5.61 0.02 0.34 0.02 628.7 41.3 15.1 21.3 15.6 21.9
LC-11 NS(2)-ve long. LL, LWL, Min LL Lead, EP1962.47

Acc 300.304 0 -11215 41.2774 -5.71 0.02 0.24 0.02 462.0 41.3 16.8 21.4 17.4 22.0
LC-12 NS(2)-ve long. LL, HFL, Min LL Lead, EP1870.17
Acc 286.267 0 -10912 41.2774 -5.83 0.02 0.12 0.02 215.5 41.3 17.1 19.3 17.7 19.9

2711.84 565.649 158.282 -14331 914.534 -5.28 0.34 0.67 0.34 1804.1 914.5 11.4 29.4 24.2 42.2
2730.19 576.98 163.22 -14295 983.854 -5.24 0.36 0.71 0.36 1949.3 983.9 10.4 29.8 24.1 43.6
2488.94 534.61 158.282 -13448 914.534 -5.40 0.37 0.55 0.37 1361.7 914.5 11.4 25.0 24.2 37.8
2500.7 545.941 163.22 -13393 983.854 -5.36 0.39 0.59 0.39 1486.1 983.9 10.4 25.3 24.2 39.0

2617.57 588.93 158.282 -13952 914.534 -5.33 0.35 0.62 0.35 1622.8 914.5 11.4 27.6 24.2 40.3
2635.92 600.261 163.22 -13916 983.854 -5.28 0.37 0.67 0.37 1768.0 983.9 10.4 28.0 24.1 41.7
2397.63 560.249 158.282 -13072 914.534 -5.45 0.38 0.50 0.38 1194.1 914.5 11.4 23.3 24.1 36.0
2409.39 571.58 163.22 -13017 983.854 -5.40 0.41 0.55 0.41 1318.6 983.9 10.4 23.5 24.1 37.3

2718.33
Sx=1,Sz=0.3,Sy=0.3
515.039 163.22 -14643 983.854 -5.39 0.36 0.56 0.36 1531.4 983.9 12.4 27.6 26.1 41.4
2619.21
Sx=1,Sz=0.3,Sy=0.3
498.525 163.22 -14349 983.854 -5.48 0.38 0.47 0.38 1235.8 983.9 12.9 25.2 26.6 38.9
NET BASE PRESSRE CALCULATION
T-T
LWL A' A1' D' D1' Comb-1 Comb-2 Comb-3
B B1 C1 C Earth fill 17 14.8 0 0 1.35 1 1.35
eL footing 2 4.75 2 4.75 1.35 1 1.35
8.5 Comb-1 25.65 26.3925 2.7 6.4125

L-L eT Comb-2 19 19.55 2 4.75
Comb-3 25.65 26.3925 2.7 6.4125
HFL A' A1' D' D1' Comb-1 Comb-2 Comb-3

1.1 Earth fill 17.00 14.8 0 0 1.35 1 1.35
A A1 D1 D A' A1' D1' D' 0.8 footing 2 4.75 2 4.75 1.35 1 1.35
8.6 1.2 2.1 8.6 1.2 2.1 Bouancy -4.01 -4.01 -0.8 -1.9 0.15 0.15 0.15
11.9 11.9 Comb-1 25.0485 25.791 2.58 6.1275

Comb-2 18.3985 18.9485 1.88 4.465
Comb-3 25.0485 25.791 2.58 6.1275
DESIGN OF HEEL SLAB
SUMMERY OF FORCES : Gross Base Pressure = P/ A ± M TT Average Gross Base Pressure at
NET BASE PRESSURE
*x / I TT ± M LL *z / I LL Critical points
S.N. Description base pressure at footing corners base pressure at footing corners base pressure at footing corners
A D B C A' A1' D' D1' A' A1' D' D1'
T/m2 T/m2 T/m2 T/m2 T/m2 T/m2 T/m2 T/m2 T/m2 T/m2 T/m2 T/m2
LC-1 NS(1), LWL, Min LL Acc, EP Lead 18.7 33.7 19.3 34.3 19.0 29.8 34.0 31.35 -6.7 3.4 31.3 24.9
LC-2 NS(1), LWL, Min LL Lead, EP Acc 21.4 30.0 22.0 30.6 21.7 27.9 30.3 28.79 -4.0 1.5 27.6 22.4
LC-3 NS(1), HFL, Min LL Acc, EP Lead 19.8 30.3 20.3 30.8 20.1 27.6 30.5 28.67 -5.0 1.8 27.9 22.5
LC-4 NS(1), HFL, Min LL Lead, EP Acc 21.8 27.5 22.5 28.2 22.2 26.3 27.9 26.86 -2.9 0.5 25.3 20.7
LC-5 NS(1), -ve long. LL, LWL, Min LL Lead, EP Acc

23.7 27.6 24.4 28.3 24.1 26.9 27.9 27.26 -1.6 0.5 25.2 20.8
LC-6 NS(1), -ve long. LL, HFL, Min LL Lead, EP Acc
24.2 25.2 24.9 25.8 24.6 25.2 25.5 25.32 -0.5 -0.6 22.9 19.2
LC-7 NS(2), LWL, Min LL Acc, EP Lead 12.4 26.9 12.8 27.3 12.6 23.1 27.1 24.54 -6.4 3.5 25.1 19.8
LC-8 NS(2), LWL, Min LL Lead, EP Acc 14.8 23.5 15.3 24.1 15.0 21.3 23.8 22.22 -4.0 1.8 21.8 17.5
LC-9 NS(2), HFL, Min LL Acc, EP Lead 13.2 23.8 13.7 24.2 13.5 21.1 24.0 22.16 -4.9 2.1 22.1 17.7
LC-10 NS(2), HFL, Min LL Lead, EP Acc 15.1 21.3 15.6 21.9 15.4 19.9 21.6 20.52 -3.0 0.9 19.7 16.1
LC-11 NS(2)-ve long. LL, LWL, Min LL Lead, EP Acc

16.8 21.4 17.4 22.0 17.1 20.4 21.7 20.89 -1.9 0.9 19.7 16.1
LC-12 NS(2)-ve long. LL, HFL, Min LL Lead, EP Acc
17.1 19.3 17.7 19.9 17.4 19.0 19.6 19.18 -1.0 0.0 17.7 14.7

11.4 29.4 24.2 42.2 17.8 30.8 35.8 32.63 -7.8 4.4 33.1 26.2
10.4 29.8 24.1 43.6 17.3 31.3 36.7 33.28 -8.4 4.9 34.0 26.9
11.4 25.0 24.2 37.8 17.8 27.6 31.4 29.00 -7.8 1.2 28.7 22.6
10.4 25.3 24.2 39.0 17.3 28.0 32.1 29.52 -8.3 1.6 29.4 23.1

11.4 27.6 24.2 40.3 17.8 29.5 34.0 31.11 -7.3 3.7 31.4 25.0
10.4 28.0 24.1 41.7 17.2 30.0 34.9 31.76 -7.8 4.2 32.3 25.6
11.4 23.3 24.1 36.0 17.8 26.4 29.7 27.56 -7.3 0.6 27.1 21.4
10.4 23.5 24.1 37.3 17.2 26.7 30.4 28.07 -7.8 1.0 27.8 21.9

12.4
Sx=1,Sz=0.3,Sy=0.3
27.6 26.1 41.4 19.2 30.3 34.5 31.81 -6.4 3.9 31.8 25.4
12.9
Sx=1,Sz=0.3,Sy=0.3
25.2 26.6 38.9 19.7 28.6 32.1 29.88 -5.3 2.8 29.5 23.8
FINDING BENDING MOMENT & SHEAR FORCE AT CRITICAL SECTION
T-T
B B1 C1 C
eL Overall depth at deff = 1.236 m
deff at criticacal section = 1.113 m
8.5
L-L eT deff
Design Bending Moment & Shear Force :
l1 1.113 Description Max BM SF. Max SF. BM
Tm T T Tm
1.1 Heel Slab (BM. Downward) -185.4 -28.8 -29.4 -180.5
A A1 D1 D A' A1' D1' E' D' 0.8
8.6 1.2 2.1 8.6 1.2 2.1 Heel Slab (BM. upward) 0.0
11.9 11.9 Toe slab (face of support) 69.7 63.9 63.9 69.7
l1 = Ponit of zero net base pressure
Toe slab (at deff from face of support) 33.8 24.5
DESIGN OF HEEL SLAB
SUMMERY OF FORCES : Ponit of BM at
NET BASE PRESSURE zero net Point of BENDING MOMENT & SHEAR FORCE
base zero base
S.N. Description base pressure at footing corners pressure pressure Heel Slab Toe Slab
A' A1' D' D1' E1' l1 BM BM SF BM|face SF|face SF|deff BM|deff
T/m2 T/m2 T/m2 T/m2 T/m2 m Tm Tm T Tm T T Tm

LC-1 NS(1), LWL, Min LL Acc, EP Lead -6.7 3.4 31.3 24.9 26.8 0 0 -121.5 -13.8 64.3 59.1 32.6 23.6
LC-2 NS(1), LWL, Min LL Lead, EP Acc -4.0 1.5 27.6 22.4 23.6 0 0 -78.9 -10.5 57.0 52.5 29.0 20.6
LC-3 NS(1), HFL, Min LL Acc, EP Lead -5.0 1.8 27.9 22.5 24.6 0 0 -99.9 -13.5 57.6 53.0 30.1 21.5
LC-4 NS(1), HFL, Min LL Lead, EP Acc -2.9 0.5 25.3 20.7 22.1 0 0 -64.6 -10.2 52.4 48.3 27.2 19.2
LC-5 NS(1), -ve long. LL, LWL, Min LL Lead, EP Acc

-1.6 0.5 25.2 20.8 22.1 0.00 0.00 -33.3 -4.8 52.4 48.4 27.3 19.2
LC-6 NS(1), -ve long. LL, HFL, Min LL Lead, EP Acc
-0.5 -0.6 22.9 19.2 20.6 0.00 0.00 -19.1 -4.5 47.8 44.2 25.5 17.8
LC-7 NS(2), LWL, Min LL Acc, EP Lead -6.4 3.5 25.1 19.8 21.5 0 0 -114.1 -12.3 51.4 47.1 26.1 19.0
LC-8 NS(2), LWL, Min LL Lead, EP Acc -4.0 1.8 21.8 17.5 18.6 0 0 -75.5 -9.3 44.8 41.2 22.7 16.3
LC-9 NS(2), HFL, Min LL Acc, EP Lead -4.9 2.1 22.1 17.7 19.5 0 0 -95.4 -12.0 45.6 41.8 23.8 17.2
LC-10 NS(2), HFL, Min LL Lead, EP Acc -3.0 0.9 19.7 16.1 17.3 0 0 -63.5 -9.1 40.8 37.6 21.2 15.1
LC-11 NS(2)-ve long. LL, LWL, Min LL Lead, EP Acc

-1.9 0.9 19.7 16.1 17.3 0.00 0.00 -36.1 -4.4 40.8 37.6 21.3 15.1
LC-12 NS(2)-ve long. LL, HFL, Min LL Lead, EP Acc-1.0 0.0 17.7 14.7 16.0 0.00 0.00 -24.0 -4.1 36.8 34.0 19.8 13.9

-7.8 4.4 33.1 26.2 27.0 0 0 -138.6 -14.7 67.9 62.3 32.9 23.8
-8.4 4.9 34.0 26.9 27.8 0 0 -145.7 -14.8 69.7 63.9 33.8 24.5
-7.8 1.2 28.7 22.6 23.4 0 0 -177.8 -28.4 58.8 53.8 28.6 20.6
-8.3 1.6 29.4 23.1 24.0 0 0 -185.4 -28.8 60.2 55.2 29.3 21.2

-7.3 3.7 31.4 25.0 25.7 0 0 -133.5 -15.3 64.5 59.2 31.4 22.6
-7.8 4.2 32.3 25.6 26.5 0 0 -140.6 -15.5 66.3 60.8 32.3 23.3
-7.3 0.6 27.1 21.4 22.2 0 0 -172.9 -29.0 55.6 50.9 27.1 19.5
-7.8 1.0 27.8 21.9 22.8 0 0 -180.5 -29.4 57.0 52.2 27.8 20.0

-6.4
Sx=1,Sz=0.3,Sy=0.3
3.9 31.8 25.4 26.2 0 0 -110.2 -10.9 65.4 60.1 32.0 23.0
LC-22 SIS(3)-ve long. LL, HFL, Min LL Lead, Seismic-5.3
Sx=1,Sz=0.3,Sy=0.3
2.8 29.5 23.8 24.6 0 0 -95.9 -10.6 60.8 55.9 30.2 21.5
DESIGN OF TOE SLAB :
(ULS) CHECK FOR BENDING MOMENT
Design Bending Moment MED = 69.7 Tm
al = d (shifting moment curve by a distance al )

1.1
D = 1.9 m */ overall depth at face of support
d = 1.815 m */ deff at face of support 0.8
D' = 0.949 m */ overall depth at d from face of support

d' = 0.86429 m */ deff at d from face of support
Clear Cover = 75 mm al
2.1
Ast Provided = 20 f @ 200 c/c
+ 20 f @ 200 c/c ALTERNATE
2
= 3141.59 mm /m
Grade of Concrete fck = 35 Mpa fyk = 500 Mpa

Grade of steel fyk = 500 Mpa euk = 0.0045
eud = 0.00405
xu = 0.87 fyk Ast / 0.362 fck b fck = 35 Mpa
= 107.861 mm ecu2 = 0.0035
xumax/d = 0.46358
xumax = 0.464 d'
= 400.662 mm UNDER REINFORCED
Ast calculated = M/ 0.87 fyk (d'-0.416 xu)
2
= 1956.51 mm /m
Ast minimum = 0.15% * b*d

2
= 2722.5 mm /m
Ast required = Max( 1956.51 , 2722.5 )

2 2
= 2722.5 mm /m < 3141.59 mm /m OK
Distribution steel = 25% of Ast.main (Refer clause 16.6.1 of IRC :112-2011)

2
= 785.398 mm /m
Provide distribution steel as 12 f @ 130 c/c
2
869.98 mm /m OK
(SLS) CHECK FOR STRESSES (RARE & QUASI PERMANENT LOAD COMBINATIONS)
Design Bending Moment MRARE = 45.72 Tm

MQP = 39.82 Tm
MST = MRARE - MQP (Bending Moment due to short term loading)
= 5.89 Tm
For short term loading Ecm = 32308.2 Mpa
Creep coefficent f = 1
For long term loading Ecm' = 16154.1 Mpa
2
Reinf. modulus of elasticity Es = 200000 N/mm
Modular ratio for QP Combination = Es / Ecm' = 12.381
Equavelent Modulus of Elasticity for Rare Combination :

Ec,eq = Ecm*(MQP+MST) = 17267 MPa
MST +(1+f)* MQP
Modular ratio for Rare Combination = Es/ Ec,eq = 11.58
Formula used for calculation of stress

dc (depth of neutral axis) = -m*As +  ( m2 * As2 + 2* m*As*b* d )
b
INA (Transformed) = b *dc3/3 + m* As *(d-dc)2
Compressive stress in concrete sc = MRARE* dc / INA

Tensile stress in steel ss = m* MRARE* (d - dc ) / INA
Description Stress Check For Rare Combination Stress Check For QP Combination
Design Moment = 45.72 Tm = 39.82 Tm
Total Depth at section = 1.9 m = 1.9 m
deff = 1.815 m = 1.815 m
width b = 1m = 1m
2 2
Ast, provided = 3141.59 mm /m = 3141.59 mm /m
Modular ratio = 11.58 = 12.38
dc (depth of neutral axis) = 328.87 mm = 338.86 mm
INA (Transformed) = 9.22E+10 mm4 = 9.77E+10 mm4
2 2
Compressive stress in concrete sc = 1.63 N/mm = 1.38 N/mm
2 2
Permissible Compressive stress = 16.8 N/mm OK = 12.6 N/mm OK
2 2
Tensile stress in steel ss = 85.33 N/mm = 74.48 N/mm
2 2
Permissible tensile stress = 400 N/mm OK = 400 N/mm OK
(SLS) CHECK FOR CRACK WIDTH (QUASI PERMANENT LOAD COMBINATIONS)
Minimum Reinforcement for crack control :
As,min = kc k fct,eff Act / ss ( IRC 112 / clause 12.3.3 (2) )
For Web
kc = 0.4 For Bending member
h = 1.9 m , b = 1m
k = 0.65
fcteff = fctm
= 2.77 Mpa
Act = Area of concrete within tensile zone just before the first crack form, section behaves
elastically until the tensile fiber stress reaches fctm. hence Neutral axis depth will be
considered for gross section
Act = b * h/2
2
= 0.95 m
ss = Maximum stress permitted in reinf. Immediately after formation of crack

= fyk
= 500 Mpa
2 2
Asmin = 1369.01 mm /m < 3141.59 mm /m OK
Calculation of crack width : ( IRC 112 / clause 12.3.4)

wk,max = 0.3 mm
Clear cover c = 75 mm
Bar dia feq = 20.00 mm
5 (c +feq/2) = 425 mm
Spacing b/w bars = 100 mm < 425 mm

The Following formula can be used for
srmax = Maximum crack spacing calculation of maximum crack spacing.
= 3.4c + 0.17 f /rPeff
= 484.979 mm
hc,eff = Min 2.5 ( h - d ) h = 1.9 m

( h - x/3 ) d = 1.815 m
h/2 x = 0.33886 m */ (for Quasi Permanent Load
= 0.2125 m combination)
width b = 1m
2
Ac,eff = hc,eff *b = 0.2125 m
rP,eff = As/ Ac,eff

= 3141.59 / 212500
= 0.01478
ssc = Stress in tension Reinforcement assuming cracked section
= 74.48 Mpa */ (for Quasi Permanent Load combination)
Es = 200000 Mpa
Ecm' = 16154.1 Mpa */ (for Long term loading)
ae = Es/Ecm
ae = 12.3807
kt = 0.5 (factor dependent on duration of load)
esm - ecm = Max ssc - kt fct,eff ( 1+ ae rP,eff ) / rP,eff

Es
0.6 ssc / Es
= 0.00022
wk = srmax ( esm - ecm )

= 0.108 mm < 0.3 mm OK
(ULS) CHECK FOR SHEAR FORCE (Section At deff from face of Support)
Factored Shear Force VED = 33.80 T
Corresponding BM MED = 24.47 Tm
VCCD = Reductin in Shear force due to inclined compression chord

= MED / d * sinb
b = 27.646 deg */Inclination amgle of compression chord.
VCCD = 10.005 T
Design Shear Force VNS = VED - VCCD

= 23.79 Tonne
Reduction in Design Shear For Within Zone ( av = 0.5d to 2d)

av = 1.815 m
Reduction factor b1 = av/2d

= 0.5
Design Shear Force VNS' = b1 * VNS

= 11.90 Tonne
Max Shear Capacity of section

n = 0.6 * ( 1- fck /310) */ fck in Mpa
= 0.53226
fcd = 0.447 *fck

= 15.63 Mpa
VRDC, max = 0.5 bw d n fcd
= 359.585 Tonne > 11.90 Tonne OK
D' = 0.949 m */ overall depth at face of support

d' = 0.864 m */ deff at face of support
Check for Design Shear Reinforcement :

k = Min 1 + √ 200/d d is depth in mm
2
k = 1.48105
r1 = Min Asl /bw d

0.02
r1 = 0.00363
scp = 0 Mpa
nmin = 0.031 k3/2 fck1/2

= 0.33056
VRdc = Max ( 0.12 k (80 r1 fck )0.33 + 0.15 scp ) bw d ( IRC 112 / clause 10.3.2 (2) )
(nmin +0.15scp ) bw d
= 33.0318 Tonne > 11.90 Tonne NO SHEAR REINFORCEMENT REQUIRED

DESIGN OF HEEL SLAB :
(ULS) CHECK FOR BENDING MOMENT
al = d (shifting moment curve by a distance al )

1.1
d = 1.815 m */ deff at face of support 0.8
D' = 1.668 m */ overall depth at d from face of support

d' = 1.583 m */ deff at d from face of support
Clear Cover = 75 mm al
8.6
+ 20 f @ 200 c/c ALTERNATE
2
= 3141.59 mm /m

eud = 0.00405
= 107.861 mm ecu2 = 0.0035
xumax/d = 0.46358
xumax = 0.464 d
Ast calculated = M/ 0.87 fyk (d-0.416 xu)

2
= 2771.27 mm /m

2
= 2722.5 mm /m
Ast required = Max( 2771.27 , 2722.5 )

2 2
= 2771.27 mm /m < 3141.59 mm /m OK
Distribution steel = 25% of Ast.main (Refer clause 16.6.1 of IRC :112-2011)

2
= 785.398 mm /m
Provide distribution steel as 16 f @ 150 c/c
2
1340.41 mm /m OK
(ULS) CHECK FOR SHEAR FORCE (Section At Face of Support)
Factored Shear Force VED = 29.43 T
Corresponding BM MED = 180.54 Tm
VCCD = Reduction in Shear force due to inclined compression chord

= MED / d * sinb
b = 7.28895 deg */Inclination amgle of compression chord.
VCCD = 12.6201 T
Design Shear Force VNS = VED - VCCD

= 16.81 Tonne

n = 0.6 * ( 1- fck /310) */ fck in Mpa
= 0.53226
fcd = 0.447 *fck

= 15.63 Mpa

= 755.128 Tonne > 16.81 Tonne OK

d = 1.815 m */ deff at face of support
Check for Design Shear Reinforcement :

2
k = 1.33195
r1 = Min Asl /bw d

0.02
r1 = 0.00173
scp = 0 Mpa
nmin = 0.031 k3/2 fck1/2

= 0.28192
= 51.1689 Tonne > 16.81 Tonne NO SHEAR REINFORCEMENT REQUIRED

MQP = 22.11 Tm
= 64.40 Tm
2
Modular ratio for QP Combination = Es / Ecm = 6.19037

Ec,eq = Ecm*(MQP+MST) = 25732.3 MPa
MST +(1+f)* MQP

b

deff = 1.815 m = 1.815 m
width b = 1m = 1m
2 2
INA (Transformed) = 6.48E+10 mm4 = 5.28E+10 mm4
2 2
2 2
2 2
2 2
h = 1.9 m , b = 1m
k = 0.65
fcteff = fctm = 2.77 Mpa
2
Act = b * h/2 = 0.95 m
ss = fyk = 500 Mpa
2 2
Asmin = 1369.01 mm /m < 3141.59 mm /m OK

wk,max = 0.3 mm
5 (c +feq/2) = 425 mm

= 3.4c + 0.17 f /rPeff
= 484.979 mm
hc,eff = Min 2.5 ( h - d ) h = 1.9 m

( h - x/3 ) d = 1.815 m
width b = 1m
2
rP,eff = As/ Ac,eff

= 3141.59 / 212500
= 0.01478

Es = 200000 Mpa
ae = Es/Ecm
ae = 12.3807

esm - ecm = ssc
Max- kt fct,eff ( 1+ ae rP,eff ) / rP,eff
Es
0.6 ssc / Es
= 0.00012

= 0.059 mm < 0.3 mm OK
'------
DESIGN OF FOUNDATION
SLS LOAD COMBINATION
LC-1 QP, LWL Forces about toe LC-1

2) Backfill 992.5 -7721.738 0.0 1
5) Surfacing 13.5 -37.7 0.0 1

V HL HT MTT MLL
LC-1 QP, LWL 1944.8792 289.62855 0 -11174.28 0
LC-2 QP, HFL Forces about toe LC-2

2) Backfill 992.5 -7721.738 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 0.15

V HL HT MTT MLL
LC-2 QP, HFL 1845.7617 273.11399 0 -10880.17 0

LC-3 RARE, LWL, Min LL Leading Forces about toe LC-3
2) Backfill 992.5 -7721.738 0.0 1
5) Surfacing 13.5 -37.7 0.0 1

V HL HT MTT MLL
LC-3 RARE, LWL, Min LL Leading 1972.2515 374.95037 0 -10791.03 31.751855
LC-4 RARE, HFL, Min LL Leading Forces about toe LC-4

2) Backfill 992.5 -7721.738 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 0.15

V HL HT MTT MLL
LC-4 RARE, HFL, Min LL Leading 1873.134 358.43582 0 -10496.92 31.751855

LC-5 RARE,-ve LL long ,LWL, Min LL Leading Forces about toe LC-5
2) Backfill 992.5 -7721.738 0.0 1
5) Surfacing 13.5 -37.7 0.0 1

V HL HT MTT MLL
LC-5 RARE,-ve LL long ,LWL, Min LL Leading 1972.2515 333.74845 0 -11108.91 31.751855
LC-6 RARE, -ve LL long,HFL, Min LL Leading Forces about toe LC-6
2) Backfill 992.5 -7721.738 0.0 1
5) Surfacing 13.5 -37.7 0.0 1
8) Buoyancy -357.7 2338.5 0.0 0.15

V HL HT MTT MLL
LC-6 RARE, -ve LL long,HFL, Min LL Leading 1873.134 317.2339 0 -10814.79 31.751855
BASE PRESSRE CALCULATION
SLS LOAD COMBINATIONS
T-T Coordinates of basecorner Properties of Base

2
Edges x (m) z (m) Area 11.9x8.5 = 101.15 m
4
B B1 C1 C A -5.950 -4.250 ITT 8.5x11.9^3/12 = 1193.65 m
4
eL D 5.950 -4.250 ILL 11.9x8.5^3/12 = 609.007 m
B -5.950 4.250
8.5 C 5.950 4.250
L-L eT
A A1 D1 D
8.6 1.2 2.1
11.9

SUMMERY OF FORCES : Eccentricity of Eccentricity of Moment and Gross Base Pressure = P/ A ± M TT
*x / I TT ± M LL *z / I LL
V HL HT MTT MLL MTT/ V MLL/ V B/2-eL1 eT1 V*eL V*eT A D B C

2 2 2
Tonne Tonne Tonne Tm Tm m m m m Tm Tm T/m T/m T/m T/m2
LC-1 QP, LWL 1944.88 289.629 0 -11174.3 0 -5.75 0.00 0.20 0.00 397.8 0.0 17.2 21.2 17.2 21.2
LC-2 QP, HFL 1845.76 273.114 0 -10880.2 0 -5.89 0.00 0.06 0.00 102.1 0.0 17.7 18.8 17.7 18.8
LC-3 RARE, LWL, Min LL Leading 1972.25 374.95 0 -10791 31.7519 -5.47 0.02 0.48 0.02 943.9 31.8 14.6 24.0 15.0 24.4
LC-4 RARE, HFL, Min LL Leading 1873.13 358.436 0 -10496.9 31.7519 -5.60 0.02 0.35 0.02 648.2 31.8 15.1 21.5 15.5 22.0
LC-5 RARE,-ve LL long ,LWL, Min LL Leading1972.25 333.748 0 -11108.9 31.7519 -5.63 0.02 0.32 0.02 626.0 31.8 16.2 22.4 16.6 22.8
LC-6 RARE, -ve LL long,HFL, Min LL Leading1873.13 317.234 0 -10814.8 31.7519 -5.77 0.02 0.18 0.02 330.4 31.8 16.7 19.9 17.1 20.4
NET BASE PRESSRE CALCULATION
T-T
LWL A' A1' D' D1' Comb-1
B B1 C1 C Earth fill 17 14.8 0 0 1
eL footing 2 4.75 2 4.75 1
8.5 Comb-1 19 19.55 2 4.75

L-L eT
HFL A' A1' D' D1' Comb-1

1.1 Earth fill 17.00 14.8 0 0 1
A A1 D1 D A' A1' D1' D' 0.8 footing 2 4.75 2 4.75 1
8.6 1.2 2.1 8.6 1.2 2.1 Bouancy -4.01 -4.01 -0.8 -1.9 0.15
11.9 11.9 Comb-1 18.3985 18.9485 1.88 4.465
DESIGN OF HEEL SLAB

SUMMERY OF FORCES :
Gross Base Pressure = P/ A ± M TT Average Gross Base Pressure at
NET BASE PRESSURE
*x / I TT ± M LL *z / I LL Critical points
S.N. Description base pressure at footing corners base pressure at footing corners base pressure at footing corners
A D B C A' A1' D' D1' A' A1' D' D1'
T/m2 T/m2 T/m2 T/m2 T/m2 T/m2 T/m2 T/m2 T/m2 T/m2 T/m2 T/m2
LC-1 QP, LWL 17.2 21.2 17.2 21.2 17.2 20.1 21.2 20.51 -1.8 0.6 19.2 15.8
LC-2 QP, HFL 17.7 18.8 17.7 18.8 17.7 18.5 18.8 18.58 -0.7 -0.5 16.9 14.1
LC-3 RARE, LWL, Min LL Leading 14.6 24.0 15.0 24.4 14.8 21.6 24.2 22.54 -4.2 2.0 22.2 17.8
LC-4 RARE, HFL, Min LL Leading 15.1 21.5 15.5 22.0 15.3 20.0 21.7 20.61 -3.7 0.4 19.7 15.9
LC-5 RARE,-ve LL long ,LWL, Min LL Leading 16.2 22.4 16.6 22.8 16.4 20.9 22.6 21.52 -2.6 1.3 20.6 16.8
LC-6 RARE, -ve LL long,HFL, Min LL Leading 16.7 19.9 17.1 20.4 16.9 19.3 20.2 19.58 -2.1 -0.3 18.2 14.8
FINDING BENDING MOMENT & SHEAR FORCE AT CRITICAL SECTION
T-T
B B1 C1 C
eL Overall depth at deff = 1.236 m
deff at criticacal section = 1.113 m
8.5
L-L eT deff
Design Bending Moment & Shear Force :
l1 1.113 Description Rare QS
Tm Tm
1.1 Heel Slab (BM. Downward) LWL -78.5 -36.4
A A1 D1 D A' A1' D1' E' D' 0.8 HFL -86.5 -22.1
8.6 1.2 2.1 8.6 1.2 2.1
Toe slab (face of support) LWL 45.7 39.8
11.9 11.9 HFL 40.7 35.2
l1 = Ponit of zero net base pressure
DESIGN OF HEEL SLAB

