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Analysis and Design of RCC Bridges and BoxCulvert

RESEARCH · APRIL 2015

DOI: 10.13140/RG.2.1.2919.8882

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National Institute of Technology Karnataka

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N LYSIS ND DESIGN OF BRIDGE ND CULVERT

Practical Training Report

Submitted in partial fulfillment for the requirements of the degree

MASTER OF TECHNOLOGY

In

STRUCTURAL ENGINEERING

By

PAUL TOM P.

13ST17F

DEPARTMENT OF CIVIL ENGINEERING

NATIONAL INSTITUTE OF TECNOLOGY KARNATAKA

SURATHKAL, MANGALORE –

575025July 2014



CERTIFICATE

This is to certify that the Practical Training Report entitled ANALYSIS AND DESIGN

OF BRIDGE AND CULVERT submitted by PAUL TOM P. (Register Number: 13ST17F) as

the record of the work carried out by him, is accepted as the Practical Training Report submission

in partial fulfillment of the requirements for the award of degree of Master of Technology in

Structural Engineering in the Department of Civil Engineering.

Head of Department Faculty Advisor

Dr. Katta Venkataramana Dr. K. Swaminathan

Department of Civil Engineering Professor - Civil Engineering

NIT Karnataka, Surathkal NIT Karnataka, Surathkal



i

ACKNOWLEDGEMENT

I am extremely thankful to Dr. Katta Venkataraman, Professor & Head,

Department of Civil Engineering, National Institute of Technology, Karnataka for giving

me the opportunity to undergo internship training at Larsen & Toubro, Chennai.

My special thanks to Dr. K. Swaminathan, Professor of the Civil Engineering

Department for all his help and guidance.

I would like to express my deepest sense of respect and indebtedness to my

Internship Supervisor, Mr. Sadasivam V. and Mrs. Nisha K.C., EDRC-Transportation

IC, Larsen & Toubro, Chennai, for their consistent support, guidance, encouragement and

advice during the project.

I owe my wholehearted thanks to Mr. Lingarajan K., who has been my Internship

Mentor for taking time out of his busy schedule for my doubts and clarifications. I also

thank the entire staff of the company for their cooperation and assistance during the course

of my project.

I hope that I can build upon the experience and knowledge that I have gained and

make a valuable contribution towards this industry in the coming future.



ii

CONTENTS

ACKNOWLEDGEMENT…………………………………….…………………………. iCONTENTS……………………………………………………………………………... ii

CHAPTER 1: INTRODUCTION

1.1 BRIDGES……………………………………………………………...………….1

1.2 CULVERT……………………………………………………………… .…….….1

1.3 LOADS AND STRESSES………………………………………………………. ..2

1.4 VEHICLE CLASSIFICATIONS……………………………………………….....2

CHAPTER 2: ANALYSIS AND DESIGN OF SUBSTRUCTURE

2.1 DETAILS OF THE STRUCTURE …………………………………………….…4

2.1.1 Determination of Permissible Stresses…………………………………….…6

2.2 CALCULATION OF LOADS AND MOMENTS………………………………...7

2.2.1 Dead Load Analysis……………………………………………………….....7

2.2.2 Live Load Analysis………………………………………………….….........8

2.2.3 Calculation of Longitudinal Forces ………………………………………....9

2.2.4 Bearings……………..……………………………………………….............9

2.2.4.1 Fixed Bearing………………………………………………….…10

2.2.4.3 Free Bearing……………………………………………………...10

2.2.5 Wind Forces …………………………………………………………….….10

2.2.6 Seismic Forces……………………………………………………………. ..11

2.2.7 Load Combinations…………………………………………………...……12

2.3 PIER DESIGN………...……………………………………………………….…13

2.3.1 Design of Pier Cap ……………………………………………………..…..14

2.3.2 Design of Footing ………………...……………………………………..…15

CHAPTER 3: ANALYSIS AND DESIGN OF SUPERSTRUCTURE

3.1 SECTION PROPERTIES……………………………………………………… ...17

3.2 LOAD ANALYSIS…………………………………………………………...….18

3.2.1 Live Load Positions……………………………………………………… ...18

3.2.2 Load Summary……………………………………………..…………........20

3.2.3 Load Combinations…………………………………………...…………....20



iii

3.3 GIRDER DESIGN……………………………………………………………….20

3.4 SHEAR CONNECTOR DESIGN…………………………………………...…...21

3.5 DIFFERENTIAL SHRINKAGE STRESS……………………………………….21 3.6 DIAPHRAGM DESIGN……………………………………………………...….22

CHAPTER 4: ANALYSIS AND DESIGN OF BOX CULVERT

4.1 DETAILS OF THE STRUCTURE..……………………………………………...25

4.2 MODELLING OF THE STRUCTURE………………………………………......25

4.3 LOAD CALCULATIONS…………………………………………………...…..25

4.3.1 Dead Load……………………………………………………………….....25

4.3.2 Live Load…………………………………………………………………..26

4.3.3 Load Combinations…………………………………………………...……284.4 DESIGN OF BOX SECTION……………………………………………………29

4.4.1 Design for Flexure………………………………………………………….29

4.4.2 Design for Shear……………………………………………………………31

REFERENCES ………………………………………………………………… ..……..32

ANNEXURE 1 : SAMPLE DESIGN OF SUB-STRUCTURE

ANNEXURE 2 : SAMPLE DESIGN OF SUPER-STRUCTURE



1

1. INTRODUCTION

This internship was carried out at Larsen & Toubro , EDRC, Transportation IC , with the

objective of gaining first-hand knowledge about the technical practices in a structural

design office, office ethics and corporate lifestyle. L & T Transportation In fr astructure

handles major roadway projects which includes National and State Highways all around

India and associated structures like flyovers, Vehicle Underpass (VUP), Pedestrian

Underpass (PUP), Rail Over Bridge (ROB), major & minor bridges and cross-drainage

works like culverts. The structural design wing of this department handles these structures

of all Infrastructure Projects. The design of the VUP Sub-structure & Super-structure and

box culvert included in this internship report are designed based on the Working Stress

Method as per the design codes published by The Indian Roads Congress.

1.1 BRIDGES

A bridge is a structure having a total length above 6m between the inner face of the dirt

walls for carrying traffic or other moving loads over a depression or obstruction such as

channel, road or railway. They are classified as minor or major bridges as per the criteria

given below:

Minor Bridges – Span greater than 6m upto 60m

Major Bridges – Span greater than 60m

1.2 CULVERT

A culvert is a cross-drainage structure having a total length of 6m or less between the inner

faces of the dirt wall or extreme vent-way boundaries measured at right angles thereto.

The types of culverts are:

Box Culvert

Pipe Culvert

RCC Solid Slab Culvert



2

1.3 LOADS, FORCES AND STRESSES

The loads and stresses considered in the design are as follows (as per IRC 6-2010):

1. Dead Load

2. Live Load

3. Impact factor due to vehicular live load

4. Vehicle Collision Load

5. Wind Load

6. Longitudinal forces due to braking

7. Earth Pressure (including live load surcharge)

8. Temperature Effect

9. Seismic Forces

1.4 VEHICLE CLASSIFICATIONS

The major classifications of vehicles considered as live load for design are

CLASS 70R WHEELED

Adopted on all roads on which permanent bridges and culverts are constructed.

Should also be checked for Class A Loading.



3

CLASS 70R TRACKED

40 TONNES BOGIE LOAD

CLASS A

Adopted on all roads on which permanent bridges and culverts are constructed.



4

2. ANALYSIS AND DESIGN OF SUBSTRUCTURE

2.1 DETAILS OF THE STRUCTURE

Fig 1: Typical section of a pier

This includes all the details required by the designer for carrying out analysis. For the

substructure design of abutment piers the details required are:

Grade of concrete and steel

Span of Bridge

Slope

Wearing coat

3000

1500

3500

RCC DIAPHRAGM

JACK LOCATION

RCC PIER CAP

RCC PIER

1

1.5 1 1.5

FREE

FIXED



5

Width of carriageway and percentage of camber

Reduced levels of ground, footing, pier cap, etc.

Type of bearing

Nature of traffic (live load)

Seismic Zone, importance factor, type of soil, etc.

Basic Wind Speed

Safe Bearing Capacity of Soil

Fig 3: Elevation and plan of an Abutment Pier



7

For M35 concrete,

Permissible flexural compressive stress in

concrete, σcbc

Normal 11.70 MPa

Wind (33% increase) 15.56 MPa

Seismic(50% increase) 17.55 MPa

Permissible flexural tensile stress in steel, σst

Normal 240.00 MPa

Wind(33% increase) 319.20 MPa


Permissible compressive stress in steel, σst

Normal 205.00 MPa

Wind (33% increase) 272.65 MPa


As per table 1 of IRC 6-2010, for wind load case the permissible stresses are increased by

33% and for seismic case it is increased by 50%.

2.2 CALCULATION OF LOADS AND MOMENTS

The first step in the design of any structure is the analysis of various dead loads, Super-

Imposed Dead Load (SIDL), live loads, seismic loads, wind loads and longitudinal loads.

2.2.1 DEAD LOAD ANALYSIS

Dead load reactions can be directly taken from the STAAD model or can be manually

calculated by considering the dead load due to superstructure (girder, diaphragm and deck

slab). Longitudinal moments are calculated in the same way by multiplying reactions with

the longitudinal eccentricity which is the distance between the centerline of pier and

bearing.

The reaction on each bearing due to girder, diaphragm and deck slab and due to Super-

imposed Dead Load, SIDL (wearing coat and crash barrier) is found out separately.



8

The dead load due to self-weight of pier cap, pier shaft and footing is also separately

calculated by multiplying the unit weight of concrete (25kN/m3) by their respective

volumes

2.2.2 LIVE LOAD ANALYSIS

The live load for each load combination can be calculated manually as well as with the

help of a STAAD model.

For the STAAD model vehicle definitions has to be provided as per IRC 6-2010, for the

load calculations and position of load has to be inputted as per IRC 6-2010.

A point worth noting is that STAAD requires the distance to the centerline of the outermost

wheel away from the origin along the transverse direction, while during manual calculation

of transverse moments the eccentricity of the center of gravity from the centerline of the

carriage-way is used.

As per IRC 6-2010 table 2, for a 3 lane, 12m wide carriage-way, 2 critical load

combinations are possible.

One Class 70R + One Class A Three Class A

One Class 70R; this configuration is checked for criticality as it generates maximum

transverse moment.

The reactions on each bearing is noted down from the STAAD model for design of pier

cap and for the calculation of transverse and longitudinal moments.

As per IRC 6-2010 Cl. 205, for 3 lane traffic, a 10% reduction is to be considered for the

longitudinal effect as the probability of the characteristic loads acting simultaneously is

low.



9

2.2.3 CALCULATION OF LONGITUDINAL FORCES

Longitudinal forces in bridges are generated due to the following factors:

Braking Effect

Frictional resistance due to change of temperature or any other cause.

2.2.4 BEARINGS

Fig 4: Bearings

Type of BearingVertical

Reaction

Horizontal Reaction

along longitudinal

direction

Horizontal Reaction

along transverse

direction

Fixed Pot Bearing

Guided Bearing along

transverse direction

Guided Bearing along

longitudinal direction

Free Bearing

Free-End Pier Fixed-End Pier

G1

G2

G3

G4



10

2.2.4.1 FIXED BEARING

They are restrained against movement along transverse and longitudinal direction. The

longitudinal forces due to fixed bearing are calculated using the formula:

F h - μ (Rg + R q )

Or

F h /2 + μ (Rg + R q )

Where, μ is the coefficient of friction at the movable bearing (values obtained from IRC 6 -

2010 Cl. 211.5.1).

R g is the reaction due to dead load

Rq is the reaction due to live load

F b is the applied horizontal force (due to braking)

2.2.4.2 FREE BEARING

Braking forces which act in the longitudinal direction above bearing level are zero as the

bearing is free in the longitudinal direction in a free-end pier. They are only restrained in

the transverse direction. They don’t resist braking forces. The longitudinal forces due to

friction generated due to movement of bearings are calculated using the formula:

μ (Rg + R q )

2.2.5 WIND FORCES (Cl 209 IRC 6-2010)

The IRC code mentioned gives equations for the transverse and vertical wind force, the

variables being Drag coefficient, CD (for horizontal force), lift coefficient (CL) , gust factor

(G) , area resisting the force and hourly mean wind pressure (P z), all of which are given in

the above mentioned clause.

The hourly mean wind pressure is given for varying heights (height exposed above mean

retarding surface) with a basic wind speed of 33ms-1 in table 4 of IRC 6-2010, which has



11

to be multiplied by the ratio of squares of basic wind speed at the location to the base wind

speed corresponding to table 4 (ie. 33ms-1) to obtain the wind pressure corresponding to

the considered location. Intermediate values can be interpolated.

The longitudinal wind load is taken as 25% of the transverse wind load.

The lever arm distance to the center of gravity of the considered portion is also determined

for calculation of moments.

Transverse Wind F orce, F t = P z x A x G x C D

Verti cal Wind Force, F v = P z x A x G x C L

2.2.6 SEISMIC FORCES

The Seismic Coefficient Ah is given by the equation,

Ah = (Z/2) x (I /R) x (S a /g)

Where, Z is the zone factor

I - Importance factor

R - Response Reduction Factor

S a /g - Seismic Response Acceleration Coefficient for 5% damping.

The values for zone factor, importance factor and Response Reduction Factor are given in

IRC 6-2010 in tables 6, 7 and 8 respectively.

The value for the Seismic Response Acceleration Coefficient depends on the type of soil

and time period of vibration and is given in Cl 219.5.1 in IRC 6-2010 for various types of

soils.

The time period for vibration is given by,

T = 2 x (D/1000F) 1/2

Where D – Approximate Dead Load of Superstructure or Live Load

F – Horizontal force in kN required to be applied at the center of mass of the superstructure

for 1mm horizontal deflection at the top of the pier/abutment along the considered direction

of the horizontal force. (Stiffness in kN/mm)



12

The value of sti ff ness is taken as, F = 3EI /L 3

E – Modulus of Elasticity of concrete

I – Moment of Inertia of the section about the axis considered

L – Length of the member

The seismic horizontal force are separately determined for the dead load on superstructure,

SIDL, dirt wall, substructure, pier and live load. Longitudinal Seismic forces are taken as

zero for dead load due to super structure, SIDL and for live load as the pier being designed

has free bearings.

2.2.7 LOAD COMBINATIONS

The following load combinations will be considered in the analysis for determination of

critical values of bending moment and shear force.

1. DL + SIDL (without live load)

2. DL + SIDL + LL-70R + Longitudinal Frictional Forces

3. DL + SIDL + LL-70R+Class A + Longitudinal Frictional Forces

4. DL + SIDL + LL-3 Class A + Longitudinal Frictional Forces

5.

