ANALYSIS AND DESIGN OF BRIDGE AND CULVERTPractical 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 – 575025 July 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 C. 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. I also thank the entire staff of the company for their cooperation and assistance during the course of my project. Department of Civil Engineering. My special thanks to Dr. and Mrs. Nisha K. Sadasivam V. Mr. Chennai. EDRC-Transportation IC.. i . Larsen & Toubro. Professor & Head. National Institute of Technology. I would like to express my deepest sense of respect and indebtedness to my Internship Supervisor. who has been my Internship Mentor for taking time out of his busy schedule for my doubts and clarifications. I owe my wholehearted thanks to Mr. Karnataka for giving me the opportunity to undergo internship training at Larsen & Toubro. Lingarajan K. Professor of the Civil Engineering Department for all his help and guidance. K. for their consistent support. Chennai. encouragement and advice during the project.. Swaminathan. guidance.ACKNOWLEDGEMENT I am extremely thankful to Dr. Katta Venkataraman. ...2 CALCULATION OF LOADS AND MOMENTS……………………………….14 2..3..……………………………………...2..2.1 Fixed Bearing…………………………………………………..…15 CHAPTER 3: ANALYSIS AND DESIGN OF SUPERSTRUCTURE 3.9 2..10 2...18 3..3 Calculation of Longitudinal Forces ……………………………………….1 Live Load Positions……………………………………………………….1 SECTION PROPERTIES………………………………………………………..2 1.2..…4 2.…………......2.4....2 Load Summary…………………………………………….17 3.11 2...….1 1..…………..…...7 Load Combinations…………………………………………………...2..1 DETAILS OF THE STRUCTURE ……………………………………………..…….20 3.2 LOAD ANALYSIS…………………………………………………………..9 2.………………………………………………...CONTENTS ACKNOWLEDGEMENT…………………………………….2 Live Load Analysis………………………………………………….…..2...1 BRIDGES…………………………………………………………….……12 2. i CONTENTS……………………………………………………………………………..3 PIER DESIGN……….2..2.18 3.1 Dead Load Analysis……………………………………………………….3 Free Bearing……………………………………………………..2 CHAPTER 2: ANALYSIS AND DESIGN OF SUBSTRUCTURE 2.....3 LOADS AND STRESSES……………………………………………………….1...2.2.4.2 CULVERT……………………………………………………………….2...20 ii ....….1 Determination of Permissible Stresses…………………………………….…6 2.3 Load Combinations…………………………………………....7 2.3.8 2....…13 2.…10 2.…....4 VEHICLE CLASSIFICATIONS………………………………………………..2 Design of Footing ………………...…………. ii CHAPTER 1: INTRODUCTION 1...7 2.1 Design of Pier Cap …………………………………………………….………………………….1 1...4 Bearings…………….6 Seismic Forces……………………………………………………………...10 2..……………………………………………………….5 Wind Forces …………………………………………………………….2. 3 LOAD CALCULATIONS…………………………………………………..….2 MODELLING OF THE STRUCTURE……………………………………….25 4.….4.4.29 4.3 Load Combinations…………………………………………………...6 DIAPHRAGM DESIGN…………………………………………………….....…….4 SHEAR CONNECTOR DESIGN…………………………………………...25 4.….1 Design for Flexure………………………………………………………….……28 4.22 CHAPTER 4: ANALYSIS AND DESIGN OF BOX CULVERT 4..26 4.3.1 Dead Load………………………………………………………………..2 Design for Shear……………………………………………………………31 REFERENCES …………………………………………………………………..25 4..3 GIRDER DESIGN………………………………………………………………..3.1 DETAILS OF THE STRUCTURE..…………………………………………….4 DESIGN OF BOX SECTION……………………………………………………29 4.32 ANNEXURE 1 : SAMPLE DESIGN OF SUB-STRUCTURE ANNEXURE 2 : SAMPLE DESIGN OF SUPER-STRUCTURE iii .....2 Live Load………………………………………………………………….21 3.3.5 DIFFERENTIAL SHRINKAGE STRESS……………………………………….20 3..25 4..3..21 3..... The structural design wing of this department handles these structures of all Infrastructure Projects.1. L & T Transportation Infrastructure handles major roadway projects which includes National and State Highways all around India and associated structures like flyovers. 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. Transportation IC. major & minor bridges and cross-drainage works like culverts. 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 1.1 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. 1. Vehicle Underpass (VUP). INTRODUCTION This internship was carried out at Larsen & Toubro. Pedestrian Underpass (PUP). The types of culverts are: Box Culvert Pipe Culvert RCC Solid Slab Culvert 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. office ethics and corporate lifestyle. Rail Over Bridge (ROB). with the objective of gaining first-hand knowledge about the technical practices in a structural design office. EDRC. Earth Pressure (including live load surcharge) 8.1.4 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. Longitudinal forces due to braking 7. FORCES AND STRESSES The loads and stresses considered in the design are as follows (as per IRC 6-2010): 1. Wind Load 6. 