SUMMERY OF FORCES : Ponit of BM at
NET BASE PRESSURE zero net Point of BENDING MOMENT & SHEAR FORCE
base zero base
S.N. Description base pressure at footing corners pressure pressure Heel Slab Toe Slab
A' A1' D' D1' E1' l1 BM BM SF BM|face SF|face SF|deff BM|deff
T/m2 T/m2 T/m2 T/m2 T/m2 m Tm Tm T Tm T T Tm

LC-1 QP, LWL -1.8 0.6 19.2 15.8 16.6077 0.00 0.00 -36.4 -5.1 39.8 36.7 20.4532 14.4467
LC-2 QP, HFL -0.7 -0.5 16.9 14.1 15.0739 0.00 0.00 -22.1 -4.9 35.2 32.5 18.6822 13.0249
LC-3 RARE, LWL, Min LL Leading -4.2 2.0 22.2 17.8 19.0291 0.00 0.00 -78.5 -9.3 45.7 42.0 23.2347 16.7017
LC-4 RARE, HFL, Min LL Leading -3.7 0.4 19.7 15.9 17.3207 0.00 0.00 -86.5 -14.2 40.7 37.4 21.1873 15.1737
LC-5 RARE,-ve LL long ,LWL, Min LL Leading -2.6 1.3 20.6 16.8 18.0372 0.00 0.00 -48.1 -5.5 42.6 39.3 22.1163 15.7624
LC-6 RARE, -ve LL long,HFL, Min LL Leading -2.1 -0.3 18.2 14.8 16.3289 0.00 0.00 -56.1 -10.4 37.6 34.6 20.0689 14.2344
UNFACTORED FORCES FOR DESIGN OF SHAFT :
SELFWEIGHT OF ABUTMENT
RCC Density = 2.5 t/m3
water density gwater = 1 t/m3
Soil Density gsoil = 2 t/m3
Thickness of wearing coat = 0.065 m

Depth of super-structure = 1.52 m
ABUTMENT COMPONENT :-
Length of Abutment = 8.5 m
1.52
0.3 1.22
FRL : 239.000
1 0.5 2.169
Cap Top : 236.831
2 0.6
4 3 5
0
0.5 4a
0.52 1 0 7.4 HFL : 233.71
4.631
LWL : 231.6
6
7 8
SHAFT BOTTOM : 231.6
0 0.2 1.1
8.6 1.2 2.1
0.8 FDN 229.7
Calculating Selfweight of Sub-structure :

Forces @ Base of abutment shaft
eL = Cg. w.r.t. c/L of shaft, at bottom of abutment shaft.
eY = Cg. From base of abutment shaft.
Element Area Factor B H L V W eY eL

3
m m m m Tonne m m
Dirt Wall & Abutment Cap
1 1 0.3 2.169 8.5 5.53 13.83 6.32 -0.97
2 1 1.52 0.6 8.5 7.752 19.38 4.93 -0.36
3 1 1 0 8.5 0 0.00 4.63 -0.1
4 0.5 0.52 0 8.5 0.00 0.00 4.63 -0.77333
4a 0.5 0.52 0.5 8.5 1.11 2.76 4.46 -0.77333
5 0.5 0 0 8.5 0.00 0.00 4.63 0.400
Total 14.39 35.97 5.43 -0.63

*/ Increase Abutment cap weight by 0% on account of bearing, bearing pedestal, stopper etc.
Abutment Cap weight Considered 14.39 35.97 5.43 -0.63
Abutment Shaft
6 1 1 4.63 8.5 39.36 98.4 2.32 -0.1
7 0.5 0 4.63 8.5 0.00 0.0 1.54 -0.6
8 0.5 0.2 4.63 8.5 3.94 9.8 1.54 0.467
Abutment shaft weight considered. 43.30 108.24 2.25 -0.05
Total Sub-structure self weight at base of shaft 57.69 144.21 3.04 -0.19
Total Weight of sub-structure & foundation = 144.21 T

Calculation of Byouency
Element Area Factor No.s B H L V W eY eL
3
m m m m Tonne m m
Earth Fill Weight

6 1 -1 1.11 2.11 8.50 -19.89 -19.89 1.06 -0.05
7 0.5 -1 0.00 2.11 8.50 0.00 0.00 0.70 -0.60
8 0.5 -1 0.09 2.11 8.50 -0.82 -0.82 0.70 0.53925
Total Earth Fill -20.70 -20.70 1.04 -0.02
Total buoyant weight = -20.70 T

Forces due to Super-Structure DL, at Shaft Bottom:

Vertical Load (Sup DL Reaction) = 107.96 Tonne
Cg. From Deck Top = 0.56 m

Moment MLL = 0 Tm
Cg. From base slab bottom = 6.775 m

Forces due to Super-Structure SIDL, at Shaft Bottom:
Vertical Load (Sup SIDL Reaction) = 17.96 Tonne
Cg. above Deck Top = 0.40 m

Forces due to Super-Structure Surfacing , at Shaft Bottom:

Vertical Load (Sup Surfacing Reaction) = 13.47 Tonne
Cg. above Deck Top = 0.03 m

Forces due to LL , at Shaft Bottom: Max Reaction Min Reaction

Vertical Load (CW LL Reaction) = 72.63 Tonne 27.37 Tonne
Lever arm about toe (along L-L axis) = -0.1 m -0.1 m
Moment MTT = -7.26277 Tm -2.73723 Tm
Lever arm about c/L base (along T-T axis) = 1.16 m 1.16 m
Moment MLL = 84.25 Tm 31.75 Tm
Forces due to LL Longitudinal Forces, at Shaft Bottom:

Longitudinal Force = 20.6 Tonne
Lever arm from footing base = 5.815 m
Moment in about transverse axis MTT = 119.8 tm
Seismic Component of Permanent Load (DL+SIDL+SURFACING), at Shaft Bottom:

At Fixed End, Force about V HL HT ey eL MLL MTT
toe T T T m m Tm Tm

Summery of LL seismic component transferred from super-structure, at Shaft Bottom:
T T T m m Tm Tm

T T T m m Tm Tm
SEISMIC COMPONENT OF SUB-STRUCTURE :

Sub-structure seismic component :

Description W ey ex W = Weight of sub-structure
Tonne m m ey = Cg. above base slab in vertical direction
Sub-structure = 144.2 3.0 -0.2
Seismic Component V HL HT ey eL MLL MTT

T T T m m Tm Tm
Earthfill seismic component :

Description W ey Seismic Over Earth Fill is considered over Traingular
Tonne m wedge of earth only.
Backfill Weight = 242.30 4.933
Seismic Component V HL HT ey eL MLL MTT

T T T m m Tm Tm
Seismic Vertical 0.0 0.0

FLUID PRESSURE CALCULATION FOR SHAFT DESIGN :
3
Fluid density = 0.48 t/m
FRL 239.000
7.4
1
SHAFT BOTTOM 231.600
2
3.55 t/m
Fluid Pressure
Total Fluid Presure

T/m2 m m Tonne m
1 0.5 3.552 7.4 8.5 111.71 2.46667
Total 111.71 2.467
Total fluid Pressure = 111.71 Tonne

Lever arm = 2.47
SUMMARY FLUID PRESSURE :

Description Fluid Pressure
Tonne Tm
EARTH PRESSURE CALCULATION FOR SHAFT DESIGN :

o
f = 35 = 0.611 Radians
o
d = 22.5 = 0.393 Radians
o
o
i = 0 = 0 Radians
o
a = 90.00 = 1.571 Radians
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
2

Shaft width B = 1.2 m
Ko Dry = 0.42642
Ko' Submerged = 0.42642
1) LWL CONDITION
Ko = 0.42642
Ko' = 0.42642
3
gdry = 2 t/m
3
gsub = 1 t/m
o
d = 22.5
o
dsubmerged = 11.25
2
q = 2.4 t/m
L = 8.5 m
B = 1.2 m
FRL 239.000
7.4 4
1
LWL 231.600 1.023 t/m2
2
6.311 t/m
0 2 5
3
2
Kagh = 6.311 t/m Ka*q 1.023 t/m2

1 0.5 6.31107 7.4 8.5 198.48 22.5 183.37 3.108 75.96 -0.6
2 1 6.31107 0 8.5 0.00 11.25 0.00 0 0.00 -0.6
3 0.5 0 0 8.5 0.00 11.25 0.00 0.000 0.00 -0.6
Total 198.483 183.374 2.871 75.9562 -0.6

Lever arm = 2.87

Lever arm = -0.60 m

2
T/m m m Tonne m
4 1 1.02342 7.4 8.5 64.3729 3.7

5 1 1.02342 0 8.5 0 0
Total 64.3729 3.7

2) HFL CONDITION
Ko = 0.42642
Ko' = 0.42642
3
gdry = 2 t/m
3
gsub = 1 t/m
o
d = 22.5
o
dsubmerged = 11.25
2
q = 2.4 t/m
L = 8.5 m
B = 1.2 m
FRL 239.000
5.29 4
1
2
HFL 233.710 1.023 t/m
2
4.512 t/m
2.11 2 5
3
2 2
Kagh = 5.411 t/m Ka*q 1.023 t/m

2
1 0.5 4.51156 5.29 8.5 101.43 22.5 93.71 4.3318 38.82 -0.6
2 1 4.51156 2.11 8.5 80.91 11.25 79.36 1.055 15.79 -0.6
3 0.5 0.89975 2.11 8.5 8.07 11.25 7.91 0.703 1.57 -0.6
Total 190.415 180.984 2.601 56.17583 -0.6

Lever arm = 2.60

Lever arm = -0.60 m

T/m2 m m Tonne m
4 1 1.02342 5.29 8.5 46.0179 4.755

5 1 1.02342 2.11 8.5 18.355 1.055
Total 64.3729 3.7

SUMMERY EARTH PRESSURE :
Tonne Tm Tonne Tm
75.96 -45.6

56.18 -33.7
SUMMERY SURCHARGE PRESSURE :

Tonne Tm

DYNAMIC EARTH PRESSURE CALCULATION FOR SHAFT DESIGN :
Ko Dry = 0.426
Ko' Ssubmerged = 0.426

o
f = 35 = 0.61087 Radians
o
d = 22.5 = 0.3927 Radians
o
o
i = 0 = 0 Radians
a = 90 o = 1.5708 Radians
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
2

Shaft width B = 1.2 m
ah = 0.18
av = 0.36
1 ± av
-1
(gsat - 1) (1 ± av)


Ka = 0.42642
Ka' = 0.42642
Ca = 0.447
Ca' = 0.592
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
d = 22.5 deg
2
q = 2.4 t/m
L = 8.5 m
B = 1.2 m
0.50 =3*(Ca'-Ka')
0.06 =3*(Ca-Ka)
FRL
Water Level
h'
SHAFT BOTTOM
0.92 1.19
0.23 0.15
FRL 239.000
7.4 7.4
7.4
LWL 231.600
0 0

Pressure

p_mid_height = 0.23 t/m2 p_mid_height = 0.92 t/m2
h = 7.4 m h = 7.4 m
y = 3.7 m y = -3.7 m
L = 8.5 m L = 8.5 m
T deg. T m T m

Lever arm = 3.70

Lever arm = -0.60 m

2 2
2 2
h-h' = 7.4 m h = 0m
L = 8.5 m L = 8.5 m

T/m m


Ka = 0.42642
Ka' = 0.42642
Ca- = 0.296
Ca-' = 0.562
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
d = 22.5 deg
2
q = 2.4 t/m
L = 8.5 m
B = 1.2 m
0.41 =3*(Ca'-Ka')
0.00 =3*(Ca-Ka)
FRL
Water Level
h'
SHAFT BOTTOM
0.75 0.97
0.00 0.00
FRL 239.000
7.4 7.4
7.4
LWL 231.600
0 0

Pressure

h = 7.4 m h = 7.4 m
y = 3.7 m y = -3.7 m
L = 8.5 m L = 8.5 m

T deg. T m T m
Total Dynamic Earth Pressure 0.0 0.0 0.0 0.0 0

Lever arm = 0.00

Lever arm = 0.00 m
Moment MTT = 0 Tm

2 2
2 2
h-h' = 7.4 m h = 0m
L = 8.5 m L = 8.5 m

T/m m


Ka = 0.42642
Ka' = 0.42642
Ca = 0.447
Ca' = 0.592
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
d = 22.5 deg
2
q = 2.4 t/m
L = 8.5 m
B = 1.2 m
0.50 =3*(Ca'-Ka')
0.06 =3*(Ca-Ka)
FRL
Water Level
h'
SHAFT BOTTOM
0.92 1.19
0.23 0.15
FRL 239.000
5.29 7.4
7.4
HFL 233.710
2.11 2.11

Pressure

h = 7.4 m h = 7.4 m
y = 1.59 m y = -1.59 m
L = 8.5 m L = 8.5 m

T deg. T m T m

Lever arm = 2.79

Lever arm = -0.60 m

2 2
2 2
h-h' = 5.29 m h = 2.11 m
L = 8.5 m L = 8.5 m

T/m m


Ka = 0.42642
Ka' = 0.42642
Ca- = 0.296
Ca-' = 0.562
3
gdry = 2 t/m
3
gsat = 2 t/m
3
gsub = 1 t/m
d = 22.5 deg
2
q = 2.4 t/m
L = 8.5 m
B = 1.2 m
0.41 =3*(Ca'-Ka')
0.00 =3*(Ca-Ka)
FRL
Water Level
h'
SHAFT BOTTOM
0.75 0.97
0.00 0.00
FRL 239.000
5.29 7.4
7.4
HFL 233.710
2.11 2.11

Pressure

h = 7.4 m h = 7.4 m
y = 1.59 m y = -1.59 m
L = 8.5 m L = 8.5 m

T deg. T m T m

Lever arm = 1.37

Lever arm = -0.60 m

2 2
2 2
h-h' = 5.29 m h = 2.11 m
L = 8.5 m L = 8.5 m

T/m m
Trapozial Portion above water Level 0.00 0

SUMMERY DYNAMIC EARTH PRESSURE :

Tonne Tm Tonne Tm

Vertical Component 0.00 0.00



Tonne Tm
------
DESIGN OF SHAFT
ULS LOAD COMBINATION
LC-1 NS, LWL, EP Lead, Min LL Acc Forces about toe LC-1
1) Sub-structure & Foundation 144.2 -27.8 0.0 1
5) Surfacing 13.5 -1.3 0.0 1
S.N. Description Forces at bottom of abutment shaft

V HL HT MTT MLL
LC-1 NS, LWL, EP Lead, Min LL Acc 315.08277 376.00031 0 1168.5335 36.514634
LC-2 NS, LWL, EP Acc, Min LL Lead Forces about toe LC-2
5) Surfacing 13.5 -1.3 0.0 1

V HL HT MTT MLL
LC-2 NS, LWL, EP Acc, Min LL Lead 324.66307 291.52341 0 946.23124 47.627783
LC-3 SIS, LWL, Min LL, Seismic Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-3
5) Surfacing 13.5 -1.3 0.0 1
14) Dynamic Surcharge Pressure 0.3
21) Super-Structure DL, SIDL, & Surfacing Component 50.2 -5.0 0.45

V HL HT MTT MLL
LC-3 SIS, LWL, Min LL, Seismic Sx=1,Sz=0.3,Sy=0.3 335.9099 329.42408 70.246219 1161.7337 359.89665
LC-4 SIS, LWL, Min LL, Seismic Sx=1,Sz=0.3,Sy=-0.3 Forces about toe LC-4
5) Surfacing 13.5 -1.3 0.0 1
21) Super-Structure DL, SIDL, & Surfacing Component 50.2 -5.0 -0.45

V HL HT MTT MLL
LC-4 SIS, LWL, Min LL, Seismic Sx=1,Sz=0.3,Sy=-0.3242.24828 314.57821 70.246219 1118.7525 359.89665
LC-5 NS, HFL, EP Lead, Min LL Acc Forces about toe LC-5
5) Surfacing 13.5 -1.3 0.0 1
8) Buoyancy -20.7 0.5 0.0 0.15

V HL HT MTT MLL
LC-5 NS, HFL, EP Lead, Min LL Acc 311.97705 372.41427 0 1084.8321 36.514634
LC-6 NS, HFL, EP Acc, Min LL Lead Forces about toe LC-6
5) Surfacing 13.5 -1.3 0.0 1
8) Buoyancy -20.7 0.5 0.0 0.15

V HL HT MTT MLL
LC-6 NS, HFL, EP Acc, Min LL Lead 321.55735 289.13271 0 890.45359 47.627783
LC-7 SIS, HFL, Min LL, Seismic Sx=1,Sz=0.3,Sy=0.3 Forces about toe LC-7
5) Surfacing 13.5 -1.3 0.0 1
8) Buoyancy -20.7 0.5 0.0 0.15
21) Super-Structure DL, SIDL, & Surfacing Component 50.2 -5.0 0.45

V HL HT MTT MLL
LC-7 SIS, HFL, Min LL, Seismic Sx=1,Sz=0.3,Sy=0.3 332.80419 336.38675 70.246219 1118.7601 359.89665
LC-8 SIS, HFL, Min LL, Seismic Sx=1,Sz=0.3,Sy=-0.3 Forces about toe LC-8
5) Surfacing 13.5 -1.3 0.0 1
8) Buoyancy -20.7 0.5 0.0 0.15
21) Super-Structure DL, SIDL, & Surfacing Component 50.2 -5.0 -0.45

V HL HT MTT MLL
LC-8 SIS, HFL, Min LL, Seismic Sx=1,Sz=0.3,Sy=-0.3239.14256 322.08555 70.246219 1076.5205 359.89665
ULS CHECK FOR ABUTMENT SHAFT :
Check For Biaxial Bending Moment
As1 NRD = Ac fcd+As fyd
= 18023.9 Tonne
T T= a a
8500 MEDT MEDL
+ ≤ 1
As4 MEDT MRDL
L
As3
fck = 35 Mpa
As2 fcd = 15.6 Mpa
fyd = 434.8 Mpa
Ac = 10200000 mm2
2
L= 1200 As = 47790.7 mm

CHECK FOR MOMENT CAPACITY
Forces at bottom of abutment shaft
S.N. NED/ (MEDT /MRDT)a
Description MRTT MRLL
NED HL HT METT MELL NRD a +(MEDL /MRDL)a
Tonne Tonne Tonne Tm Tm Tm Tm Check
LC-1 NS, LWL, EP Lead, Min LL Acc 315.083 376 0 1168.53 36.5146 0.0 1 1626.3 8400.6 0.72 OK
LC-2 NS, LWL, EP Acc, Min LL Lead 324.663 291.523 0 946.231 47.6278 0.0 1 1631.2 8434.2 0.59 OK
335.91 329.424 70.2462 1161.73 359.897 0.02 1 1637.0 8473.7 0.75 OK
242.248 314.578 70.2462 1118.75 359.897 0.01 1 1589.1 8145.0 0.75 OK
LC-5 NS, HFL, EP Lead, Min LL Acc 311.977 372.414 0 1084.83 36.5146 0.02 1 1624.7 8389.7 0.67 OK
LC-6 NS, HFL, EP Acc, Min LL Lead 321.557 289.133 0 890.454 47.6278 0.02 1 1629.6 8423.3 0.55 OK
332.804 336.387 70.2462 1118.76 359.897 0.02 1 1635.4 8462.8 0.73 OK
239.143 322.086 70.2462 1076.52 359.897 0.01 1 1587.5 8134.1 0.72 OK
ULS SHEAR CHECK FOR ABUTMENT SHAFT :
Design Shear Resitance ( IRC 112 / clause 10.3.2 (2) )
As1 k = Min 1 + √ 200/d d is depth in mm
2
k = 1.40825
T T=
8500 r1 = Min Asl /bw d
As4 0.02
L 2
Asl = 31906.8 mm */ Reinforcement on tension face
As3 r1 = 0.00313
scp = Axial stress

As2
3/2 1/2
nmin = 0.031 k fck
= 0.30649
L= 1200
0.33
VRdc = Max ( 0.12 k (80 r1 fck ) + 0.15 scp ) bw d
fck = 35 Mpa (nmin +0.15scp ) bw d
fcd = 15.6333 Mpa
fyk = 500 Mpa
Max Shear Capacity
Ac = 10200000 mm2 n = 0.6 * ( 1- fck /310) */ fck in Mpa
2
As = 47790.7 mm = 0.53226

Reduction factor b = 0.5 for av < 0.5d = 4243.69 Tonne

Forces at bottom ( SHEAR CAPACITY (LONGITUDINAL DIRn)
S.N. of abutment shaft scp = Check
Description VRdc
NED HL bHL NED/AC
bHL < VRdc
Tonne Tonne Tonne N/mm2 Tonne
LC-1 NS, LWL, EP Lead, Min LL Acc 315.083 376 188 0.31 400.01 PROVIDE MINIMUM SHEAR LINKS
LC-2 NS, LWL, EP Acc, Min LL Lead 324.663 291.523 145.762 0.32 401.45 PROVIDE MINIMUM SHEAR LINKS
335.91 329.424 164.712 0.33 403.14 PROVIDE MINIMUM SHEAR LINKS
LC-5 NS, HFL, EP Lead, Min LL Acc 311.977 372.414 186.207 0.31 399.55 PROVIDE MINIMUM SHEAR LINKS
LC-6 NS, HFL, EP Acc, Min LL Lead 321.557 289.133 144.566 0.32 400.98 PROVIDE MINIMUM SHEAR LINKS
Minimum shear reinforcement
Overall width of section = 8500 mm
Overall depth of section = 1200 mm
Effective Cover at section = 123 mm
Effective depth of section = 1077 mm
Minimum shear reinforcement ratio (rmin) 0.072√fck = 0.00085

fyk
Shear reinforcement ratio (rw) ASW
(Refer clause 16.5.2 (5) of IRC :112-2011) s. bw .sina
Therefore,
2
ASW (min) /s = 7241.28 mm /m
Provide 10 f links @ 200 c/c in trans dirn & 300 c/c vertically
2
Asw/s provided 11126.5 mm /m OK
CHECK FOR ABUTMENT SHAFT SLENDERNESS RATIO: ( IRC 112 / clause 8.3.2 (3))
Ac = 10200000 mm2
2
As1 As = 47790.7 mm
fcd = 15.6 Mpa
fyd = 434.8 Mpa
Selenderness crateria
T
As4 Moment of Inertia about TT axis ITT = 1.224E+12 mm4
Moment of Inertia about LL axis ILL = 6.14125E+13 mm4
As3 L T=
8500 Radius of gyration along LL axis iL =  ITT /A
= 346.41 mm
Radius of gyration along TT axis iT =  ILL /A

As2 = 2453.74 mm
L= 1200
Clear Height of compression member lo = 5.23 m

Effective Length of column along LL -axis leL = 1.4 *lo
= 7.32 m
Selenderness ratio along L-L axis lL = leL/ iL

= 21.1393
Effective Length of column along TT -axis leT = 2.3 *lo

= 12.03 m
Selenderness ratio along TT axis lT = leT/ iT

= 4.90
Check lL / lT = 4.31 > 2 Check for limiting slenderness ratio

And lT / lL = 0.23 < 2 Ignore second order effect
SUMMERY OF FORCES AT BOTTOM OF SHAFT: CHECK FOR SLENDERNESS RATIO
eL = eT = (eL/L) / (eT/T) /
NED HL HT METT MELL eL /L eT /T CHECK
MTT/NED MLL/NED (eT/T) (eL/L)
LC-1 NS, LWL, EP Lead, Min LL Acc 315.1 376.0 0.0 1168.5 36.5 3.7 0.1 3.1 0.014 226.7 0.004 Check for limiting slenderness ratio
LC-2 NS, LWL, EP Acc, Min LL Lead 324.7 291.5 0.0 946.2 47.6 2.9 0.1 2.4 0.017 140.7 0.007 Check for limiting slenderness ratio
335.9 329.4 70.2 1161.7 359.9 3.5 1.1 2.9 0.126 22.9 0.044 Check for limiting slenderness ratio
LC-5 NS, HFL, EP Lead, Min LL Acc 312.0 372.4 0.0 1084.8 36.5 3.5 0.1 2.9 0.014 210.4 0.005 Check for limiting slenderness ratio
LC-6 NS, HFL, EP Acc, Min LL Lead 321.6 289.1 0.0 890.5 47.6 2.8 0.1 2.3 0.017 132.4 0.008 Check for limiting slenderness ratio
CHECK FOR ABUTMENT SHAFT SECOND ORDER FORCES: ( IRC 112 / clause 11.2.1)
Ac = 10200000 mm2
2
As1 As = 47790.7 mm
fcd = 15.6 Mpa
fyd = 434.8 Mpa
Selenderness crateria
T
As4 Moment of Inertia about TT axis ITT = 1.224E+12 mm4
T= Moment of Inertia about LL axis ILL = 6.14125E+13 mm4
As3 L 8500
Radius of gyration along LL axis iL =  ITT /A
= 346.41 mm
Radius of gyration along TT axis iT =  ILL /A

As2 = 2453.74 mm
L= 1200
Clear Height of compression member lo = 5.23 m

Effective length of column along L-L leL = 1.4 *lo
= 7.32 m
Selenderness ratio along L-L axis lL = leL/ iL

= 21.14
Effective Length of column along TT -axis leT = 2.3 *lo

= 12.03 m
Selenderness ratio along TT axis lT = leT/ iT

= 4.90
Finding Limiting Value of Slenderness Ratio.

llim = 20 A B C/ n
f(,to) = 1.11 Creep for abutment shaft

MoEqp/MoEd = Ratio of BM in Quasi Permanent LC of SLS to BM in Design LC of ULS
fef = f(,to) * MoEqp/MoEd
A = 1/ (1+0.2 fef)
w = As fyd / (Ac fcd)

= 0.130
B =  ( 1 + 2w )
= 1.123
rm = Mo1 /Mo2 (Ratio of First order moments at two ends of members

= 0
C = 1.7 - rm
= 1.7
n = NED / (Ac fcd)

= NED / 15946 */ (NED in Tonne)
SUMMERY OF FORCES AT BOTTOM OF SHAFT: CHECK FOR SECOND ORDER EFFECT ( along LL Axis)
S.N. ULS FORCES SLS (QP LC) Second Order Effect
MoEqp
NED METT MELL METT MELL fef A n llim (l <llim) : Ignore
/MoEd
Tonne Tm Tm Tm Tm (l >llim) : Consider
LC-1 315.1 1168.5 36.5 484.8 0.0 0.41 0.46 0.92 0.02 248.62 Ignore second order effect
CHECK FOR SECOND ORDER EFFECT ( along TT Axis)

Load Second Order Effect
MoEqp
Case fef A n llim (l <llim) : Ignore
/MoEd
(l >llim) : Consider
LC-1 0.00 0.00 1.00 0.02 271.57 Ignore second order effect
INTERACTION DIAGRAM : (P : MTT) SECTION AT SHAFT BOTTOM
Section Dimensions: Material Properties:

2
D = 1200 mm fck = 35 N/mm
2
As1 B = 8500 mm fyk = 500 N/mm
2
Es = 200000 N/mm
Reinforcement Details :
Dia Spacing Cover From To Y_Cg Remark
Reinf. Nos. Spacing
As3 mm mm mm m m m
T As4 8442 REINFORCEMENT ACROSSAXIS OF BENDING:
As1 16 130 50 217.5 1012 4192 7 132.417
T = 8500 As2 16 130 50 217.5 1012 -4192 7 132.417
L REINFORCEMENT ALONG AXIS OF BENDING:
As3 25 130 75 58 8442 -512.5 65 131
0 130 0 0 0 0 0 0 NONE
As4 16 130 50 58 8442 542 65 131
As2
2
As tension face (Length) = 31906.8 mm
2
1012 18000 As Compression face (Length) = 13069 mm
2
L= 1200 INTERACTION DIAGRAM (Pu : MuTT) As tension face (wiidth) = 1407.43 mm
16000 2
As Compression face (width) = 1407.43 mm
2
NA xu 14000 Total As = 47790.7 mm
= 0.47 %
12000
Pu Mu
xu/D
T Tm Balance Failure
Pu ( T )
10000
1E-09 -2078.9 401.388 d1 1112.5 mm
0.2 1646.47 2307.56 8000 xu 686.728 mm
0.4 4286.9 3094.15 xu/D 0.57227
0.6 7094.53 3262.4 6000 Pu 6562.69 T
0.8 10570.8 2560.14 Mu 3343.76 Tm
4000
1 13704.9 1531.71
1.2 15354.2 802.93 2000
1.4 16135.9 454.806
1.6 16574.4 258.147 0
0 500 1000 1500 2000 2500 3000 3500 4000
1.8 16848.4 134.506
2 17032.9 50.7862 Mu (Tm)
Formula Used In Construction of Intraction Diagram :
Pu = Cc+ Cs
Mu = Mc + Ms
Cc = 0.361*fck*xu*b xu ≤ D
0.447*fck*(1 - 4*g/21)*b *D xu > D
2
g = 16 / ( 7xu / D - 3 )
Cs = S ( fsi -fci) Asi
fci = 0 esi ≤ 0
0.447fck esi ≥ 0.002
2
0.447fck [ 2 * (esi / 0.002) -(esi / 0.002) ] otherwise
fsi = -0.87 fy esi ≤ -0.00217

esi* Es esi > -0.00217 esi ≤ 0.00217
0.87 fy esi > 0.00217
Mc = Cc * ( 0.5D - x )
Ms = S Csi * yi
x = 0.416 xu xu ≤ D
(0.5 - 8*g /49)*{D/ (1-4*g/21)} xu > D
x = Centroid of stress blok area from most compressed edge
0.0035 * xu - D/ 2 + yi xu ≤ D
xu
esi =
0.002* 1+ yi - D/14 xu > D
xu -3D/7
INTRACTION DIAGRAM : (P : MLL) SECTION AT SHAFT BOTTOM
Section Dimensions: Material Properties:

As1 D = 8500 mm fck = 35 N/mm22
xu B = 1200 mm fyk = 500 N/mm
2
Es = 200000 N/mm
NA Reinforcement Details :
As3 Dia Spacing Cover From To Y_Cg Remark
Reinf. Nos. Spacing
As4 8442 mm mm mm m m m
T REINFORCEMENT ACROSSAXIS OF BENDING:
T = 8500 As3 25 130 75 58 8442 -512.5 65 131
L 0 130 0 0 0 0 0 0 NONE
As4 16 130 50 58 8442 542 65 131
REINFORCEMENT ALONG AXIS OF BENDING:
As1 16 130 50 217.5 1012 4192 7 132.417
As2 As2 16 130 50 217.5 1012 -4192 7 132.417
1012 Balance Failure

L= 1200 20000 d1 8442
xu 5211.1111 mm
18000 INTRACTION DIAGRAM (Pu : MuLL)
xu/D 0.6130719
Pu Mu 16000 Pu 8305.6485 T
xu/D
T Tm Mu 20031.339 Tm
14000
1E-09 -2078.9 5.5E-05
0.2 1392.07 12179.8 12000
Pu
0.4 4739.46 18713.3

10000
0.6 8086.84 20118.3
0.8 11299.3 17116.5 8000
1 14269 10948.9
6000
1.2 15780.2 6393.74
1.4 16478.7 4289.87 4000
1.6 16861.3 3136.77 2000
1.8 17095.1 2431.47
2 17249.1 1965.58 0
0 5000 10000 15000 20000 25000
100 17793.3 15.4802
Mu
------
DESIGN OF SHAFT
SLS LOAD COMBINATION
LC-1 RARE, LWL, Min LL Leading Forces about toe LC-1

5) Surfacing 13.5 -1.3 0.0 1

V HL HT MTT MLL
LC-1 RARE, LWL, Min LL Leading 310.97692 255.47377 0 792.43067 31.751855
LC-2 RARE, HFL, Min LL Leading Forces about toe LC-2

5) Surfacing 13.5 -1.3 0.0 1
8) Buoyancy -20.7 0.5 0.0 0.15

V HL HT MTT MLL
LC-2 RARE, HFL, Min LL Leading 307.87121 253.08307 0 736.65301 31.751855

LC-3 QP, LWL Forces about toe LC-3
5) Surfacing 13.5 -1.3 0.0 1

V HL HT MTT MLL
LC-3 QP, LWL 283.60463 183.37448 0 484.82952 0
LC-4 QP, HFL Forces about toe LC-4

5) Surfacing 13.5 -1.3 0.0 1
8) Buoyancy -20.7 0.5 0.0 0.15

V HL HT MTT MLL
LC-4 QP, HFL 280.49892 180.98379 0 429.05187 0

FORCES AT SHAFT BOTTOM:
SLS LOAD COMBINATION :
As1
T T=
8500
As4
L
As3
As2
L= 1200
SLS CHECK FOR ABUTMENT SHAFT :
Forces at bottom of abutment shaft

S.N.
Description
NED HL HT METT MELL
LC-1 RARE, LWL, Min LL Leading 310.977 255.474 0 792.431 31.7519
LC-2 RARE, HFL, Min LL Leading 307.871 253.083 0 736.653 31.7519
LC-3 QP, LWL 283.605 183.374 0 484.83 0
LC-4 QP, HFL 280.499 180.984 0 429.052 0
STRESS CHECK SECTION AT SHAFT BOTTOM
Section Dimensions:
2 3 D = 1200 mm
As1 B = 8500 mm
Material Properties:
2
fck = 35 N/mm
2
As3 fyk = 500 N/mm
2
As4 8442 Es = 200000 N/mm
T = 8500
T
As2
1 4
1012 L
dy L= 1200
f NA xu
NA
Reinforcement Details :
Eff. From To As per
Dia Spacing Cover Nos. Spacing
Reinf. cover Total As L T L T unit
mm mm mm mm Nos. mm mm2 mm mm mm mm mm2/mm
As1 16 130 50 58 7 147.0 1407.4 130 8442 1012 8442 1.6
As2 16 130 50 58 7 147.0 1407.4 130 58 1012 58 1.6
As3 25 130 75 87.5 65 131.0 31907 87.5 58 87.5 8442 3.8
0 130 0 0 65 131.0 0 0 58 0 8442 0.0
As4 16 130 50 58 65 131.0 13069 1142 58 1142 8442 1.6
Closed
SECTION COORDINATE
S.N x y Properties of Gross Cross-section
1 0 0 Properties @ XY axis @ centrodial axis
2 2
2 0 8500 A = 1E+07 mm 1E+07 mm
3 1200 8500 cgL = 600 mm 600 mm
4 1200 0 cgT = 4250 mm 4250 mm
4 4
5 0 0 ILL = 2E+14 mm 6E+13 mm
4 4
Closed ITT = 5.E+12 mm 1.E+12 mm
4 4
ILT = 3.E+13 mm 0.E+00 mm

MQP = 484.83 Tm
= 307.60 Tm
2
Equivalent Modulus of Elasticity for Rare Combination :

Ec,eq = Ecm*(MQP+MST) = 20044.5 MPa
MST +(1+f)* MQP
Forces Finding Position of Neutral Axs

P MTT MLL Modular First Trail Valuse Adopted Value suggested by program
LC T Tm Tm ratio f dy f dy f dy NA_stress
radian mm radian mm radian mm Mpa
LC-1 310.977 792.431 31.7519 9.98 4.7 -7E+05 4.7 -1E+06 4.7 -1E+06 0.00
LC-2 307.871 736.653 31.7519 9.98 4.7 -7E+05 4.7 -1E+06 4.7 -1E+06 0.00
LC-3 283.605 484.83 1 12.38 4.7 -1E+07 4.7 -2E+07 4.7 -2E+07 0.00
LC-4 280.499 429.052 1 12.38 4.7 -1E+07 4.7 -2E+07 4.7 -2E+07 0.00
x y x y Dist.
1200 0 0 8500 from
Max. Concrete Permissible conc. Max. Tensile Stress Permissible steel N.A
LOAD COMBIANTIONS Stress (Mpa) stresses(Mpa) (Mpa) stresses (Mpa) (mm) (4)
LC-1 6.853 16.8 OK -211.272 -400 OK -294.947
LC-2 RARE COMBINATION 6.381 16.8 OK -193.686 -400 OK -298.561
LC-3 QUASI PERMANENT 3.811 12.6 OK -117.231 -400 OK -344.469
LC-4 COMBIANTION 3.380 12.6 OK -99.626 -400 OK -355.041
First Trail NA
tan (f)= MLL * ITT/ MTT / ILL
tan (f)= (eL-eL') * ILL - (eT-eT')*ILT

(eT-eT') * ITT - (eL-eL')*ILT
s (L1 , T1) = P/Aeff + P*(eL-eL') - P*(eT-eT')*(ILTeff / ILeff)

( L1 - CgLeff )
ITeff - (ILTeff2 / ILeff)
+ P*(eT-eT') - P*(eL-eL')*(ILTeff / ITeff)

( T1 - CgTeff )
ILeff - (ILTeff2 / ITeff)

For Web
h = 1.2 m , b = 1m
k = 0.65
fcteff = fctm
= 2.77 Mpa
Act = b * h/2
2
= 0.6 m

= fyk
= 500 Mpa
2 2
Asmin = 864.635 mm /m < 3753.74 mm /m on tension face OK
2
< 1537.5 mm /m on compression face OK
wk,max = 0.3 mm
5 (c +feq/2) = 437.5 mm
Spacing b/w bars = 130 mm < 437.5 mm

= 3.4c + 0.17 f /rPeff
= 850.822 mm
hc,eff = Min 2.5 ( h - d ) h = 1.2 m

( h - x/3 ) d = 0.9895 m
width b = 1m
2
rP,eff = As/ Ac,eff

= 3753.7 / 526250
= 0.00713

Es = 200000 Mpa
ae = Es/Ecm
ae = 12.3807

Es
0.6 ssc / Es
= 0.00035

= 0.299 mm < 0.3 mm OK
DESIGN OF DIRT WALL :
3
Density of Earth = 2 T/m
Earth Pressure coefficent Ko = 0.42642
0.3
Earth Pressure = 1/2 Ko g h2
= 2.007 T/m
Lever arm = 0.42 *h 2.2

= 0.911 m
Moment at bottom MEP = 1.828 Tm/m
2
Live Load surcharge intensity q = 2.4 t/m
Live load surcharge Pressure = Ko*q*h
= 2.22017 T/m
Lever arm = 0.5 *h

= 1.085 m
Moment at bottom MSP = 2.408 Tm/m
ULS DESIGN FORCES:

LOADS Unfactored Factored Forces
Load
Force BM Factor Force BM
T Tm T Tm
Earth Pressure = 2.007 1.828 1.5 3.01024 2.74275
Surcharge Pressure = 2.220 2.408 1.2 2.66421 2.88983
Total 5.67 5.63
SLS DESIGN FORCES:

LOADS Unfactored SLS RARE COMB. SLS QUASI PER. COMB.
Force BM Load Force BM Load Force BM
T Tm Factor T Tm Factor T Tm
Earth Pressure = 2.007 1.828 1 2.00683 1.8285 1 2.00683 1.8285
Surcharge Pressure = 2.220 2.408 0.8 1.77614 1.92656 0 0 0
Total 3.78 3.76 2.01 1.83

SEISMIC CASE :
Seismic case (Coefficent of Earth Pressure) Ca = 0.447
*/For sumberged Condition
Dynamic Earth Pressure Increment

2
Horizontal force = 1/2 (Ca-Ko) g * h = 0.09799 T
Lever arm = 0.5 *h = 1.0847 m
Moment at base MDEP = 0.10629 Tm
Dynamic Surcharge Pressure Increment

Horizontal force = 3/2*(Ca-Ko) *q * h = 0.163 T
Lever arm = 0.670 *h = 1.453 m
Moment at base MDEP = 0.236 Tm
ULS DESIGN FORCES:

LOADS Unfactored Factored Forces
Load
Force BM Force BM
Factor
T Tm T Tm
NON-SEISMIC COMPONENT
Earth Pressure = 2.007 1.828 1 2.007 1.8285
SEISMIC COMPONENT
Earth Pressure = 0.098 0.106 1.5 0.147 0.15944
Total 2.65 2.54
ULS DESIGN :
D = 0.3 m */ overall depth at d from face of support

d = 0.258 m */ deff at d from face of support
Clear Cover = 50 mm

2
= 1340.41 mm /m

eud = 0.00405
= 46.0205 mm ecu2 = 0.0035
xumax/d = 0.46358
xumax = 0.464 d'
Ast calculated = M/ 0.87 fyk (d'-0.416 xu)

2
= 542.104 mm /m

2
= 450 mm /m
Ast required = Max( 542.104 , 450 )

2
= 542.104 mm /m
Increase required reinforcement by 50%
2 2
= 813.157 mm /m < 1340.41 mm /m OK
(ULS) CHECK FOR SHEAR FORCE

Factored Shear Force VED = 5.67 Tonne

d = 0.258 m */ deff at face of support
Design Shear Resitance

2
= 1.88045
r1 = Min Asl /bw d

0.02
= 0.0052
scp = 0 Mpa
nmin = 0.031 k3/2 fck1/2

= 0.47292
= 14.09 Tonne > 5.67 Tonne OK

n = 0.6 * ( 1- fck /310) */ fck in Mpa
= 0.532258
fcd = 0.446667 *fck

= 15.63333 Mpa

= 107.3405 Tonne > 5.67 Tonne OK

MQP = 1.83 Tm
= 1.93 Tm
Creep coefficent f = 1.11
2

Ec,eq = Ecm*(MQP+MST) = 20956 MPa
MST +(1+f)* MQP

b

deff = 0.258 m = 0.258 m
width b = 1m = 1m
2 2
4 4
INA (Transformed) = 5.66E+08 mm = 7.26E+08 mm
2 2
2 2
2 2
2 2

For Web
h = 0.3 m , b = 1m
k = 1
fcteff = fctm
= 2.77 Mpa
Act = b * h/2
2
= 0.15 m

= fyk
= 500 Mpa
2 2
Asmin = 332.5521 mm /m < 1340.41 mm /m OK

wk,max = 0.3 mm
Bar dia feq = 16 mm
5 (c +feq/2) = 290 mm

= 3.4c + 0.17 f /rPeff
= 383.0687 mm
hc,eff = Min 2.5 ( h - d ) h = 0.3 m

( h - x/3 ) d = 0.258 m */ (for Quasi
h/2 x = 0.07918 m Permanent Load
width b = 1m
2
rP,eff = As/ Ac,eff

= 1340.413 / 105000
= 0.012766

Es = 200000 Mpa
ae = Es/Ecm
ae = 13.07687

Es
0.6 ssc / Es
= 0.000177

= 0.068 mm < 0.3 mm OK
DESIGN OF RETURN WALL
c1 0 a= 8.6
C B
c2 0.75 A
C'
c3 0.75
b =
7.95
A''
Y direction
X direction
A' B'
8.6
Width of Solid return wall (a) = 8.6 m

Height of Solid return wall (b) = 7.95 m
Width of Cantilever return wall c1 = 0 m

Height of Cantilever return at Tip c2 = 0.75 m
Height of Cantilever return taper c3-c2 = 0.00 m
Height of Cantilever return at Root c3 = 0.75 m
Thickness of Solid Return at farther end t1 = 0.5 m

Thickness of Solid Return at top t2 = 0.5 m
Thickness of Solid Return at bottom t3 = 0.6 m
Thickness of Cantilever return = 0.5 m
Unit wt of Soil = 2 t/m3
Grade of concrete = M 35 MPa
Grade of Reinforcement = Fe 500 MPa
scbc = 1166.67 t/m2
modular ratio m = 10
sst = 24000 t/m2
k = 0.327
j = 0.891
R = 170.005 t/m2
a/b = 0.900
Case (1) For uniformly distributed load over entire plate

For a/b = 0.75 For a/b = 1.000 For a/b = 0.900
b1 = 1.246 b1 = 1.769 b1 = 1.560
b2 = 1.186 b2 = 1.769 b2 = 1.536
g1 = 1.129 g1 = 1.183 g1 = 1.161
g2 = 0.829 g2 = 1.183 g2 = 1.041
Live Load Surcharge:
2
q = 0.244 x 2 x 1.2 = 0.5856 t/m
sbmax = b1 x q x b2
2
t
samax = b2 x q x b2
2
t
2
sbmax = 1.5598 x 0.5856 x 63.2025 = 160.362 t/m
0.36
For 1000 mm of width
3
Z = 1000 x 360000 = 6.00E+07 mm
3
6 = 0.06000 m
Hence Moment /m width along Y direction

MY /m width = 160.362 x 0.06 = 9.622 t-m/m
2
samax = 1.5358 x 0.5856 x 63.2025 = 157.895 t/m
0.36
Z = 1000 x 360000 = 60000000 mm3
6 = 0.06000 m3
Hence Moment /m width along X direction
MX /m width = 157.895 x 0.06 = 9.474 t-m/m
Case (2) For Triangular loading due to earth pressure

For a/b = 0.75 For a/b = 1 For a/b = 0.900
b1 = 0.537 b1 = 0.695 b1 = 0.632
b2 = 0.276 b2 = 0.397 b2 = 0.349
g1 = 0.551 g1 = 0.559 g1 = 0.556
g2 = 0.23 g2 = 0.192 g2 = 0.207
Earth pressure:
2
q = 0.244 x 2 x 7.95 = 3.8796 t/m
sbmax = b1 x q x b2
t2
samax = b2 x q x b2
t2
2
sbmax = 0.6318 x 3.8796 x 63.2025 = 430.327 t/m
0.36
Z = 1000 x 360000 = 6.000E+07 mm3
6 = 0.060 m3
Hence Moment /m width along Y direction

MY /m width = 430.327 x 0.06 = 25.8196 t-m/m
2
samax = 0.3486 x 3.8796 x 63.2025 = 237.436 t/m
0.36
3
Z = 1000 x 360000 = 6.000E+07 mm
3
6 = 0.060 m
Hence Moment /m width along X direction

MX /m width = 237.436 x 0.0600 = 14.246 t-m/m
Total Moment in Solid Return /m height = 23.72 t-m/m Along X-direction

Total Moment in Solid Return /m width = 35.44 t-m/m Along Y-direction
Forces at the cantilevr return wall (AA'')

Forces at Due to earth pressure Due to surcharge pressure
Force at CC' 1/2 x 0.244 x 2 x 0.75^2 0.244 x 1.2 x 2 x 0.75

= 0.137 t/m = 0.439 t/m
Force at AA'' 1/2 x 0.244 x 2 x 0.75^2 0.244 x 1.2 x 2 x 0.75

= 0.137 t/m = 0.439 t/m
Total Force (0.137+0.137)/2 * 0 (0.439+0.439)/2 * 0

= 0.000 T = 0.000 T
Lever arm from AA'' (2 x 0.13725 + 0 ) / ( + 0) x (2 x 0.4392 + 0 ) / ( + 0) x 0

0/3 /3
= 0 m = 0 m
Moment at Face AA'' 0*0 0*0

0.000 Tm 0.000 Tm
Moment at AA' per m 0/0.75 0/0.75

/height = 0.000 tm/m = 0.000 tm/m
Lever arm from BB' 8.6 + 0 8.6 + 0

= 8.6 m = 8.6 m
Moment at Face BB' 0*8.6 0*8.6

= 0.000 Tm = 0.000 Tm
Moment at BB' per m 0/3.975 0/3.975

/height = 0.00 tm/m = 0.00 tm/m
*/ Assumed 50% height is effective
Lever arm from A'B' 7.95000000000001-(0.75+0.75)*2/3 7.95000000000001-(0.75+0.75)/2

= 6.950 m = 7.20 m
Moment at Face BB' 0*6.95 0*7.2

= 0.000 Tm = 0.000 Tm
Moment at AB' per m 0/4.3 0/4.3

/width = 0.00 tm/m = 0.00 tm/m
*/ Assumed 50% width is effective
Design Bending Moment at face of Cantilever return wall (horiozontal reinforcement):
Force due to Unfactored Load Factor
Bending Moment SLS
at Face AA'' ULS Rare QP
Earth Pressure 0.00 tm/m 1.5 1 1
Surcharge Pressure 0.00 tm/m 1.2 0.8 0
ULS Design Bending moment = 0.00 Tm/m

SLS Rare Design Bending moment = 0.00 Tm/m
SLS QP Design Bending moment = 0.00 Tm/m
Design Forces for Solid Return wall:

Bending Moment At Face BB' ( Horizontal Reinforcement)
Bending Moment SLS
at Face BB' ULS Rare QP
Earth Pressure From cantilever return wall 0.00 tm/m 1.5 1 1
Earth Pressure over solid return wall 14.246 tm/m 1.5 1 1
Surcharge Pressure From cantilever return wall 0.00 tm/m 1.2 0.8 0
Surcharge Pressure over solid return wall 9.474 tm/m 1.2 0.8 0
ULS Design Bending moment = 32.74 Tm

SLS Rare Design Bending moment = 21.83 Tm
SLS QP Design Bending moment = 14.25 Tm
Design Bending Moment At Face A'B' (Vertical Reinforcement)

Bending Moment SLS
at Face A'B' ULS Rare QP
Earth Pressure From cantilever return wall 0.00 tm/m 1.5 1 1
Earth Pressure over solid return wall 25.82 tm/m 1.5 1 1
Surcharge Pressure From cantilever return wall 0.00 tm/m 1.2 0.8 0
Surcharge Pressure over solid return wall 9.62 tm/m 1.2 0.8 0
ULS Design Bending moment = 50.28 Tm

SLS Rare Design Bending moment = 33.52 Tm
SLS QP Design Bending moment = 25.82 Tm

Clear cover = 75 mm
For short Term loading Ecm = 32308.2 Mpa
For long Term loading Ecm' = 16154.1 Mpa
fcteff = 2.77 Mpa
fcd = 15.63 Mpa
f = 1.00
euk = 0.0045
eud = 0.0041
ecu2 = 0.0035
xumax/d = 0.4636
Design of Section At Face AA''
Overall depth = 500 mm
Effective depth provided = 419 mm
I Structural design
M xmax xu Check Ast Calculated Check Ast min Check
2 2
Load comb. (tm/m) (mm) (mm) (mm ) Ast Calc. < Ast Provided (mm ) Ast P > Ast min
ULS 0.00 194.416 25.8865 UR, OK 0 OK 628.5 OK
II Stress Check
Rare comb. Ec,eq = Ecm*(MQP+MST) = 0 MPa
MST +(1+f)* MQP
m = Es/ Ec,eq = 0 MPa
QP comb. m = Es / Ecm' = 12.3807 MPa
M modular N.A. INA Comp Max C. Check Tensile Max T Check
Load comb. ratio depth stress Stress stress Stress
(tm/m) m mm mm4 Mpa Mpa Mpa Mpa
SLS (R Comb.) 0.00 0.00 0 0E+00 0.00 16.8 OK 0.00 400 OK
SLS (QP Comb.) 0.00 12.38 79.6019 1E+09 0.00 12.6 OK 0.00 400 OK
III Crack width check

kc = 0.4 For Bending member kt = 0.5
k = max 0.86 ae Es/Ecm' = 12.38
Load Act
spacing check hceff Aceff rPeff esm - ecm srmax wk check As,min check
2 2 2
comb. mm mm mm As/Ac,eff (mm) (mm )
SLS QP 250000 405.00 OK 202.50 202500 0.0037 0.00000 802.89 0.00 OK 476.658 OK
Area of steel provided, A st P

2
Provide 12 mm dia @ 150 mm c/c providing 753.982 mm on earth face.
2
Provide 12 mm dia @ 150 mm c/c providing 753.982 mm on other face.
Along Horizontal direction.
Design of Section At Face BB''

I Structural design
Load comb. (tm/m) (mm) (mm) (mm2) Ast Calc. < Ast Provided (mm )
2
Ast P > Ast min
ULS 32.74 214.368 46.0205 UR, OK 1699.4 Revise 693 OK
II Stress Check
Rare comb. Ec,eq = Ecm*(MQP+MST) = 19548.3 MPa
MST +(1+f)* MQP
m = Es/ Ec,eq = 10.2311 MPa
SLS (R Comb.) 21.83 10.23 99.6867 2E+09 10.21 16.8 OK 379.74 400 OK
SLS (QP Comb.) 14.25 12.38 108.343 2E+09 6.17 12.6 OK 249.55 400 OK
k = max 0.83 ae Es/Ecm' = 12.38
Load Act
spacing check hceff Aceff rPeff esm - ecm srmax wk check As,min check
2 2 2
SLS QP 272500 415.00 OK 207.50 207500 0.0065 0.00075 676.06 0.51 Revise 500.527 OK

2
2
Along Horizontal direction.
Design of Section At Face AB''

I Structural design
Load comb. (tm/m) (mm) (mm) (mm2) Ast Calc. < Ast Provided (mm )
2
Ast P > Ast min
ULS 50.28 239.888 46.0205 UR, OK 2321.47 Revise 775.5 OK
II Stress Check
Rare comb. Ec,eq = Ecm*(MQP+MST) = 18249.7 MPa
MST +(1+f)* MQP
m = Es/ Ec,eq = 10.9591 MPa
SLS (R Comb.) 33.52 10.96 109.427 3E+09 12.75 16.8 OK 520.37 400 Revise
SLS (QP Comb.) 25.82 12.38 115.446 3E+09 9.35 12.6 OK 402.54 400 Revise

k = 0.79 ae Es/Ecm' = 12.38
max
Load A ct spacing check hceff Aceff rPeff esm - ecm srmax wk check As,min check
2 2 2
SLS QP 300000 415.00 OK 207.50 207500 0.0065 0.00121 676.06 0.82 Revise 525.432 OK

2
2
Along Vertical direction.
SHEAR CHECK FOR RETURN WALL :

Case (1) For uniformly distributed load over entire plate
2
R1= g1qb = 1.161 x 0.586 x 7.95 = 5.40692 t-m/m
2
R2= g2qb = 1.041 x 0.586 x 7.95 = 4.84826 t-m/m
Case (2) For Triangular loading due to earth pressure
2
R1= g1qb = 0.556 x 3.880 x 7.95 = 17.142 t-m/m
2
R2= g2qb = 0.207 x 3.880 x 7.95 = 6.391 t-m/m
D = 600 mm
deff = 520 mm
Finding creep coefficent
fck = 35 Mpa (Considering Precat Beam material)
fcm = 45 Mpa
t = 25550 days
to = 90 days
f (t, to) = fo b c( t , to )
fo = fRH b(fcm) b(to)
fRH = 1+ 1 - RH/100 for fcm ≤ 45 Mpa

0.1 ( ho )1/3
1+ 1 - RH/100 for fcm > 45 Mpa

a1 * a2
0.1 ( ho )1/3
RH = Relative humidity
= 80 %
ho = 2400 mm
a1 = [ 43.75 / fcm ]0.7 = 0.98047
a2 = [ 43.75 / fcm ]0.2 = 0.99438
fRH = 1.14938
b(fcm) = 18.78 / √fcm

= 2.79956
b(to) = 1/ (0.1+ to0.2)

= 0.3907
fo = 1.25718
b c( t , to) = [ (t-to) / (b H +t -to) ]0.3
bH = Min 1.5 [ 1+ (0.012 RH)18 ] ho +250 for fcm ≤ 35 Mpa

1500
Min 1.5 [ 1+ (0.012 RH)18 ] ho +250 a3 for fcm > 35 Mpa

1500* a3
a2 = [ 43.75 / fcm ]0.5 = 0.986
bH = 1479.02
b c( t , to) = 0.983
f (t, to) = 1.24

Design of RCC T-Beam
Span: 18.0 m c/c of exp.joint
SALIENT FEATURES OF THE BRIDGE DECK:
Span c/c of Exp. J. = 18 m
Exp. Gap = 40 mm
c/L of brg. c/L of exp. J = 0.7 m
Span c/c of brg. = 16.6 m
Overall Length of Girder = 17.6 m
Thickness of Cross-Girder = 0.6 m
Overall carriageway width = 12 m
Wearing Coat Thickness = 65 mm
Depth of Precast Beam = 1.3 m

Thickness of Cast-in-situ deck = 0.22 m
Overall depth Beam + slab = 1.52 m
c/c of girder (transverse direction) = 3 m
Deck cantilever in transverse direction = 1.5 m
3
Density of Concrete = 2.5 t/m
Size of bearing = 0.7 m circular
STAGES : Girder Age Deck Age

Casting of Precast concrete at day 0 -
Erection of T-Beam 28 -
Casting of deck 29 1
Placing of SIDL 43 14
Open to LL 57 28
At ∞ ∞ ∞
PROPORTINING OF PRECAST BEAM
0.75 0.75
0.2 0.2
ht1 0.1 0.00
0.325 1.3 1.3
0.2
0.25
bw2 = 0.75 0.75
Section at Mid Span Section at Support

Web Thickening
0.6
0.4 c/L
0.75 0.325
0.2
0.7 1.5 1.3 6

8.3
web thickness variation along span
Web Thickening
Section At c/L brg. deff L/8 TS 2L/8 3L/8 4L/8
Dist. From c/L brg. m 0 1.29 2.075 2.3 4.15 6.225 8.3
bw m 0.75 0.75 0.562 0.48846 0.325 0.325 0.325
Overall depth of composite girder = 1.52 m

deff = 1.29 */Assumed 0.85 times of overall depth)
MATERIAL USED :
Grade of Reinforcement = Fe 500
fyk = 500 Mpa
Cast insitu deck = M 35

fck = 35 Mpa
fcm = 45 MPa
Ecm = 32000 MPa
Precast Beam = M 35
fck = 35
fcm = 45 MPa
Ecm = 32000 MPa
ANALYSES ASSUMPTION
Environmental parameters
Relative humidity = 80 %
Exposure condition = Severe
TEMPERATURE
o
Coefficient of thermal expansion = 1.2E-05 / C
FOR PRECAST BEAM
Modulus of Elasticity
For short Term loading Ecm = 32000 Mpa
For long Term loading Ecm' = Ecm/ (1+f)
f = Creep coefficient
Creep
Cross-sectional Area Ac = 1.34m2 (Composite Outer Girder at mid span
Perimeter in contact with atmosphere u = 6.80m considered)
Age of concrete at the time of loading to = 90days
t considered = 25550 days
f = 1.37(Refer Appendix B)
@ 1.24*(Reduced by 10% on the conservative side)
2
Ecm' = 14304.3 N/mm
Shrinkage
2
Cross-sectional Area Ac = 0.68 m (Precast Beam considered)
Final autogenonus shrinkage eca, = 2.0 *(fck-12.5)*10-6