DL + SIDL + LL-70R + Longitudinal Frictional Forces + Wind

6. DL + SIDL + LL-70R+Class A + Longitudinal Frictional Forces +Wind

7. DL + SIDL + LL-3 Class A + Longitudinal Frictional Forces + Wind

8. DL + SIDL + Long. Seismic Force (without live load)

9. DL + SIDL + 20% LL- 70R + Long. Frictional Forces + Long. Seismic Force

10. DL + SIDL + 20% LL- 70R+Class A + Long. Frictional Forces + Long. Seismic

Force

11. DL + SIDL + 20% LL- 3 Class A+ Long. Frictional Forces + Long. Seismic Force

12. DL + SIDL + Long. Frictional Forces + Trans. Seismic Force (without live load)

13. DL + SIDL + 20% LL- 70R+Long. Frictional Forces + Trans. Seismic Force

14. DL + SIDL + 20% LL- 70R+Class A + Long. Frictional Forces + Trans. Seismic

Force

15. DL + SIDL + 20% LL- 3 Class A+ Long. Frictional Forces + Trans. Seismic Force



13

Only 20% of Live Load is taken for the load combinations involving Seismic forces under

the assumption that only 20% of the live load acts on the super-structure in the event of an

earthquake. (Cl. 219.5.2, IRC 6-2010)

The vertical force, horizontal force in transverse and longitudinal direction and Moments

in transverse and longitudinal direction are found out for these load combinations at the

bottom of pier and bottom of foundation. All load cases are checked if they are within

permissible limits of stresses in steel and concrete.

Note: Seismic loads are increased by 25% in seismic cases for calculating the forces at the

bottom of the footing and all moment are recalculated for lever arm distance increased by

the depth of the footing.

2.3 PIER DESIGN

The area of concrete required for pier to resist axial load is calculated by dividing the

maximum axial load value amongst all the load combinations by the permissible stress in

concrete for the respective load case. The area of steel provided in any case shall not be

less than 0.3% of the gross sectional area of concrete (Cl. 306.2.2 IRC 21-2000).

The cross-sectional area of longitudinal reinforcement shall not be less than 0.8% nor more

than 8% of the gross cross-sectional area. (Cl. 306.2.1 IRC 21-2000).

As per Cl. 306.3 the diameter of transverse reinforcement of any type shall not be less than

one quarter the diameter of the largest longitudinal bar in that region of the column and in

no case less than 8mm. The pitch of transverse reinforcement shall not exceed 300mm or

the least of the least lateral dimension of the column or 12 times the diameter of the smallest

longitudinal reinforcement in the column.

It may be noted that permissible stress in steel as well concrete is increased by 33% for

wind load case and by 50% for seismic cases.



15

Area of steel r equi red, Ast req = M / ( σ st x j x d)

Note : Value of Q & j varies for each load case as permissible stresses in steel and concrete

are increased for wind by 33% and seismic case, it is increased by 50%.

Side face reinforcement of 0.05% of gross area is provided on each face. The sections are

also designed for shear and torsion by providing the appropriate reinforcement as per the

design procedure in IRC 21-2000 Cl 304.7.

2.3.2 DESIGN OF FOOTING

Firstly the additional load on the footing bottom due to self-weight of footing, soil above

footing and due to earth-fill are calculated. The earth-fill and the eccentricity between the

centerline of pier and footing exerts a moment on the footing in the longitudinal direction,

this value is added to the existing moments at the bottom of the footing.

The revised values of vertical load, longitudinal and transverse moments are calculated

after which the stresses at the corners of the footing is calculated using the formula,

P/A ± M L /Z L ± M T /Z T

The net pressure is calculated by reducing the stress due to self-weight of footing and soil

from the total stress and stresses are interpolated to obtain the stress at the center of each

face of the location of the pier.

The critical value of bending moment for section along traffic direction and across traffic

direction is calculated for each load case to determine the reinforcement required at each

face using working stress equations used for pier cap design.

Critical sections are taken at a distance deff along the traffic direction and across the trafficdirection and critical values of shear fore is calculated for the punching shear check.

Punching Shear Stress, τ cp = V p / Aps

Punching Shear, V p = (P 1 + P 2 + P 3 + P 4 ) / 4 x Ef fective area in carrying punching shear

A ps – Area resisting punching shear



16

The value of shear stress has to be within permissible limits as per IRC 21-2000 Cl.

307.2.5.5, which states that punching shear stress shall not be less than 0.16 x (f ck ) 1/2 .

Fig 5: Dimensional Reinforcement Detail of Sub-structure & Foundation



17

3. ANALYSIS AND DESIGN OF SUPERSTRUCTURE

The superstructure consists of the girder, deck slab and crash barriers. The girders rest

on the bearings through which forces and moments are transferred to the sub-structure.

3.1 SECTION PROPERTIES

The section properties of the girders are initially assumed as per standards or from previous

experience and later checks are done in the design stages to ensure safety. From

calculations the Moment of inertia, area of cross-section and center of gravity of the section

is calculated.

Fig 6: Dimensional Section details of a Girder

The section properties for the composite section, i.e. the section including the deck slab is

also determined from the properties of the individual sections by considering unit width of



18

deck slab for each girder. These section properties are used in creating a STAAD Pro

grillage model for analysis.

3.2 LOAD ANALYSIS

The various load cases considered for the design on the superstructure are:

Dead Load (Girder + Deck Slab + Diaphragm)

Super-imposed Dead Load ( Crash Barrier + Wearing Coat)

Live Load Cases

o Class 70R eccentric

o

Class 70R on the inner girder

o Class 70R + 1 Class A

o 3 Class A

The live load cases shown above are for a 3 lane carriage way. The live load combinations

may be changed based on the carriageway width as per IRC 6-2010, table 2.

The shear force and bending moment for each of these load cases are determined at a

distance, ‘d’ away from the support m, at 0.25leff from the support and at the mid-span.

The section is designed for the flexure requirement at mid-span. The longitudinal

reinforcement obtained may be curtailed at a section of 0.25leff from the support based on

the moments at that section.

3.2.1 LIVE LOAD POSITIONS

CLASS 70R Eccentric

4 0 1m

CLASS 70R



19

CLASS 70R ON INNER GIRDER

CLASS 70R + 1 CLASS A

3 CLASS A

5 465m

4 0 1m

10m

CLASS A

LASS 70R

2 65

CLASS A CLASS A

CLASS A

6 15m

9 65m

CLASS 70R



20

3.2.2 LOAD SUMMARY

The load analysis is summarized for the section at effective depth, ‘d’, away from the

support and at the mid-span for design purposes.

All the loads and moments are tabulated by taking into considerations the impact factor

for the live load and the longitudinal effect for the various lane configurations.

Also each live load case is analyzed for maximum shear force and maximum bending

moment condition from the STAAD model and are listed as separated load cases.

Loads are listed separately for the inner and outer girder.

3.2.3

LOAD COMBINATIONS

All the live load cases are each combined with the Super-imposed Dead Load (SIDL)

as these come under the service condition and the critical value is taken as the

maximum results from inner and outer girder results, which is used for carrying out the

design.

3.3 GIRDER DESIGN

The girder design is carried out at the mid-span for the construction stage where only dead

load is considered followed by the curtailment design at the required distance from the

support. After this design is carried out for the composite section in service stage in a

similar fashion and stresses are now combined and checked whether they are within

permissible limits.

The design of girders are carried as a T flange, by determining the neutral axis depth and

this depth is used to determine the revised stresses in steel and concrete due to axial force

combined with biaxial bending.

For the construction stage only the dead load is considered along with the self-weight of

the deck slab as it is cast at a later stage. The SIDL along with live load case is considered

in the service stage and design is carried out. The stresses in concrete and steel are checked

if they exceed the permissible limits.



21

Shear reinforcement is also determined at these 2 sections as per IRC 21-2000 Cl. 304.7.1.

Fig 7: Dimensional Reinforcement Details of Girders

3.4 SHEAR CONNECTOR DESIGN

The deck slab and girder being cast and placed separately are not monolithic and hence

requires a connection for load transfer. This is facilitated with the help of shear connectors

which are cast in the girders in the casting yard with the shear connectors projecting above

the top of the girder. The deck slab is cast around this thereby helping the superstructure

withstand shear.

The maximum shear force due to live load and SIDL are considered for the design as 1.3DL

+1.5 LL, as these are the only loads on the deck slab. Dead load is not considered.

3.5 DIFFERENTIAL SHRINKAGE STRESS

As the various components of the superstructure are cast at different times, the concrete is

of different age and shrinkage occurs in the various components non-uniformly. This

generates a stress known as Differential Shrinkage Stress.



22

It is calculated as per BS 5400-4 1990 Cl. 7.4.3.5

M cs = e diff x E cf x Acf x a cent

Where, ediff – Differential Shrinkage Strain

E cf – Modulus of elasticity of the concrete flange

Acf – Area of the effective concrete flange

acent – Distance of the centroid of the concrete flange from the centroid of the composite

section

Φ – Reduction coefficient to allow for creep, taken as 0.43

3.6

DIAPHRAGM DESIGN

Fig 8 : BMD of Diaphragm from STAAD Pro

The diaphragm beam is also modelled on STAAD to obtain the maximum sagging and

hogging moments, from which the top and bottom reinforcements are designed.

The loads to be considered on the diaphragm are taken for the critical condition, which is

often during jacking. The superstructure is jacked up from time to time, for replacement of

the bearings which may wear off with use. The structure is closed down for vehicle usage

G1

G2 G3

G4

Jacking Point



23

during such maintenance and so live loads can be ignored. The loads considered to be

acting on the diaphragm during jacking are the self-weight of girder, deck slab, crash

barrier, wearing coat and self-weight of diaphragm itself

The diaphragm is also provided with shear reinforcement and side face reinforcement as

per IRC 21-2000 Cl. 304.7.1.



25

4.1 DETAILS OF THE STRUCTURE

The basic design data required for analysis of the structure is as follows:

1. Clear span

2. Clear height

3. Dimension of Box Culvert

4. Depth of fill and wearing coat

5. Width of carriage way

6. Soil Properties

4.2 MODELLING OF THE STRUCTURE

The box culvert in modelled as a 2-D member for a 1m strip, restrained with spring

supports. The center-line dimensions of the box culvert are taken for modelling

The stiffness of the supports in the vertical direction is based on ‘Foundation Analysis and

Design’ by Joseph E. Bowles, who states that the Modulus of sub-grade reaction is given

by,

F s = 40 x S.F . x q a Where, S.F. is the safety factor

qa is the Safe Bearing Capacity of the soil.

The sti f fness, k = ½x F s x (D istance between adjacent supports)

4.3 LOAD CALCULATIONS

4.3.1 DEAD LOAD

The dead loads are calculated by considering 1m of the box section. The dead load for top

slab, bottom slab and side walls are calculated separately as a Uniformly Distributed Load

applied on the respective members. The concrete density is generally taken as 25kN/m3.

The Super Imposed Dead Load (SIDL) includes wearing coat, fill and parapet wall. The

wearing coat thickness is generally increased to accommodate future overlay and is also

considered for 1m width and applied as a UDL on the top slab. The parapet wall is of 0.3m



26

width generally and height is provided as required which is including the height of fill. As

the parapet wall is constructed at the sides of the carriage-way, the parapet load is given

throughout the span of the top slab.

Surcharge Live Load is considered to be equivalent to 1.2m of earth fill as per Cl. 214.1

IRC 6.2010. The unit weight of soil fill is taken as 20kN/m 3 and the load is applied

horizontally on the side walls.

Earth pressure is considered for the at rest condition. The pressures at top and bottom slab

level are computed and applied on the side walls.

For the High Flood Level (HFL) condition, the water pressure inside the box culvert is

applied vertical down on the bottom slab and the Submerged Soil Pressure is also

calculated and applied horizontally on the side walls. Water pressure acting horizontally

inside and outside will balance each other and is therefore ignored.

4.3.2 LIVE LOAD

For calculation of load dispersion along the traffic direction, as per Cl 305.16.3, IRC 21-

200-, the effect of contact of wheel or track load in the direction of span length shall be

taken as equal to the dimension of the tyre contact area over the wearing surface of the slab

in the direction of the span plus twice the overall depth of the slab inclusive of the thickness

of the wearing surface.

The calculation of load dispersion in the direction across traffic, as per Cl. 305.16.2 IRC

21-2000,

The eff ective width, b eff = α x (1 – a/l o ) + b l

α – a constant having values as per the table in Cl. 305.16.2, IRC 21-2000, depending uponthe b / l o ratio, where b is the width of the slab.

a – the distance of the center of gravity of the concentrated load from the nearer support.

l o – the effective span



28

1,3 – Critical Section for Bending Moment for bottom slab

4,6 - Critical Section for Bending Moment for top slab

7,10 - Critical Section for Bending Moment for side wall

2 - Critical Section for Shear Force for bottom slab

5 - Critical Section for Shear Force for top slab

8,9 - Critical Section for Shear Force for side wall

The braking force is also calculated as per Cl. 211.2 IRC 6-2010 from the load intensity

value, and half of the value so obtained are applied on each edge of the top slab in the

STAAD model.

The pressure on the base slab due to maximum reaction in the supports from STAAD Pro

model should be less than the Safe Bearing Capacity of the soil.

4.3.3 LOAD COMBINATIONS

The critical load combinations considered for design are as follows:

1. DL+SIDL+EP

2. DL+SIDL+EP+LLS-L

3.

DL+SIDL+EP+LLS-R

4. DL+SIDL+EP+LLS-BOTH

5. DL+SIDL+EP+LLS-L+LL

6. DL+SIDL+EP+LLS-R+LL

7. DL+SIDL+EP+LLS-BOTH+LL

8. DL+SIDL+EP+LLS-L+LL+BR-L

9.

DL+SIDL+EP+LLS-R+LL+BR-R

10.

DL+SIDL+EP+LLS-BOTH+LL+BR-L

11. DL+SIDL+EP+LLS-BOTH+LL+BR-R

DL – Dead Load SIDL – Super Imposed Dead Load

EP – Earth Pressure LLS – Live Load Surcharge

BR – Braking Force LL – Live Load



29

The above load combinations are for Low Flood Level, in case of floods, the High Flood

Level (HFL) is considered where Submerged Earth Pressure and water pressure are

additional forces instead of Dry Earth Pressure.

The combinations for HFL are as follows:

1. DL+SIDL+SEP+WP

2. DL+SIDL+SEP+WP+LLS-L

3. DL+SIDL+SEP+WP+LLS-R

4. DL+SIDL+SEP+WP+LLS-BOTH

5. DL+SIDL+SEP+WP+LLS-L+LL

6. DL+SIDL+SEP+WP+LLS-R+LL

7. DL+SIDL+SEP+WP+LLS-BOTH+LL

8. DL+SIDL+SEP+WP+LLS-L+LL+BR-L

9. DL+SIDL+SEP+WP+LLS-R+LL+BR-R

SEP – Submerged Earth Pressure WP – Water Pressure

The design moments are taken as the maximum value at the critical sections considered.