2 . Should also be checked for Class A Loading. Temperature Effect 9.3 LOADS. Vehicle Collision Load 5. Live Load 3. Seismic Forces 1. Impact factor due to vehicular live load 4. Dead Load 2. CLASS 70R TRACKED 40 TONNES BOGIE LOAD CLASS A Adopted on all roads on which permanent bridges and culverts are constructed. 3 . For the substructure design of abutment piers the details required are: Grade of concrete and steel Span of Bridge 4 . ANALYSIS AND DESIGN OF SUBSTRUCTURE 2.5 1 1.1 DETAILS OF THE STRUCTURE 1.5 1 FIXED FREE Wearing coat Slope 3000 RCC DIAPHRAGM JACK LOCATION 1500 3500 RCC PIER CAP RCC PIER Fig 1: Typical section of a pier This includes all the details required by the designer for carrying out analysis.2. type of soil. etc. importance factor. Basic Wind Speed Safe Bearing Capacity of Soil Fig 3: Elevation and plan of an Abutment Pier 5 . Type of bearing Nature of traffic (live load) Seismic Zone. Width of carriageway and percentage of camber Reduced levels of ground. etc. pier cap. footing. Fig 2: Transverse Section of a Pier 2.1 DETERMINATION OF PERMISSIBLE STRESSES As per IRC 21-2000 (Cl.1. for long piers. 306.4.3). Stresses are increased when analyzing for wind and seismic consideration by 33% and 50% respectively. β = 1. long columns are subject to a Stress Reduction Factor given by.5 – lef /(100 x rmin) lef – Effective length of pier rmin – Least radius of gyration This is applicable only if the Slenderness ratio (lef / rmin) is greater than 50. 6 . ie. Permissible flexural compressive stress in concrete.50 MPa As per table 1 of IRC 6-2010.65 MPa Seismic(50% increase) 307. diaphragm and deck slab and due to Superimposed Dead Load. wind loads and longitudinal loads.20 MPa Seismic(50% increase) 360.00 MPa 319.2 CALCULATION OF LOADS AND MOMENTS The first step in the design of any structure is the analysis of various dead loads. for wind load case the permissible stresses are increased by 33% and for seismic case it is increased by 50%.00 MPa Wind (33% increase) 272. σcbc Normal 11.00 MPa Permissible compressive stress in steel. diaphragm and deck slab). σst Normal 205. 2. seismic loads. SIDL (wearing coat and crash barrier) is found out separately. SuperImposed Dead Load (SIDL).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.56 MPa Seismic(50% increase) 17. 2. 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.2.70 MPa Wind (33% increase) 15. The reaction on each bearing due to girder.For M35 concrete. σst Wind(33% increase) 240. 7 .55 MPa Normal Permissible flexural tensile stress in steel. live loads. for 3 lane traffic.The dead load due to self-weight of pier cap. One Class 70R + One Class A Three Class A One Class 70R.2. 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. 8 . For the STAAD model vehicle definitions has to be provided as per IRC 6-2010.2 LIVE LOAD ANALYSIS The live load for each load combination can be calculated manually as well as with the help of a STAAD model. 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. 12m wide carriage-way. pier shaft and footing is also separately calculated by multiplying the unit weight of concrete (25kN/m3) by their respective volumes 2. a 10% reduction is to be considered for the longitudinal effect as the probability of the characteristic loads acting simultaneously is low. 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. for a 3 lane. 2 critical load combinations are possible. this configuration is checked for criticality as it generates maximum transverse moment. 205. 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.4 BEARINGS G1 G2 G3 G4 Free-End Pier Fixed-End Pier Fig 4: Bearings Type of Bearing Vertical Horizontal Reaction Horizontal Reaction along longitudinal along transverse direction direction Reaction Fixed Pot Bearing Guided Bearing along transverse direction Guided Bearing along longitudinal direction Free Bearing 9 .2.2. 