= 4.5E-05
Final drying shrinkage ecd, = 0.0002 (Refer Appendix C)
FOR CAST -IN SITU DECK SLAB

Shrinkage
2
Cross-sectional Area Ac = 0.66 m
2
Final autogenonus shrinkage eca, = 2.0 *(fck-12.5)*10-6

= 4.5E-05
Final drying shrinkage ecd, = 0.0002 (Refer Appendix C)
SERVICEABILITY LIMIT STATE :

Max permissible Stress in Concrete
Rare Combination = 0.48*fck
= 16.8 Mpa
Quasi permanent Combination = 0.36*fck

= 12.6 Mpa
Max permissible Stress in Steel = 0.8*fyk

= 400 Mpa
Permissible crack width wk,max = 0.3 mm

c/L Brg.
CRASH BARRIER 0.5
12
11
CRASH BARRIER 0.5
16.6
17.96
PLAN
12
0.22
c/L jack Nos of Girder = 4 1.3 1.52
0.8
1.5 3
Super-structure Cross-section
PROPERTY CALCULATION of PRECAST BEAM:-
Density of concrete = 2.5 t/m3
A) INNER/ OUTER GIRDER :
0.75 0.75
1 0.2 1 0.2
2 0.1 2 0.000
3
0.325 1.3 1.3

3
4 0.2
5 0.25
0.75 0.75
Section Property At Mid Span

Element B D A cgy' IZZ cgz' Iyy
Factor Nos. 2 4
No. m m m m m m m4
1 1 0.213 0.2 2 0.085 0.1 0.028 0.26875 0.00646
2 0.5 0.213 0.1 2 0.0213 0.23333 0.004 0.23333 0.00121
3 1 0.325 1.3 1 0.423 0.65 0.060 0 0.00372
4 0.5 0.2125 0.2 2 0.043 0.98 0.004 0.26875 0.00318
5 1 0.2125 0.25 2 0.106 1.18 0.028 0.23333 0.00618
Total 0.678 0.671 0.124 0.0207
UDL = 0.678 x 2.5

= 1.69 t/m
Section Property At Support Section

Factor Nos.
No. m m m 2
m m 4
m m4
1 1 0.000 0.2 2 0.000 0.1 0.000 0.375 0
2 0.5 0.000 0.00 2 0.0000 0.2 0.000 0.375 0
3 1 0.75 1.3 1 0.975 0.65 0.137 0 0.0457
Total 0.975 0.650 0.137 0.0457
UDL = 0.975 x 2.5

= 2.44 t/m
Section At unit c/L brg. deff L/8 TS 2L/8 3L/8 4L/8

Dist. From c/L brg. m 0 1.292 2.075 2.3 4.15 6.225 8.3
web width bw m 0.75 0.75 0.56202 0.48846 0.325 0.325 0.325

Area A m2 0.975 0.975 0.843 0.792 0.678 0.678 0.678
yt m 0.650 0.650 0.659 0.663 0.671 0.671 0.671
yb m 0.650 0.650 0.641 0.637 0.629 0.629 0.629
4
IZZ m 0.137 0.137 0.131 0.129 0.124 0.124 0.124
Iyy m4 0.046 0.046 0.035 0.030 0.021 0.021 0.021
EFFECTIVE WIDTH CALCULATION :
Effective Span lo = Min Distance from bearing to bearing

Clear distance b/w supports + Effective depth
Bearing Size in Longitudinal dir.n = 0.7 m
lo = Min 16.6
15.9 + 1.292 */ (Effective depth assumed 0.85 times
of Overall depth)
lo = 16.6 m
bef
bef1 bef2
1.338 bw = 0.325 1.52

b1,2= 1.338
3 b= 3
1.5 3
beff. CALCULATION FOR INNER GIRDER :

b1,2 = 1.3375
beff1,2 = Min 0.2 bi + 0.1 lo = 1.9 m

0.2 lo = 3.32 m
beff1,2 = 1.9275 m
beff = Min  beff,i + bw = 4.18 m

b = 3 m
beff = 3m
beff. CALCULATION FOR OUTER GIRDER :

b1 = 1.3375 m b2 = 1.34 m
beff1 = Min 0.2 bi + 0.1 lo = 1.9 m

0.2 lo = 3.32 m
beff1 = 1.9275 m
beff2 = Min 0.2 bi + 0.1 lo = 1.9 m
0.2 lo = 3.3 m
beff2 = 1.9275 m
beff = Min  beff,i + bw = 4.18 m
b = 3 m
beff = 3m
PROPERTY CALCULATION OF COMPOSITE BEAM
fcm = Mean value of concrete compressive strength

fcm = fck + 10 */ fcm & fck are in Mpa
Ecm = Secant modulus of elasticity

0.3
Ecm = 22 * ( fcm /12.5 )
Material Concrete Grade fcm Ecm

(fck) Mpa MPa MPa
Deck slab = 35 45 32
Pre-cast section = 35 45 32
Modular ratio (EcmP / EcmD) = 1.00
A) OUTER GIRDER :
(Equivalent to Precast Beam grade) (Equivalent to Precast Beam grade)
3 @ 3.00 3 @ 3.00
1 0.75 0.22 1 0.75 0.22
2 0.2 2 0.2
3 0.1 3 0.00
4
1.52 1.52
0.325 1.3 1.3
4
5 0.2
6 0.25
0.75 0.75

Element B D A cgy' IZZ cgz' Iyy Perimeter (with atmosphere. (m) )
Factor Nos.
No. m m m
2
m m
4
m m
4
Composite Precast Deck
1 1 3.000 0.22 1 0.660 0.11 0.106 0 0.495 3.0 3.00
2 1 0.213 0.2 2 0.085 0.32 0.003 0.26875 0.00646 0.4 0.40
3 0.5 0.213 0.1 2 0.0213 0.45333 0.000 0.23333 0.00121 0.5 0.47
4 1 0.325 1.3 1 0.423 0.87 0.116 0 0.00372 1.1 1.10
5 0.5 0.2125 0.2 2 0.043 1.20 0.021 0.26875 0.00318 0.6 0.58
6 1 0.2125 0.25 2 0.106 1.40 0.085 0.23333 0.00618 1.3 1.25
Total 1.338 0.506 0.330 0.5157 6.80 3.80 3.00

Factor Nos.
No. m m m
2
m m
4
m m4
1 1 3.000 0.22 1 0.660 0.11 0.138 0 0.495
2 1 0.000 0.2 2 0.000 0.32 0.000 0.375 0.000
3 0.5 0.000 0.00 2 0.000 0.42 0.000 0.375 0.000
4 1 0.75 1.3 1 0.975 0.87 0.229 0 0.046
Total 1.635 0.563 0.367 0.5407

Composite cross-section properties
Section At unit c/L brg. deff TS L/8 2L/8 3L/8 4L/8
Dist. From c/L brg. m 0 1.29 2.3 2.075 4.15 6.225 8.30
web width bw m 0.75 0.75 0.48846 0.56202 0.325 0.325 0.325

2
Area A m 1.635 1.635 1.452 1.503 1.338 1.338 1.338
yt m 0.563 0.563 0.528 0.538 0.506 0.506 0.506
yb m 0.957 0.957 0.992 0.982 1.014 1.014 1.014
IZZ m4 0.367 0.367 0.344 0.351 0.330 0.330 0.330
Iyy m4 0.541 0.541 0.525 0.530 0.516 0.516 0.516
A) INNER GIRDER :
(Equivalent to Precast Beam grade) (Equivalent to Precast Beam grade)
3 @ 3.00 3 @ 3.00
1 0.75 0.22 1 0.75 0.22
2 0.2 2 0.2
3 0.1 3 0.00
4
1.52 1.52
0.325 1.3 1.3
4
5 0.2
6 0.25
0.75 0.75

Factor Nos.
No. m m m2
m m 4
m m4
1 1 3.000 0.22 1 0.660 0.11 0.106 0 0.495
2 1 0.213 0.2 2 0.085 0.32 0.003 0.269 0.006
3 0.5 0.213 0.1 2 0.0213 0.45333 0.000 0.233 0.001
4 1 0.325 1.3 1 0.423 0.87 0.116 0 0.004
5 0.5 0.2125 0.2 2 0.043 1.20 0.021 0.269 0.003
6 1 0.2125 0.25 2 0.106 1.40 0.085 0.233 0.006
Total 1.338 0.506 0.330 0.516

Factor Nos.
No. m m m2
m m 4
m m4
1 1 3.000 0.22 1 0.660 0.11 0.138 0 0.495
2 1 0.000 0.2 2 0.000 0.32 0.000 0.375 0
3 0.5 0.000 0.00 2 0.0000 0.42 0.000 0.375 0
4 1 0.75 1.3 1 0.975 0.87 0.229 0 0.0457
Total 1.635 0.563 0.367 0.541

Composite cross-section properties
Section At unit c/L brg. deff TS L/8 2L/8 3L/8 4L/8
Dist. From c/L brg. m 0 1.292 2.3 2.075 4.15 6.225 8.3
web width bw m 0.75 0.75 0.48846 0.56202 0.325 0.325 0.325

Area A m2 1.635 1.635 1.452 1.503 1.338 1.338 1.338
yt m 0.563 0.563 0.528 0.538 0.506 0.506 0.506
yb m 0.957 0.957 0.992 0.982 1.014 1.014 1.014
IZZ m4 0.367 0.367 0.344 0.351 0.330 0.330 0.330
Iyy m4 0.541 0.541 0.525 0.530 0.516 0.516 0.516
PROPERTY OF END CROSS GIRDER :

1.738
1 0.22
1.27
2
1.05
0.6
Section Property
Factor Nos.
No. m m m2 m m4 m m4
1 1 1.738 0.22 1 0.382 0.11 0.061 0 0.09616
2 1 0.600 1.05 1 0.630 0.745 0.094 0 0.0189
Total 1.012 0.505 0.155 0.1151

FORCES DUE TO SELF WEIGHT
Total Depth (including deck) = 1.52 m

Density of Concrete = 2.50 t/m3
Precast Beam
2.44 t/m
1.69 t/m
c/L
0.5 1 1.3 6
8.3
Span -0.5 1 1.3 6

UDL 2.44 1.69
Bending Moment & Shear Force at critical Sections

Precast Beam Dead Load
Support Reaction = 16.504 T
Section At Unit c/L brg. deff TS L/8 2L/8 3L/8 4L/8
Dist. From c/L brg. m 0 1.292 2.3 2.075 4.15 6.225 8.3
Bending Moment Tm -0.30 17.41 28.61 26.28 44.52 55.46 59.10
Shear Force T 15.29 12.16 10.16 10.56 7.03 3.51 0.00
DECK SLAB SELF WEIGHT

Thickness of deck slab = 0.22 m
Width of deck slab over Outer Girder = 3 m
Width of deck slab over Inner Girder = 3 m
UDL over Girder (Inner Girder) = 1.65 t/m

UDL over Girder (Outer Girder) = 1.65 t/m
1.65 t/m Outer Girder

1.65 t/m Inner Girder
1.65 t/m Outer Girder
1.65 t/m Inner Girder
c/L
0.5 1 1.3 6
8.3
Outer Girder
Span -0.5 1 1.3 6
UDL 1.65 1.65
Inner Girder
Span -0.5 1 1.3 6
UDL 1.65 1.65
Bending Moment & Shear Force at critical Sections

Deck Slab Dead Load, Outer Girder
Dist. From c/L brg. m 0 1.292 2.3 2.075 4.15 6.225 8.3
Shear Force T 13.70 11.56 9.90 10.27 6.85 3.42 0.00
Deck Slab Dead Load, Inner Girder

Dist. From c/L brg. m 0 1.292 2.3 2.075 4.15 6.225 8.3
Shear Force T 13.70 11.56 9.90 10.27 6.85 3.42 0.00
SUMMERY OF BENDING MOMENT DUE TO SELFWEIGT OF BEAM & DECK

Dist. From c/L brg. m 0 1.292 2.3 2.075 4.15 6.225 8.3
Precast Beam Tm -0.30 17.41 28.61 26.28 44.52 55.46 59.10
Deck slab (Outer Girder) Tm -0.21 16.11 26.93 24.66 42.42 53.08 56.63
Deck slab (Inner Girder) Tm -0.21 16.11 26.93 24.66 42.42 53.08 56.63
SUMMERY OF SHEAR FORCE DUE TO SELFWEIGT OF BEAM & DECK

Dist. From c/L brg. m 0 1.292 2.3 2.075 4.15 6.225 8.3
Precast Beam T 15.29 12.16 10.16 10.56 7.03 3.51 0.00
Deck slab (Outer Girder) T 13.70 11.56 9.90 10.27 6.85 3.42 0.00
Deck slab (Inner Girder) T 13.70 11.56 9.90 10.27 6.85 3.42 0.00
Calculation of SIDL :
3
Density of Concrete = 2.5 t/m
12
0.5 0 11 0 0.5
0.065 thick WC

Crash barrier weight = 1.2 t/m
Cg. From crash barrier bottom = 0.4 m
2
Wearing coat = 0.2 t/m
0.00
Footpath weight = 0.000 t/m
0
2
Footpath Live load = 0.360 t/m
= 0.000 t/m
SUMMERY OF FORCES FOR OUTER GIRDER:
Impact Factor For LL.
Class A = 0.199
Class 70 R wh. = 0.199
BENDING MOMENT OUTER GIRDER DUE TO PERMANENT LOAD

Dist. From c/L brg. m 0.00 1.29 2.075 2.3 4.15 6.225 8.3
Precast Beam Tm -0.3 17.4 28.6 26.3 44.5 55.5 59.1

Deck Outer Girder Tm -0.2 17.7 29.6 27.1 46.7 58.4 62.3
SIDL Tm 0.0 13.7 21.9 23.6 37.4 46.5 49.5
Surfacing Tm 0.0 6.0 9.5 10.3 16.3 20.3 21.7
FPDL Tm
FPLL Tm
Governing LL with Impact
Mz MTon-m Tm 0.0 44.3 67.4 72.6 112.5 137.2 149.3
Corresponding Fy Mton Tm 40.8 40.8 39.0 34.0 30.2 22.2 14.6
MAX. SHEAR FORCES OUTER GIRDER

Dist. From c/L brg. m 0.00 1.29 2.075 2.3 4.15 6.225 8.3
Precat Beam T 15.3 12.2 10.2 10.6 7.0 3.5 0.0

Deck Outer Girder T 15.1 12.7 10.9 11.3 7.5 3.8 0.0
SIDL T 10.5 10.5 10.5 7.4 7.4 4.4 1.4
Surfacing T 4.5 4.5 4.4 3.5 3.1 1.8 0.5
FPDL
FPLL
Maximum S.F T 39.3 35.7 34.1 29.7 26.5 19.4 12.7
ULS CHECK FOR COMPOSITE SECTION: BENDING MOMENT
Design Parameters
Design yield strength of reinforcement fyd = 434.78 Mpa
Concrete Characteristic Strength fck = 35 Mpa
fcd = 0.447 *fck = 15.63 Mpa
Using Rectangular stress block
Effective height factor l = 0.8
Compression zone factor h = 1
hfcd = 15.63 Mpa
Limiting value of xu,max/d = 0.464
Modular ratio (EcmP / EcmD) = 1 (Precast Beam / Cast insitu deck)
A) OUTER GIRDER SUMMERY OF LOADS

BENDING MOMENT OUTER GIRDER
LC-1
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Precast Beam Tm -0.30 17.41 28.61 26.28 44.52 55.46 59.10 1.35
Deck Outer Girder Tm -0.21 17.72 29.62 27.12 46.66 58.38 62.29 1.35
SIDL Tm 0.03 13.75 21.90 23.59 37.37 46.47 49.47 1.35
Surfacing Tm -0.04 6.05 9.47 10.26 16.27 20.33 21.68 1.75
FP DL
FP LL
Live Load Tm 0.00 44.26 67.45 72.64 112.52 137.21 149.27 1.5
Factored Bending Moment

LC-1 Basic Comb Tm -0.72 142.96 225.93 230.86 370.80 457.81 492.52
A) OUTER GIRDER AT MID SPAN
(Equivalent to Precast Beam grade)

3 @ 3.00 hfcd = 15.63
1 0.75 0.22 x1
2 0.2 Cu
3 0.1 xu lxu
4 1.52
0.325 1.3 z
Ast
0.2 Tu
0.25
0.75
Clear Cover = 61 mm
Dia of spacer Bar = 32 mm
Total Depth = 1.52 mm
Reeinforcement at different sections
At 4L/8 y from At 3L/8 At 2L/8 At L/8
Layer Dia Nos bottom Dia Nos Dia Nos Dia Nos
mm (m) mm mm mm
Layer-1 32 6 0.0770 32 6 32 6 32 6
Layer-2 32 6 0.1410 32 6 32 6 32 6
Layer-3 32 2 0.2050 32 2 32 0 32 0
Layer-4 32 0 0.2690 32 0 32 0 32 0
Layer-5 32 0 0.3330 32 0 32 0 32 0
Layer-6 32 0 0.3970 32 0 32 0 32 0
Total Ast = 0.0113 m2 0.0113 m2 0.0097 m2 0.0097 m2

deff = 1.397 m 1.397 m 1.411 m 1.411 m
dast_o = 1.443 m 1.443 m 1.443 m 1.443 m
hcef1 = (h-d)*2.5 = 0.307 m 0.307 m 0.273 m 0.273 m
Reinforcement provided
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dia of bars mm 32 32 32 32 32 32 32
Nos. Nos. 12 12 12 12 12 14 14
Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113
deff w.r.t Composite m 1.411 1.411 1.411 1.411 1.411 1.397 1.397
dast_o section m 1.443 1.443 1.443 1.443 1.443 1.443 1.443
deff 1.191 1.191 1.191 1.191 1.191 1.177 1.177

w.r.t Precasts section
dast_o 1.223 1.223 1.223 1.223 1.223 1.223 1.223
deff = deff up to cg. Of total steel

dast_o = deff up to cg. Of outer most steel
Check for Minimum & Maximum reinforcement percentage ( IRC 112 / clause 16.5.1.1)
As, min = Max 0.26 (fctm/fyk ) btd

0.0013 btd
fctm = 2.77 Mpa
fyk = 500 Mpa
Asmax = 0.025Ac

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
d m 1.411 1.411 1.411 1.411 1.411 1.397 1.397

bt m 0.750 0.750 0.750 0.750 0.750 0.750 0.750
As, min m2 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015
2
As, provided m 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113
check Asmin < Asprovided OK OK OK OK OK OK OK
Ac m2 1.635 1.635 1.503 1.452 1.338 1.338 1.338
Asmax m2 0.041 0.041 0.038 0.036 0.033 0.033 0.033
check Asmax > Asprovided OK OK OK OK OK OK OK
Anchorage of Span Reinforcemet at end : ( IRC 112 / clause 16.5.1.4)
Tensile Force = VED * (al/d) +NED
VED = 122.02 T Factored Shear Force at face of support
d = 1.41 deff at face of support
al = 0.5 *z*(cot q)
z = 1.37 m (z at face of support)
q = 45 deg (angle of concrete strut with longitudinal axis)
NED = 0T
al = 0.683
Tensile Force = 59.0777 Tonne
2
Area of tensile reinforcement at support section As = 0.0097 m
Maximum tensile stress in reinforcement fyd = fyk /gm = 500 /1.15
= 434.783 Mpa
Tensile capacity of anchorage reinforcement Ft = 419.608 Tonne OK

Anchorage provided upto l b.net distance from face of support starting after leaving w/3
CHECK FOR ULTIMATE LIMIT STATE CAPACITY: ( IRC 112 / clause 8.2.1)
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113

deff m 1.4110 1.4110 1.4110 1.4110 1.4110 1.3973 1.3973
lxu m 0.089 0.089 0.089 0.089 0.089 0.104 0.104
CArea m2 0.268 0.268 0.268 0.268 0.268 0.313 0.313
x1 m 0.045 0.045 0.045 0.045 0.045 0.052 0.052
Cu T 419.61 419.61 419.61 419.61 419.61 489.54 489.54
Tu T 419.61 419.61 419.61 419.61 419.61 489.54 489.54
Check (C-T =Zero) 0 0 0 0 0 0 0
xu m 0.112 0.112 0.112 0.112 0.112 0.130 0.130
xu/d 0.079 0.079 0.079 0.079 0.079 0.093 0.093
Check ( xu/d < xu,max/d ) UR,OK UR,OK UR,OK UR,OK UR,OK UR,OK UR,OK
z =(d-x1) m 1.37 1.37 1.37 1.37 1.37 1.35 1.35

MRD = Tu*z Tm 573.30 573.30 573.30 573.30 573.30 658.48 658.48
MED Tm -0.72 142.96 225.93 230.86 370.80 457.81 492.52

check MED < MRD OK OK OK OK OK OK OK
Additional Tensile force due to shear

DFd T 62.16 58.47 54.41 48.30 40.23 26.04 12.30
MED/z +DFD T 61.64 163.10 219.77 217.27 311.63 366.39 378.46
MRD/z 419.61 419.61 419.61 419.61 419.61 489.54 489.54
Check MRD > MED/z +DFD OK OK OK OK OK OK OK
Check for anchorage of bars
Basic anchorage length lb = (f/4) (fyd / fbd) ( IRC 112 / clause 15.2.3.3 (1) )
Grade of Concrete fck = 35 Mpa
Ultimate bond stress fbd = 3.00 Mpa ( IRC 112 / table 15.3 )
fyd = fyk/ 1.1.5
fy = 500 Mpa
fyd = 434.783 Mpa
Basic anchorage length lb = (f/4) (fyd / fbd)
Design anchorage Length

lbd = Max aa lb As,req / As,prov
lb,min = Max ( 0.3 lb , 10f , 100mm ) for anchorage in tension
aa = 0.7
As,req / As,prov = 1

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dia of bar 32 32 32 32 32 32 32
Basis anchorage length l b mm 1159.4 1159.4 1159.4 1159.4 1159.4 1159.4 1159.4
l b,min mm 347.8 347.8 347.8 347.8 347.8 347.8 347.8
l bd mm 811.6 811.6 811.6 811.6 811.6 811.6 811.6
ULS CHECK FOR COMPOSITE SECTION: SHEAR FORCE
Design Parameters
fck = 35.0 Mpa
fcd = acc fck/ym

acc = 0.67
gm = 1.5
fcd = 15.63 Mpa
fyk = 500 Mpa

gs = 1.15
fyd = fyk /gs

fyd = 434.78 Mpa
fywd = 0.8 fyk /gs

fywd = 347.83 Mpa
Reduction factor for section b/w 0.5d ≤ av ≤ 2d

b = av / 2d ( IRC 112 / clause 10.3.3.3 (7) )
SHEAR FORCE SUMMERY
LC-1
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Precast Beam T 15.29 12.16 10.16 10.56 7.03 3.51 0.00 1.35
Deck Outer Girder T 15.06 12.72 10.89 11.30 7.53 3.77 0.00 1.35
SIDL T 10.52 10.52 10.52 7.45 7.45 4.39 1.45 1.35
Surfacing T 4.50 4.50 4.38 3.47 3.08 1.76 0.45 1.75
FP DL
FP LL
LL (with Impact) T 39.31 35.74 34.14 29.74 26.46 19.40 12.75 1.5
LL (correspond to Max BM) T 40.84 40.84 39.01 33.98 30.25 22.17 14.57 1.5
Factored Shear Force

LC-1 Basic Comb
VED T 122.02 109.28 101.50 90.23 74.80 47.93 21.87
VED(Correspod to Max BM) T 124.32 116.94 108.81 96.60 80.47 52.08 24.60
deff m 1.41 1.41 1.41 1.41 1.41 1.40 1.40
Reduction factor b 0.50 0.50 0.74 0.82 1.00 1.00 1.00
VED' = VED* b T 61.01 54.64 74.63 73.54 74.80 47.93 21.87


2
r1 = Min Asl /bw d

0.02
scp = 0 Mpa
3/2 1/2
nmin = 0.031 k fck
Check of Shear Reinforcement Requirement

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
2
Asl m 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113
d T 1.411 1.411 1.411 1.411 1.411 1.397 1.397
k 1.38 1.38 1.38 1.38 1.38 1.38 1.38
bw m 0.750 0.750 0.562 0.488 0.325 0.325 0.325
r1 0.009 0.009 0.012 0.014 0.020 0.020 0.020
nmin 0.296 0.296 0.296 0.296 0.296 0.297 0.297
VRdc T 50.921 50.921 41.970 38.205 28.593 28.353 28.353
VED' T 61.012 54.640 74.631 73.540 74.795 47.927 21.866
Provide Design
Provide Design
Provide Design
Provide Design
Provide Design
Provide Design
Provide min.
Shear Reinf.
Shear Reinf.
Shear Reinf.
Shear Reinf.
Shear Reinf.
Shear Reinf.
Check Shear Reinf.
shear reinf.
Requirement
CHECK FOR SECTION MAXIMUM SHEAR CAPACITY :
Vccd = 0 T
Vtd = 0 T
'
VNS = VED -Vccd -Vtd
VNS = VED'
Variation of q 45
o
≥ q ≥ 21.80 o
Considering q = 45 o
for maximum shear capacity of section
VRdmax = acw * bw * z * n1 * fcd / ( cot q +tan q) ( IRC 112 / clause 10.3.3.2 Eq 10.8 )
acw = 1
z = 0.9*d
n1 = 0.6 for fck ≤ 80 Mpa
= Max 0.9- fck/250 for fck > 80 Mpa

0.5
= 0.6
Section At unit c/L brg. deff L/8 L/8 2L/8 3L/8 4L/8
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
VNS T 61.012 54.640 74.631 73.540 74.795 47.927 21.866

bw m 0.750 0.750 0.562 0.488 0.325 0.325 0.325
d m 1.411 1.411 1.411 1.411 1.411 1.397 1.397
z m 1.27 1.27 1.27 1.27 1.27 1.26 1.26
VRdmax T 446.69 446.69 334.73 290.92 193.56 191.68 191.68
Check OK/ REVISE OK OK OK OK OK OK OK
FINDING VALUE OF q AT DESIGN SECTIONS FOR DESIGN SHEAR REINFORCEMENT

VRdmax = VNS
-1
q = 0.5 sin [ 2*VNS / (acw * bw * z * v1 * fcd) ] ( IRC 112 / clause 10.3.3.2 Eq 10.8 )

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
VNS T 61.01 54.64 74.63 73.54 74.80 47.93 21.87

bw m 0.750 0.750 0.562 0.488 0.325 0.325 0.325
d m 1.411 1.411 1.411 1.411 1.411 1.397 1.397
z m 1.270 1.270 1.270 1.270 1.270 1.258 1.258
q deg 3.93 3.51 6.44 7.32 11.37 7.24 3.28
q adopted deg 45 45 45 45 45 45 45
FINDING DESIGN SHEAR REINFORCEMENT REQUIREMENT
VNS = VRds = (Asw/s) *z *fywd *cotq ( IRC 112 / clause 10.3.3.2 Eq 10.7 )
Asw/s = VNS / z fywd cotq
Minimum shear reinforcement ( IRC 112 / clause 10.3.3.5 Eq 10.20 )

Asw, min = rw,min * s * bw
rw, min = ( 0.072 √ fck ) / fyk

= 0.00085

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
VNS T 61.012 54.640 74.631 73.540 74.795 47.927 21.866

bw m 0.750 0.750 0.562 0.488 0.325 0.325 0.325
z m 1.27 1.27 1.27 1.27 1.27 1.26 1.26
qdesign deg 45.000 45.000 45.000 45.000 45.000 45.000 45.000
Asw/s mm2/m 1381.29 1237.02 1689.62 1664.91 1693.33 1095.69 499.893
Additional requirement (suspension reinf) 1351.46
Asw,min /s mm2/m 76.67 76.67 57.46 49.94 33.22 55.37 55.37
Legs nos 4 2 2 2 2 2 2
Provide Asw dia mm 12 12 12 12 12 12 12
spacing mm 120 120 120 120 120 200 200
Asw/s provide 3769.9 1885.0 1885.0 1885.0 1885.0 1131.0 1131.0
Check Ok/Revise OK OK OK OK OK OK OK
Additional Tensile force DFd to be accounted in longitudinal reinforcement ( IRC 112 / clause 10.3.3.2 (6) )
DFd = 0.5 VED (cotq - cot a)
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
VED(Correspond to Max BM) T 124.32 116.94 108.81 96.60 80.47 52.08 24.60
z m 1.27 1.27 1.27 1.27 1.27 1.26 1.26
DFd(Correspond to Max BM) T 62.16 58.47 54.41 48.30 40.23 26.04 12.30
Check for Shear Reinforcement within 0.75av support region ( IRC 112 / clause 10.3.3.2 (7)& (8))
Check required if b factor is considered for