4.4 DESIGN OF BOX SECTION

The critical case is taken for maximum shear force and maximum bending moment

condition at the critical sections 1, 3, 4, 6, 7 and 10 as shown in the figure above.

The design for flexure is done as per Working Stress Design Methodology.

4.4.1 DESIGN FOR FLEXURE

The effective depth for the top slab, bottom slab and side wall are calculated by deducting

the clear cover and depth of stirrup and diameter of the reinforcement bar.

The effective depth required is calculated as per the following procedure and the depth is

checked if safe or not. If not section dimensions need to be revised.

Ef fective depth r equi red, d req = (M /Qb) 1/2



30

where d req- Effective depth required

M – Bending Moment at the section

Q = (1/2) x j x k σ cbc

j = 1 – (k/3)

k = (280/ (3 σ cbc)) / (280/ (3 σ cbc) + σ st)

σ cbc & σ st are the permissible flexural strength in steel and concrete respectively.

The area of steel required is calculated as per the following formula and adequate steel is

provided and spacing of bars are computed. The steel provided has to be greater than the

minimum steel required that is 0.12% of the gross area of section.

Area of steel r equi red, Ast req = M / (σ st jd )

The area of distribution steel is considered by considering the load combination 0.2DL +

0.3LL. The bending moment at critical section are computed and required steel is provided

as per the procedure for main reinforcement.

Fig 11: Typical Detailing of a Box Culvert



31

4.4.2 DESIGN FOR SHEAR

The critical cases for shear force in the maximum bending moment and maximum shear

force conditions are considered at the critical sections 2, 5, 8 & 9.

The design shear stress is computed as follows (Cl. 304.7 IRC 21-2000):

Design Shear Stress, τ v = V / (b x d)

b – breadth of the member

d – effective depth of the member

V – Design Shear across the section

The value of design shear stress must be less than the maximum shear stress allowed in the

section as per IRC 21-2000 table 12A. The permissible shear stress, τc is determined based

on the percentage of steel provided as given in table 12B IRC 21-2000, and the shear

reinforcement is computed for the unbalanced shear force.

Vertical Shear Reinf orcement, A sw = V s x S / (σ s x d)

A sw – Total Cross-sectional area of stirrup legs

V s = V - τ c x b x d

S – Spacing of the stirrups

σ s – Permissible tensile stress in shear reinforcement

d – effective depth



32

REFERENCES

1. IRC 6-2010, Standard Specifications and Code of Practice for Road Bridges

Section II – Loads and Stresses (5th Revision)

2. IRC 21-2000, Standard Specifications and Code of Practice for Road Bridges,

Section III – Cement Concrete (Plain and Reinforced) (3 rd Revision)

3. IRC-78-2000, Standard Specifications and Code of Practice for Road Bridges,

Section VII- Foundations and Substructures.

4. Dr. V.K. Raina, Concrete Bridge Practice: Analysis, Design and Economics, page

387-396, Design of a RCC section subject to combined Axial Thrust and Biaxial

Bending.

5. Foundation Analysis and Design, 5th edition, by Joseph E.Bowles, McGraw-Hill,

1996.



7.3 SEISMIC COMBINATIONS FOR FOOTING BOTTOM…………………………. 15

7.4 WIND LOAD FOR FOOTING BOTTOM…………………………………………. 15

8 LOAD COMBINATIONS 16

8.1 PIER BOTTOM………………………………………………………………… ....... 16

8.2 FOOTING BOTTOM……………………………………………………………….. 20

9 LOAD SUMMARY 24

9.1 BOTTOM OF PIER …………………………………………………………………. 24

9.2 BOTTOM OF FOOTING………………………………………………………… .... 25

10 DESIGN OF FREE-END PIER 26

11 MATERIAL STRESSES 27

12 PIER CAP DESIGN 28

13 FOOTING DESIGN 32

13.1 SECTIONAL PROPERTIES……………………………………………………… ... 32

13.2 EARTHFILL………………………………………………………………………… 33

13.3 FOOTING CORNER STRESSES…………………………………………………... 34

13.4 NET PRESSURE………………………………………………………………… ..... 37

13.5 DESIGN AT CRITICAL SECTIONS……………………………………………..... 38

13.6 FOOTING SHEAR ………………………………………………………………….. 43



1. DETAILS OF SUBSTRUCTURE

Grade of Concrete 35.00 MPa

Grade of Steel 500.00 MPa

Density of concrete 25.00 kN/m3

Overall span of RCC Girder 20.00 m

Effective Span 19.00 m

Size of Pier Transverse Direction 3.00 m

Longitudinal Direction (Thickness) 1.00 m

Equivalent width of pier in transverse direction 2.79 m

Depth of pier cap 1.50 m

Thickness of dirt wall 0.30 m

Spacing between bearings 3.00 m

Eccentricity between C/L OF Pier & Bearings 0.11 m

Height of Crash barrier 1.15 m

Thickness of wearing coat 0.06 m

Thickness of deck slab 0.23 m

Depth of RCC Girder 1.50 m

Thickness of bearing 0.07 mMinimum height of pedestal 0.20 m

% camber 2.50 %

Average thickness of bearing pedestal 0.31 m

Total width of deck slab 12.00 m

Depth of founding level from GL 2.00 m

Depth of footing 1.00 m

GL to footing top level 1.00 m

FRL at pier location 621.59 m

Existing ground level 613.64 m

Average bearing Top level 619.67 m

Pier cap top level 619.30 m

Footing top level 612.64 mFounding level 611.64 m

Height of pier from GL to pier cap top 5.65 m

Height from bearing level to footing top 7.03 m

Height of pier (i.e.. Footing top to pier cap top) 6.65 m

Cross-sectional Area of Pier (A) 2.79 m2

Least moment of inertia (I) 0.23 m4

Least radius of gyration r min = 0.29 m√(I/A)

1



Note 3 Table 13 IRC 21-2000 lef =1.75l 11.65

Slenderness Ratio ( lef /r min) 40.34 <50

Hence, Short pier

Stress Reduction factor (only for long column) (1.5-lef /(100*r min) 1.00

1.1 PERMISSIBLE STRESSES

(Stress increase as per IRC 21-2000)

Permissible flexural compressive stress in concrete σcbc Normal 11.70 MPa Table 9

Wind 15.56 MPa

Seismic 17.55 MPa

Permissible flexural tensile stress in steel σst Normal 240.00 MPa Table 10

Wind 319.20 MPa

Seismic 360.00 MPa

Permissible compressive stress in steel σst Normal 205.00 MPa Table 10

Wind 272.65 MPa

Seismic 307.50 MPa

Safe Bearing Capacity of Soil 440.00 kN/m2

2



3. LIVE LOAD

3.1 CLASS 70R

120 120 170 170 170

6.58 1.52 2.13 1.37 1.37

A1 = 256.27 kN

A2 = 743.73 kN

Total Reaction due to Class 70R = 1000.00 kN

0.45 1.20 2.79 6.00

2.96

Maximum Reaction = 743.73 kN

Transverse Moment = 2197.72 kNm

Longitudinal Moment = 81.81 kNm

3.98 3.05

80 170

A2A1

4



3.2 CLASS 70R + 1 CLASS A

27 27 114 114 68 68 68 68

1.1 3.2 1.2 4.3 3.0 3.0 3.0 5.50

A1 = 142.84 kN

A2 = 357.16 kN

1.95 2.30

7.50

70R A

0.45 1.20 2.79 6.00

2.96 3.10

Transverse Moment = 1090.53 kNm Maximum Reaction = 357.16 kN

Longitudinal Moment = 39.29 kNm Total Reaction due to Class A = 554.00 kN

10% reduction for longitudnal effect as per IRC 6-2010 Cl. 205 Total Reaction = 1100.89 kN

Reaction = 990.80 kN


Longitudinal Moment = 35.36 kNM

A2A1

5



3.3 3-CLASS A

0.4

6

0.45 0 2.3 1.2 2.3 1.2 2.3

4.25 2.75

0.75

Reaction due to 1 Class A vehicle = 357.16




10% reduction due to longitudnal effect




6



4. LONGITUDINAL FORCES

4.1 FRICTIONAL FORCE

As per Cl. 211.5.1 OF IRC 6-2010, following values of horizontal force have been considered.

μ - Coefficient of friction at movable bearing = 0.05Rg - Reaction at free end due to dead load = 1882.00 kN

Rq - Reaction at free end due to live load

Class 70R 743.73 kN

Class 70R + Class A 990.80 kN

3 Class A 964.33 kN

S.No. Description of traffic load Horizontal Force = μ(Rg + Rq) kN

1 DL+SIDL+Class 70R 131.29

2 DL+SIDL+Class 70R + 1 Class A 143.64

3 DL+SIDL+3 Class A 142.32

Free pier will have no braking forces acting on pier

Bearing Deformation only needs to be calculated for elastomeric bearing

7



5. WIND FORCE

The project stretch contains less obstructions for wind hence the terrain is considered

to be plain as per table 4 of IRC 6-2010

Basic wind speed for the project stretch 42.5 m/s

Height of the superstructure 8.85 m

Height from GL to bottom of superstructure 5.92 m

For height of 9m & for basic wind speed of 33m/s,

Horizontal wind pressure 463.7 N/m2

For basic wind speed of 42.5m/s,

Horizontal wind pressure, Pz 769.1076 N/m

Transverse wind force , FT ( Cl. 209.3.3 of IRC 6-2010)

FT = Pz x A1 x G x CD

A1 - Solid Area in m

2

G - Gust factor

CD - Drag Coefficient

Longitudinal wind force FL for superstructure shall be taken as 25% of the

transverse wind force as per Cl. 209.3.4 of IRC 6-2010.

Vertical wind force , FT ( Cl. 209.3.5 of IRC 6-2010)

FL = Pz x A3 x G x CD

A3 -Area in plan in m2

G - Gust factor CL - Lift Coefficient = 0.75

5.1 DEAD LOAD

5.1.1 Superstructure

Length of superstructure resisting wind, l = 10.00 m

Depth of superstructure resisting wind, d = 2.93 m

Area of deck resisting wind, A1 = 29.31 m

Width of cross-section, b = 12.00 m

b/d = 4.09

CD for structures supported by single beam = 1.40

CD for structures supported by 2 or more beams = 2.09

Gust factor (G) for spans upto 150m = 2.00

Transverse force on superstructure due to wind, FT = 94.36 kN

Longitudinal force on superstructure due to wind, FL = 23.59 kN

C.G. of the force from bearing level = 1.44 m

8



Vertical Wind Load, FL

Width of superstructure = 12.00 m

Area in plan, A3 = 120.00 m

Vertical Wind Load, FL = 138.44 kN

5.1.2 Sub-structure =

Dimension of pier in longitudinal direction, b = 1.00 mDimension of pier in transverse direction, t = 3.00 m

Height of pier exposed to wind, h = 5.65 m

t/b = 3.00

h/b = 5.65

As per note 4 of IRC 6-2010 page 30, h/b = 40.00

From table 5 of IRC 6-2010, CD = 1.20

As per IRC 6-2010, Cl. 209.4 Note 1, CD value should be multiplied with maximum of

(1-1.5r/b) or 0.5 for piers with rounded corners, where r is the radius of rounded pier corner.

0.50

For pier with r = 0.5m, (1-1.5r/b) = 0.25

CD multiplication factor = 0.50

CD is multiplied by 0.5 = 0.60Gust factor, G = 2.00

Solid area of projected elevation, A1 = 5.65 m

Transverse force on substructure due to wind = 5.22 kN

Longitudinal force on substructure due to wind = 1.30 kN

Lever arm (from top of footing to C.G. of exposed area)

for wind force acting on substructure = 3.82 m

5.2 Live Load

(Cl. 209.3.3 IRC 6-2010)

Height of deck from GL = 7.64 mFor basic wind speed of 42.5m/s,

Hourly mean speed of wind at deck level = 35.80 m/s

Height of live load from ground level = 10.65 m

For height of 10.95m & for basic wind speed 33m/s

Horizontal wind pressure = 473.00 N/m2

For height of 10.95m & for basic wind speed 42.5m/s

Horizontal wind pressure = 784.53 N/m2

Total length of superstructure exposed to wind force = 10.00 m

Height of exposed area of live load (excluding height of crash barrier)

for calculating wind force = 1.85 m

Area of live load resisting wind = 18.50 m2

CD value as per Cl. 209.3.6 of IRC 6-2010 = 1.20

Gust factor (G) for spans upto 150m = 2.00

Transverse wind force due to live load = 34.83 kN

Longitudinal wind force = 8.71 kN

C.G. of force from bearing level = 3.81 m

9



6. SEISMIC FORCES

6.1 SELF-WEIGHT CALCULATION OF PIER

12

1.4

0.4

1.1

4.4

3.2

Area of pier cap above section 1-1 = 4.8 m2

Area of pier cap between section 1-1 & 2-2 = 8.36 m2

Total area of pier cap per unit width = 13.16 m2

Volume of pier cap = 18.424 m3

C.G. of pier cap above 1-1 from top = 0.2 m

C.G. of pier cap between 1-1 & 2-2 from top = 0.84386 m

C.G. of pier cap from top = 0.60902 m

Self weight of pier cap = 460.6 kN

Height of straight portion of pier = 5.15 m

Area of pier = 2.79 m2

Volume of pier = 14.3685 m3

Self weight of straight portion of pier = 359.213 kN

C/s area of dirt wall = 0.77 m2

Weight if dirt wall = 231 kN

Longitudinal moment due to dirt wall over piercap = 127.05 kNm

Calculation of Seismic Coefficient

Zone Factor = 0.1

Response Reduction Factor (table 5) = 2.5

11

2 2

10



6.6 SUB-STRUCTURE

6.6.1 Pier cap

Total Load = 460.60 kN

Seismic force in Transverse Direction = 27.636 kN

Seismic force in Longitudinal Direction = 27.636 kN

CG of pier cap from top of pier cap = 0.61 m

CG of pier cap from top of footing = 6.05 m

6.6.2 Pier

Height from GL to pier cap bottom = 4.15 m



Seismic force in Longitudinal Direction = 17.3887 kN

CG of pier cap from top of footing = 3.0775 m

6.7 LIVE LOAD

Only 20% Live load is considered for seismic case

6.7.1 Class 70RTotal Load = 743.73 kN


Seismic force in Longitudinal Direction = 0 kN

6.7.2 Class 70R + Class A




6.7.3 3-Class A

Total Load = 964.33 kNSeismic force in Transverse Direction = 11.572 kN


Horizontal seismic force acts at 1.2m above FRL

C.G. of live load from bearing top = 2.98 m

12



7.1 FORCES AND MOMENTS FOR FOOTING TOP

7.03 m

Dead Load

1.1

Self weight of

superstructure 1472.00 161.92

1.2

Weight of dirt

wall+approach slab 231.00 -127.05

1.3 Weight of pier cap 460.60

1.4 Weight of pier 359.21

2 SIDL 410.00 45.10

3 Live Load

3.1 Class 70R 743.73 81.81 2197.72

3.2 Class 70R + Class A 990.80 35.36 981.47

3.3 3 Class A 964.33 106.08 723.25

4 Longitudinal Forces

4.1 Frictional Force

4.1.1 DL+SIDL+Class 70R 131.29 7.03 922.68

4.1.2

DL+SIDL+Class 70R +

Class A 143.64 7.03 1009.50

4.1.3 DL+SIDL+3 Class A 142.32 7.03 1000.20

5 Wind Load

5.1 On superstructure

5.1.1 Wind over permanent load -138.44 23.59 94.36 8.47 8.47 199.76 799.04

5.1.2 Wind over live load 8.71 34.83 10.83 10.83 94.34 377.35

Net force on superstructure -138.44 32.30 129.19 294.10 1176.39

5.2 On substructure 1.30 5.22 3.82 3.82 4.98 19.94

The elevation difference between top of bearing to top of

7. LOAD CASES

eT (m)