2.2. They are only restrained in the transverse direction.5.4.1 FIXED BEARING They are restrained against movement along transverse and longitudinal direction. which has 10 .4. all of which are given in the above mentioned clause. Rg is the reaction due to dead load Rq is the reaction due to live load Fb is the applied horizontal force (due to braking) 2. The longitudinal forces due to friction generated due to movement of bearings are calculated using the formula: μ (Rg + Rq) 2.5 WIND FORCES (Cl 209 IRC 6-2010) The IRC code mentioned gives equations for the transverse and vertical wind force. lift coefficient (CL) .μ (Rg + Rq) Or Fh/2 + μ (Rg + Rq) Where.2. area resisting the force and hourly mean wind pressure (Pz).2.2.2 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. μ is the coefficient of friction at the movable bearing (values obtained from IRC 62010 Cl. They don’t resist braking forces. CD (for horizontal force). The longitudinal forces due to fixed bearing are calculated using the formula: Fh .1). 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 6-2010.2. the variables being Drag coefficient. gust factor (G) . 211. 5. Ah= (Z/2) x (I/R) x (Sa/g) Where. Z is the zone factor I . Ft = Pz x A x G x CD Vertical Wind Force. The values for zone factor. importance factor and Response Reduction Factor are given in IRC 6-2010 in tables 6.Response Reduction Factor Sa/g .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. (Stiffness in kN/mm) 11 . 33ms-1) to obtain the wind pressure corresponding to the considered location.Importance factor R . 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.1 in IRC 6-2010 for various types of soils. The longitudinal wind load is taken as 25% of the transverse wind load. Transverse Wind Force. The value for the Seismic Response Acceleration Coefficient depends on the type of soil and time period of vibration and is given in Cl 219.6 SEISMIC FORCES The Seismic Coefficient Ah is given by the equation. The time period for vibration is given by.2. 7 and 8 respectively. The lever arm distance to the center of gravity of the considered portion is also determined for calculation of moments. Fv = Pz x A x G x CL 2.Seismic Response Acceleration Coefficient for 5% damping. Intermediate values can be interpolated. 1. DL + SIDL + LL-70R + Longitudinal Frictional Forces 3. Frictional Forces + Long. 2.70R+Class A + Long. Frictional Forces + Long. Seismic Force 12.The value of stiffness is taken as. DL + SIDL + LL-70R+Class A + Longitudinal Frictional Forces +Wind 7. DL + SIDL + 20% LL. Seismic Force 10. Seismic Force 11.2. dirt wall.7 LOAD COMBINATIONS The following load combinations will be considered in the analysis for determination of critical values of bending moment and shear force. pier and live load. Seismic Force (without live load) 9. Seismic Force 14.70R+Class A + Long. DL + SIDL + 20% LL. SIDL. F = 3EI/L3 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. Seismic Force 12 .70R + Long. DL + SIDL + 20% LL. Seismic Force 15. DL + SIDL + LL-3 Class A + Longitudinal Frictional Forces + Wind 8. Frictional Forces + Trans. Frictional Forces + Trans. substructure. DL + SIDL + LL-70R+Class A + Longitudinal Frictional Forces 4. DL + SIDL + Long. SIDL and for live load as the pier being designed has free bearings. DL + SIDL + 20% LL. DL + SIDL (without live load) 2. Frictional Forces + Long.3 Class A+ Long. DL + SIDL + 20% LL. DL + SIDL + 20% LL. Longitudinal Seismic forces are taken as zero for dead load due to super structure. DL + SIDL + LL-3 Class A + Longitudinal Frictional Forces 5.3 Class A+ Long. Seismic Force (without live load) 13. DL + SIDL + LL-70R + Longitudinal Frictional Forces + Wind 6. DL + SIDL + Long. Frictional Forces + Trans.70R+Long. Frictional Forces + Trans. 3% of the gross sectional area of concrete (Cl.5. 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.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 cross-sectional area of longitudinal reinforcement shall not be less than 0. All load cases are checked if they are within permissible limits of stresses in steel and concrete.2.8% nor more than 8% of the gross cross-sectional area.2. 2. 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.2. 306.1 IRC 21-2000).2 IRC 21-2000). The area of steel provided in any case shall not be less than 0. 306. (Cl. 13 . 219. 