VED = 61.0 T
Asw provided within central 0.75 av zone.
calculation of shear reinforcement.

av = deff = 1.41 m
0.75 av = 1.05825 m
2
Asw provided = 3769.9 mm /m
2
Asw_0.75av = 3989.51 mm
VED ≤ Asw * fywd
Asw_0.75av ≥ VED/fywd
2 2
≥ 1754.09 mm < 3989.51 mm OK
DESIGN FOR INTERFACE SHEAR : ( IRC 112 / clause 10.3.4)

vEdi = b VEd /z bi
b = Ratio of longitudinal force in new concrete and total longitudinal force
= 1
bi = 0.75 m bi = 0.75
vRdi = Min msn + r fyd [ msina +cos a]

0.5nfcd = 4.16 Mpa
r = As /Ai
As = Area of reinforcement crossing the inter face
Aj = Interface area of joint
2
Aj = 750000 mm Considering 1 m length
m = 0.6 Assuming smooth surface

sn = 0 Mpa
a = 90 deg
n = 0.6 [ 1 - fck /310 ]

= 0.532
As min = 0.15 % of interface area

= 0.15 * bi *1000 / 100 mm2/m
2
= 1125 mm /m
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
VED T 122.02 109.28 101.50 90.23 74.80 47.93 21.87

z m 1.270 1.270 1.270 1.270 1.270 1.258 1.258
vEdi N/mm2 1.281 1.147 1.066 0.947 0.785 0.508 0.232
Legs nos 4 4 4 4 4 4 4
spacing mm 120 120 120 120 120 200 200
Asw/s provide 3769.9 3769.9 3769.9 3769.9 3769.9 2261.9 2261.9
Check As ≥ As,min OK OK OK OK OK OK OK
r 0.005 0.005 0.005 0.005 0.005 0.003 0.003
vRdi N/mm2 1.311 1.311 1.311 1.311 1.311 0.787 0.787
Check vEDi ≤ vRdi OK OK OK OK OK OK OK
CHECK FOR MINIMUM TRANSVERSE REINFORCEMENT DECK SLAB (COMPRESSIN FLANGE):

CHECK FOR SHEAR IN FLANGED PORTION

fcd = 0.45 *fck
= 15.75 Mpa
fyd = fyk /gs
fyd = 434.78 Mpa
b = Ratio of longitudinal force in deck and total longitudinal force ( IRC 112 / clause 10.3.5)
= 1
vEd = bVED/z hf Total Longitudinal Shear Stress
Longitudinal force on the one side of flange (section A-A)
vEdf = vEd * beff1/ beff
hf = 0.22 m
beff1/beff = 0.375
o
Variation of qf 45 ≥ q ≥ 26.5 o For compression flange
CHECK FOR SECTION MAXIMUM PERMISSBLE LONGITUDINAL SHEAR STRESS:
vEdf,max = n fcd sinqf cosqf
Considering qf = 26.5
o
n = 0.6 [ 1 - fck /310 ] , fck in MPA

= 0.532
beff = 3 m
vEdf,max = 3.32 Mpa A
0.75 hf = 0.22
beff1 = 1.125
A
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
VED Tm 122.02 109.28 101.50 90.23 74.80 47.93 21.87

z m 1.27 1.27 1.27 1.27 1.27 1.26 1.26
vEd Mpa 4.37 3.91 3.63 3.23 2.68 1.73 0.79
vEdf Mpa 1.638 1.467 1.362 1.211 1.004 0.650 0.296
FINDING q f
qf = 0.5 sin-1 [ 2vEDf / n fcd ]
qf deg 11.59 10.32 9.56 8.46 6.98 4.49 2.04
Check OK/ REVISE qf < qfmax OK OK OK OK OK OK OK
Check OK/ REVISE vEDf < vEdf,max OK OK OK OK OK OK OK
REINFORCEMENT REQUIREMENT IN DECK FOR LONGITUDINAL SHEAR

Transverse reinforcement per unit length
Asf /sf = vEDf * hf / fyd cot qf

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
vEdf Mpa 1.47 1.36 1.21 1.00 0.65 0.30

qdesign deg 26.50 26.50 26.50 26.50 26.50 26.50
2
Asf /sf mm /m 370.05 343.70 305.55 253.28 163.89 74.77
No exta reinforcement is required if v Edf 0.4fcd = 6.25 Mpa

< 0.4fcd
As there will be transverse bending will exist along with shear b/w precast beam & deck
Check for Minimum Requirement in transverse direction
Reinforcement requirement for transverse bending of deck

2
As, deck = 2000 mm /m ( Including Top & Bottom Both reinf)
As,trans = Max Asf if vEdf > 0.4fcd

0.5 Asf + As,deck
As,deck if vEdf < 0.4fcd

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Asf, exta mm2/m 0.00 0.00 0.00 0.00 0.00 0.00

2
As, deck mm /m 2000 2000 2000 2000 2000 2000
2
As,trans mm /m 2000 2000 2000 2000 2000 2000
dia mm 16 16 16 16 16 16
At Top spacing mm 100 100 100 100 100 100
dia mm 12 12 12 12 12 12
At Bottom spacing mm 150 150 150 150 150 150
As,trans 2764.6 2764.6 2764.6 2764.6 2764.6 2764.6
Check OK/ REVISE OK OK OK OK OK OK

SLS STRESS CHECK:
BENDING MOMENT SUMMERY
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Precat Beam Tm -0.30 17.41 28.61 26.28 44.52 55.46 59.10

SIDL Tm 0.03 13.75 21.90 23.59 37.37 46.47 49.47
Surfacing Tm -0.04 6.05 9.47 10.26 16.27 20.33 21.68
FP DL Tm
FP LL Tm
Live Load Tm 0.00 44.26 67.45 72.64 112.52 137.21 149.27
A) OUTER GIRDER
Modular ratio for Section Analsys of Concrete
For short term = Ecm = 32000 Mpa
Creep factor = f = 1.24
For long term = Ecm' = 14304.3 Mpa
FINDING OUT STRESSES IN BEAM DUE TO SELFWEIGHT OF BEAM & DECK SLAB
Es = 200000 Mpa ( IRC 112 / clause 12.2 )
Eceff = 14304.3 Mpa
Modular ratio = Es/Eceff
= 13.98
Bending Moment due to Selfweight of Beam + Deck slab

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Precat Beam Tm -0.30 17.41 28.61 26.28 44.52 55.46 59.10

Precast Beam + Deck Tm -0.51 35.13 58.23 53.41 91.18 113.84 121.39
0.75
ec
2 0.2
3 0.1 dc
4
0.325 1.3
d-dc
Ast
0.2 es
0.25
0.75 Stresses Strains

Reinforcement provided at section
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113

deff m 1.19 1.19 1.19 1.19 1.19 1.18 1.18
dAst_O m 1.22 1.22 1.22 1.22 1.22 1.22 1.22
Finding compressive stresses at girder top & tensile stress in steel

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
BM (BEAM +DECK) Tm -0.51 35.13 58.23 53.41 91.18 113.84 121.39

Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113
deff m 1.19 1.19 1.19 1.19 1.19 1.18 1.18
dc m 0.532 0.532 0.532 0.532 0.532 0.560 0.560
Iz (Transformed) m4 0.093 0.093 0.093 0.093 0.093 0.100 0.100
N/mm2
Stresses At
Gtop 2.01 3.33 3.05 5.21 6.41 6.83

Girder Ast_cg N/mm2 -34.84 -57.75 -52.96 -90.41 -98.62 -105.17
Ast_outer N/mm2 -36.53 -60.55 -55.53 -94.80 -105.93 -112.96
FINDING OUT STRESSES IN COMPOSITE SECTION DUE TO SIDL & SURFACING

Es = 200000 Mpa
Eceff = 14304.3 Mpa

= 13.98
Bending Moment due to SIDL + Surfacing + FPDL +FPLL

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
SIDL Tm 0.03 13.75 21.90 23.59 37.37 46.47 49.47

Surfacing Tm -0.04 6.05 9.47 10.26 16.27 20.33 21.68
FPDL 0.00 0.00 0.00 0.00 0.00 0.00 0.00
FPLL 0.00 0.00 0.00 0.00 0.00 0.00 0.00
SIDL+Surfaing Tm -0.01 19.79 31.38 33.85 53.64 66.80 71.16

beff = 3.00
1 0.75 0.22 ec
2 0.2
3 0.1 dc
4
0.325 1.3
d-dc
Ast
0.2 es
0.25

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113

deff m 1.41 1.41 1.41 1.41 1.41 1.40 1.40
dAst_O m 1.44 1.44 1.44 1.44 1.44 1.44 1.44

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
BM (SIDL +Surfacing) Tm -0.01 19.79 31.38 33.85 53.64 66.80 71.16

Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113
deff m 1.4110 1.4110 1.4110 1.4110 1.4110 1.3973 1.3973
dc m 0.33 0.33 0.33 0.33 0.33 0.35 0.35
Iz (Transformed) m4 0.19 0.19 0.19 0.19 0.19 0.21 0.21
Dtop 0.000 N/mm2 0.33 0.53 0.57 0.91 1.09 1.16
Deck
N/mm2
Stresses At
Dbottom 0.220 0.11 0.17 0.19 0.29 0.41 0.43

2
Gtop 0.220 N/mm 0.11 0.17 0.19 0.29 0.41 0.43
Girder Ast_cg 1.397 N/mm 2
-15.59 -24.72 -26.67 -42.27 -45.72 -48.71
2
Ast_outer 1.443 N/mm -16.05 -25.45 -27.45 -43.51 -47.72 -50.83
FINDING OUT STRESSES IN COMPOSITE SECTION DUE TO LIVE LOAD
Es = 200000 Mpa
Eceff = 32000 Mpa
= 6.25
Bending Moment due to Live Load

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Live Load Tm 0.00 44.26 67.45 72.64 112.52 137.21 149.27
beff = 3.00
1 0.75 0.22
ec
2 0.2
3 0.1 dc
4
0.325 1.3
d-dc
Ast
0.2 es
0.25

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113

deff m 1.41 1.41 1.41 1.41 1.41 1.40 1.40
dAst_O m 1.44 1.44 1.44 1.44 1.44 1.44 1.44

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
BM (Live Load) Tm 0.00 44.26 67.45 72.64 112.52 137.21 149.27

Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113
deff m 1.4110 1.4110 1.4110 1.4110 1.4110 1.3973 1.3973
dc m 0.22 0.22 0.22 0.22 0.22 0.23 0.23
Iz (Transformed) m4 0.10 0.10 0.10 0.10 0.10 0.11 0.11
Dtop 0.000 N/mm2 1.01 1.53 1.65 2.56 2.97 3.23
Deck
N/mm2
Stresses At
Dbottom 0.220 0.00 -0.01 -0.01 -0.01 0.18 0.19

2
Gtop 0.220 N/mm 0.00 -0.01 -0.01 -0.01 0.18 0.19
-34.28 -52.23 -56.25 -87.14 -92.34 -100.46
Ast_outer 1.443 N/mm2 -35.20 -53.63 -57.76 -89.48 -95.97 -104.40
SUMMERY OF STRESSES
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Stresses due to Precast Beam & Deck slab
Dtop N/mm2
Deck
N/mm2
Stresses At
Dbottom
Gtop N/mm2 2.01 3.33 3.05 5.21 6.41 6.83
Girder Ast_cg N/mm2 -34.84 -57.75 -52.96 -90.41 -98.62 -105.17
2
Ast_outer N/mm -36.53 -60.55 -55.53 -94.80 -105.93 -112.96
Stresses due to SIDL+Surfacing +FPDL +FPLL

Dtop N/mm2 0.33 0.53 0.57 0.91 1.09 1.16
Deck
N/mm2
Stresses At
Dbottom 0.11 0.17 0.19 0.29 0.41 0.43

Gtop N/mm2 0.11 0.17 0.19 0.29 0.41 0.43
Girder Ast_cg N/mm2 -15.59 -24.72 -26.67 -42.27 -45.72 -48.71
2
Ast_outer N/mm -16.05 -25.45 -27.45 -43.51 -47.72 -50.83
Stresses due to Live Load

Dtop N/mm2 1.01 1.53 1.65 2.56 2.97 3.23
Deck 2
Stresses At
Dbottom N/mm 0.00 -0.01 -0.01 -0.01 0.18 0.19

Gtop N/mm2 0.00 -0.01 -0.01 -0.01 0.18 0.19
Girder Ast_cg N/mm2 -34.28 -52.23 -56.25 -87.14 -92.34 -100.46
2
Ast_outer N/mm -35.20 -53.63 -57.76 -89.48 -95.97 -104.40
Stresses at section due to differential shrinkage

Dtop N/mm2 -0.23 -0.21 -0.20 -0.18 -0.18 -0.18
Deck
N/mm2
Stresses At
Dbottom -0.52 -0.51 -0.50 -0.46 -0.46 -0.46

Gtop N/mm2 1.13 1.15 1.16 1.19 1.19 1.19
Girder Ast_cg N/mm2 -6.38 -5.59 -5.85 -4.90 -4.90 -4.90
2
Ast_outer N/mm -7.24 -6.44 -6.70 -5.74 -5.74 -5.74
+ve temperature differences

Dtop N/mm2 3.60167 3.65 3.67 3.71 3.71 3.71
Deck
N/mm2
Stresses At
Dbottom -1.41 -1.41 -1.41 -1.41 -1.41 -1.41

Gtop N/mm2 -1.41 -1.41 -1.41 -1.41 -1.41 -1.41
Girder Ast_cg N/mm2 9.14 8.22 7.86 7.07 7.07 7.07
2
Ast_outer N/mm 11.60 10.35 9.86 8.77 8.77 8.77
-ve temperature differences

Dtop N/mm2 -2.11 -2.09 -2.08 -2.05 -2.05 -2.05
Deck
N/mm2
Stresses At
Dbottom 0.92 0.95 0.96 0.98 0.98 0.98

Gtop N/mm2 0.92 0.95 0.96 0.98 0.98 0.98
Girder Ast_cg N/mm2 -9.07 -8.94 -8.89 -8.77 -8.77 -8.77
2
Ast_outer N/mm -12.02 -11.89 -11.84 -11.72 -11.72 -11.72
1) Rare Combination LC-1
Load Factor
Beam +Deck slab 1 Max Concrete stress = 7.458 Mpa
SIDL + Surfacing +FPDL+FPLL 1 Max permissible stress = 16.8 Mpa OK
Live Load 1
Differential Shrinkage 0 Max Tensle Stress in steel = -268.19 Mpa
+ve Temperature 0 Max permissible stress = -300 Mpa OK
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 1.34 2.07 2.23 3.47 4.06 4.40
Deck
N/mm2
Stresses At
Dbottom 0.22 0.10 0.16 0.18 0.28 0.58 0.63

Gtop 0.22 N/mm2 2.11 3.50 3.23 5.50 6.99 7.46
Girder Ast_cg 1.40 N/mm2 -84.71 -134.70 -135.88 -219.82 -236.69 -254.33
Ast_outer 1.44 N/mm2 -87.78 -139.63 -140.75 -227.79 -249.62 -268.19

Load Factor
SIDL + Surfacing 1 Max permissible stress = 16.8 Mpa OK
Live Load 1
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 1.11 1.85 2.02 3.29 3.89 4.22
Deck
N/mm2
Stresses At
Dbottom 0.22 -0.42 -0.34 -0.32 -0.18 0.12 0.16

Gtop 0.22 N/mm2 3.24 4.65 4.39 6.69 8.18 8.65
Girder Ast_cg 1.40 N/mm2 -91.09 -140.29 -141.73 -224.72 -241.59 -259.23
Ast_outer 1.44 N/mm2 -95.02 -146.07 -147.45 -233.53 -255.36 -273.93

Load Factor
Live Load 1
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 4.94 5.72 5.90 7.18 7.78 8.11
Deck
N/mm2
Stresses At
Dbottom 0.22 -1.31 -1.25 -1.23 -1.13 -0.83 -0.78

Gtop 0.22 N/mm2 0.70 2.08 1.82 4.09 5.58 6.05
Girder Ast_cg 1.40 N/mm2 -75.57 -126.48 -128.02 -212.75 -229.62 -247.26
Ast_outer 1.44 N/mm2 -76.18 -129.28 -130.89 -219.02 -240.85 -259.42
Load Factor
Live Load 1
-ve Temperature 1

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 -0.77 -0.02 0.15 1.42 2.01 2.35
Deck
N/mm2
Stresses At
Dbottom 0.22 1.03 1.11 1.14 1.26 1.57 1.61

Gtop 0.22 N/mm2 3.04 4.44 4.19 6.48 7.97 8.44
Girder Ast_cg 1.40 N/mm2 -93.78 -143.63 -144.77 -228.59 -245.46 -263.10
Ast_outer 1.44 N/mm2 -99.80 -151.52 -152.58 -239.51 -261.34 -279.92

Load Factor
Live Load 1
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 4.72 5.50 5.69 7.01 7.60 7.93
Deck
N/mm2
Stresses At
Dbottom 0.22 -1.83 -1.75 -1.73 -1.59 -1.29 -1.25

Gtop 0.22 N/mm2 1.83 3.23 2.98 5.28 6.77 7.24
Girder Ast_cg 1.40 N/mm2 -81.96 -132.07 -133.87 -217.65 -234.52 -252.16
Ast_outer 1.44 N/mm2 -83.42 -135.72 -137.59 -224.76 -246.58 -265.16

Load Factor
Live Load 1
-ve Temperature 1

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 -1.00 -0.23 -0.05 1.24 1.84 2.17
Deck
N/mm2
Stresses At
Dbottom 0.22 0.50 0.61 0.64 0.80 1.10 1.14

Gtop 0.22 N/mm2 4.17 5.59 5.35 7.67 9.16 9.63
Girder Ast_cg 1.40 N/mm2 -100.16 -149.23 -150.62 -233.49 -250.36 -268.00
Ast_outer 1.44 N/mm2 -107.04 -157.96 -159.28 -245.25 -267.08 -285.65
1) Quasi-Permanent Combination LC-1
Load Factor
Live Load 0
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 0.33 0.53 0.57 0.91 1.09 1.16
Deck
N/mm2
Stresses At
Dbottom 0.22 0.11 0.17 0.19 0.29 0.41 0.43

Gtop 0.22 N/mm2 2.12 3.50 3.24 5.51 6.81 7.27
Girder Ast_cg 1.40 N/mm2 -50.43 -82.47 -79.63 -132.68 -144.35 -153.87
Ast_outer 1.44 N/mm2 -52.58 -86.00 -82.98 -138.31 -153.65 -163.79

Load Factor
Live Load 0
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 0.11 0.32 0.37 0.73 0.92 0.99
Deck
N/mm2
Stresses At
Dbottom 0.22 -0.42 -0.33 -0.31 -0.17 -0.06 -0.03

Gtop 0.22 N/mm2 3.25 4.65 4.40 6.70 8.01 8.46
Girder Ast_cg 1.40 N/mm2 -56.81 -88.06 -85.48 -137.58 -149.25 -158.77
Ast_outer 1.44 N/mm2 -59.83 -92.44 -89.68 -144.05 -159.39 -169.53

Load Factor
Live Load 0
+ve Temperature 0.5 Max permissible stress = -400 Mpa OK
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 2.14 2.36 2.41 2.76 2.95 3.02
Deck
N/mm2
Stresses At
Dbottom 0.22 -0.60 -0.53 -0.52 -0.41 -0.30 -0.27

Gtop 0.22 N/mm2 1.41 2.80 2.53 4.80 6.11 6.56
Girder Ast_cg 1.40 N/mm2 -45.87 -78.36 -75.70 -129.15 -140.81 -150.34
Ast_outer 1.44 N/mm2 -46.78 -80.82 -78.05 -133.93 -149.27 -159.41
Load Factor
Live Load 0
-ve Temperature 0.5

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 -0.72 -0.51 -0.47 -0.12 0.07 0.14
Deck
N/mm2
Stresses At
Dbottom 0.22 0.57 0.65 0.67 0.78 0.90 0.92

Gtop 0.22 N/mm2 2.58 3.98 3.72 6.00 7.31 7.76
Girder Ast_cg 1.40 N/mm2 -54.97 -86.94 -84.07 -137.06 -148.73 -158.26
Ast_outer 1.44 N/mm2 -58.59 -91.94 -88.90 -144.17 -159.51 -169.65

Load Factor
Live Load 0
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 1.91 2.14 2.20 2.59 2.77 2.85
Deck
N/mm2
Stresses At
Dbottom 0.22 -1.12 -1.04 -1.02 -0.88 -0.76 -0.74

Gtop 0.22 N/mm2 2.54 3.95 3.70 5.99 7.30 7.75
Girder Ast_cg 1.40 N/mm2 -52.25 -83.95 -81.55 -134.05 -145.72 -155.24
Ast_outer 1.44 N/mm2 -54.03 -87.26 -84.75 -139.66 -155.00 -165.14

Load Factor
Live Load 0
-ve Temperature 0.5

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 -0.95 -0.73 -0.67 -0.30 -0.11 -0.04
Deck
N/mm2
Stresses At
Dbottom 0.22 0.04 0.14 0.17 0.32 0.43 0.46

Gtop 0.22 N/mm2 3.71 5.13 4.88 7.19 8.50 8.95
Girder Ast_cg 1.40 N/mm2 -61.35 -92.53 -89.92 -141.96 -153.63 -163.16
Ast_outer 1.44 N/mm2 -65.84 -98.38 -95.60 -149.91 -165.25 -175.39
LIMIT STATE OF CRACKING :
Asmin = kc k fct,eff Act / ss ( IRC 112 / clause 12.3.3 (2) )
For Web
k = 0.65 For web with h>800mm
fcteff = fctm
= 2.77 Mpa
Act = Area of concrete within tensile zone just before the first crack form
section behaves elastically until the tensile fiber stress reaches fctm.
hence Neutral axis depth will be considered for gross section
Spacing = 216.667 mm
ss = fyk
= 500 Mpa

3 @ 3.0
1 0.8 0.22
2 0.2
3 0.1 yt
4
1.52
0.325 1.3
NA
5 0.2
6 0.25
0.75

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
h m 1.52 1.52 1.52 1.52 1.52 1.52 1.52

yt m 0.56 0.56 0.54 0.53 0.51 0.51 0.51
bw m 0.75 0.75 0.56 0.49 0.33 0.33 0.33
Act (D-yt)*bw m2 1.01 1.01 0.85 0.78 0.62 0.62 0.62
Asmin mm2 1459.2 1459.2 1220.6 1123.5 900.2 900.2 900.2
As,provided mm2 9651.0 9651.0 9651.0 9651.0 9651.0 11259.5 11259.5
wk,max = 0.3 mm

srmax = Maximum crack spacing
= 0.17 f
3.4c +
rPeff
Bar dia f = 32 mm
5 (c +f/2) = 385 mm
Spacing b/w bars = 104.667 mm < 385
rP,eff = As/ Ac,eff
Ac,eff = Min 2.5 ( h - d )

( h - x/3 )
h/2

Es
0.6 ssc / Es
ae = Es/Ecm
Es = 200000 Mpa
Ecm = 32000 Mpa
ae = 6.25

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
As m2 0.00965 0.00965 0.009651 0.009651 0.009651 0.01126 0.011259

h m 1.52 1.52 1.52 1.52 1.52 1.52 1.52
d m 1.41 1.41 1.41 1.41 1.41 1.40 1.40
hcef1 2.5*(h-d) m 0.27 0.27 0.27 0.27 0.27 0.31 0.31
Avg web width of tension zone m 0.750 0.750 0.750 0.750 0.750 0.750 0.750
Acef1 m2 0.204 0.204 0.204 0.204 0.204 0.230 0.230
rP,eff 0.047 0.047 0.047 0.047 0.047 0.049 0.049
srmax mm 322.60 322.60 322.60 322.60 322.60 318.57 318.57
Finding Out Cracak width for Load case LC-1 Quasi permanent Load combination
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
ssc N/mm2 -52.5839 -86.00 -82.98 -138.31 -153.65 -163.79
esm - ecm 0.00016 0.000258 0.000249 0.000502 0.00058 0.000634
wk mm 0.05 0.08 0.08 0.16 0.19 0.20
Check OK OK OK OK OK OK
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
ssc N/mm2 -59.83 -92.44 -89.68 -144.05 -159.39 -169.53
esm - ecm 0.00018 0.000277 0.000269 0.00053 0.00061 0.000663
wk mm 0.06 0.09 0.09 0.17 0.19 0.21
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
ssc N/mm2 -46.78 -80.82 -78.05 -133.93 -149.27 -159.41
esm - ecm 0.00014 0.000242 0.000234 0.00048 0.00056 0.000612
wk mm 0.05 0.08 0.08 0.15 0.18 0.20
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
ssc N/mm2 -58.59 -91.94 -88.90 -144.17 -159.51 -169.65
esm - ecm 0.00018 0.000276 0.000267 0.000531 0.00061 0.000663
wk mm 0.06 0.09 0.09 0.17 0.20 0.21
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
ssc N/mm2 -54.03 -87.26 -84.75 -139.66 -155.00 -165.14
esm - ecm 0.00016 0.00026 0.00025 0.00051 0.00059 0.00064
wk mm 0.05 0.08 0.08 0.16 0.19 0.20
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
ssc N/mm2 -65.84 -98.38 -95.60 -149.91 -165.25 -175.39
esm - ecm 0.00020 0.00030 0.00029 0.00056 0.00064 0.00069
wk mm 0.06 0.10 0.09 0.18 0.20 0.22
STRESS CALCULATION DUE TO TEMPERATURE OUTER GIRDER:
Coefficent of thermal expansion = 1.2E-05
2
Ec = 32000 N/mm
2
Es = 200000 N/mm
OUTER GIRDER, MID SPAN

POSITIVE TEMPERATURE DIFFERENCES
3.00 NEGATIVE TEMPERATURE DIFFERENCES
17.8 f1 f1 -10.6
0.15 0.75
f2
4 0.22 0.25
f3 f2
0.25 f3 -0.7
f4 0.2 f4 0.2
f5 f5
f6 0.1 f6
1.52
1.52
1 1.52 0.325 0.55 0.62
f7 f7
0.2
f9 f8
f8 0.2
f9
-0.8
0.15 f10 0.25 f10 0.25
2.1 0.75 -6.6
+ve Temperature
POSITIVE TEMPERATURE DIFFERENCES h Temp
Points Depth temp b1 b2 Av. width Area y A*y A*y2 av. temp A*t A*t*y 0 17.8
o 2 3 4 o 2o 3o
mm C m m m m m C m C m C 0.15 4
0 0.4 0
f1 0 17.8 1.37 0
f2 0.15 4 3.00 3.00 3.00 0.45 0.08 0.03 0.00 10.90 4.91 0.37 1.52 2.1
f3 0.22 2.88 3.00 3.00 3.00 0.21 0.19 0.04 0.01 3.44 0.72 0.13
f4 0.42 0 0.75 0.75 0.75 0.15 0.32 0.05 0.02 1.44 0.22 0.07
f5 0.4 0 0.75 0.84 0.79 -0.02 0.41 -0.01 0.00 0.00 0.00 0.00
f6 0.52 0 0.84 0.33 0.58 0.07 0.47 0.03 0.02 0.00 0.00 0.00
f7 1.37 0 0.33 0.33 0.33 0.28 0.95 0.26 0.25 0.00 0.00 0.00
f8 1.07 0 0.33 0.33 0.33 -0.10 1.22 -0.12 -0.15 0.00 0.00 0.00
f9 1.27 0 0.33 0.75 0.54 0.11 1.16 0.12 0.14 0.00 0.00 0.00
f10 1.52 2.1 0.75 0.75 0.75 0.19 1.40 0.26 0.36 1.05 0.20 0.27
1.52
Total 1.3375 0.67475 0.648 6.040 0.845
e0 x SA - q x SAy = a x SAt
e0 x 1.338 - q x 0.675 = 1.2E-05 x 6.040 ------------------- (1)
e0 SAy - q x SAy2 = a x SAyt

e0 x 0.67475 - q x 0.648 = 1.2E-05 x 0.845 ------------------- (2) + ve = compression
- ve = tension
By solving equation (1) & (2)
e0 = 9.8E-05
q = 8.6E-05 rad./m
STRESSES AT
3.71
Dtop Dbottom Gtop Ast_cg Ast_outer
Points Depth f ei = Ec ( at + yq - eo ) ytop 0.00 0.22 0.22 1.40 1.44
2 2 2 2 2
mm N/mm Eigen stresses N/mm N/mm N/mm N/mm N/mm2
0 0 -2.02
f1 0 3.71
f2 0.15 -1.17 3.714 -1.410 -1.410 7.065 8.772
f3 0.22 -1.41
f4 0.42 -1.97
f5 0.4 -2.02 Stresses At cg. Of steel & outermost
f6 0.52 -1.69 steel is in steel
f7 1.37 0.64
f8 1.07 -0.18
f9 1.27 0.37 1.86
f10 1.52 1.86
Positive temp. stress
1.52 0
NEGATIVE TEMPERATURE DIFFERENCES
Points Depth temp b1 b2 Av. width Area y A*y A*y2 av. temp A*t A*t*y -ve Temperature
o 2 3
mm C m m m m m4 o
C m2 oC m3 oC h Temp
0 0 -10.6
f1 0 -10.6 0.25 -0.7
f2 0.22 -1.89 3.00 3.00 3.00 0.66 0.11 0.07 0.01 -6.24 -4.12 -0.45 0.45 0
f3 0.25 -0.70 0.75 0.75 0.75 0.02 0.24 0.01 0.00 -1.29 -0.03 -0.01 1.07 0
f4 0.42 -0.11 0.75 0.75 0.75 0.13 0.34 0.04 0.01 -0.40 -0.05 -0.02 1.27 -0.8
f5 0.45 0.00 0.75 0.62 0.69 0.02 0.44 0.01 0.00 -0.05 0.00 0.00 1.52 -6.6
f6 0.52 0.00 0.62 0.33 0.47 0.03 0.49 0.02 0.01 0.00 0.00 0.00
f7 1.27 -0.80 0.75 0.75 0.75 0.56 0.90 0.50 0.45 -0.40 -0.23 -0.20
f8 1.07 0.00 0.75 0.75 0.75 -0.15 1.17 -0.18 -0.21 -0.40 0.06 0.07
f9 1.27 -0.80 0.75 0.75 0.75 0.15 1.17 0.18 0.21 -0.40 -0.06 -0.07
f10 1.52 -6.60 0.75 0.75 0.75 0.19 1.40 0.26 0.36 -3.70 -0.69 -0.97
1.52
Total 1.61375 0.91077 0.851 -5.121 -1.647
e0 x 1.614 - q x 0.91077 = 1.2E-05 x -5.121 ------------------- (1)

e0 x 0.91077 - q x 0.851 = 1.2E-05 x -1.647 ------------------- (2)

e0 = -6.3E-05
q = -4.4E-05 rad./m
STRESSES AT
Dtop Dbottom Gtop Ast_cg Ast_outer -2.05
Points Depth f ei = Ec ( at + yq - eo ) ytop 0.00 0.22 0.22 1.40 1.44 1.40
mm N/mm2 Eigen stresses N/mm2 N/mm2 N/mm2 N/mm2 N/mm2