ML

(kNm)

MT

(kNm)S.No. Description of loads P (kN)

HL

(kN) HT (kN) eL (m)

13



6 Seismic Loads

6.1 Longitudinal Seismic Case

6.1.1

Dead load on

superstructure 0.00 8.23 0.00

6.1.2 SIDL 0.00 8.98 0.00

6.1.3 Dirt Wall 13.86 7.71 106.85

6.1.4 Pier Cap 27.64 6.05 167.09

6.1.5 Pier 17.39 3.08 53.51

6.1.6 Live Load6.1.6.1 Class 70R 0.00 10.01 0.00

6.1.6.2 Class 70R + Class A 0.00 10.01 0.00

6.1.6.3 3 Class A 0.00 10.01 0.00

6.2 Transverse Seismic Case

6.2.1

Dead load on


6.2.2 SIDL 24.60 8.98 220.86

6.2.3 Dirt Wall 13.86 7.71 106.85

6.2.4 Pier Cap 27.64 6.05 167.09

6.2.5 Pier 17.39 3.08 53.51

6.2.6 Live Load

6.2.6.1 Class 70R 8.92 10.01 89.33

6.2.6.2 Class 70R + Class A 11.89 10.01 119.00

6.2.6.3 3 Class A 11.57 10.01 115.82

7.2 SEISMIC COMBINATIONS FOR FOOTING TOP

1

Longitudinal Seismic

Case

1.1 L+0.3T (DL+SIDL) 58.88 51.54 327.45 382.50

1.2

L+0.3T (DL+SIDL+ Class

70R) 58.88 54.22 327.45 409.30

1.3


70R+ Class A) 58.88 55.11 327.45 418.20

1.4

L+0.3T (DL+SIDL+ 3 Class

A) 58.88 55.01 327.45 417.25

2 Transverse Seismic Case

2.1 T+0.3L (DL+SIDL) 17.67 171.80 98.23 1275.00

2.2

T+0.3L (DL+SIDL+ Class

70R) 17.67 180.73 98.23 1364.33

2.3


70R+ Class A) 17.67 183.69 98.23 1394.01

2.4

T+0.3L (DL+SIDL+ 3 Class

A) 17.67 183.38 98.23 1390.83

ML

(kNm)

MT


HL

(kN) HT (kN)

14



7 Seismic Loads

7.1 Longitudinal Seismic Case

7.1.1

Dead load on


7.1.2 SIDL 0.00 9.98 0.00

7.1.3 Dirt Wall 17.33 8.71 150.88

7.1.4 Pier Cap 34.55 7.05 243.40

7.1.5 Pier 21.74 4.08 88.637.1.6 Live Load

7.1.6.1 Class 70R 0.00 11.01 0.00

7.1.6.2 Class 70R + Class A 0.00 11.01 0.00

7.1.6.3 3 Class A 0.00 11.01 0.00

7.2 Transverse Seismic Case

7.2.1

Dead load on


7.2.2 SIDL 30.75 9.98 306.82

7.2.3 Dirt Wall 17.33 8.71 150.88

7.2.4 Pier Cap 34.55 7.05 243.40

7.2.5 Pier 21.74 4.08 88.63

7.2.6 Live Load

7.2.6.1 Class 70R 11.16 11.01 122.82

7.2.6.2 Class 70R + Class A 14.86 11.01 163.627.2.6.3 3 Class A 14.46 11.01 159.24

7.3 SEISMIC COMBINATIONS FOR FOOTING BOTTOM

1


Case

1.1 L+0.3T (DL+SIDL) 73.61 64.43 482.91 542.55

1.2


70R) 73.61 67.77 482.91 579.40

1.3L+0.3T (DL+SIDL+ Class70R+ Class A) 73.61 68.89 482.91 591.64

1.4

L+0.3T (DL+SIDL+ 3 Class

A) 73.61 68.77 482.91 590.33

2 Transverse Seismic Case

2.1 T+0.3L (DL+SIDL) 22.08 214.76 144.87 1808.51

2.2


70R) 22.08 225.91 144.87 1931.33

2.3


70R+ Class A) 22.08 229.62 144.87 1972.13

2.4

T+0.3L (DL+SIDL+ 3 Class

A) 22.08 229.22 144.87 1967.75

7.4 WIND LOAD FOR FOOTING BOTTOM

5 Wind Load

5.1 On superstructure

5.1.1 Wind over permanent load -138.44 23.59 94.36 9.47 9.47 223.35 893.40

5.1.2 Wind over live load 8.71 34.83 11.83 11.83 103.05 412.18

Net force on superstructure -138.44 32.30 129.19 326.40 1305.58

5.2 On substructure 1.30 5.22 4.82 4.82 6.29 25.16

ML

(kNm)

MT


HL

(kN) HT (kN)

For Footing bottom , depths are increased by 1m and seismic forces are increased by

15



8.1 PIER BOTTOM

8.1.1 DL+SIDL (Without Live Load)

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10Total 2932.81 79.97

8.1.2 DL+SIDL+LL Class 70R+Longitudinal Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.103 LL - Class 70R 743.73 81.81 2197.72

4 Longitudinal Frictional Force 131.29 7.03 922.68Total 3676.54 131.29 0.00 1084.46 2197.72

8.1.3 DL+SIDL+LL Class 70R+Class A+Longitudinal Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - Class 70R+Class A 990.80 35.36 981.47

4 Longitudinal Frictional Force 143.64 7.03 1009.50Total 3923.61 143.64 0.00 1124.83 981.47

8.1.4 DL+SIDL+LL 3 Class A+Longitudinal Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - 3 Class A 964.33 106.08 723.254 Longitudinal Frictional Force 142.32 7.03 1000.20

Total 3897.14 142.32 0.00 1186.25 723.25

8. LOAD COMBINATIONS

S.No. Description of loads P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm)


eT (m) ML (kNm) MT (kNm)

S.No. Description of loads P (kN) HL (kN) HT (kN) eL (m) eT (m)

S.No. Description of loads P (kN) HL (kN) HT (kN) eL (m)

ML (kNm) MT (kNm)

16



1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - Class 70R 743.73 81.81 2197.724 Longitudinal Frictional Force 131.29 7.03 922.68

5 Wind Load

5.1 On superstructure -138.44 32.30 129.19 294.10 1176.39

5.2 On substructure 1.30 5.22 3.82 3.82 4.98 19.94Total 3538.10 164.89 134.41 1383.54 3394.05

8.1.6 DL+SIDL+LL Class 70R +Class A+Longitudinal Forces+Wind Load

1 Dead Load 2522.81 34.872 SIDL 410.00 45.10

3 LL - Class 70R+Class A 990.80 35.36 981.47

4 Longitudinal Frictional Force 143.64 7.03 1009.50

5 Wind Load



8.1.7 DL+SIDL+LL 3 Class A+Longitudinal Forces+Wind Load

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - 3 Class A 964.33 106.08 723.25


5 Wind Load



8.1.5 DL+SIDL+LL Class 70R+Longitudinal

Negative because wind is assumed to act upwards for critical condition





ML (kNm) MT (kNm)

17



8.1.8 DL+SIDL+Longitudinal Seismic Case (Without Live Load)

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 Longitudinal Seismic Force 58.88 51.54 327.45 382.50Total 2932.81 58.88 51.54 407.42 382.50

8.1.9 DL+SIDL+20% LL Class 70R+Longitudinal Forces+Longitudinal Seismic Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - Class 70R 148.75 16.36 439.54



8.1.10 DL+SIDL+20% LL Class 70R+Class A+Longitudinal Forces+Longitudinal Seismic Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - Class 70R+Class A 198.16 7.07 196.294 Longitudinal Frictional Force 143.64 7.03 1009.50


8.1.11 DL+SIDL+20% LL 3 Class A+Longitudinal Forces+Longitudinal Seismic Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - 3 Class A 192.87 21.22 144.65

4 Longitudinal Frictional Force 142.32 7.03 1000.205 Longitudinal Seismic Force 58.88 55.01 327.45 417.25

Total 3125.68 201.20 55.01 1428.83 561.90





ML (kNm) MT (kNm)


18



1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 Transverse Seismic Force 17.67 171.80 98.23 1275.00

Total 2932.81 17.67 171.80 178.20 1275.00

8.1.13 DL+SIDL+20% LL Class 70R+Longitudinal Forces+Transverse Seismic Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - Class 70R 148.75 16.36 439.54


5 Transverse Seismic Force 17.67 180.73 98.23 1364.33Total 3081.56 148.95 180.73 1117.25 1803.88

8.1.14 DL+SIDL+20% LL Class 70R+Class A+Longitudinal Forces+Transverse Seismic Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - Class 70R+Class A 198.16 7.07 196.29



1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - 3 Class A 192.87 21.22 144.65


5 Transverse Seismic Force 17.67 183.38 98.23 1390.83

Total 3125.68 159.98 183.38 1199.62 1535.48

8.1.15 DL+SIDL+20% LL 3 Class A+Longitudinal Forces+Transverse Seismic Forces


S.No. Description of loads P (kN) HL (kN) ML (kNm) MT (kNm)


HT (kN)


eL (m) eT (m)


8.1.12 DL+SIDL+Transverse Seismic Case (Without Live Load)

19



8.2 FOOTING BOTTOM

8.2.1 DL+SIDL (Without Live Load)

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10Total 2932.81 79.97

8.2.2 DL+SIDL+LL Class 70R+Longitudinal Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.103 LL - Class 70R 743.73 81.81 2197.72

4

Longitudinal Frictional

Force 131.29 8.03 1053.97Total 3676.54 131.29 0.00 1215.75 2197.72

8.2.3 DL+SIDL+LL Class 70R+Class A+Longitudinal Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.103 LL - Class 70R+Class A 990.80 35.36 981.47

4


Force 143.64 8.03 1153.14Total 3923.61 143.64 0.00 1268.47 981.47

8.2.4 DL+SIDL+LL 3 Class A+Longitudinal Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.103 LL - 3 Class A 964.33 106.08 723.25

4


Force 142.32 8.03 1142.52Total 3897.14 142.32 0.00 1328.56 723.25

It may be noted that Seismic loads are increased by 25% in seismic cases for






ML (kNm) MT (kNm)

20



8.2.5 DL+SIDL+LL Class 70R+Longitudinal Forces+Wind Load

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - Class 70R 743.73 81.81 2197.72

4Longitudinal FrictionalForce 131.29 8.03 1053.97

5 Wind Load



8.2.6 DL+SIDL+LL Class 70R +Class A+Longitudinal Forces+Wind Load

1 Dead Load 2522.81 34.872 SIDL 410.00 45.10

3 LL - Class 70R+Class A 990.80 35.36 981.47

4


Force 143.64 8.03 1153.14

5 Wind Load



8.2.7 DL+SIDL+LL 3 Class A+Longitudinal Forces+Wind Load

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - 3 Class A 964.33 106.08 723.25

4


Force 142.32 8.03 1142.52

5 Wind Load



Negative because wind is assumed to act upwards for critical condition





ML (kNm) MT (kNm)

21



8.2.8 DL+SIDL+Longitudinal Seismic Case (Without Live Load)

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10


8.2.9 DL+SIDL+20% LL Class 70R+Longitudinal Forces+Longitudinal Seismic Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - Class 70R 148.75 16.36 439.54

4Longitudinal FrictionalForce 131.29 8.03 1053.97


8.2.10 DL+SIDL+20% LL Class 70R+Class A+Longitudinal Forces+Longitudinal Seismic Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.103 LL - Class 70R+Class A 198.16 7.07 196.29

4


Force 143.64 8.03 1153.14


8.2.11 DL+SIDL+20% LL 3 Class A+Longitudinal Forces+Longitudinal Seismic Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - 3 Class A 192.87 21.22 144.65

4


Force 142.32 8.03 1142.52






ML (kNm) MT (kNm)


22



8.2.12 DL+SIDL+Transverse Seismic Case (Without Live Load)

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10


8.2.13 DL+SIDL+20% LL Class 70R+Longitudinal Forces+Transverse Seismic Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - Class 70R 148.75 16.36 439.54

4


Force 131.29 8.03 1053.97


8.2.14 DL+SIDL+20% LL Class 70R+Class A+Longitudinal Forces+Transverse Seismic Forces

1 Dead Load 2522.81 34.87

2 SIDL 410.00 45.10

3 LL - Class 70R+Class A 198.16 7.07 196.29

4


Force 143.64 8.03 1153.14


8.2.15 DL+SIDL+20% LL 3 Class A+Longitudinal Forces+Transverse Seismic Forces

1 Dead Load 2522.81 34.872 SIDL 410.00 45.10

3 LL - 3 Class A 192.87 21.22 144.65

4


Force 142.32 8.03 1142.52


MT (kNm)

ML (kNm) MT (kNm)

S.No. Description of loads P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm)





23



9.2 BOTTOM OF FOOTING

1 DL+SIDL+Longitudinal Forces (Without Live Load) 2932.81 0.00 0.00 79.97 0.00

2 DL+SIDL+LL Class 70R+Longitudinal Forces 3676.54 131.29 0.00 1215.75 2197.72

3 DL+SIDL+LL Class 70R+Class A+Longitudinal Forces 3923.61 143.64 0.00 1268.47 981.47

4 DL+SIDL+LL 3 Class A+Longitudinal Forces 3897.14 142.32 0.00 1328.56 723.25

5 DL+SIDL+LL Class 70R+Longitudinal Forces+WindLoad

3538.10 164.89 134.41 1548.43 3528.46

6DL+SIDL+LL Class 70R +Class A+Longitudinal

Forces+Wind Load3785.17 177.24 134.41 1601.16 2312.21

7DL+SIDL+LL 3 Class A+Longitudinal Forces+Wind

Load3758.71 175.92 134.41 1661.25 2053.99

8DL+SIDL+Longitudinal Forces+Longitudinal Seismic

Case (Without Live Load)2932.81 73.61 64.43 562.88 542.55

9DL+SIDL+20% LL Class 70R+Longitudinal

Forces+Longitudinal Seismic Forces3081.56 204.89 67.77 1633.21 1018.94

10DL+SIDL+20% LL Class 70R+Class A+Longitudinal


11DL+SIDL+20% LL 3 Class A+Longitudinal


12 DL+SIDL+Longitudinal Forces+Transverse SeismicCase (Without Live Load)

2932.81 22.08 214.76 224.84 1808.51

13DL+SIDL+20% LL Class 70R+Longitudinal

Forces+Transverse Seismic Forces3081.56 153.37 225.91 1295.17 2370.87

14DL+SIDL+20% LL Class 70R+Class A+Longitudinal


15DL+SIDL+20% LL 3 Class A+Longitudinal


S.No. Description of Load Combination P (kN) HL (kN) HT (kN)

SEISMIC

TRANSVERSE

ML (kNm) MT (kNm)

NORMAL

WIND

SEISMIC

LONGITUDINAL

25



10. DESIGN OF FREE-END PIER

Length of section along tranverse direction 2.79 m

Length of section along longitudinal direction 1.00 m

Effective Cover 60 mm

End Spacing 0.1 m

No. of bars along tranverse direction (on one side) 16 Nos.

Bar Diameter 16 mm

Area of steel along transverse direction 3216.990877 mm2

No. of bars along longitudinal direction (on one side) 6 Nos.

Bar Diameter 16 mm

Area of steel along longitudinal direction 1206.371579 mm2

IRC 21-2000 Table 9 Note 1

Modular Ratio 10

Grade of Concrete 35.00 Mpa

Permissible flexural compressive stress in concrete σcbc Normal 11.70 MPa

Wind 15.56 MPa

Seismic 17.55 MPa

Permissible flexural tensile stress in steel σst Normal 240.00 MPa

Wind 319.20 MPa

Seismic 360.00 MPa

Permissible compressive stress in steel σst Normal 205.00 MPaWind 272.65 MPa

Seismic 307.50 MPa

Area of Concrete 2.79 m2

Area of steel 8846.724913 mm

Percentage of Steel 0.317086914 %

Area of concrete to resist axial load only 335351.58 mm2

Minimum Area of steel 2682.81265 mm2

Area of steel required 8370 mm2

SAFE

26



11. MATERIAL STRESSES

Longitudinal Direction (Thickness) 1.00 m

Equivalent width of pier in transverse direction 2.79 m

Effective Cover 60 mm

Area of steel along transverse direction on one face 3216.99 mm2

Distance to C.G. transverse steel from NA 440.00 mm Area of steel along longitudinal direction on one face 1206.37 mm2

Distance to C.G. of longitudinal steel from NA 1335.00 mm

Total Area of Steel = 8846.72 mm2

Modular Ratio 10.00

Effective Area = 1.47E+06 mm2

Section Modulus in transverse direction, ZTT 4.90E+08 mm3

Section Modulus in the longitudinal direction, ZLL 1.35E+09 mm3

STEEL TENSION m(bd^3/12+MT/ZT-ML/ZL)

CONCRETE COMP (bd^3/12+MT/ZT+ML/ZL)

S.No. P (kN)

Mx (Trans.)

kNm

My (Long.)

kNm ex (m) ey (m)

σ concrete

(Mpa)

σ steel

tension (Mpa)

1 2932.81 79.97 0.00 0.03 0.00 2.15 21.32

2 3676.54 1084.46 2197.72 0.29 0.60 6.33 59.98

3 3923.61 1124.83 981.47 0.29 0.25 5.68 53.76

4 3897.14 1186.25 723.25 0.30 0.19 5.60 52.85

5 3538.10 1383.54 3394.05 0.39 0.96 7.74 72.89

6 3785.17 1423.91 2177.80 0.38 0.58 7.08 66.67

7 3758.71 1485.33 1919.58 0.40 0.51 7.00 65.76

8 2932.81 407.42 382.50 0.14 0.13 3.10 29.91

9 3081.56 1346.46 848.84 0.44 0.28 5.47 51.09

10 3130.97 1423.99 614.50 0.45 0.20 5.48 51.15

11 3125.68 1428.83 561.90 0.46 0.18 5.45 50.83

12 2932.81 178.20 1275.00 0.06 0.43 3.30 32.13

13 3081.56 1117.25 1803.88 0.36 0.59 5.71 53.74

14 3130.97 1194.78 1590.30 0.38 0.51 5.74 53.96

15 3125.68 1199.62 1535.48 0.38 0.49 5.70 53.62

TRANSVERSE

SEISMIC

LONGITUDINAL

SEISMIC

WIND

NORMAL

27



12. PIER CAP DESIGN

Effective depth, d = 1.4025 m

Width of pier cap 1.4 m

0.105 3.00

1.4025 1.70 1.5

Depth @ 'd' away

from face of pier 0.41.20

1.1

14.04

0.20 4.40

Results from STAAD after 10% reduction due to longitudinal effect for 3 lanes traffic for live load

Description

B1 B2

1 Dead Load 357.00 379.00

2 SIDL 174.00 31.003 Live Load

3.1 Class 70R 343.00 405.00

3.2 Class 70R + Class A 297.00 337.50

3.3 3 Class A 285.30 266.40

Impact Factor (As per IRC-6-2010 Cl. 208)

For Class A and combination 1.17 (Cl. 208.2)

For Class 70R 1.17 (Cl. 208.4 Fig 5)

Loads @ face of pier considering impact factor

S.No. DescriptionShear Force

(kN)

Bending

Moment

(kNm)

Torsion

(kNm)

1 Dead Load 736.00 1148.28 80.96

2 SIDL 205.00 543.53 22.55

3 Class 70R 875.16 1295.82 96.27

4 Class 70R + Class A 744.32 1123.36 81.87

5 3 Class A 647.19 1071.99 71.19

Loads @ distance 'd' from the face of pier considering impact factor

S.No. DescriptionShear Force

(kN)BendingMoment

(kNm)

Torsion(kNm)

1 Dead Load 357.00 607.79 39.27

2 SIDL 174.00 296.24 19.14

3 Class 70R 343 683.23 44.14

4 Class 70R + Class A 297 593.16 38.32

5 3 Class A 285.3 569.79 36.81

Reaction of Bearing (kN)S.No.

B2

B

28



Bending Moment and Shear Force due to self weight of cantilever portion of pier cap

1.50 m 1.20 m

157.06 kN 89.70 kN

172.77 kN 98.67 kN

1.85 m 1.33 m

319.92 kNm 131.66 kNm88.65 kN 61.65 kN

2.30 m 1.60 m

204.11 kNm 98.71

Load Combination

Torsion SF (kN) BM (kNm) Torsion SF (kN) BM (kNm)

1 DL+SIDL+Class 70R 199.78 5065.20 3187.40 102.55 1034.32 1817.63

2DL+SIDL+Class 70R+Class A 185.38 3638.54 3442.71 96.73 988.32 1727.56

3 DL+SIDL+3 Class A 174.70 3541.40 3391.34 95.22 976.62 1704.19

Maximum 199.78 5065.20 3442.71 102.55 1034.32 1817.63

Calculation of Equivalent Shear force and bending moment due to torsion

Load Combination

Torsion Eq. SF (kN)Eq. BM

(kNm)Torsion

Eq. SF

(kN)

Eq. BM

(kNm)

1 DL+SIDL+Class 70R 199.78 228.32 243.43 102.55 117.20 112.06

2 DL+SIDL+Class 70R +Cl 185.38 211.87 225.89 96.73 110.55 105.703 DL+SIDL+3 Class A 174.70 199.66 212.87 95.22 108.83 104.05

Eq. SF = 1.6T/b

Eq. BM = T(1+D/b)/1.7

at distance 'd' away from pier face

at pier face at distance 'd' away from pier face

at distance d awayat pier face

Depth of pier cap

Shear due to pier cap

Increase shear by 10% for bearing

C.G. of pier cap section from

Bending Moment due to self weightShear due to dirt wall

Lever arm of shear force due to

Bending Moment due to dirt wall

S.No.

S.No.at pier face

29



Total Shear Force and Bending Moments

S.No. Load Combination

SF (kN) BM (kNm) SF (kN) BM (kNm)

1 DL+SIDL+Class 70R 2305.89 3954.86 1151.53 1929.69

2 DL+SIDL+Class 70R +Cl 2158.60 3668.60 1098.88 1833.26

3 DL+SIDL+3 Class A 2049.26 3604.21 1085.45 1808.24

Maximum 2305.89 3954.86 1929.69 1929.69



Modular Ratio 10.00

Permissible flexural compressive stress in concrete σcbc Normal 11.70 MPa

Permissible flexural tensile stress in steel σst Normal 240.00 MPa

Permissible compressive stress in steel σst Normal 205.00 MPa

k 0.31

j 0.90

Q 1.64

Clear Cover 40.00 mmTotal Depth, D 1500.00 m

Width of pier cap, b 1400.00 m

Design Shear Force at column face 2305.89 kN

Maximum Bending Moment 3954.86 kNm

Effective Depth Required, dreq 1312.73 mm

Depth provided, d 1402.50 mm

Design for flexure

Ast req 13117.32 mm2

Diameter of bar 25.00 mm

No. of bars required 28.00

1st layer 14 Nos. of 25 mm dia bars2nd layer 14 Nos. of 25 mm dia bars

Provided Reinforcement 13744.47

Side face reinforcement (0.05%) 1050.00 mm2

Diameter of bars 12.00 mm

No. of bars required 10.00

Provide 10 Nos. of 12 mm dia bars along each side face

at distance 'd' awayat pier face

30



Design for shear

At the face of pier

Table 12A IRC 21-2000

For M35 concrete, τc max 2.30 Mpa

Effective depth 1402.50 mm

Design Shear Stress, τv 1.17 < 2.3

SAFE

% reinforcement 0.65

Table 12B IRC 21-2000

Shear stress in concrete, τc 0.35 MPa

Shear force for which reinforcement is required 1618.67 kN

Area of shear reinforcement required 788.19 mm2

Provide 4 legged 16 mm dia stirrups

Asv 804.25 mm2

Spacing Required 142.85 mm

4 legged 16

mm dia

stirrups @ 140 mm

Area of shear reinforcement provided 804.25 mm2

> 788.185 SAFE

Transverse Reinforcement

As per IRC 21-2000 Cl 304.7.2.4.3

Maximum Torsion 199.78 kNm

Average effective width, b1 1263.00 mm

Average effective depth, d1 813.00 mmTorsional transverse reinforcement required, Aswt 480.41 mm2

< 804.248 OK

Provide Fe415 grade

31



13.2 EARTHFILL

Distance between pier and RE wall 0.40 m

Height of soil retained by RE wall 7.95 m

Weight of soil retained by RE wall 2361.45 kN

Eccentricity of wt of soil on footing along longitudinal direction 1.40 m

Moment due to soil above GL 3306.03 kNm

Eccentricity of pier from centre of footing 0.85 m

S.No. Ptop (kN) Pbottom (kN) Ml (kNm) ML (Mx) kNm MT (Mx) kNm

1 2932.81 6587.33 79.97 893.11 0.00

2 3676.54 7331.06 1215.75 1396.71 2197.72

3 3923.61 7578.14 1268.47 1239.43 981.47

4 3897.14 7551.67 1328.56 1322.02 723.25

5 3538.10 7192.63 1548.43 1847.07 3528.46

6 3785.17 7439.70 1601.16 1689.78 2312.21

7 3758.71 7413.23 1661.25 1772.38 2053.99

8 2932.81 6587.33 562.88 1376.02 542.55

9 3081.56 6736.08 1633.21 2319.92 1018.94

10 3130.97 6785.49 1723.10 2367.80 787.93

11 3125.68 6780.20 1726.62 2375.82 734.98

12 2932.81 6587.33 224.84 1037.98 1808.51

13 3081.56 6736.08 1295.17 1981.88 2370.87

14 3130.97 6785.49 1385.06 2029.76 2168.42

15 3125.68 6780.20 1388.58 2037.78 2112.40

NORM

AL

WIND

LONGITUDINAL

SEISMIC

TRANSVERSE

SEISMIC

33



13.3 FOOTING CORNER STRESSES

P1 (kN/m2) P2 (kN/m

2) P3 (kN/m

2) P4 (kN/m

2)

1 185.55 185.55 249.97 249.97

2 271.24 112.72 213.46 371.98

3 241.21 170.42 259.82 330.61

4 228.05 175.88 271.24 323.40

5 298.41 43.91 177.14 431.63

6 268.39 101.62 223.49 390.26

7 255.22 107.07 234.91 383.06

8 187.71 148.57 247.82 286.95

9 175.76 102.27 269.60 343.09

10 167.34 110.51 281.29 338.12

11 164.97 111.95 283.31 336.32

12 245.55 115.11 189.98 320.42

13 236.71 65.71 208.65 379.65

14 229.31 72.91 219.31 375.71

15 226.83 74.47 221.45 373.81

Summary of Base Pressure at bottom of footing

SBC (kN/m2)

Max. Pressure

(kN/m2)

Min. Pressure

(kN/m2)

440.00 371.98 112.72 OK

550.00 431.63 43.91 OK

550.00 343.09 102.27 OK

550.00 379.65 65.71 OKTransverse Seismic

Wind

Normal

Load Case

NORM

AL

WIND

LONGITUD

INAL

SEISM

IC

TRANSVERSE

SEISMIC


Footing Corner Stresses

34



1.355

2.79 5.5

9.96

1.355

3.1 1.00 1.4

5.5

P

P2 P3

P4

P21

P12

P14 P41

P43

P34

P32P23

P

C

P

D

P

A

P

B

P

F

P

G

P

H

P

E

35



P12 (kN/m2) P21 (kN/m

2) P23 (kN/m

2) P32 (kN/m

2) P34 (kN/m

2) P43 (kN/m

2) P41 (kN/m

2P14 (kN/m

2)

1 185.55 185.55 221.86 233.57 249.97 249.97 233.57 221.86

2 232.18 151.77 169.50 187.82 252.51 332.92 346.33 328.02

3 223.77 187.86 220.81 237.06 277.26 313.17 307.85 291.60

4 215.20 188.73 229.63 246.96 284.09 310.55 299.13 281.79

5 235.71 106.61 119.00 143.23 239.83 368.93 397.72 373.50

6 227.30 142.70 170.31 192.47 264.58 349.18 359.24 337.08

7 218.72 143.57 179.13 202.37 271.41 346.56 350.52 327.27

8 178.06 158.21 204.51 222.56 257.46 277.31 261.69 243.64

9 157.66 120.38 196.58 227.01 287.70 324.98 300.50 270.07

10 153.34 124.51 206.77 237.82 295.29 324.12 294.65 263.60

11 151.91 125.01 208.54 239.69 296.37 323.26 292.71 261.55

12 213.41 147.25 157.31 170.92 222.11 288.28 301.36 287.75

13 194.58 107.84 146.28 172.27 250.78 337.53 343.27 317.28

14 190.78 111.45 155.43 182.05 257.84 337.18 338.45 311.83

15 189.29 112.01 157.31 184.04 258.98 336.27 336.39 309.67

Load CaseFooting Corner Stresses

NORMAL

WIND

LONGITUDINA

LSEISMIC

TRAN

SVERSE

SE

ISMIC

36



13.4 NET PRESSURE

Self weight of footing + soil 1293.08 kN

Area of base at footing 30.25 m2

Pressure at 4 corners of footing 42.75 kN/m2

Net pressure = Pressure due to load and moment - Pressure at 4 corners due to footing and soil