0 0
f1 0 -2.05
f2 0.22 0.98 -2.05165 0.98187 0.98187 -8.77066 -11.7211
f3 0.25 1.40
f4 0.42 1.38
f5 0.45 1.38 Stresses At cg. Of steel & outermost
f6 0.52 1.28 steel is in steel
f7 1.27 -0.09
f8 1.07 0.50 -2.67
f9 1.27 -0.09
f10 1.52 -2.67
1.52 0
OUTER GIRDER, SUPPORT SECTION

POSITIVE TEMPERATURE DIFFERENCES NEGATIVE TEMPERATURE DIFFERENCES
3.00
17.8 f1 f1 -10.6
0.15 0.75
f2
4 0.22 0.25
f3 f2
0.25 f3 -0.7
f4 0.2 f4 0.2
f5 f5
f6 0.00 f6
1.52
1.52
1 1.52 1.10 0.62
f7
f8
0.2
f7
-0.8
0.15 f8 f9 0.25
2.1 0.75 -6.6
Points Depth temp b1 b2 Av. width Area y A*y A*y2 av. temp A*t A*t*y +ve Temperature
o 2 3
mm C m m m m m4 o
0 0 17.8
f1 0 17.8 0.15 4
f2 0.15 4 3.000 3.000 3.000 0.450 0.075 0.034 0.0025 10.9 4.905 0.368 0.4 0
f3 0.22 2.88 3.000 3.000 3.000 0.210 0.185 0.039 0.0072 3.44 0.722 0.134 1.37 0
f4 0.42 0 0.750 0.750 0.750 0.150 0.320 0.048 0.0154 1.44 0.216 0.069 1.52 2.1
f5 0.420 0 0.750 0.750 0.750 0.000 0.420 0.000 0.0000 0 0.000 0.000
f6 0.4 0 0.750 0.750 0.750 -0.015 0.410 -0.006 -0.0025 0 0.000 0.000
f7 1.37 0 0.750 0.750 0.750 0.728 0.885 0.644 0.5698 0 0.000 0.000
f8 1.52 2.1 0.750 0.750 0.750 0.113 1.445 0.163 0.2349 1.05 0.118 0.171
1.52
Total 1.635 0.921 0.827 5.962 0.741
e0 x 1.635 - q x 0.92085 = 1.2E-05 x 5.962 ------------------- (1)

- ve = tension
e0 = 0.0001
q = 0.0001 rad./m
STRESSES AT 3.60
2 2 2 2 2
-1.87
0 0
f1 0 3.60
f2 0.15 -1.21 3.60 -1.41 -1.41 9.14 11.60
f3 0.22 -1.41
f4 0.42 -1.87
f7 1.37 1.23
2.52
f8 1.52 2.52
1.52 0

Points Depth temp b1 b2 Av. width Area y A*y A*y2 av. temp A*t A*t*y -ve Temperature
o 2 3
mm C m m m m m4 o
0 0 -10.6
f1 0 -10.6 0.25 -0.7
f2 0.22 -1.888 3.000 3.000 3.000 0.660 0.110 0.0726 0.0080 -6.244 -4.121 -0.453 0.45 0
f3 0.25 -0.7 0.750 0.750 0.750 0.023 0.235 0.0053 0.0012 -1.294 -0.029 -0.007 1.07 0
f4 0.42 -0.105 0.750 0.750 0.750 0.128 0.335 0.0427 0.0143 -0.4025 -0.051 -0.017 1.27 -0.8
f5 0.42 -0.105 0.750 0.750 0.750 0.000 0.420 0.0000 0.0000 -0.105 0.000 0.000 1.52 -6.6
f6 0.45 -1.1E-16 0.750 0.750 0.750 0.023 0.435 0.0098 0.0043 -0.0525 -0.001 -0.001
f7 1.07 0 0.750 0.750 0.750 0.465 0.760 0.3534 0.2686 -5.6E-17 0.000 0.000
f8 1.27 -0.8 0.750 0.750 0.750 0.150 1.170 0.1755 0.2053 -0.4 -0.060 -0.070
f9 1.52 -6.6 0.750 0.750 0.750 0.188 1.395 0.2616 0.3649 -3.7 -0.694 -0.968
1.52
Total 1.635 0.92085 0.867 -4.956 -1.516
e0 x 1.635 - q x 0.92085 = 1.2E-05 x -4.956 ------------------- (1)

e0 x 0.92085 - q x 0.867 = 1.2E-05 x -1.516 ------------------- (2)

e0 = -6.1E-05
q = -4.4E-05 rad./m
STRESSES AT
Points Depth f ei = Ec ( at + yq - eo ) ytop 0.00 0.22 0.22 1.40 1.44 1.34
2 2 2 2 2 2
mm N/mm Eigen stresses N/mm N/mm N/mm N/mm N/mm
0 0
f1 0 -2.11
f2 0.22 0.92 -2.11345 0.92225 0.92225 -9.07054 -12.0181
f3 0.25 1.34
f4 0.42 1.33
f7 1.07 0.45
f8 1.27 -0.14 -2.72
f9 1.52 -2.72
1.52 0
Summery of stresses at sections (+ve Temperature

Summery of stresses at sections (+ve Temperature Differences) Differences)
Section At unit c/L brg. deff L/8 TS 2L/8 3L/8 4L/8 STRESSES AT
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30 Dtop Dbottom Gtop Ast_cg Ast_outer
Dist
1 from 0 0.22 0.22 1.39729 1.443
Dtop 0.00 N/mm2 3.60 3.60 3.65 3.67 3.71 3.71 3.71
2
2 c/L brg. N/mm N/mm N/mm N/mm N/mm
2 2 2 2
N/mm2
STRESSES AT
Dbottom 0.22 -1.41 -1.41 -1.41 -1.41 -1.41 -1.41 -1.41 3 0 3.60 -1.41 -1.41 9.14 11.60
Gtop 0.22 N/mm2 -1.41 -1.41 -1.41 -1.41 -1.41 -1.41 -1.41 4 1.5 3.60 -1.41 -1.41 9.14 11.60
2
Ast_cg 1.40 N/mm 9.14 9.14 8.22 7.86 7.07 7.07 7.07 5 2.8 3.71 -1.41 -1.41 7.07 8.77
Ast_outer 1.44 N/mm2 11.60 11.60 10.35 9.86 8.77 8.77 8.77 6 8.8 3.71 -1.41 -1.41 7.07 8.77
Summery of stresses at sections (-ve Temperature

Summery of stresses at sections (-ve Temperature Differences) Differences)
Dist
1 from 0 0.22 0.22 1.39729 1.443
Dtop 0.00 N/mm2 -2.11 -2.11 -2.09 -2.08 -2.05 -2.05 -2.05
2
2 c/L brg. N/mm N/mm N/mm N/mm N/mm
2 2 2 2
2
STRESSES AT
Dbottom 0.22 N/mm 0.92 0.92 0.95 0.96 0.98 0.98 0.98 3 0 -2.11 0.92 0.92 -9.07 -12.02
Gtop 0.22 N/mm2 0.92 0.92 0.95 0.96 0.98 0.98 0.98 4 1.5 -2.11 0.92 0.92 -9.07 -12.02
Ast_cg 1.40 N/mm2 -9.07 -9.07 -8.94 -8.89 -8.77 -8.77 -8.77 5 2.8 -2.05 0.98 0.98 -8.77 -11.72
2
Ast_outer 1.44 N/mm -12.02 -12.02 -11.89 -11.84 -11.72 -11.72 -11.72 6 8.8 -2.05 0.98 0.98 -8.77 -11.72
FORCES DUE TO DIFFERENTIAL SHRINKAGE
SHRINKAGE AT  FOR DECK SLAB
ecs ,D,  = eca,D, ecd,D, 
eca ,D,  = 4.5E-05
ecd ,D,  = 0.0002
ecs ,D,  = 4.5E-05 + 0.0002

= 0.00024
SHRINKAGE AT  FOR PRECAST BEAM

ecs ,P,  = eca,P, ecd,P, 
eca ,P,  = 4.5E-05
ecd ,P,  = 0.0002
ecs ,P,  = 4.5E-05 + 0.0002

= 0.00025
SHRINKAGE AT TIME t (AT THE TIME OF CASTING OF DECK SLAB) IN PRECAST BEAM
t = 180 days
ecs ,P, ( t ) = eca,P ( t )ecd,P ( t )
eca ,P, ( t ) = bas(t) * eca,  0.00025 0.00012

0.50137
bas(t) = 1 - exp(-0.2 √t )
= 0.93166
eca ,P, ( t ) = 0.93166 x 4.5E-05

= 4.2E-05
ho kh
ecd ,P, ( t ) = bds(t,ts) * kh * ecd, 0 100 1
200 0.85
ecd, 0 = 0.00028 300 0.75
500 0.7
bds(t,ts) = ( t - ts ) 5000 0.7
(t-ts) + 0.04 √ ho3
ts = 1 days (Age at which drying shrinkage starts)
ho = 356 mm
bds(t,ts) = 0.400
kh = 0.736
ecd ,P, ( t ) = 8.1E-05
ecs ,P, ( t ) = 4.2E-05 + 8.1E-05

= 0.00012
CALCULATING STRESSES DUE TO DIFFERENTIAL SHRINKAGE :
Differential shrinkage strain
ediff = ecs ,D (  ) - [ ecs,P () - ecs,P ( t ) ]
= 0.00024 - [ 0.00025 - 0.00012 ]
= 0.00012
Restarined Force in slab 3.00

Fs = ediff Ecf Aslab (1-ef) / f
0.22
f = 2 dcen
1.52
f
(1- e ) / f = 0.432 1.30
Ecf = Modulus of elasticity of flange concrete

= 32000 Gpa
Finding Restrained stress in deck slab

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Acef m2 0.66 0.66 0.66 0.66 0.66 0.66 0.66
Fs T 109.31 109.31 109.31 109.31 109.31 109.31 109.31
2
Restrained stress Fs/Acef N/mm -1.66 -1.66 -1.66 -1.66 -1.66 -1.66 -1.66
Equilibrium Forces in composite section

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
A m2 1.64 1.64 1.50 1.45 1.34 1.34 1.34

4
Composite section Izz m 0.37 0.37 0.35 0.34 0.33 0.33 0.33
yt m 0.56 0.56 0.54 0.53 0.51 0.51 0.51
dcen m 0.45 0.45 0.43 0.42 0.40 0.40 0.40

2
Fs/Ac N/mm 0.67 0.67 0.73 0.75 0.82 0.82 0.82
Mcs Fs*dcen Tm 49.54 49.54 46.76 45.67 43.25 43.25 43.25
Top N/mm2 0.76 0.76 0.72 0.70 0.66 0.66 0.66

due to Moment
Stress at fibers
deck
Component
2
Bottom N/mm 0.46 0.46 0.42 0.41 0.37 0.37 0.37
Top N/mm2 0.46 0.46 0.42 0.41 0.37 0.37 0.37
Girder 2
Bottom N/mm -1.29 -1.29 -1.31 -1.32 -1.33 -1.33 -1.33
Net Stresses at deck/ bottom fibers
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Top N/mm2 0.00 -0.23 -0.23 -0.21 -0.20 -0.18 -0.18 -0.18
due to Moment
Stress at fibers
deck
Component
2
Bottom N/mm 0.22 -0.52 -0.52 -0.51 -0.50 -0.46 -0.46 -0.46
Top N/mm2 0.22 1.13 1.13 1.15 1.16 1.19 1.19 1.19
Girder 2
Bottom N/mm 1.52 -0.62 -0.62 -0.58 -0.56 -0.51 -0.51 -0.51
1.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-1.00 0.00 1.00 2.00 -1.00 0.00 1.00 2.00

-0.23 -0.18
-0.63 1.13 -0.63 1.19
-0.62 -0.51 Mid Span

Support Section
Stresses Due to differential Shrinkage
Summery of stresses at sections

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
1 2 3 5 4 6 7 8
Dtop 0.00 N/mm2 -0.23 -0.23 -0.21 -0.20 -0.18 -0.18 -0.18
STRESSES AT
Dbottom 0.22 N/mm2 -0.52 -0.52 -0.51 -0.50 -0.46 -0.46 -0.46
Gtop 0.22 N/mm2 1.13 1.13 1.15 1.16 1.19 1.19 1.19
2
Ast_cg 1.40 N/mm -6.38 -6.38 -5.59 -5.85 -4.90 -4.90 -4.90
Ast_outer 1.44 N/mm2 -7.24 -7.24 -6.44 -6.70 -5.74 -5.74 -5.74
2
Es = 200000 N/mm Stresses At cg. Of steel & outermost
2
Eceff = 14304.3 N/mm steel is in steel
*(Long term Eceff is considered)
SUMMERY OF FORCES FOR INNER GIRDER :
Impact Factor For LL.
Class A = 0.199
Class 70 R wh. = 0.199
Class 70 R T = 0.1
BENDING MOMENT INNER GIRDER DUE TO PERMANENT LOAD

Dist. From c/L brg. m 0.00 1.29 2.075 2.3 4.15 6.225 8.3
Precat Beam Tm -0.3 17.4 28.6 26.3 44.5 55.5 59.1

Deck Inner Girder Tm -0.2 17.7 29.6 27.1 46.7 58.4 62.3
SIDL Tm 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Surfacing Tm 0.0 5.4 8.5 9.2 14.5 18.2 19.4
FPDL Tm
FPLL Tm
Mz MTon-m Tm 0.0 59.9 91.0 97.3 148.3 180.4 193.3
Corresponding Fy Mton T 60.8 55.3 52.6 45.0 40.0 30.4 22.4
MAX. SHEAR FORCES INNER GIRDER

Dist. From c/L brg. m 0.00 1.29 2.075 2.3 4.15 6.225 8.3
Precat Beam T 15.3 12.2 10.2 10.6 7.0 3.5 0.0

Deck Inner Girder T 15.1 12.7 10.9 11.3 7.5 3.8 0.0
SIDL T 3.5 3.2 3.2 2.3 2.3 1.3 0.4
Surfacing T 4.0 4.0 3.9 3.1 2.7 1.6 0.4
FPDL T
FPLL T
Maximum S.F. 53.2 48.4 46.0 39.4 35.0 26.6 19.6
ULS CHECK FOR COMPOSITE SECTION: BENDING MOMENT
Design Parameters
Design yield strength of reinforcement fyd = 434.78 Mpa
Concrete Characteristic Strength fck = 35 Mpa
fcd = 0.447 *fck = 15.63 Mpa
Using Rectangular stress block
Effective height factor l = 0.8
Compression zone factor h = 1
hfcd = 15.63 Mpa
Limiting value of xu,max/d = 0.464
Modular ratio (EcmP / EcmD) = 1.000 (Precast Beam / Cast insitu deck)
A)INNER GIRDER SUMMERY OF LOADS

BENDING MOMENT INNER GIRDER
LC-1
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Precat Beam Tm -0.30 17.41 28.61 26.28 44.52 55.46 59.10 1.35
Deck Outer Girder Tm -0.23 17.72 29.62 27.12 46.66 58.38 62.29 1.35
SIDL Tm 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1
Surfacing Tm 0.00 5.41 8.46 9.16 14.55 18.18 19.40 1.75
FPDL Tm
FPLL Tm
Live Load Tm 0.00 59.92 90.96 97.34 148.35 180.41 193.25 1.5
Factored Bending Moment

LC-1 Basic Comb Tm -0.72 146.78 229.86 234.15 371.07 456.12 487.70
A) INNER GIRDER AT MID SPAN

3 @ 3.00 hfcd = 15.63
1 0.75 0.22 x1
2 0.2 Cu
3 0.1 xu lxu
4 1.52
0.325 1.3 z
Ast
0.2 Tu
0.25
0.75
Clear Cover = 56 mm
Dia of spacer Bar = 32 mm
Total Depth = 1.52 mm
Reeinforcement at different sections
At 4L/8 y from At 3L/8 At 2L/8 At L/8
Layer Dia Nos bottom Dia Nos Dia Nos Dia Nos
mm (m) mm mm mm
Layer-1 32 6 0.0720 32 6 32 6 32 6
Layer-2 32 6 0.1360 32 6 32 6 32 6
Layer-3 32 2 0.2000 32 2 32 0 32 0
Layer-4 32 0 0.2640 32 0 32 0 32 0
Layer-5 32 0 0.3280 32 0 32 0 32 0
Layer-6 32 0 0.3920 32 0 32 0 32 0
Total Ast = 0.0113 m2 0.0113 m2 0.0097 m2 0.0097 m2

deff = 1.402 m 1.402 m 1.416 m 1.416 m
dast_o = 1.448 m 1.448 m 1.448 m 1.448 m
hcef1 = (h-d)*2.5 = 0.294 m 0.294 m 0.260 m 0.260 m
Reinforcement provided
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dia of bars mm 32 32 32 32 32 32 32
Nos. Nos. 12 12 12 12 12 14 14
Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113
deff w.r.t Composite m 1.4160 1.4160 1.416 1.4160 1.416 1.402 1.402
dast_o section m 1.4480 1.4480 1.448 1.4480 1.448 1.448 1.448
deff 1.1960 1.1960 1.1960 1.1960 1.1960 1.1823 1.1823

w.r.t Precasts section
dast_o 1.2280 1.2280 1.2280 1.2280 1.2280 1.2280 1.2280
deff = deff up to cg. Of total steel

dast_o = deff up to cg. Of outer most steel
Check for Minimum & Maximum reinforcement percentage ( IRC 112 / clause 16.5.1.1)
As, min = Max 0.26 (fctm/fyk ) btd

0.0013 btd
fctm = 2.77 Mpa
fyk = 500 Mpa
Asmax = 0.025Ac

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
d m 1.416 1.416 1.416 1.416 1.416 1.402 1.402

bt m 0.750 0.750 0.750 0.750 0.750 0.750 0.750
As, min m2 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015
2
As, provided m 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113
check Asmin < Asprovided OK OK OK OK OK OK OK
Ac m2 1.6350 1.6350 1.5034 1.4519 1.3375 1.3375 1.3375
Asmax m2 0.0409 0.0409 0.0376 0.0363 0.0334 0.0334 0.0334
check Asmax > Asprovided OK OK OK OK OK OK OK
Anchorage of Span Reinforcemet at end : ( IRC 112 / clause 16.5.1.4)
Tensile Force = VED * (al/d) +NED
VED = 122.02 T Factored Shear Force at face of support
d = 1.42 deff at face of support
al = 0.5 *z*(cot q)
z = 1.37 m (z at face of support)
q = 45 deg (angle of concrete strut with longitudinal axis)
NED = 0T
al = 0.686
Tensile Force = 59.0845 Tonne
2
Area of tensile reinforcement at support section As = 0.0097 m
Maximum tensile stress in reinforcement fyd = fyk /ym = 500 /1.15
= 434.783 Mpa
Tensile capacity of anchorage reinforcement Ft = 419.608 Tonne OK
CHECK FOR ULTIMATE LIMIT STATE CAPACITY: ( IRC 112 / clause 8.2.1)
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Ast m2 0.01 0.01 0.01 0.01 0.01 0.01 0.01

deff m 1.42 1.42 1.42 1.42 1.42 1.40 1.40
lxu m 0.09 0.09 0.09 0.09 0.09 0.10 0.10
CArea m2 0.27 0.27 0.27 0.27 0.27 0.31 0.31
x1 m 0.04 0.04 0.04 0.04 0.04 0.05 0.05
Cu T 419.61 419.61 419.61 419.61 419.61 489.54 489.54
Tu T 419.61 419.61 419.61 419.61 419.61 489.54 489.54
Check (C-T =Zero) 0 0 0 0 0 0 0
xu m 0.112 0.112 0.112 0.112 0.112 0.130 0.130
xu/d 0.079 0.079 0.079 0.079 0.079 0.093 0.093
Check ( xu/d < xu,max/d ) UR,OK UR,OK UR,OK UR,OK UR,OK UR,OK UR,OK
z =(d-x1) m 1.37 1.37 1.37 1.37 1.37 1.35 1.35

MRD = Tu*z Tm 575.39 575.39 575.39 575.39 575.39 660.93 660.93
MED Tm -0.72 146.78 229.86 234.15 371.07 456.12 487.70

check MED < MRD OK OK OK OK OK OK OK
Additional Tensile force due to shear

DFd T 71.33 63.33 58.63 52.39 43.37 29.72 17.36
MED/z +DFD T 70.80 170.37 226.25 223.14 313.98 367.56 378.59
MRD/z 419.61 419.61 419.61 419.61 419.61 489.54 489.54
Check MRD/z > MED/z +DFD OK OK OK OK OK OK OK
Check for anchorage of bars
Basic anchorage length lb = (f/4) (fyd / fbd) ( IRC 112 / clause 15.2.3.3 (1) )
Ultimate bond stress fbd = 3.00 Mpa ( IRC 112 / table 15.4 )
fyd = fyk/ 1.1.5
fy = 500 Mpa
fyd = 434.783 Mpa
Basic anchorage length lb = (f/4) (fyd / fbd)
Design anchorage Length

lbd = Max aa lb As,req / As,prov
lb,min = Max ( 0.3 lb , 10f , 100mm ) for anchorage in tension
aa = 0.7

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Ast provided m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113

Dia of bar 32 32 32 32 32 32 32
Nos. 12 12 12 12 12 14 14
Basis anchorage length l b mm 1159.4 1159.4 1159.4 1159.4 1159.4 1159.4 1159.4
l b,min mm 347.8 347.8 347.8 347.8 347.8 347.8 347.8
l bd mm 811.6 811.6 811.6 811.6 811.6 811.6 811.6
ULS CHECK FOR COMPOSITE SECTION: SHEAR FORCE
Design Parameters
fck = 35.0 Mpa
fcd = acc fck/ym
acc = 0.67
ym = 1.5
fcd = 15.63 Mpa
fyk = 500 Mpa

gs = 1.15
fyd = fyk /gs

fyd = 434.783 Mpa
fywd = 0.8 fyk /gs

fywd = 347.826 Mpa
A) INNER GIRDER SUMMERY OF LOADS

Reduction factor for section b/w 0.5d ≤ av ≤ 2d
b = av / 2d ( IRC 112 / clause 10.3.3.3 (7) )
SHEAR FORCE SUMMERY

LC-1
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Precat Beam T 15.29 12.16 10.16 10.56 7.03 3.51 0.00 1.35
Deck Outer Girder T 15.06 12.72 10.89 11.30 7.53 3.77 0.00 1.35
SIDL T 3.48 3.16 3.16 2.32 2.32 1.30 0.42 1
Surfacing T 4.01 4.01 3.89 3.12 2.74 1.55 0.39 1.75
FPDL
FPLL
LL(with Impact) T 48.35 48.35 46.00 39.37 34.99 26.60 19.62 1.5
LL(Correspond to Max BM) T 60.79 55.26 52.57 44.99 39.98 30.40 22.42 1.5
Factored Shear Force

LC-1 Basic Comb
VED T 124.00 116.30 107.40 96.35 79.25 53.75 30.51
VED(Correspod to Max BM) T 142.65 126.66 117.25 104.78 86.74 59.44 34.72
deff m 1.41 1.41 1.41 1.41 1.41 1.40 1.40
Reduction factor b 0.50 0.50 0.74 0.82 1.00 1.00 1.00
VED' = VED* b T 62.00 58.15 78.97 78.53 79.25 53.75 30.51


2
r1 = Min Asl /bw d

0.02
scp = 0 Mpa
nmin = 0.031 k3/2 fck1/2

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
2
Asl m 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113
d T 1.416 1.416 1.416 1.416 1.416 1.402 1.402
k 1.376 1.376 1.376 1.376 1.376 1.378 1.378
bw m 0.750 0.750 0.562 0.488 0.325 0.325 0.325
r1 0.009 0.009 0.012 0.014 0.020 0.020 0.020
nmin 0.296 0.296 0.296 0.296 0.296 0.297 0.297
VRdc T 51.017 51.017 42.049 38.277 28.681 28.441 28.441
'
VED T 62.001 58.151 78.967 78.526 79.246 53.745 30.514
Provide Design
Provide Design
Provide Design
Provide Design
Provide Design
Provide Design
Provide Design
Shear Reinf.
Shear Reinf.
Shear Reinf.
Shear Reinf.
Shear Reinf.
Shear Reinf.
Shear Reinf.
Check Shear Reinf.
Requirement
Vccd = 0 T
Vtd = 0 T
VNS = VED' -Vccd -Vtd

VNS = VED'
Variation of q 45
o
≥ q ≥ 21.80
o
Considering q = 45
o
VRdmax = acw * bw * z * n1 * fcd / ( cot q +tan q) ( IRC 112 / clause 10.3.3.2 Eq 10.8 )
acw = 1
z = 0.9*d
n1 = 0.6 for fck ≤ 80 Mpa
= Max 0.9- fck/250 for fck > 80 Mpa

0.5
= 0.6

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
VNS T 62.001 58.151 78.967 78.526 79.246 53.745 30.514

bw m 0.750 0.750 0.562 0.488 0.325 0.325 0.325
d m 1.416 1.416 1.416 1.416 1.416 1.402 1.402
z m 1.274 1.274 1.274 1.274 1.274 1.262 1.262
VRdmax T 448.270 335.915 291.950 194.250 192.369 192.369
FINDING VALUE OF q AT DESIGN SECTIONS FOR DESIGN SHEAR REINFORCEMENT
VRdmax = VNS
q = 0.5 sin-1 [ 2*VNS / (acw * bw * z * v1 * fcd) ] ( IRC 112 / clause 10.3.3.2 Eq 10.8 )

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
VNS T 62.001 58.151 78.967 78.526 79.246 53.745 30.514

bw m 0.750 0.750 0.562 0.488 0.325 0.325 0.325
d m 1.416 1.416 1.416 1.416 1.416 1.402 1.402
z m 1.274 1.274 1.274 1.274 1.274 1.262 1.262
q deg 3.975 3.727 6.798 7.801 12.038 8.112 4.564
q adopted deg 45 45 45 45 45 45 45
VNS = VRds = (Asw/s) *z *fywd *cotq ( IRC 112 / clause 10.3.3.2 Eq 10.7 )
Asw/s = VNS / z fywd cotq
Minimum shear reinforcement ( IRC 112 / clause 10.3.3.5 Eq 10.20 )

Asw, min = rw,min * s * bw
rw, min = ( 0.072 √ fck ) / fyk

= 0.00085

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
VNS T 62.00 58.15 78.97 78.53 79.25 53.75 30.51

bw m 0.75 0.75 0.56 0.49 0.33 0.33 0.33
z m 1.27 1.27 1.27 1.27 1.27 1.26 1.26
qdesign deg 45.00 45.00 45.00 45.00 45.00 45.00 45.00
Asw/s mm2/m 1398.72 1311.86 1781.47 1771.51 1787.76 1224.33 695.123
Additional requirement (suspension reinf) 0
Asw,min /s mm2/m 76.67 76.67 57.46 49.94 33.22 41.53 55.37
Legs nos 2 2 2 2 2 2 2
spacing mm 120 120 120 120 120 150 200
Asw/s provide 1884.96 1884.96 1884.96 1884.96 1884.96 1507.96 785.40
Check Ok/Revise OK OK OK OK OK OK OK
Additional Tensile force DFd to be accounted in longitudinal reinforcement ( IRC 112 / clause 10.3.3.2 (6) )
DFd = 0.5 VED (cotq - cot a)
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
VED T 142.65 126.66 117.25 104.78 86.74 59.44 34.72

z m 1.27 1.27 1.27 1.27 1.27 1.26 1.26
DFd T 71.33 63.33 58.63 52.39 43.37 29.72 17.36
Check for Shear Reinforcement within 0.75av support region ( IRC 112 / clause 10.3.3.2 (7)& (8))
VED = 62.0 T
Check required if b factor is considered for

Asw provided within central 0.75 av zone.
av = deff = 1.41 m
calculation of shear reinforcement.