Load Case P A (kN/m2) PB (kN/m

2) PC (kN/m

2) PD (kN/m

2) PE (kN/m

2) PF (kN/m

2) PG (kN/m

2) PH (kN/m

2)

1 179.12 175.02 190.83 175.02 142.81 184.97 207.22 184.97

2 206.01 159.40 224.33 239.81 149.23 135.92 249.97 294.43

3 213.46 189.82 229.71 225.73 163.07 186.19 252.47 256.98

4 212.96 193.66 230.30 220.13 159.22 195.55 254.57 247.71

5 203.50 130.48 227.73 259.58 128.42 88.37 261.64 342.86

6 210.95 160.89 233.11 245.49 142.26 138.64 264.13 305.42

7 210.45 164.74 233.70 239.89 138.40 148.00 266.24 296.15

8 181.33 165.09 199.38 184.94 125.39 170.79 224.64 209.92

9 190.58 161.29 221.01 198.57 96.27 169.05 263.60 242.54

10 192.44 167.15 223.49 195.98 96.18 179.55 266.96 236.38

11 192.30 167.95 223.45 194.84 95.71 181.37 267.07 234.38

12 179.78 141.93 193.39 208.10 137.58 121.37 212.45 251.81

13 189.03 136.56 215.02 223.31 108.46 116.52 251.41 287.53

14 190.88 141.90 217.50 221.24 108.37 125.99 254.77 282.39

15 190.75 142.75 217.47 220.04 107.90 127.93 254.88 280.29

NORMAL

WIND

LONGITUDINA

LSE

ISMIC

TRANSVERSE

SEISMIC

37



13.5 DESIGN AT CRITICAL SECTIONS

Effective cover 75 mm

Diameter of reinforcement along traffic direction 16 mm

Diameter of reinforcement across traffic direction 16 mm

Effective depth along traffic direction 0.917 m

Effective depth across traffic direction 0.901 m

0.45

1.36

0.901 0.901

2.79

0.901 0.901

0.45 1.355

2.2 0.917 1.00 0.917 0.5

3.1 1.4

4

P

P2 P3

P4

2

4

3

P

C

P

D

P

A

P

B

P

F

P

G

P

H

P

E

2

3

d

d

b

a

b

c

c

Traffic Direction

38



Moment at 1-1 due to earth retained by RE wall -751.37 kNm

1 38.62 k 0.28

2 311.52 j 0.91

3 620.94 Q 1.49

4 548.68

5 77.37 k 0.23

6 232.06 j 0.92

7 159.80 Q 1.63

8 325.92 k 0.21

9 757.53 j 0.93

10 742.85 Q 1.68

11 752.25

12 124.81 k 0.21

13 556.42 j 0.93

14 541.74 Q 1.68

15 551.13

mm2

NORMAL

WIND

LONGITUDINAL

SEISMIC

TRANSVERSE

SEISMIC

259.76 1792.50

Maximum Ast 3111.87

301.57 2416.05

97.32 285.87

168.56 857.47

259.18 2749.73

Moment

about 1-1

(kNm)

Depth Required

(mm)Ast Required (mm2)Load Case

257.54 1761.94

303.47 2446.60

123.61 405.93

261.00 1809.70

199.76 1060.03

304.54 2463.80

68.76 193.53

139.87 590.47

195.29 1561.17

275.72 3111.87

39



1 1087.48 k 0.28

2 1301.28 j 0.91

3 1319.92 Q 1.49

4 1328.53

5 1349.30 k 0.23

6 1367.94 j 0.92

7 1376.55 Q 1.63

8 1165.42 k 0.21

9 1344.27 j 0.93

10 1360.80 Q 1.68

11 1361.15

12 1110.86 k 0.21

13 1289.71 j 0.93

14 1306.24 Q 1.68

15 1306.59

mm2Maximum Ast 6657.99

368.79 3612.98

TRANSVER

SE

SEISMIC397.36 4194.65

399.90 4248.42

399.96 4249.56

377.73 3790.42

LONGITUDINAL

SEISMIC

405.68 4372.09

408.17 4425.86

408.22 4427.00

406.44 4985.72

WIND

409.24 5054.59

410.52 5086.42

NORMAL

399.14 6521.42

401.99 6614.82

403.30 6657.99

Load Case

Moment

about 2-2

(kNm)

Depth Required

(mm)Ast Required (mm2)

364.88 5449.96

40



1 917.18 k 0.28

2 1394.66 j 0.91

3 1244.91 Q 1.49

4 1204.30

5 1590.96 k 0.23

6 1441.21 j 0.92

7 1400.60 Q 1.63

8 1017.87 k 0.21

9 1150.61 j 0.93

10 1125.50 Q 1.68

11 1116.85

12 1197.83 k 0.21

13 1343.66 j 0.93

14 1322.89 Q 1.68

15 1313.79

mm2Maximum Ast 4520.67

382.95 3292.17

TRANSVER

SE

SEISMIC405.59 3692.96

402.44 3635.89

401.06 3610.86

353.01 2797.54

LONGITUDINAL

SEISMIC

375.32 3162.37

371.21 3093.35

369.78 3069.60

441.34 4520.67

WIND

420.06 4095.16

414.09 3979.75

335.10 2856.06

NORMAL

413.22 4342.91

390.40 3876.60

383.98 3750.13

Load Case

Moment

about 3-3

(kNm)

Depth Required


41



1 917.18 k 0.28

2 725.77 j 0.91

3 946.19 Q 1.49

4 984.17

5 517.05 k 0.23

6 737.47 j 0.92

7 775.45 Q 1.63

8 852.74 k 0.21

9 840.48 j 0.93

10 885.68 Q 1.68

11 893.16

12 647.40 k 0.21

13 622.06 j 0.93

14 662.92 Q 1.68

15 670.86

mm2

Minimum Area of reinforcement = 0.12% of cross-sectional area (As per IRC 78-2000 Cl. 707.2.7)

Minimum reinforcement 6600 mm2

Reinforcement required along traffic direction 6657.99 mm2 SAFE

Diameter of bar 16

Provide 16 mm diameter bars @ 160 mm c/c

Reinforcement provided 6911.50 mm2 SAFE

Reinforcement required across traffic direction 5019.78 mm2 PROVIDE MINIMUM REINFORCEMENT

Diameter of bar 16 mm

Provide 16 mm diameter bars @ 160 mm c/c

Reinforcement provided 6911.50 mm2 SAFE

Maximum Ast 5019.78

264.49 3214.49

TRANSVERSE

SEISMIC

259.27 3088.69

267.64 3291.54

269.24 3330.97

303.55 4234.03

LONGITUDINA

LSEISMIC

301.37 4173.19

309.36 4397.62

310.67 4434.74

240.34 2586.10

WIND

287.03 3688.60

294.33 3878.55

335.10 4678.11

NORMAL

298.09 3701.80

340.36 4826.08

347.12 5019.78

Load Case

Moment

about 4-4

(kNm)

Depth Required


42



13.6 FOOTING SHEAR

Weight of soil retained by RE wall beyond section a-a per meter 347.14 kN/m

Reduction in shear along section a-a due to flaring depth Moment(a-a) x tanβ / da-a

tanβ = 0.10

Effective depth at section a-a 0.83 m

Moment about a-a due to soil 433.71 kNm

Area resisting shear at a distance 'd' away from the face of the pier

along traffic direction (section c-c & d-d) 5.05 m2

across traffic direction (section a-a & b-b) 4.56 m2

Permissible Shear Stress is obtained from Table 12B of IRC 21-2000

Load

Case

Stress atsection a-

a, kN/m2

BM about

a-a, kNm

SF along

a-a, kN

Stress atsection b-

b, kN/m2

SFalong b-

b, kN

ShearStress

(τv), Mpa

Permissi

ble

Shear

Stress

(τc) Mpa

1 168.38 -73.12 5.84 SAFE 202.37 544.05 0.12 SAFE 0.20

2 189.22 -46.37 152.33 SAFE 242.39 653.98 0.14 SAFE 0.20

3 198.55 -16.96 272.57 SAFE 245.74 661.74 0.15 SAFE 0.20

4 197.07 -24.27 245.19 SAFE 247.39 666.73 0.15 SAFE 0.20

5 181.29 -85.73 5.07 SAFE 251.61 681.72 0.15 SAFE 0.27

6 190.63 -56.33 125.31 SAFE 254.96 689.48 0.15 SAFE 0.27

7 189.14 -63.63 97.94 SAFE 256.61 694.47 0.15 SAFE 0.27

8 164.79 -103.64 -100.66 SAFE 217.17 586.83 0.13 SAFE 0.30

9 162.68 -151.57 -257.30 SAFE 251.00 683.51 0.15 SAFE 0.30

10 163.96 -150.70 -250.75 SAFE 254.10 692.09 0.15 SAFE 0.30

11 163.73 -151.63 -254.35

SAFE

254.17 692.34 0.15

SAFE

0.30

12 167.30 -82.28 -26.11 SAFE 206.81 556.88 0.12 SAFE 0.30

13 165.20 -130.21 -182.75 SAFE 240.64 653.57 0.14 SAFE 0.30

14 166.48 -129.34 -176.20 SAFE 243.74 662.15 0.15 SAFE 0.30

15 166.24 -130.27 -179.80 SAFE 243.81 662.39 0.15 SAFE 0.30

NORMAL

WIND

LONGITUDINAL

SEISMIC

TRANSVERSE

SEISMIC

43



Load

Case

Stress at

section c-

c, kN/m2

SF along

c-c, kN

Shear

Stress

(τv) Mpa

Stress at

section d-

d, kN/m2

SF

along d-

d, kN

Shear

Stress

(τv), Mpa

Permissi

ble

Shear

Stress

(τc),Mpa

1 181.64 485.49 0.10 SAFE 181.64 457.71 0.09 SAFE 0.20

2 276.13 656.84 0.13 SAFE 143.78 349.20 0.07 SAFE 0.20

3 246.51 622.97 0.12 SAFE 187.41 466.44 0.09 SAFE 0.20

4 238.47 615.56 0.12 SAFE 194.92 487.50 0.10 SAFE 0.20

5 314.96 719.88 0.14 SAFE 102.48 238.27 0.05 SAFE 0.27

6 285.34 686.01 0.14 SAFE 146.10 355.50 0.07 SAFE 0.27

7 277.30 678.61 0.13 SAFE 153.61 376.56 0.07 SAFE 0.27

8 201.55 532.10 0.11 SAFE 168.88 424.08 0.08 SAFE 0.30

9 227.81 613.52 0.12 SAFE 166.45 418.87 0.08 SAFE 0.30

10 222.84 611.51 0.12 SAFE 175.39 443.14 0.09 SAFE 0.30

11 221.13 609.52 0.12 SAFE 176.87 447.27 0.09 SAFE 0.30

12 237.16 561.34 0.11 SAFE 128.26 311.66 0.06 SAFE 0.30

13 266.01 645.99 0.13 SAFE 123.24 299.34 0.06 SAFE 0.30

14 261.90 645.06 0.13 SAFE 131.32 321.26 0.06 SAFE 0.30

15 260.10 642.95 0.13SAFE

132.89 325.63 0.06SAFE

0.30

Area of footing at base 30.25 m2

Area available at d/2 away from face of pier 7.11 m2

Area effective in carrying punching shear 23.14 m2

Average depth at d/2 away from pier 0.86 m

Area resisting punching shear, Aps 8.07 m2

Punching shear, Vp = Net Load, P - (P1+P2+P3+P4)/4 x Area effective in carrying punching shear

Punching Shear Stress, τcp = Vp/Aps

Grade of concrete 35.00 Mpa

Allowable Punching Shear - 0.16 x (f ck)0.5

NORMA

L

TRANSVERSE

SEISMIC

LONGITUDIN

AL

SEISMIC

WIND

44



Load

Case

Punching

Shear, kN τcp , MPa

Allowable

Shear

Stress,

Mpa

1 1547.49 0.19 0.95 SAFE

2 1722.21 0.21 0.95 SAFE

3 1780.25 0.22 0.95 SAFE

4 1774.03 0.22 0.95 SAFE

5 1689.69 0.21 1.26 SAFE

6 1747.73 0.22 1.26 SAFE

7 1741.51 0.22 1.26 SAFE

8 1547.49 0.19 1.42 SAFE

9 1582.44 0.20 1.42 SAFE

10 1594.05 0.20 1.42 SAFE

11 1592.80 0.20 1.42 SAFE

12 1547.49 0.19 1.42 SAFE

13 1582.44 0.20 1.42 SAFE

14 1594.05 0.20 1.42 SAFE

15 1592.80 0.20 1.42 SAFE

Reinforcement at top of footing

As per IRC 78-2000 Cl. 707.2.8)

Minimum area of reinforcement = 250 mm2/m in each direction

Along traffic direction = 1375 mm2

Across traffic direction = 1375 mm2

Spacing Calculation & Actual provided area of reinforcement

TRANSVERSE

SEISMIC

LONGITUDINAL

SEISM

IC

WIND

NORMAL

45



ANNEXURE 2 : SAMPLE DESIGN OF SUPER-STRUCTURE

CONTENTS

DETAILS OF THE STRUCTURE 1

1. SECTION PROPERTIES 2

1.1 NEAR SUPPORT………………………………………………………………………….. ....2

1.2 MID-SPAN…………………………………………………………………………………. ...3

1.3 INTERMEDIATE SECTION……………………………………………………………….. ..4

1.4 DIAPHRAGM……………………………………………………………………………… ...4

2. LOAD CALCULATION 5

2.1 DEAD LOAD………………………………………………………………………… .……...5

2.2 SIDL……………………………………………………………………………………..…… .5

2.3 LIVE LOADS……………………………………………………………………………… ....5

2.4 ANALYSIS RESULTS……………………………………………………………………….6

2.5 LOAD COMBINATIONS……………………………………………………………… .……7

3. GIRDER DESIGN 8

3.1 CONSTRUCTION STAGE………………………………………………………………… ...8

3.2 SERVICE STAGE…………………………………………………………………………...10

4. SHEAR DESIGN 16

5. SHEAR CONNECTOR DESIGN 17

6. DIFFERENTIAL SHRINKAGE STRESSES 18

7. DIAPHRAGM DESIGN 19

STAAD Input file for Girder Design………………………………………………………..…21

STAAD Input file for Diaphragm Design…………………………………………………..…26



DETAILS OF SUPERSTRUCTURE



Density of concrete 25.00 kN/m3

Overall span of RCC Girder 18.00 m

Effective Span 17.50 m

Spacing between bearings 3.00 m


Depth of RCC Girder 1.50 m

% camber 2.50 %

Total width of deck slab 12.00 m

FRL at pier location 621.59 m

Existing ground level 613.64 m

Pier cap top level 621.34 m

Height of pier from GL to pier cap top 7.70 m

1



1.2 MID-SPAN

750

150

75

225

1500

150

150

250

300

600

S.No. C.G. (mm) A x CG (mm3) Iself (mm

4) Ibase (mm

4) Iyy (mm

4)

1 750 3.38E+08 8.44E+10 3.38E+11 3.38E+09

2 1425 9.62E+07 1.27E+08 1.37E+11 4.94E+09

3 1325 2.24E+07 5.27E+06 2.96E+10 9.02E+08

4 125 9.38E+06 3.91E+08 1.56E+09 3.94E+09

5 300 6.75E+06 2.81E+07 2.05E+09 9.28E+08

Total 4.72E+08 5.08E+11 1.41E+10

Area 0.63 m2

C.G. from bottom 747.26 mm

Distance of N.A. from top 752.74 mm

Distance of N.A. from bottom 747.26 mm

Moment of inertia 0.16 m4

Ztop 0.21 m

Zbottom 0.21 m

Composite Section at mid-span

Thickness of deck slab 230.00 mm

Actual Width of deck slab 3000.00 mm

Effective width of deck slab 3000.00 mm

Grade of concrete in deck slab 40.00 Mpa

Grade of concrete in girder 40.00 Mpa

S.No. C.G. (mm) A x CG (mm3) Iself (mm

4) Ibase (mm

4) Iyy (mm

4)

Girder 747.26 4.72E+08 1.55E+11 5.08E+11 1.41E+10

Slab 1615 1.11E+09 3.04E+09 1.80E+12 5.18E+11

Total 1.59E+09 2.31E+12 5.32E+11

Total Area 1.32 m2

Total depth of section 1.73 m

C.G. of composite section from bottom 1.20 m

Distance of N.A. from top of slab 0.53 m

Distance of N.A. from bottom 1.20 m

Distance of N.A. from top of girder 0.30 m

Moment of Inertia 0.41 m4

Ztop slab 0.77 m

Ztop girder 1.36 m

Zbottom 0.34 m

Moment of inertia about y-y axis 0.53 m4

1321875

690000

631875

Area (mm2)

631875

22500

75000

16875

67500

450000

Area (mm2)

1

2

2

3

4

4

5

3



2. LOAD CALCULATION

Thickness of deck slab 0.23 m

Distance between bearings 3.00 m


Cross-sectional area of crash barrier 0.30 m2

2.1 DEAD LOADDead load of girder at the support 23.11 kN/m

Dead load of girder at midspan 15.80 kN/m

Dead load due to deck slab 17.25 kN/m

2.2 SIDL

SIDL due to wearing coat on girder 6.60 kN/m

SIDL due to crash barrier 7.50 kN/m

2.3 LIVE LOADS

Class 70R - Maximum Eccentricity

Class 70R

4.01

Class 70R - on 2nd girder

Class 70R

5.465

Class 70R + Class A

10

Class 70R Class A

4.01

3 Class A

6.15

Class A Class A Class A

2.65

9.65

5



2.5 LOAD COMBINATIONS

Load Combinations for Outer Girder

daway

(1.5m

from

support)

0.25 leff

(4.25m

from

support)

At

midspan

0.25 leff (4.25m

from support)

Combo 1 333.51 195.20 1655.54 1370.16

Combo 2 193.06 118.65 1026.76 785.25

Combo 3 307.60 178.43 1525.14 1262.03

Combo 4 297.70 181.56 1628.35 1145.49

Combo 5 396.14 247.72 2104.19 1531.37

Combo 6 214.71 142.93 1192.94 871.63

Combo 7 343.15 248.85 1914.57 1386.79

Combo 8 286.28 170.39 1671.87 1164.73

396.14 248.85 2104.19 1531.37

Load Combinations for Inner Girder

daway

(1.5m

from

support)

0.25 leff

(4.25m

from

support)

At

midspan

0.25 leff (4.25m

from support)

Combo 1 262.47 134.21 1207.64 1087.48

Combo 2 320.62 165.92 1464.26 1334.69

Combo 3 247.82 131.56 1146.43 1037.27

Combo 4 198.24 130.16 1173.14 792.46

Combo 5 270.10 217.49 1594.06 1116.56

Combo 6 335.31 274.25 1921.85 1372.59

Combo 7 253.75 203.40 1479.70 1054.45

Combo 8 187.54 118.92 1216.45 815.73

335.31 274.25 1921.85 1372.59

Outer girder resists approximately 10% more moment than inner girder so design is done for outer girder

and same design is adopted for inner girder as all girders are precast.

S.No. Load Case

Shear Force Bending Moment (kNm)

S.No. Load Case

Shear Force

2 + 4.3

2 + 4.4

Maximum

Bending Moment (kNm)

2 + 3.1

2 + 3.2

2 + 3.3

2 + 3.1

2 + 3.2

2 + 3.3

2 + 3.4

2 + 4.1

2 + 4.2

2 + 3.4

Maximum

2 + 4.1

2 + 4.2

2 + 4.3

2 + 4.4

7



3. GIRDER DESIGN

3.1 CONSTRUCTION STAGE

Design of girder for construction stage (Dead Load alone)

Width of the web, bw 300.00 mm

Width of the flange, bf 750.00 mm

Depth of the flange, Df 150.00 mm

Overall depth of the section, D 1500.00 mm

Clear Cover 40.00 mm


Moment to be resisted by the section, Me 1270.36 kNm

Diameter of main bar 32.00 mm at

No. of bars 5.00 Nos.

68.00 mm from bottom of girder







Effective cover provided 132.00 mm

Area of steel provided 12063.72 mm2

Grade of concrete adopted 40.00 MPa

Permissible compressive stress in bending 13.33 MPa

Permissible tensile stress in reinforcement 240.00 MPa

Modular Ratio, m 10.00

Factor for critical neutral axis 0.36

D

kd

b

f

d

Neutral Axis

c

c

st

/m

b

w

8



Check for neutral axis

If neutral axis lies within the range, for kd<Df

(bf x kd) x (kd/2) = m x Ast x (d - kd)

Solving

Neutral Axis depth, kd 521.76 mm

Neutral Axis depth factor, k 0.38

As neutral axis depth (kd) < Depth of flange, neutral axis lies in the web

For kd >Df

((bf - bw) x Df) x (kd - Df/2) + (bw x kd) x kd/2 = m x Ast x (d - kd)

6.75E+04 x kd - 5.06E+06 + 150.00 kd^2 = 1.65E+08 - 1.21E+05 kd

150.00 kd^2 + 1.88E+05 kd - 1.70E+08 = 0.00

Revised Neutral axis depth, kd 608.69 mm


Stresses for given moment

Bending Moment , M = (bf x (0.5 x σc x kd) x (d - kd/3)) - ((bf - bw) x (0.5 x σc' x (kd - Df) x (d - Df - (kd - Df)/3))

1.27E+09 = 2.66E+08 σc - 8.28E+07

1.27E+09 = 1.83E+08 σc

where σc' = (σc x (kd - Df)/kd)

Actual stress in concrete, σc 6.94 Mpa

Actual stress in bottom most steel layer, 93.84 Mpa

σst = (D-d1'-kd) x σc x m/kd

6.94

MPa

93.84

MPa

Top of Girder

9



Curtailment Design of girder for construction stage (DL alone)





Clear Cover 40.00 mmEffective depth 1400.00 mm












Area of steel provided 8042.48 mm2Grade of concrete adopted 40.00 MPa





D

kd

b

f

d

Neutral Axis

c

c

st

/m

b

w

10






Solving




For kd >Df


6.75E+04 x kd - 5.06E+06 + 150.00 kd^2 = 1.13E+08 - 8.04E+04 kd

150.00 kd^2 + 1.48E+05 kd - 1.18E+08 = 0.00


Neutral Axis depth factor, k 0.37Stresses for given moment


9.67E+08 = 2.39E+08 σc - 6.69E+07

9.67E+08 = 1.73E+08 σc



Actual stress in bottom most steel layer 98.08 Mpa

σst = (D-d1'-kd) x σc x m/kd5.6 MPa

98.08

MPa

Top of Girder

11



3.2 SERVICE STAGE

Design of Composite girder for Service stage



Depth of the flange, Df 230.00 mmOverall depth of the section, D 1730.00 mm












196.00 mm from bottom of girder Effective cover provided 132.00 mm







D

kd

b

f

d

Neutral Axis

c

c

st

/m

b

w

12






Solving




For kd >Df


6.21E+05 x kd - 7.14E+07 + 150.00 kd^2 = 1.93E+08 - 1.21E+05 kd

150.00 kd^2 + 7.42E+05 kd - 2.64E+08 = 0.00




2.10E+09 = 7.44E+08 σc - 5.80E+07

2.10E+09 = 6.86E+08 σc





Final Stresses

Actual stess in concrete at top of girder flange, σc 7.89 Mpa

Actual Stress in bottom most steel layer, σst 215.90 MPa

Actual stress within permissible limit

3.07 MPa

122.06

MPa

Top of Girder

13



Curtailment Design of Composite girder for Service stage
























D

kd

b

f

d

Neutral Axis

c

c

st

/m

b

w

14






Solving




For kd >Df


6.21E+05 x kd - 7.14E+07 + 150.00 kd^2 = 1.31E+08 - 8.04E+04 kd

150.00 kd^2 + 7.01E+05 kd - 2.03E+08 = 0.00




1.53E+09 = 6.30E+08 σc - 1.26E+07

1.53E+09 = 6.17E+08 σc





Modular Ratio 10.00

Final Stresses (Curtailment design)

Actual stess in concrete at top of girder flange, σc 5.99 Mpa

Actual Stress in bottom most steel layer, σst 224.43 MPa

Actual stress within permissible limit

Adding stress due to differential shrinkage

Final stress in steel 226.79 Mpa

2.48 MPa

126.35MPa

Top of Girder

15



4. SHEAR DESIGNDesign for shear at distance 'd' away from the support of girder

Shear at 'd' distance away from support 648.39 kN

Nominal shear stress, τv 1.35 MPa

Permissible Shear Stress, τc,max 2.50 MPa

Refer IRC 21-200 Table 12A , corresponding to M40 concrete

Percentage Reinforcement at the section 2.52 %

Design shear strength in concrete 0.60 MPa

Shear in concrete, Vuc 287.64 kN

Provide 2 legged 12 mm dia stirrups @ 125 mm spacing

Asv 226.19 mm2

Sv 125.00 mm

σsv 200.00 MPa

Shear resistance of vertical stirrups 578.33 kN

Total Shear resistance at the section 865.97 kN

Minimum shear reinforcement, Asv,min 41.55 mm2

Design for shear at distance 0.25leff (4.25m) from the support of girder

Shear at 4.25m distance away from support 274.25 kN

Nominal shear stress, τv 0.56 MPa

Permissible Shear Stress, τc,max 2.50 MPa

Refer IRC 21-200 Table 12A , corresponding to M40 concrete

Percentage Reinforcement at the section 1.64 %

Design shear strength in concrete 0.51 MPa

Shear in concrete, Vuc 249.39 kN

Provide 2 legged 12 mm dia stirrups @ 250 mm spacing

Asv 226.19 mm2

Sv 250.00 mm

σsv 200.00 MPa

Shear resistance of vertical stirrups 294.96 kN

Total Shear resistance at the section 544.35 kN

Minimum shear reinforcement, Asv,min 83.09 mm2

Section is adequate

Section is adequate

SAFE

SAFE

SAFE

SAFE

16



5. SHEAR CONNECTOR DESIGN

Inertia of composite section 0.41 m4

Maximum shear due to SIDL ('d' away) 119.70 kN

Maximum shear due to live load ('d' away) 310.11 kN

Total shear (1.3DL + 1.5LL) 620.78 kN

3000

1500

1274

300

Transformed compressive area of concrete flange, Ac 0.69 m2

CG of composite section 1273.55 mm

Y,( Distance between CG of compressive area and that of composite section) 0.32 m

Design Shear = VAY / I 338.23 kN/m

Provide 2 legged 12 mm dia shear connectors @ 150 mm spacing

Area of connector, As 226.19 mm2

Permissible Shear Stress for fy 500 435.00 Mpa

Shear Capacity of connector, C 98.39 kN

Spacing Required 290.91 mm

Provided 150.00 mm

SAFE

230

321

C.G. of composite section

C.G. of compressive area

17



6. DIFFERENTIAL SHRINKAGE STRESSES

Sectional properties at mid span of composite section of girder and slab


Total Area 1.32 m2

Total Depth of section 1.73 m

CG 1.20 mDistance of NA from top of slab 0.53 m

Distance of NA from bottom 1.20 m

Moment of inertia 0.41 m4

Ztop 0.77 m3

Zbottom 0.34 m3

As per BS 5400-4 1990 Cl 7.4.3.5

Mcs = ediff x Ecf x Acf x acent

ediff - Differential Shrinkage Strain 1.00E-04

Ecf - Modulus of elasticity of the concrete flange 31622.78 Mpa

Acf - Area of the effective concrete flange 0.69 m

2

acent - Distance of the centroid of the concrete flange from the

centroid of the concrete section 0.34 m

Φ - Reduction coefficient to allow for creep 0.43

Mcs 320.36 kNm

Fcs 938.25 kN

Stress in compression flange -1.36 Mpa

Stress due to direct compression 0.71 Mpa

Stress at top due to flexural bending 0.42 Mpa

Stress at bottom due to flexural bending -0.95 Mpa

Tension negative

Total stress at top due to differential shrinkage -0.23 Mpa

Total stress at bottom due to differential shrinkage -0.24 Mpa

+ + =

(-)

(+)

(-)

-1.36 MPa

(+)

0.71 MPa

0.42 MPa

-0.95 MPa -0.24 MPa

-0.23 MPa

(-)