0.75 av = 1.05825 m
2
Asw provided = 1885.0 mm /m
2
Asw_0.75av = 1994.75 mm
VED ≤ Asw * fywd
Asw_0.75av ≥ VED/fywd
2 2
≥ 1782.52 mm < 1994.75 mm OK
DESIGN FOR INTERFACE SHEAR : ( IRC 112 / clause 10.3.4)

vEdi = b VEd /z bi
b = Ratio of longitudinal force in new concrete and total longitudinal force

= 1
bi = 0.75 m bi = 0.75
vRdi = Min msn + r fyd [ msina +cos a]

0.5nfcd = 4.16 Mpa
r = As /Ai
As = Area of reinforcement crossing the inter face
Ai = Interface area of joint
2
Ai = 750000 m Considering 1 m length
m = 0.6 Assuming smooth surface

sn = 0 Mpa
a = 90 deg
n = 0.6 [ 1 - fck /310 ]

= 0.532
As min = 0.15 % of interface area

= 0.15 * bi *1000 / 100 mm2/m
2
= 1125 mm /m
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
VED T 124.00 116.30 107.40 96.35 79.25 53.75 30.51

z m 1.27 1.27 1.27 1.27 1.27 1.26 1.26
2
vEdi N/mm 1.30 1.22 1.12 1.01 0.83 0.57 0.32
Legs nos 4 4 4 4 4 4 4
spacing mm 120 120 120 120 120 150 200
Asw/s provide 3769.91 3769.91 3769.91 3769.91 3769.91 3015.93 1570.80
Check As ≥ As,min OK OK OK OK OK OK OK
r 0.0050 0.0050 0.0050 0.0050 0.0050 0.0040 0.0021
vRdi N/mm2 1.311 1.311 1.311 1.311 1.311 1.049 0.546
Check vEDi ≤ vRdi OK OK OK OK OK OK OK
CHECK FOR MINIMUM TRANSVERSE REINFORCEMENT DECK SLAB (COMPRESSIN FLANGE):

CHECK FOR SHEAR IN FLANGED PORTION

fcd = 0.45 *fck
= 15.75 Mpa
fyd = fyk /gs
fyd = 434.78 Mpa
b = Ratio of longitudinal force in deck and total longitudinal force ( IRC 112 / clause 10.3.5)
= 1
vEd = bVED/z hf Total Longitudinal Shear Stress
Longitudinal force on the one side of flange (section A-A)
vEdf = vEd * beff1/ beff
hf = 0.22 m
beff1/beff = 0.375
o
Variation of qf 45 ≥ q ≥ 26.5
o
For compression flange
CHECK FOR SECTION MAXIMUM PERMISSBLE LONGITUDINAL SHEAR STRESS:
vEdf,max = n fcd sinqf cosqf
Considering qf = 26.5
o
n = 0.6 [ 1 - fck /310 ] , fck in MPA

= 0.532
beff = 3.00 m
vEdf,max = 3.32 Mpa A
0.75 hf = 0.22
beff1 = 1.125
A
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
VED Tm 124.00 116.30 107.40 96.35 79.25 53.75 30.51

z m 1.27 1.27 1.27 1.27 1.27 1.26 1.26
vEd Mpa 4.42 4.15 3.83 3.44 2.83 1.94 1.10
vEdf Mpa 1.659 1.556 1.436 1.289 1.060 0.726 0.412
FINDING q f
qf = 0.5 sin-1 [ 2vEDf / n fcd ]
qf deg 11.75 10.98 10.10 9.02 7.38 5.02 2.84
Check OK/ REVISE qf < qfmax OK OK OK OK OK OK OK
Check OK/ REVISE vEDf < vEdf,max OK OK OK OK OK OK OK
REINFORCEMENT REQUIREMENT IN DECK FOR LONGITUDINAL SHEAR

Transverse reinforcement per unit length
Asf /sf = vEDf * hf / fyd cot qf

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
vEdf Mpa 1.56 1.44 1.29 1.06 0.73 0.41

qdesign deg 26.50 26.50 26.50 26.50 26.50 26.50
2
Asf /sf mm /m 392.44 362.39 325.11 267.40 183.13 103.97
No exta reinforcement is required if v Edf 0.4fcd = 6.25 Mpa

< 0.4fcd
As there will be transverse bending will exist along with shear b/w precast beam & deck
Reinforcement requirement for transverse bending of deck

2
As, deck = 2000 mm /m ( Including Top & Bottom Both reinf)
As,trans = Max Asf if vEdf > 0.4fcd

0.5 Asf + As,deck
As,deck if vEdf < 0.4fcd

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Asf, exta mm2/m 0.00 0.00 0.00 0.00 0.00 0.00

As, deck mm2/m 2000 2000 2000 2000 2000 2000
As,trans mm2/m 2000 2000 2000 2000 2000 2000
dia mm 16 16 16 16 16 16
At Top spacing mm 150 150 150 150 150 150
dia mm 12 12 12 12 12 12
At Bottom spacing mm 100 100 100 100 100 100
As,trans 2471.39 2471.39 2471.39 2471.39 2471.39 2471.39

SLS STRESS CHECK:
A) INNER GIRDER SUMMERY OF LOADS
BENDING MOMENT SUMMERY
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Precat Beam Tm -0.30 17.41 28.61 26.28 44.52 55.46 59.10

SIDL Tm 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Surfacing Tm 0.00 5.41 8.46 9.16 14.55 18.18 19.40
FPDL Tm 0.00 0.00 0.00 0.00 0.00 0.00 0.00
FPLL Tm 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Live Load Tm 0.00 59.92 90.96 97.34 148.35 180.41 193.25
A) OUTER GIRDER
Modular ratio for Section Analsys of Concrete
Creep factor = f = 1.24
For long term = Ecm' = 14304.3 Mpa
FINDING OUT STRESSES IN BEAM DUE TO SELFWEIGHT OF BEAM & DECK SLAB
Es = 200000 Mpa ( IRC 112 / clause 12.2 )
Eceff = 14304.3 Mpa
= 13.98
Bending Moment due to Selfweight of Beam + Deck slab

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Precast Beam Tm -0.30 17.41 28.61 26.28 44.52 55.46 59.10

Precast Beam + Deck Tm -0.53 35.13 58.23 53.41 91.18 113.84 121.39
0.75
ec
2 0.2
3 0.1 dc
4
0.325 1.3
d-dc
Ast
0.2 es
0.25

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113

deff m 1.20 1.20 1.20 1.20 1.20 1.18 1.18
dAst_O m 1.23 1.23 1.23 1.23 1.23 1.23 1.23

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
BM (BEAM +DECK) Tm -0.53 35.13 58.23 53.41 91.18 113.84 121.39

Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113
deff m 1.20 1.20 1.20 1.20 1.20 1.18 1.18
dc m 0.533 0.533 0.533 0.533 0.533 0.562 0.562
Iz (Transformed) m4 0.094 0.094 0.094 0.094 0.094 0.101 0.101
N/mm2
Stresses At
Gtop 2.00 3.31 3.03 5.18 6.37 6.79

Girder Ast_cg N/mm2 -34.68 -57.49 -52.72 -90.01 -98.18 -104.69
Ast_outer N/mm2 -36.36 -60.27 -55.27 -94.36 -105.42 -112.41
FINDING OUT STRESSES IN COMPOSITE SECTION DUE TO SIDL & SURFACING

Es = 200000 Mpa
Eceff = 14304.3 Mpa

= 13.98
Bending Moment due to SIDL + Surfacing

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
SIDL Tm 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Surfacing Tm 0.00 5.41 8.46 9.16 14.55 18.18 19.40
FPDL Tm 0.00 0.00 0.00 0.00 0.00 0.00 0.00
FPLL Tm 0.00 0.00 0.00 0.00 0.00 0.00 0.00
SIDL+Surfaing Tm 0.00 5.41 8.46 9.16 14.55 18.18 19.40

beff = 3.00
1 0.75 0.22
ec
2 0.2
3 0.1 dc
4
0.325 1.3
d-dc
Ast
0.2 es
0.25

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113

deff m 1.42 1.42 1.42 1.42 1.42 1.40 1.40
dAst_O m 1.45 1.45 1.45 1.45 1.45 1.45 1.45

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
BM (SIDL +Surfacing) Tm 0.00 5.41 8.46 9.16 14.55 18.18 19.40

Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113
deff m 1.4160 1.4160 1.4160 1.4160 1.4160 1.4023 1.4023
dc m 0.33 0.33 0.33 0.33 0.33 0.35 0.35
Iz (Transformed) m4 0.19 0.19 0.19 0.19 0.19 0.22 0.22
Dtop 0.000 N/mm2 0.09 0.14 0.15 0.24 0.30 0.32
Deck
N/mm2
Stresses At
Dbottom 0.220 0.03 0.05 0.05 0.08 0.11 0.12

2
Gtop 0.220 N/mm 0.03 0.05 0.05 0.08 0.11 0.12
-4.25 -6.64 -7.19 -11.42 -12.40 -13.23
2
Ast_outer 1.448 N/mm -4.37 -6.84 -7.41 -11.76 -12.94 -13.80
FINDING OUT STRESSES IN COMPOSITE SECTION DUE TO LIVE LOAD
Es = 200000 Mpa
Eceff = 32000 Mpa
= 6.25
Bending Moment due to Live Load

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Live Load Tm 0.00 59.92 90.96 97.34 148.35 180.41 193.25
beff = 3.00
1 0.75 0.22
ec
2 0.2
3 0.1 dc
4
0.325 1.3
d-dc
Ast
0.2 es
0.25

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113

deff m 1.42 1.42 1.42 1.42 1.42 1.40 1.40
dAst_O m 1.45 1.45 1.45 1.45 1.45 1.45 1.45

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
BM (Live Load) Tm 0.00 59.92 90.96 97.34 148.35 180.41 193.25

Ast m2 0.0097 0.0097 0.0097 0.0097 0.0097 0.0113 0.0113
deff m 1.4160 1.4160 1.4160 1.4160 1.4160 1.4023 1.4023
dc m 0.22 0.22 0.22 0.22 0.22 0.23 0.23
Iz (Transformed) m4 0.10 0.10 0.10 0.10 0.10 0.11 0.11
Dtop 0.000 N/mm2 1.36 2.06 2.20 3.36 3.88 4.16
Deck
N/mm2
Stresses At
Dbottom 0.220 0.00 -0.01 -0.01 -0.01 0.24 0.26

2
Gtop 0.220 N/mm 0.00 -0.01 -0.01 -0.01 0.24 0.26
-46.24 -70.18 -75.11 -114.47 -120.97 -129.58
Ast_outer 1.448 N/mm2 -47.47 -72.06 -77.12 -117.53 -125.70 -134.65
SUMMERY OF STRESSES
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Stresses due to Precast Beam & Deck slab
Dtop N/mm2
Deck
N/mm2
Stresses At
Dbottom
Gtop N/mm2 2.00 3.31 3.03 5.18 6.37 6.79
Girder Ast_cg N/mm2 -34.68 -57.49 -52.72 -90.01 -98.18 -104.69
2
Ast_outer N/mm -36.36 -60.27 -55.27 -94.36 -105.42 -112.41
Stresses due to SIDL+Surfacing

Dtop N/mm2 0.09 0.14 0.15 0.24 0.30 0.32
Deck
N/mm2
Stresses At
Dbottom 0.03 0.05 0.05 0.08 0.11 0.12

Gtop N/mm2 0.03 0.05 0.05 0.08 0.11 0.12
Girder Ast_cg N/mm2 -4.25 -6.64 -7.19 -11.42 -12.40 -13.23
2
Ast_outer N/mm -4.37 -6.84 -7.41 -11.76 -12.94 -13.80
Stresses due to Live Load

Dtop N/mm2 1.36 2.06 2.20 3.36 3.88 4.16
Deck 2
Stresses At
Dbottom N/mm 0.00 -0.01 -0.01 -0.01 0.24 0.26

Gtop N/mm2 0.00 -0.01 -0.01 -0.01 0.24 0.26
Girder Ast_cg N/mm2 -46.24 -70.18 -75.11 -114.47 -120.97 -129.58
2
Ast_outer N/mm -47.47 -72.06 -77.12 -117.53 -125.70 -134.65
Stresses at section due to differential shrinkage

Dtop N/mm2 -0.23 -0.21 -0.20 -0.18 -0.18 -0.18
Deck
N/mm2
Stresses At
Dbottom -0.52 -0.51 -0.50 -0.46 -0.46 -0.46

Gtop N/mm2 1.13 1.15 1.16 1.19 1.19 1.19
Girder Ast_cg N/mm2 -6.38 -5.59 -5.85 -4.90 -4.90 -4.90
2
Ast_outer N/mm -7.24 -6.44 -6.70 -5.74 -5.74 -5.74
+ve temperature differences

Dtop N/mm2 3.60 3.65 3.67 3.71 3.71 3.71
Deck
N/mm2
Stresses At
Dbottom -1.41 -1.41 -1.41 -1.41 -1.41 -1.41

Gtop N/mm2 -1.41 -1.41 -1.41 -1.41 -1.41 -1.41
Girder Ast_cg N/mm2 9.14 8.22 7.86 7.07 7.07 7.07
2
Ast_outer N/mm 11.60 10.35 9.86 8.77 8.77 8.77
-ve temperature differences

Dtop N/mm2 -2.11 -2.09 -2.09 -2.07 -2.07 -2.07
Deck
N/mm2
Stresses At
Dbottom 0.92 0.95 0.96 0.99 0.99 0.99

Gtop N/mm2 0.92 0.95 0.96 0.99 0.99 0.99
Girder Ast_cg N/mm2 -9.07 -8.50 -8.28 -7.78 -7.78 -7.78
2
Ast_outer N/mm -12.02 -11.43 -11.20 -10.69 -10.69 -10.69
Load Factor
Live Load 1
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 1.45 2.20 2.36 3.60 4.18 4.48
Deck
N/mm2
Stresses At
Dbottom 0.22 0.03 0.04 0.04 0.07 0.35 0.37

Gtop 0.22 N/mm2 2.02 3.35 3.08 5.25 6.71 7.16
Girder Ast_cg 1.40 N/mm2 -85.17 -134.31 -135.03 -215.90 -231.55 -247.50
Ast_outer 1.45 N/mm2 -88.20 -139.16 -139.79 -223.64 -244.06 -260.86

Load Factor
Live Load 1
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 1.22 1.99 2.15 3.43 4.00 4.30
Deck
N/mm2
Stresses At
Dbottom 0.22 -0.50 -0.47 -0.45 -0.39 -0.12 -0.09

Gtop 0.22 N/mm2 3.15 4.50 4.24 6.44 7.91 8.35
Girder Ast_cg 1.40 N/mm2 -91.55 -139.90 -140.87 -220.80 -236.45 -252.40
Ast_outer 1.45 N/mm2 -95.44 -145.60 -146.49 -229.38 -249.80 -266.60

Load Factor
Live Load 1
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 5.05 5.85 6.03 7.32 7.90 8.19
Deck
N/mm2
Stresses At
Dbottom 0.22 -1.39 -1.37 -1.37 -1.34 -1.06 -1.04

Gtop 0.22 N/mm2 0.61 1.94 1.67 3.84 5.30 5.75
Girder Ast_cg 1.40 N/mm2 -76.03 -126.09 -127.16 -208.83 -224.48 -240.43
Ast_outer 1.45 N/mm2 -76.60 -128.81 -129.93 -214.87 -235.28 -252.09
Load Factor
Live Load 1
-ve Temperature 1

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 -0.67 0.11 0.27 1.53 2.11 2.41
Deck
N/mm2
Stresses At
Dbottom 0.22 0.95 0.99 1.01 1.06 1.34 1.36

Gtop 0.22 N/mm2 2.94 4.30 4.04 6.24 7.71 8.15
Girder Ast_cg 1.40 N/mm2 -94.24 -142.81 -143.30 -223.68 -239.33 -255.28
Ast_outer 1.45 N/mm2 -100.22 -150.59 -150.99 -234.33 -254.75 -271.56

Load Factor
Live Load 1
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 4.82 5.64 5.82 7.14 7.72 8.01
Deck
N/mm2
Stresses At
Dbottom 0.22 -1.91 -1.88 -1.86 -1.80 -1.53 -1.50

Gtop 0.22 N/mm2 1.74 3.09 2.83 5.03 6.50 6.94
Girder Ast_cg 1.40 N/mm2 -82.41 -131.68 -133.01 -213.73 -229.38 -245.33
Ast_outer 1.45 N/mm2 -83.84 -135.25 -136.63 -220.61 -241.02 -257.83

Load Factor
Live Load 1
-ve Temperature 1

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 -0.89 -0.11 0.07 1.35 1.93 2.23
Deck
N/mm2
Stresses At
Dbottom 0.22 0.42 0.49 0.51 0.60 0.87 0.90

Gtop 0.22 N/mm2 4.08 5.45 5.20 7.43 8.90 9.34
Girder Ast_cg 1.40 N/mm2 -100.62 -148.40 -149.15 -228.58 -244.23 -260.18
Ast_outer 1.45 N/mm2 -107.46 -157.03 -157.69 -240.07 -260.49 -277.30
Load Factor
Live Load 0
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 0.09 0.14 0.15 0.24 0.30 0.32
Deck
N/mm2
Stresses At
Dbottom 0.22 0.03 0.05 0.05 0.08 0.11 0.12

Gtop 0.22 N/mm2 2.03 3.36 3.08 5.26 6.48 6.91
Girder Ast_cg 1.40 N/mm2 -38.93 -64.13 -59.92 -101.43 -110.58 -117.92
Ast_outer 1.45 N/mm2 -40.73 -67.10 -62.68 -106.11 -118.36 -126.21

Load Factor
Live Load 0
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 -0.14 -0.07 -0.05 0.07 0.12 0.14
Deck
N/mm2
Stresses At
Dbottom 0.22 -0.50 -0.46 -0.45 -0.38 -0.35 -0.35

Gtop 0.22 N/mm2 3.16 4.51 4.25 6.45 7.67 8.10
Girder Ast_cg 1.40 N/mm2 -45.31 -69.72 -65.77 -106.33 -115.48 -122.82
Ast_outer 1.45 N/mm2 -47.97 -73.54 -69.37 -111.85 -124.09 -131.95

Load Factor
Live Load 0
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 1.89 1.97 1.99 2.10 2.15 2.17
Deck
N/mm2
Stresses At
Dbottom 0.22 -0.68 -0.66 -0.66 -0.63 -0.59 -0.59

Gtop 0.22 N/mm2 1.32 2.65 2.38 4.56 5.77 6.20
Girder Ast_cg 1.40 N/mm2 -34.36 -60.02 -55.99 -97.90 -107.05 -114.39
Ast_outer 1.45 N/mm2 -34.93 -61.93 -57.75 -101.73 -113.97 -121.83
Load Factor
Live Load 0
-ve Temperature 0.5

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 -0.97 -0.91 -0.89 -0.79 -0.74 -0.72
Deck
N/mm2
Stresses At
Dbottom 0.22 0.49 0.52 0.53 0.57 0.61 0.61

Gtop 0.22 N/mm2 2.49 3.83 3.57 5.76 6.97 7.40
Girder Ast_cg 1.40 N/mm2 -43.47 -68.38 -64.06 -105.32 -114.47 -121.81
Ast_outer 1.45 N/mm2 -46.74 -72.82 -68.28 -111.46 -123.70 -131.56

Load Factor
Live Load 0
-ve Temperature 0

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 1.66 1.76 1.79 1.93 1.98 2.00
Deck
N/mm2
Stresses At
Dbottom 0.22 -1.20 -1.16 -1.15 -1.09 -1.06 -1.05

Gtop 0.22 N/mm2 2.45 3.80 3.54 5.75 6.96 7.39
Girder Ast_cg 1.40 N/mm2 -40.74 -65.61 -61.84 -102.80 -111.95 -119.29
Ast_outer 1.45 N/mm2 -42.17 -68.36 -64.44 -107.46 -119.71 -127.57

Load Factor
Live Load 0
-ve Temperature 0.5

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
Dtop 0.00 N/mm2 -1.19 -1.12 -1.09 -0.97 -0.92 -0.90
Deck
N/mm2
Stresses At
Dbottom 0.22 -0.03 0.02 0.04 0.11 0.14 0.15

Gtop 0.22 N/mm2 3.62 4.98 4.73 6.95 8.16 8.59
Girder Ast_cg 1.40 N/mm2 -49.85 -73.97 -69.90 -110.22 -119.37 -126.71
Ast_outer 1.45 N/mm2 -53.98 -79.25 -74.98 -117.20 -129.44 -137.30
LIMIT STATE OF CRACKING :
Asmin = kc k fct,eff Act / ss ( IRC 112 / clause 12.3.3 (2) )
For Web
k = 0.65 For web with h>800mm
fcteff = fctm
= 2.77 Mpa
Act = Area of concrete within tensile zone just before the first crack form
section behaves elastically until the tensile fiber stress reaches fctm.
hence Neutral axis depth will be considered for gross section
ss = fyk
= 500 Mpa
(Equavelent to Precast Beam grade)

3 @ 3.0
1 0.8 0.22
2 0.20
3 0.10 yt
4
1.52
0.325 1.3
NA
5 0.20
6 0.25
0.750

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
h m 1.52 1.52 1.52 1.52 1.52 1.52 1.52

yt m 0.56 0.56 0.54 0.53 0.51 0.51 0.51
bw m 0.75 0.75 0.56 0.49 0.33 0.33 0.33
Act (D-yt)*bw m2 1.01 1.01 0.85 0.78 0.62 0.62 0.62
Asmin mm2 1459.20 1459.20 1220.62 1123.51 900.16 900.16 900.16
As,provided mm2 9651.0 9651.0 9651.0 9651.0 9651.0 11259.5 11259.5
Calculation of crack width : ( IRC 112 /clause 12.3.4)
wk,max = 0.3 mm

srmax = Maximum crack spacing
= 3.4c + 0.17f
rPeff
Bar dia f = 32 mm
5 (c +f/2) = 360 mm
Spacing b/w bars = 106.333 mm < 360
rP,eff = As/ Ac,eff
Ac,eff = Min 2.5 ( h - d )

( h - x/3 )
h/2

Es
0.6 ssc / Es
ae = Es/Ecm
Es = 200000 Mpa
Ecm = 32000 Mpa
ae = 6.25

Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
As m2 0.00965 0.00965 0.00965 0.00965 0.009651 0.01126 0.01126

h m 1.52 1.52 1.52 1.52 1.52 1.52 1.52
d m 1.42 1.42 1.42 1.42 1.42 1.40 1.40
hcef1 2.5*(h-d) m 0.26 0.26 0.26 0.26 0.26 0.29 0.29
Avg web width of tension zone m 0.750 0.750 0.750 0.750 0.750 0.750 0.750
Acef1 m2 0.195 0.195 0.195 0.195 0.195 0.221 0.221
rP,eff 0.049 0.049 0.049 0.049 0.049 0.051 0.051
srmax mm 300.32 300.32 300.32 300.32 300.32 297.04 297.04
Finding Out Crack width for Load case LC-1 Quasi permanent Load combination
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
ssc N/mm2 -40.73 -67.10 -62.68 -106.11 -118.36 -126.21
esm - ecm 0.00012 0.0002 0.00019 0.000347 0.00041 0.00045
wk mm 0.04 0.06 0.06 0.10 0.12 0.13
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
ssc N/mm2 -47.97 -73.54 -69.37 -111.85 -124.09 -131.95
esm - ecm 0.00014 0.00022 0.00021 0.000376 0.00044 0.00048
wk mm 0.04 0.07 0.06 0.11 0.13 0.14
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
ssc N/mm2 -34.93 -61.93 -57.75 -101.73 -113.97 -121.83
esm - ecm 0.0001 0.00019 0.00017 0.000325 0.00039 0.00043
wk mm 0.03 0.06 0.05 0.10 0.12 0.13
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
ssc N/mm2 -46.74 -72.82 -68.28 -111.46 -123.70 -131.56
esm - ecm 0.00014 0.00022 0.0002 0.000374 0.00044 0.00048
wk mm 0.04 0.07 0.06 0.11 0.13 0.14
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
ssc N/mm2 -42.17 -68.36 -64.44 -107.46 -119.71 -127.57
esm - ecm 0.00013 0.00021 0.00019 0.000354 0.00042 0.00046
wk mm 0.04 0.06 0.06 0.11 0.12 0.14
Dist. From c/L brg. m 0.00 1.29 2.08 2.30 4.15 6.23 8.30
ssc N/mm2 -53.98 -79.25 -74.98 -117.20 -129.44 -137.30
esm - ecm 0.00016 0.00024 0.00022 0.000403 0.00047 0.00051
wk mm 0.05 0.07 0.07 0.12 0.14 0.15
STRESS CALCULATION DUE TO TEMPERATURE INNER GIRDER:
Coefficent of thermal expansion = 1.2E-05
2
Ec = 32000 N/mm
2
Es = 200000 N/mm
INNER GIRDER, MID SPAN

3.00
17.8 f1 f1 -10.6
0.15 0.75
f2
4 0.22 0.25
f3 f2
0.25 f3 -0.7
f4 0.2 f4 0.2
f5 f5
f6 0.1 f6
1.52
1.52
1 1.52 0.325 0.55 0.62
f7 f7
0.2
f8
f8 f9 0.2
f9
-0.8
0.15 f10 0.25 f10 0.25
2.1 0.75 -6.6

Points Depth temp b1 b2 Av. width Area y A*y A*y2 av. temp A*t A*t*y +ve Temperature
o
m2 m3
4 o
mm C m m m C m2 oC m3 oC h Temp
0 0 17.8
f1 0 17.8 0.15 4
f2 0.15 4 3.000 3.000 3.000 0.450 0.075 0.0338 0.0025 10.9 4.905 0.368 0.4 0
f3 0.22 2.88 3.000 3.000 3.000 0.210 0.185 0.0389 0.0072 3.44 0.722 0.134 1.37 0
f4 0.42 0 0.750 0.750 0.750 0.150 0.320 0.0480 0.0154 1.44 0.216 0.069 1.52 2.1
f5 0.4 0 0.750 0.835 0.793 -0.016 0.410 -0.0065 -0.0027 0 0.000 0.000
f6 0.52 0 0.835 0.325 0.580 0.070 0.469 0.0326 0.0153 0 0.000 0.000
f7 1.37 0 0.325 0.325 0.325 0.276 0.945 0.2611 0.2467 0 0.000 0.000
f8 1.07 0 0.325 0.325 0.325 -0.098 1.220 -0.1190 -0.1451 0 0.000 0.000
f9 1.27 0 0.325 0.750 0.538 0.108 1.157 0.1244 0.1439 0 0.000 0.000
f10 1.52 2.1 0.750 0.750 0.750 0.188 1.395 0.2616 0.3649 1.05 0.197 0.275
1.52
Total 1.3375 0.67475 0.648 6.040 0.845
e0 x 1.338 - q x 0.67475 = 1.2E-05 x 6.040 ------------------- (1)
+ ve = compression
e0 SAy - q x SAy
2
= a x SAyt - ve = tension
e0 x 0.67475 - q x 0.648 = 1.2E-05 x 0.845 ------------------- (2)

e0 = 9.8E-05
q = 8.6E-05 rad./m
STRESSES AT
3.71
2 2 2 2 2 2
0 0 -2.02
f1 0 3.71
f2 0.15 -1.17 3.71433 -1.41023 -1.41023 7.06513 8.77207
f3 0.22 -1.41
f4 0.42 -1.97
f7 1.37 0.64
f8 1.07 -0.18
f9 1.27 0.37 1.86
f10 1.52 1.86
1.52 0
2
Points Depth temp b1 b2 Av. width Area y A*y A*y av. temp A*t A*t*y -ve Temperature
o
mm C m m2 m m3 m4 o
0 0 -10.6
f1 0 -10.6 0.25 -0.7
f2 0.22 -1.888 3.000 3.000 3.000 0.660 0.110 0.0726 0.0080 -6.244 -4.121 -0.453 0.45 0
f3 0.25 -0.7 0.750 0.750 0.750 0.023 0.235 0.0053 0.0012 -1.294 -0.029 -0.007 1.07 0
f4 0.42 -0.105 0.750 0.750 0.750 0.128 0.335 0.0427 0.0143 -0.4025 -0.051 -0.017 1.27 -0.8
f5 0.45 -1E-16 0.750 0.623 0.686 0.021 0.435 0.0090 0.0039 -0.0525 -0.001 0.000 1.52 -6.6
f6 0.52 0 0.623 0.325 0.474 0.033 0.489 0.0162 0.0079 -5.6E-17 0.000 0.000
f8 1.27 -0.8 0.325 0.750 0.538 0.403 0.846 0.3409 0.2882 -0.4 -0.161 -0.136
f7 1.07 0 0.750 0.750 0.750 -0.150 1.170 -0.1755 -0.2053 -0.4 0.060 0.070
f9 1.27 -0.8 0.750 0.750 0.750 0.150 1.170 0.1755 0.2053 -0.4 -0.060 -0.070
f10 1.52 -6.6 0.750 0.750 0.750 0.188 1.395 0.2616 0.3649 -3.7 -0.694 -0.968
1.52
Total 1.45438 0.74821 0.688 -5.058 -1.582
e0 x 1.454 - q x 0.74821 = 1.2E-05 x -5.058 ------------------- (1)

e0 x 0.74821 - q x 0.688 = 1.2E-05 x -1.582 ------------------- (2)

e0 = -6.2E-05
q = -4E-05 rad./m
STRESSES AT
2 2 2 2 2 2
0 0 1.42
f1 0 -2.07
f2 0.22 0.99 -2.0713 0.99026 0.99026 -7.78025 -10.6942
f3 0.25 1.41
f4 0.42 1.42
f7 1.27 0.05
f8 1.07 0.62
f9 1.27 0.05 -2.50
f10 1.52 -2.50
1.52 0
INNER GIRDER, SUPPORT SECTION