18



7. DIAPHRAGM DESIGN

Design of Longitudinal Reinforcement for Diaphargm

Overall depth of diaphragm 1480.00 mm

Width of the diaphragm 400.00 mm

Gross Area, Ag 592000.00 mm2

Moment obtained from STAAD modelDesign sagging moment 294.70 kNm

Design Hogging Moment 568.15 kNm



IRC 21-2000 Table 9 &10

σst 240.00 Mpa

σsv 200.00 Mpa

σcbc 13.33 MPa

m 10.00

k 0.28

j 0.91

Q 1.69

Width of the section, b 400.00 mm

Effective depth required 916.23 mm

Clear cover 50.00 mm

Effective depth provided 1380.50 mm

Design of top reinforcement

Ast,reqd 1891.33 mm2

Minimum steel to be provided 1184.00 mm2

Area of steel to be provided 1891.33 mm2

Diameter of the bar provided 25.00 mm

Cross-sectional area of the bar 490.87 mm2

No. of bars required 4

Ast provided 1963.50 mm2

SAFE

1.5m

1.5mmm

mmm

Girder+Deck Slab+Wearing Coat

Diaphragm

Crash

Barrier

19



Design of bottom reinforcement

Ast,reqd 981.03 mm2

Minimum steel to be provided 1184.00 mm2

Area of steel to be provided 1184.00 mm2

Diameter of the bar provided 16.00 mm


No. of bars required 6 Ast provided 1206.37 mm2

SAFE

Design of shear reinforcement for Diaphragm

Maximum shear force at support 910.05 kN

Nominal Shear Stress 1.65 Mpa

As per IRC 21-2000 permissible shear stress from table 12B

Maximum shear stress 2.50 MPa

OK

% of reinforcement 0.36 %

Permissible shear stress 0.28 MPaShear to be carried by reinforcement 755.43 kN

Spacing of stirrups 180.00 mm

Shear stirrups required 410.41 mm2

Provide 12 mm, 4 LVS @ 180.00 mm spacing

Area of provided stirrups 452.39 mm2

SAFE

Design of Side reinforcement

Provide side face reinforcement 592.00 mm2

Diameter of bar to be provided 10.00 mm


No. of bars required in one direction 4.00

Spacing of bars along web 265.34 mm

Provide 4.00 bars of 10.00 mm at 250 mm spacing on each face of diaphragm

20



21

STAAD input file for Girder Design

STAAD SPACE

START JOB INFORMATION

ENGINEER DATE 20-Jun-14

END JOB INFORMATION

INPUT WIDTH 79

UNIT METER KN

JOINT COORDINATES

1 0 0 0; 2 0 0 1.5; 3 0 0 4.5; 4 0 0 7.5; 5 0 0 10.5; 6 0 0 12; 7 0.5 0 0;

8 0.5 0 1.5; 9 0.5 0 4.5; 10 0.5 0 7.5; 11 0.5 0 10.5; 12 0.5 0 12; 13 1.5 0 0;

14 1.5 0 1.5; 15 1.5 0 4.5; 16 1.5 0 7.5; 17 1.5 0 10.5; 18 1.5 0 12;

19 2.5 0 0; 20 2.5 0 1.5; 21 2.5 0 4.5; 22 2.5 0 7.5; 23 2.5 0 10.5;

24 2.5 0 12; 25 3.5 0 0; 26 3.5 0 1.5; 27 3.5 0 4.5; 28 3.5 0 7.5;

29 3.5 0 10.5; 30 3.5 0 12; 31 4.5 0 0; 32 4.5 0 1.5; 33 4.5 0 4.5;

34 4.5 0 7.5; 35 4.5 0 10.5; 36 4.5 0 12; 37 5.5 0 0; 38 5.5 0 1.5;

39 5.5 0 4.5; 40 5.5 0 7.5; 41 5.5 0 10.5; 42 5.5 0 12; 43 6.5 0 0;

44 6.5 0 1.5; 45 6.5 0 4.5; 46 6.5 0 7.5; 47 6.5 0 10.5; 48 6.5 0 12;

49 7.5 0 0; 50 7.5 0 1.5; 51 7.5 0 4.5; 52 7.5 0 7.5; 53 7.5 0 10.5;

54 7.5 0 12; 55 8.5 0 0; 56 8.5 0 1.5; 57 8.5 0 4.5; 58 8.5 0 7.5;

59 8.5 0 10.5; 60 8.5 0 12; 61 9.5 0 0; 62 9.5 0 1.5; 63 9.5 0 4.5;

64 9.5 0 7.5; 65 9.5 0 10.5; 66 9.5 0 12; 67 10.5 0 0; 68 10.5 0 1.5;

69 10.5 0 4.5; 70 10.5 0 7.5; 71 10.5 0 10.5; 72 10.5 0 12; 73 11.5 0 0;

74 11.5 0 1.5; 75 11.5 0 4.5; 76 11.5 0 7.5; 77 11.5 0 10.5; 78 11.5 0 12;

79 12.5 0 0; 80 12.5 0 1.5; 81 12.5 0 4.5; 82 12.5 0 7.5; 83 12.5 0 10.5;

84 12.5 0 12; 85 13.5 0 0; 86 13.5 0 1.5; 87 13.5 0 4.5; 88 13.5 0 7.5;

89 13.5 0 10.5; 90 13.5 0 12; 91 14.5 0 0; 92 14.5 0 1.5; 93 14.5 0 4.5;

94 14.5 0 7.5; 95 14.5 0 10.5; 96 14.5 0 12; 97 15.5 0 0; 98 15.5 0 1.5;



22

99 15.5 0 4.5; 100 15.5 0 7.5; 101 15.5 0 10.5; 102 15.5 0 12; 103 16.5 0 0;

104 16.5 0 1.5; 105 16.5 0 4.5; 106 16.5 0 7.5; 107 16.5 0 10.5; 108 16.5 0 12;

109 17.5 0 0; 110 17.5 0 1.5; 111 17.5 0 4.5; 112 17.5 0 7.5; 113 17.5 0 10.5;

114 17.5 0 12; 115 18 0 0; 116 18 0 1.5; 117 18 0 4.5; 118 18 0 7.5;

119 18 0 10.5; 120 18 0 12;

MEMBER INCIDENCES

1 1 2; 2 2 3; 3 3 4; 4 4 5; 5 5 6; 6 1 7; 7 2 8; 8 3 9; 9 4 10; 10 5 11;

11 6 12; 12 7 8; 13 8 9; 14 9 10; 15 10 11; 16 11 12; 17 7 13; 18 8 14;

19 9 15; 20 10 16; 21 11 17; 22 12 18; 23 13 14; 24 14 15; 25 15 16; 26 16 17;

27 17 18; 28 13 19; 29 14 20; 30 15 21; 31 16 22; 32 17 23; 33 18 24; 34 19 20;

35 20 21; 36 21 22; 37 22 23; 38 23 24; 39 19 25; 40 20 26; 41 21 27; 42 22 28;

43 23 29; 44 24 30; 45 25 26; 46 26 27; 47 27 28; 48 28 29; 49 29 30; 50 25 31;

51 26 32; 52 27 33; 53 28 34; 54 29 35; 55 30 36; 56 31 32; 57 32 33; 58 33 34;

59 34 35; 60 35 36; 61 31 37; 62 32 38; 63 33 39; 64 34 40; 65 35 41; 66 36 42;

67 37 38; 68 38 39; 69 39 40; 70 40 41; 71 41 42; 72 37 43; 73 38 44; 74 39 45;

75 40 46; 76 41 47; 77 42 48; 78 43 44; 79 44 45; 80 45 46; 81 46 47; 82 47 48;

83 43 49; 84 44 50; 85 45 51; 86 46 52; 87 47 53; 88 48 54; 89 49 50; 90 50 51;

91 51 52; 92 52 53; 93 53 54; 94 49 55; 95 50 56; 96 51 57; 97 52 58; 98 53 59;

99 54 60; 100 55 56; 101 56 57; 102 57 58; 103 58 59; 104 59 60; 105 55 61;

106 56 62; 107 57 63; 108 58 64; 109 59 65; 110 60 66; 111 61 62; 112 62 63;

113 63 64; 114 64 65; 115 65 66; 116 61 67; 117 62 68; 118 63 69; 119 64 70;

120 65 71; 121 66 72; 122 67 68; 123 68 69; 124 69 70; 125 70 71; 126 71 72;

127 67 73; 128 68 74; 129 69 75; 130 70 76; 131 71 77; 132 72 78; 133 73 74;

134 74 75; 135 75 76; 136 76 77; 137 77 78; 138 73 79; 139 74 80; 140 75 81;

141 76 82; 142 77 83; 143 78 84; 144 79 80; 145 80 81; 146 81 82; 147 82 83;

148 83 84; 149 79 85; 150 80 86; 151 81 87; 152 82 88; 153 83 89; 154 84 90;

155 85 86; 156 86 87; 157 87 88; 158 88 89; 159 89 90; 160 85 91; 161 86 92;

162 87 93; 163 88 94; 164 89 95; 165 90 96; 166 91 92; 167 92 93; 168 93 94;



23

169 94 95; 170 95 96; 171 91 97; 172 92 98; 173 93 99; 174 94 100; 175 95 101;

176 96 102; 177 97 98; 178 98 99; 179 99 100; 180 100 101; 181 101 102;

182 97 103; 183 98 104; 184 99 105; 185 100 106; 186 101 107; 187 102 108;

188 103 104; 189 104 105; 190 105 106; 191 106 107; 192 107 108; 193 103 109;

194 104 110; 195 105 111; 196 106 112; 197 107 113; 198 108 114; 199 109 110;

200 110 111; 201 111 112; 202 112 113; 203 113 114; 204 109 115; 205 110 116;

206 111 117; 207 112 118; 208 113 119; 209 114 120; 210 115 116; 211 116 117;

212 117 118; 213 118 119; 214 119 120;

DEFINE MATERIAL START

ISOTROPIC CONCRETE

E 2.17185e+007

POISSON 0.17

DENSITY 23.5616

ALPHA 1e-005

DAMP 0.05

END DEFINE MATERIAL

MEMBER PROPERTY AMERICAN

7 TO 10 18 TO 21 29 TO 32 40 TO 43 172 TO 175 183 TO 186 194 TO 197 -

205 TO 208 PRIS AX 1.614 IX 0.01 IY 0.547 IZ 0.466

95 TO 98 106 TO 109 117 TO 120 PRIS AX 1.32 IX 0.01 IY 0.531 IZ 0.41

51 TO 54 62 TO 65 73 TO 76 84 TO 87 128 TO 131 139 TO 142 150 TO 153 -

161 TO 164 PRIS AX 1.467 IX 0.01 IY 0.539 IZ 0.438

1 TO 6 11 17 22 28 33 39 44 50 55 61 66 72 77 83 88 94 99 105 110 116 121 -

127 132 138 143 149 154 160 165 171 176 182 187 193 198 204 209 TO 213 -

214 PRIS YD 0.01 ZD 0.01

12 TO 16 23 TO 27 34 TO 38 45 TO 49 56 TO 60 67 TO 71 78 TO 82 89 TO 93 100 -

101 TO 104 111 TO 115 122 TO 126 133 TO 137 144 TO 148 155 TO 159 166 TO 170 -

177 TO 181 188 TO 192 199 TO 203 PRIS YD 0.23 ZD 1



24

CONSTANTS

MATERIAL CONCRETE ALL

SUPPORTS

8 TO 11 110 TO 113 PINNED

DEFINE MOVING LOAD

TYPE 1 LOAD 40 60 60 85 85 85 85

DIST 3.98 1.52 2.13 1.37 3.06 1.37 WID 1.93

TYPE 2 LOAD 13.5 13.5 57 57 34 34 34 34

DIST 1.1 3.2 1.2 4.3 3 3 3 WID 1.8

LOAD 1 LOADTYPE Traffic TITLE LIVE LOAD

*CLASS 70R (Ecc)

*0.45+1.2+2.79+0.86/2

LOAD GENERATION 40

TYPE 1 -13.43 0 4.01 XINC 1

*CLASS 70R (Girder 2)

*4.5+1.93/2

LOAD GENERATION 40

TYPE 1 -13.43 0 5.465 XINC 1

*CLASS 70R + 1 CLASS A

LOAD GENERATION 40

TYPE 1 -13.43 0 4.01 XINC 1

*0.45+7.5+2.3-0.5/2=10

TYPE 2 -18.8 0 10 XINC 1

*3 CLASS A

LOAD GENERATION 40

TYPE 2 -18.48 0 2.65 XINC 1

TYPE 2 -18.48 0 6.15 XINC 1

TYPE 2 -18.48 0 9.65 XINC 1



25

LOAD 165 LOADTYPE Dead TITLE GIRDER+DECK SLAB+DIAPHRAGM

MEMBER LOAD

*Support girder - 25*0.92

7 TO 10 18 TO 21 29 TO 32 40 TO 43 172 TO 175 183 TO 186 194 TO 197 -

205 TO 208 UNI GY -23

*Mid-span Girder - 25*0.63

84 TO 87 95 TO 98 106 TO 109 117 TO 120 128 TO 131 UNI GY -15.75

*Intermediate Section Girder - 25*(0.92+0.63)/2

51 TO 54 62 TO 65 73 TO 76 139 TO 142 150 TO 153 161 TO 164 UNI GY -19.375

*Deck Slab - 25*3*0.23


96 TO 98 106 TO 109 117 TO 120 128 TO 131 139 TO 142 150 TO 153 161 TO 164 -

172 TO 175 183 TO 186 194 TO 197 205 TO 208 UNI GY -17.25

*Diaphragm - 25*0.4*(1.48-0.23)

12 TO 16 199 TO 203 UNI GY -12.5

LOAD 166 LOADTYPE Dead TITLE WEARING COAT+CRASH BARRIER

MEMBER LOAD

*Crash Barrier - 25*0.3

6 11 17 22 28 33 39 44 50 55 61 66 72 77 83 88 94 99 105 110 116 121 127 132 -

138 143 149 154 160 165 171 176 182 187 193 198 204 209 UNI GY -7.5

*Wearing Coat of thickness 100mm - 22*0.1*3


96 TO 98 106 TO 109 117 TO 120 128 TO 131 139 TO 142 150 TO 153 161 TO 164 -

172 TO 175 183 TO 186 194 TO 197 205 TO 208 UNI GY -6.6

PERFORM ANALYSIS

FINISH



26

STAAD input file for Diaphragm

STAAD SPACE

START JOB INFORMATION

ENGINEER DATE 24-Jun-14

END JOB INFORMATION

INPUT WIDTH 79

UNIT METER KN

JOINT COORDINATES

2 1.5 0 0; 3 2.5 0 0; 4 4.5 0 0; 5 7.5 0 0; 6 9.5 0 0; 7 10.5 0 0; 8 12 0 0;

9 0 0 0;

MEMBER INCIDENCES

2 2 3; 3 3 4; 4 4 5; 5 5 6; 6 6 7; 7 9 2; 8 7 8;

DEFINE MATERIAL START

ISOTROPIC CONCRETE

E 2.17185e+007

POISSON 0.17

DENSITY 23.5616

ALPHA 1e-005

DAMP 0.05

END DEFINE MATERIAL

MEMBER PROPERTY AMERICAN

2 TO 8 PRIS YD 1.48 ZD 0.4

CONSTANTS

MATERIAL CONCRETE ALL

SUPPORTS

3 6 PINNED

LOAD 1 LOADTYPE Dead TITLE DEAD LOAD



JOINT LOAD

8 9 FY -67.5

JOINT LOAD

2 4 5 7 FY -333.75

MEMBER LOAD

2 TO 6 UNI GY -12.5

JOINT LOAD

2 4 5 7 FY -59.4

PERFORM ANALYSIS

FINISH

analysis & design.pdf

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