3.00
17.8 f1 f1 -10.6
0.15 0.75
f2
4 0.22 0.25
f3 f2
0.25 f3 -0.7
f4 0.2 f4 0.2
f5 f5
f6 0.00 f6
1.52
1.52
1 1.52 1.10 0.62
f7
f8
0.2
f7
-0.8
0.15 f8 f9 0.25
2.1 0.75 -6.6
2
Points Depth temp b1 b2 Av. width Area y A*y A*y av. temp A*t A*t*y +ve Temperature
o
mm C m m2 m m3 m4 o
0 0 17.8
f1 0 17.8 0.15 4
f2 0.15 4 3.000 3.000 3.000 0.450 0.075 0.0338 0.0025 10.9 4.905 0.368 0.4 0
f3 0.22 2.88 3.000 3.000 3.000 0.210 0.185 0.0389 0.0072 3.44 0.722 0.134 1.37 0
f4 0.42 0 0.750 0.750 0.750 0.150 0.320 0.0480 0.0154 1.44 0.216 0.069 1.52 2.1
f5 0.420 0 0.750 0.750 0.750 0.000 0.420 0.0000 0.0000 0 0.000 0.000
f6 0.4 0 0.750 0.750 0.750 -0.015 0.410 -0.0062 -0.0025 0 0.000 0.000
f7 1.37 0 0.750 0.750 0.750 0.728 0.885 0.6438 0.5698 0 0.000 0.000
f8 1.52 2.1 0.750 0.750 0.750 0.113 1.445 0.1626 0.2349 1.05 0.118 0.171
1.52
Total 1.635 0.92085 0.827 5.962 0.741
e0 x 1.635 - q x 0.92085 = 1.2E-05 x 5.962 ------------------- (1)

- ve = tension
e0 = 0.0001
q = 0.0001 rad./m
STRESSES AT
3.60
2 2 2 2 2 2
-1.87
0 0
f1 0 3.60
f2 0.15 -1.21 3.60167 -1.41146 -1.41146 9.13547 11.6015
f3 0.22 -1.41
f4 0.42 -1.87
f7 1.37 1.23
f8 1.52 2.52
1.52 0 Positive temp. stress
NEGATIVE TEMPERATURE DIFFERENCES -ve Temperature

2
Points Depth temp b1 b2 Av. width Area y A*y A*y av. temp A*t A*t*y h Temp
o
mm C m m2 m m3 m4 o
C m2 oC m3 oC 0 -10.6
0 0.25 -0.7
f1 0 -10.6 0.45 0
f2 0.22 -1.888 3.000 3.000 3.000 0.660 0.110 0.073 0.008 -6.244 -4.121 -0.453 1.07 0
f3 0.25 -0.7 0.750 0.750 0.750 0.023 0.235 0.005 0.001 -1.294 -0.029 -0.007 1.27 -0.8
f4 0.42 -0.105 0.750 0.750 0.750 0.128 0.335 0.043 0.014 -0.4025 -0.051 -0.017 1.52 -6.6
f6 0.42 -0.105 0.750 0.750 0.750 0.000 0.420 0.000 0.000 -0.105 0.000 0.000
f5 0.45 -1.1E-16 0.750 0.750 0.750 0.023 0.435 0.010 0.004 -0.0525 -0.001 -0.001
f7 1.07 0 0.750 0.750 0.750 0.465 0.760 0.353 0.269 -5.6E-17 0.000 0.000
f8 1.27 -0.8 0.750 0.750 0.750 0.150 1.170 0.176 0.205 -0.4 -0.060 -0.070
f9 1.52 -6.6 0.750 0.750 0.750 0.188 1.395 0.262 0.365 -3.7 -0.694 -0.968
1.52
Total 1.635 0.92085 0.867 -4.956 -1.516
e0 x 1.635 - q x 0.92085 = 1.2E-05 x -4.956 ------------------- (1)
e0 SAy - q x SAy
2
= a x SAyt
e0 x 0.92085 - q x 0.867 = 1.2E-05 x -1.516 ------------------- (2)
e0 = -6.1E-05
q = -4.4E-05 rad./m
STRESSES AT
2 2 2 2 2
0 0 1.33
f1 0 -2.11
f2 0.22 0.92 -2.11 0.92 0.92 -9.07 -12.02
f3 0.25 1.34
f4 0.42 1.33
f7 1.07 0.45
0.00
f8 1.27 -0.14
f9 1.52 -2.72
1.52 0
Summery of stresses at sections (+ve Temperature

Summery of stresses at sections (+ve Temperature Differences) Differences)
Dist
1 from 0 0.22 0.22 1.39729 1.443
N/mm2
2 2 2 2 2
Dtop 0.00 3.60 3.60 3.65 3.67 3.71 3.71 3.71 2 c/L brg. N/mm N/mm N/mm N/mm N/mm
2
STRESSES AT
Dbottom 0.22 N/mm -1.41 -1.41 -1.41 -1.41 -1.41 -1.41 -1.41 3 0 3.60 -1.41 -1.41 9.14 11.60
2
Gtop 0.22 N/mm -1.41 -1.41 -1.41 -1.41 -1.41 -1.41 -1.41 4 1.5 3.60 -1.41 -1.41 9.14 11.60
2
Ast_cg 1.40 N/mm 9.14 9.14 8.22 7.86 7.07 7.07 7.07 5 2.8 3.71 -1.41 -1.41 7.07 8.77
2
Ast_outer 1.44 N/mm 11.60 11.60 10.35 9.86 8.77 8.77 8.77 6 8.8 3.71 -1.41 -1.41 7.07 8.77
Summery of stresses at sections (-ve Temperature
Summery of stresses at sections (-ve Temperature Differences) Differences)
Dist
1 from 0.00 0.22 0.22 1.40 1.44
2 2 2 2 2 2
Dtop 0.00 N/mm -2.11 -2.11 -2.09 -2.09 -2.07 -2.07 -2.07 2 c/L brg. N/mm N/mm N/mm N/mm N/mm
2
STRESSES AT
Dbottom 0.22 N/mm 0.92 0.92 0.95 0.96 0.99 0.99 0.99 3 0 -2.11 0.92 0.92 -9.07 -12.02
2
Gtop 0.22 N/mm 0.92 0.92 0.95 0.96 0.99 0.99 0.99 4 1.5 -2.11 0.92 0.92 -9.07 -12.02
2
Ast_cg 1.40 N/mm -9.07 -9.07 -8.50 -8.28 -7.78 -7.78 -7.78 5 2.8 -2.07 0.99 0.99 -7.78 -10.69
2
Ast_outer 1.44 N/mm -12.02 -12.02 -11.43 -11.20 -10.69 -10.69 -10.69 6 8.8 -2.07 0.99 0.99 -7.78 -10.69
Design of End diaphgram
Summery of forces for End cross-girder
Flange part is ignored in design
0.22 End Cross girder span c/c of brg. = 9m
L/D Ratio = 7.09 > 2.5

1.27 Hence design as Normal Beam
1.05
0.6
Service Condition.
Force due to Hogging Moment Sagging Moment Load Factor
(Tm ) (Tm ) (Shear Force ( T ) ULS SLS R SLS Q
DL 2.35 1.88 4.66 1.35 1 1
SIDL 2.51 0.58 1.65 1.35 1 1
Surfacing 0.35 0.19 0.39 1.75 1 1
FPDL 0 0 0 0 1 1
FPLL 0 0 0 0 1 0
LL (Governing case) 27.11 -102.09 43.12 1.5 1 0
Summery of Forces for Service condition

Hogging Sagging Shear Force
Load Combination Tm Tm Tonne
ULS 47.85 149.48 73.87
SLS Rare 32.33 99.44 49.81
SLS Quasi Permanent 5.22 2.65 6.69
Jack up condition.
Force due to Hogging Moment Sagging Moment Load Factor
(Tm ) (Tm ) Shear Force ( T ) ULS SLS R SLS Q
DL 25.57 11.46 32.94 1.35 1 1
SIDL 12.56 3.49 12.16 1.35 1 1
Surfacing 4.53 1.66 5.29 1.75 1 1
FPDL 0 0 0 1.35 1 1
Summery of Forces for Jackup condition

ULS 59.41 23.09 70.13
SLS Rare 42.66 16.61 50.38
Design Bending Moment Maximum of service & Jackup condition

ULS 59.41 149.48 73.87
SLS Rare 42.66 99.44 50.38
MATERIAL PROPERTIES :
Grade of concrete = M 35 MPa PERMISSIBLE STRESSES
Grade of Reinforcement = Fe 500 MPa 1) Premissble concrete compressive stresses
fywd = 0.8 fyk = 400 MPa Load Combi Permissble Stress
Clear cover = 50 mm SLS Rare 0.48 fck = 16.8 Mpa
Modulus of Elasticity steel Es = 200000 Mpa SLS QP 0.36 fck = 12.6 Mpa
For short Term loading Ecm = 32000 Mpa
For long Term loading Ecm' = 14304.3 Mpa
fcteff Mean tensile strength = fctm = 2.77 Mpa 2) Premissble Tensile stress in steel = 0.8 fy
fcd = 15.63 Mpa = 400 Mpa
Creep factor f = 1.24
euk = 0.0045 3) Permissible crack width wk
eud = 0.0041 SLS QP Load combination = 0.3 mm
ecu2 = 0.0035
xumax/d = 0.4636
DESIGN OF SECTION HOGGING MOMENT DESIGN OF SECTION SAGGING MOMENT

Width bw = 600 mm Width bw = 600 mm
Overall depth D = 1270 mm Overall depth D = 1270 mm
Effective depth provided d = 1207.5 mm Effective depth provided d = 1207.5 mm
Let us provide At top Let us provide At bottom

Layer-1 25 f 8 Nos. @ 67.8571 mm c/c Layer-1 25 f 8 Nos. @ 67.8571 mm c/c
Layer-2 25 f 8 Nos. @ 67.8571 mm c/c Layer-2 25 f 8 Nos. @ 67.8571 mm c/c
2 2
Ast,provided = 7853.98 mm Ast,provided = 7853.98 mm
A) ULS CAPACITY CHECK
Check Check Check
Ast / 0.362 fck
Ast,cal =M/ 0.87
MRd =0.87 fyk

xu = 0.87 fyk
fyk (d'-0.416
Ast (d-0.416
MED/z +DFD
Ast,provided > Ast
Load comb.
Ast Calc.<Ast
Ast, z = d- MED/z
MRD/z >
xu)
xu)
MED b d xmax Check Ast min DFd 0.416 xu +DFD MRD/z
Provided
Provided
min
Tm mm mm mm2 mm mm mm2 mm2 T m T Tm Tm/m
ULS Hogging 59.41 600 1207.5 7853.98 559.768 269.651 UR, OK 1246.8 OK 1811.25 OK 36.94 1095.33 91.1707 374.216 341.648 OK
ULS Sagging 149.48 600 1207.5 7853.98 559.768 269.651 UR, OK 3137.37 OK 1811.25 OK 36.94 1095.33 173.41 374.216 341.648 OK
B) SLS STRESS CHECK

Rare Load combination. Formula used for calculation of stress
2 2
Ec,eq = Ecm*(MQP+MST) = 14304.3 MPa dc (depth of neutral axis) = -m*As +  ( m * As + 2* m*As*b* d )
MST +(1+f)* MQP b
MST = MRARE -MQP = 0.00 Tm INA (Transformed) = b *dc3/3 + m* As *(d-dc)2
m = Es/ Ec,eq = 13.982 MPa
Quasi Permanent Load Combination Tensile stress in steel ss = m* MRARE* (d - dc ) / INA
m = Es / Ecm' = 13.9818 MPa
Stress Check for SLS Load Combinations
M N.A. Tensile Max T
Ast, modular depth Comp Max C. stress Stress
Check Check
Load comb. b d Provided
ratio (dc) INA stress Stress
2
(tm/m) mm mm mm mm mm4 Mpa Mpa Mpa Mpa
Check for Hogging Moment

SLS (R Comb.) 42.66 600.0 1207.5 7853.98 13.98 416.74 8E+10 2.14 16.8 OK 56.73 400 OK
SLS (QP Comb.) 42.66 600.0 1207.5 7853.98 13.98 416.74 8E+10 2.14 12.6 OK 56.73 400 OK
Check for Sagging Moment

SLS (R Comb.) 99.44 600.0 1207.5 7853.98 7.54 323.59 5E+10 6.07 16.8 OK 124.95 400 OK
SLS (QP Comb.) 16.61 600.0 1207.5 7853.98 13.98 416.74 8E+10 0.83 12.6 OK 22.09 400 OK
C) SLS CRACK WIDTH CHECK (QUASI PERMANENT LOAD COMBINATION)

1) CHECK Ast,min for crack control
Load b h d Act =bh/2 ss = fyk k kc As,min =kc k fct,eff h k
comb. mm mm mm mm
2
Mpa Act / ss As,provided check 0 1
0.3 1
Check for Hogging Moment 0.8 0.65
SLS QP 600 1270 1207.5 381000 500.00 0.65 0.4 549.044 7853.98 OK 3 0.65

SLS QP 600 1270 1207.5 381000 500.00 0.65 0.4 549.044 7853.98 OK
2) CHECK FOR MAXIMUM SPACING b/w bars.
Spacing b/w bars
Load comb. Bar dia cover Provided Calculated check
feq c mm mm

SLS QP 25 50 67.86 312.50 OK

SLS QP 25 50 67.86 312.50 OK
3) CHECK FOR CRACK WIDTH

esm - ecm =Max [[
smax =3.4c +
0.17f/rPeff
hc,eff =Min [ 2.5 ( h
Aceff = rpeff = x =neutral ae = ssc - kt fct,eff ( 1+ ae
Load comb. - d ) , ( h - x/3 ) , Asprovided ssc kt wk check
hc,eff *b As/Ac,eff axis depth Es/Ecm' rP,eff ) / rP,eff ] /Es ,
h/2]
0.6ssc/Es ]
2 2
mm mm mm mm Mpa mm

SLS QP 156.25 93750 7853.98 0.084 220.73 56.73 416.74 0.5 13.98 0.00017 0.038 OK

SLS QP 156.25 93750 7853.98 0.084 220.73 22.09 416.74 0.5 13.98 6.6E-05 0.015 OK
D) CHECK FOR SHEAR : ( IRC 112 / clause 10.3.2 (2) )
r1 = Min [ Asl/bw d
VRdc =Max [ ( 0.12

k (80 r1 fck )0.33 +
nmin = 0.031 k3/2
0.15 scp ) bw d ,
(nmin +0.15scp )
k= Min [ 1 +
200/d , 2 ]
bw d ]
, 0.02 ]
fck1/2
Load comb. VED b bVED d bw Asl scp Check
2
T T mm mm mm Mpa Tonne
ULS 73.87 1 73.87 1207.5 600 1.407 7853.98 0.0108 0.306 0 37.7256 Provide shear
reinf.
Check for Maximum Shear Capacity :
2*VNS / (acw *
q = 0.5 sin-1 [
bw * z * v1 *
Vrdmax = acw
n1 * fcd /2
q adopted
* bw * z *
fcd) ]
Load comb. VED bw d z =0.9d acw n1 Check
T mm mm mm Tonne deg deg
ULS 73.87 600 1207.5 1086.75 1 0.6 305.81 OK 6.99 45
DFd = 0.5 VED

rw,min =( 0.072
rw,min*s *bw
√ fck ) / fyk
Asw/s = VED / z Provide Asw
provide
Asw/s
Load comb. VED bw z qdesign
Asw,min =
fywd cotq
cotq
Legs dia spacing
2 2
T m m deg mm /m mm /m nos mm mm mm2/m Check T
ULS 73.87 600 1086.75 45 1699.33 + 0.00085 92.0069 36.94

Additional requirement (suspension reinf.) 1351.46 = 3050.8 4 16 180 4468.04 OK
DFd = Additional Tensile force, to be accounted in longitudinal reinforcement

DESIGN OF END CROSS GIRDER FOR TRANSVERSE BENDING
Calculation of Horizontal force
1) Live Load breaking force = 20 Tonne */For Class 70 R single lane load
2) Seismic component of permanent loads

Selfweight Sup = 296.2 Tonne
SIDL,surfacing, FPDL = 86.9 Tonne
Total = 383.2 Tonne
Seismic coefficent in long. direction = 0.54
Total Horizontal force = 4 + 383.2 x 0.54

*/20 % breakng force is considered = 210.91 Tonne
Nos. of Girder = 4
Horizontal force per girder = 52.7 Tonne
Summery of Force in End cross Girder Beam

*Refer STAAD file Unfactored ULS Load Factor
Maximum Hogging/ Sagging Moment 26.12 Tm 1.5
Maximum Shear Force 28.73 T 1.5
Factored Design Forces

Maximum Hogging/ Sagging Moment 39.17 Tm
Maximum Shear Force 43.10 T
MATERIAL PROPERTIES :
fywd = 0.8 fyk = 400 MPa
Clear cover = 50 mm
fcd = 15.63 Mpa
euk = 0.0045
eud = 0.0041
ecu2 = 0.0035
xumax/d = 0.464
DESIGN OF SECTION HOGGING MOMENT 1.27

Width bw = 1270 mm 0.22 1.05
Overall depth D = 600 mm
Effective depth provided d = 537.5 mm
Let us provide At top

Layer-1 25 f 8 Nos. @ 163.571 mm c/c 0.6
2
Ast,provided = 3926.99 mm Flange part is ignored in design
A) ULS CAPACITY CHECK

Check Check Check
xu = 0.87 fyk Ast
z = d- 0.416 xu
fyk (d'-0.416 xu)
Ast (d-0.416 xu)

Ast,cal =M/ 0.87
MRd =0.87 fyk

Ast Calc.<Ast Provided
Ast,provided > Ast min
MED/z +DFD
/ 0.362 fck b
MRD/z > MED/z

MRD/z
Ast,
MED b d xmax Check Ast min DFd
Load comb. Provided
+DFD
Tm mm mm mm2 mm mm mm2 mm2 T m T Tm Tm/m
ULS Hogging 39.17 1270 537.5 3926.99 249.17 134.83 UR, OK 1870.57 OK 806.25 OK 21.55 481.413 102.919 82.24 170.82 OK
D) CHECK FOR SHEAR : ( IRC 112 / clause 10.3.2 (2) )
r1 = Min [ Asl/bw d
VRdc =Max [ ( 0.12

k (80 r1 fck )0.33 +
nmin = 0.031 k3/2
0.15 scp ) bw d ,
(nmin +0.15scp )
k= Min [ 1 +
200/d , 2 ]
Load comb. VED b bVED d bw Asl scp Check
bw d ]
, 0.02 ]
fck1/2
2
T T mm mm mm Mpa Tonne
ULS 43.10 1 43.10 537.5 1270 1.610 3926.99 0.0058 0.375 0 33.00 Provide shear
reinf.
Check for Maximum Shear Capacity :
2*VNS / (acw *
q = 0.5 sin-1 [
q adopted
bw * z * v1 *
Vrdmax = acw
n1 * fcd /2
* bw * z *
Load comb. VED bw d z =0.9d acw n1
fcd) ]
Check
T mm mm mm Tonne deg deg
ULS 43.10 1270 537.5 483.75 1 0.6 288.14 OK 4.30 45
DFd = 0.5 VED

rw,min =( 0.072
rw,min*s *bw
√ fck ) / fyk
Asw/s = VED / z Provide Asw
provide
Asw/s
Load comb. VED bw z qdesign
Asw,min =
fywd cotq Check
cotq
Legs dia spacing
2 2
T m m deg mm /m mm /m nos mm mm mm2/m T
ULS 43.10 1270 483.75 45 2227.29 0.00085 162.29 4 12 150 3015.93 OK 21.55
DFd = Additional Tensile force, to be accounted in longitudinal reinforcement

Appendix B :
Finding creep coefficent
fck = 35 Mpa (Considering Precat Beam material)
fcm = 45 Mpa
t = 25550 days
to = 90 days
f (t, to) = fo b c( t , to )
fo = fRHbfcmbto
fRH = 1+ 1 - RH/100 for fcm ≤ 45 Mpa

0.1 ( ho )1/3
1+ 1 - RH/100 for fcm > 45 Mpa

1/3 a1 a2
0.1 ( ho )
RH = Relative humidity
= 80 %
ho = 393 mm
a1 = [ 43.75 / fcm ]0.7 = 0.98047
0.2
a2 = [ 43.75 / fcm ] = 0.99438
fRH = 1.273
bfcm = 18.78 / √fcm
= 2.79956
bto = 1/ (0.1+ to0.2)
= 0.3907
fo = 1.39239
0.3
b c( t , to) = [ (t-to) / (b H +t -to) ]
bH = Min 1.5 [ 1+ (0.012 RH)18 ] ho +250 for fcm ≤ 35 Mpa

1500
Min 1.5 [ 1+ (0.012 RH)18 ] ho +250 a3 for fcm > 35 Mpa

1500* a3
a2 = [ 43.75 / fcm ]0.5 = 0.986

bH = 1119.15
b c( t , to) = 0.987
f (t, to) = 1.37
Appendix C :
CALCULATION OF BASIC DRYING SHRINKAGE STRAIN FOR PRECAST BEAM
fck = 35 Mpa
fcm = 45 Mpa
ecd. = kh ecd.0
-6
ecd.0 = 0.85 [ (220+110 ads1) exp(-ads2. fcm /fcmo ) ] 10 b RH
b RH = 1.55 [ 1 - RH / RHo ]3
RH = 80 %
RH0 = 100 %
b RH = 0.7564
ads1 = 3 for slow setting cement

4 for normal cement
6 for rapid hardening
ads2 = 0.13 for slow setting cement

0.12 for normal cement
0.11 for rapid hardening
ads1 = 4 for normal cement

ads2 = 0.12 for normal cement
fcmo = 12.5 Mpa
ecd.0 = 0.00028
ho kh
ho = 2Ac/u 100 1
= 393.2 mm 200 0.85
300 0.75
kh = 0.7267 500 0.7
5000 0.7
ecd. = 0.0002
CALCULATION OF BASIC DRYING SHRINKAGE STRAIN FOR DECK SLAB
fck = 35 Mpa
fcm = 45 Mpa
RH = 80 %
RH0 = 100 %
b RH = 0.7564
ads1 = 4 for normal cement

ads2 = 0.12 for normal cement
fcmo = 12.5 Mpa
ecd.0 = 0.00028
ho = 2Ac/u
= 440 mm
kh = 0.715
ecd. = 0.0002
APPENDIX : D
MATERIAL PROPERTIES
REINFORCEMENT PROPERTIES :
Grade of steel = Fe 500 Mpa
Es = 200000 Mpa
fyk = 500 Mpa

fyd = 434.783 Mpa
ft = 545 MPa
gs = 1.15
Stress
fyd = fyk / gs
= 434.7826 Mpa
eyk = fyk / Es eyd = 0.22% eud = 0.41%

= 0.25% Mpa Strain
Design stress- strain diagram for
eyd = fyd / Es Reinforcing Steel
= 0.22% Mpa
euk = 0.45%
eud = 0.9 * euk

= 0.41%
fy = es*Es if es < eyd

= fyd if es >= eyd
PROPERTY OF CONCRETE (PRECAST BEAM):
Concrete Grade = M 35
fcd = 15.63 Mpa
fck = 35 Mpa
fcd = afck /gm
stress
a = 0.67
gm = 1.5 ec2 = 0.002 ecu2 = 0.0035
strain
fcd = 0.447 *fck Design stress -strain diagarm
= 15.63 Mpa for Concrete
fcm = fck+10 (fck & fcm) in Mpa

= 45 Mpa
fctm = 0.259 fck2/3 for fck ≤ 60 Mpa
= 2.27 ln[1 + fcm/12.5)] for fck > 60 Mpa
fctm = 2.77 Mpa
ec2 = (2+0.085 ( 0.8 fck - 50 )0.53)/10 For fck > 60 Mpa

0.2 % For fck <= 60 Mpa
= 0.002
ecu2 = (2.6 + 35 [ ( 90 - 0.8*fck ) / 100 ]4)/10 For fck > 60 Mpa

0.35 % For fck <= 60 Mpa
= 0.0035
Stress in concrete corresponding to starin

h
sc = fcd * ( 1 - (1-ec/ec2) ) For 0 ≤ ec ≤ 0.002
= fcd For 0.002 ≤ ec ≤ 0.0035
4
h = 1.4 + 23.4 [ ( 90 - 0.8*fck ) / 100 ] For fck > 60 Mpa
2 For fck <= 60 Mpa
= 2
Property of Rectangular stress block

hfcd
Effective height factor l = 0.8 for fck <= 60 Mpa
= 0.8- (fck-60)/500 for 60 < fck <= 110 Mpa
= 0.8
Compression zone factor h = 1 for fck <= 60 Mpa

= 1- (fck-60)/250 for 60 < fck <= 110 Mpa
= 1
0.0035 Strain fcd 1 *fcd

3/7x 0.416 x
0.002 Stress
@ 0.8 *x
x 4/7x
Strain Recatangular- Parabolic stress block Equavelent stress block

Limiting Depth of Neutral axis
Minimum Strain in reinforcement at ultimate limit state
eud = 0.41%
Ultimate strain in concrete ecu2 = 0.0035
ecu2 = 0.0035
xu ≤xu,max
d
d-xu
eud= 0.00405
Ast
xu,max 0.0035
=
d - xu,max 0.00405
xu,max = 0.464 *d

Design of Br@Ch.25+732 - 1x18

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Design of Br@Ch.25+732 - 1x18

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CONTENTS

Depth of super-structure = 1.52 m

Overall carriageway width = 8.5 m

MATERIAL USED & THERE PROPERTIES :

Modulus of Elasticity for Concrete

Creep coefficent for Foundation f = 1 ( As ho =  , For foundations)

Ecm' = 16154.1 Mpa

Max permissible Stress in Steel = 0.8*fyk = 400 Mpa

Permissible crack width wk,max = 0.3 mm

Backfill Soil Parameter

Live Load Surcharge :

1.25 3 c/c of girder

Nos. of Girder = 3 Nos.

Showing +ve Force & Moment Direction

0.52 1 0 9.30 HFL : 233.710

8.6 1.2 2.1

8.6 1.2 2.1 RETURN WALL

Calculating Selfweight of Sub-structure :

Total 14.39 35.97 7.33 -3.33 0.00

Abutment shaft weight considered. 43.30 108.24 4.15 -2.75 0.00

Calculating Selfweight Foundation:

Total Footing weight 142.16 355.41 0.74 -5.44 0.00

Total Footing weight 75.21 188.02 3.85 -7.60 0.00

Total Sub-structure + Footing 277.21 693.03 2.51 -5.48 0.00

Total Weight of sub-structure & foundation = 693.03 T

Lever arm about c/L base (along T-T axis) = 0m

Earth Fill Weight

Total Earth Fill 496.24 992.49 5.26 -7.78 0.00

Total Weight of backfill = 992.49 T

Lever arm about c/L base (along T-T axis) = 0m

Element Area Factor No.s B H L V W eY eL eT

Earth Fill Weight

Total Earth Fill -357.67 -357.67 1.92 -6.54 0.00

Total buoyant weight = -357.67 T

Lever arm about c/L base (along T-T axis) = 0.00 m

Density of RCC = 2.5 T/m

Nos of Girder = 3 1.3 1.52

Section at Mid span Section at support

Total 0.678 0.671

Section Property of Girder At Support Section

Total 0.975 0.650

Self weight of Precast Beam

Reaction due to self weight of each girder

Total Reaction 16.9428 0.664

Total weight of one Girder = 33.89 Tonne

Total Nos. of girder = 3 Nos.

Total weight of all girders = 101.66 Tonne

Weigth of Concrete Deck = 83.96 T 0.11 m

Diaphragm = 10.67 T 1.01 m

Total Concrete Weight = 196.29 T

Reaction Over Each End = 107.96 Tonne

Total Reaction at Each support = 108.0 Tone

Forces due to Super-Structure DL about base slab toe :

Lever arm about c/L base (along T-T axis) = 0m

Cg. From base slab bottom = 8.67 m

Overall span = 17.96 m

Footpath weight = 0 t/m 0.35

Forces & Moments @ Foundation base

Horizontal seismic coeff. -Long., AhL' = (Z/2)(I)(Sa/g)(Long.) = 0.54