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. As per Cl.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. 306. 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.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. IRC 6-2010) The vertical force. The impact factor is calculated for class 70R and class A vehicle. 304. the equivalent bending moment and equivalent shear force are calculated as per IRC 21-2000. which have higher values of shear force and moment and at a distance ‘d’ away from the face of the pier. The shear force and bending moment due to self-weight of pier cap. 304. where the forces and moments are lower thereby reducing the reinforcement required.2.2.3.7.2. bearing pedestal. Effective depth required.7. For the torsion (longitudinal moment) values in the pier cap. Pier cap is designed at the face of the pier. dirt wall and centrifugal forces are also calculated and added to the obtained values. the pier cap is designed as a cantilever beam. and the values are added to the values of shear force and bending moment already calculated. Cl.2.3. dreq = (M/Qb)1/2 where dreq.1 DESIGN OF PIER CAP Here only the critical reactions on bearings on one side of the pier along the transverse direction are considered for each load case. and the total shear force and bending moment are adjusted accordingly.Effective depth required M – Bending Moment at the section Q = (1/2) x j x k x σcbc j = 1 – (k/3) k = (280/(3 x σcbc)) / (280/(3 x σcbc) + σst) σcbc & σst are the permissible flexural strength in steel and concrete respectively. if a/d >1. Design is carried out at pier face and at ‘d’ distance away from face of the pier by considering the maximum value of shear force and bending moment by working stress method where. where d is the effective depth.1 and Cl. Checks for corbel action are performed where. 14 .4. P/A ± ML/ZL ± MT/ZT 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. it is increased by 50%. The earth-fill and the eccentricity between the centerline of pier and footing exerts a moment on the footing in the longitudinal direction.05% of gross area is provided on each face. Punching Shear Stress. Vp = (P1 + P2 + P3 + P4) / 4 x Effective area in carrying punching shear Aps – Area resisting punching shear 15 . 2. 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. The sections are also designed for shear and torsion by providing the appropriate reinforcement as per the design procedure in IRC 21-2000 Cl 304.2 DESIGN OF FOOTING Firstly the additional load on the footing bottom due to self-weight of footing. Ast req = M / ( σst 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. Side face reinforcement of 0.Area of steel required. soil above footing and due to earth-fill are calculated. longitudinal and transverse moments are calculated after which the stresses at the corners of the footing is calculated using the formula. this value is added to the existing moments at the bottom of the footing. The revised values of vertical load. Critical sections are taken at a distance deff along the traffic direction and across the traffic direction and critical values of shear fore is calculated for the punching shear check.3.7. τcp = Vp / Aps Punching Shear. 5.The value of shear stress has to be within permissible limits as per IRC 21-2000 Cl. Fig 5: Dimensional Reinforcement Detail of Sub-structure & Foundation 16 . which states that punching shear stress shall not be less than 0.5.2. 307.16 x (fck)1/2. ANALYSIS AND DESIGN OF SUPERSTRUCTURE The superstructure consists of the girder. i. Fig 6: Dimensional Section details of a Girder The section properties for the composite section.e. deck slab and crash barriers. the section including the deck slab is also determined from the properties of the individual sections by considering unit width of 17 . 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. area of cross-section and center of gravity of the section is calculated. From calculations the Moment of inertia.3. The girders rest on the bearings through which forces and moments are transferred to the sub-structure. The longitudinal reinforcement obtained may be curtailed at a section of 0. ‘d’ away from the support m.2. at 0.0 1m 18 .25leff from the support and at the mid-span.deck slab for each girder. 3.1 LIVE LOAD POSITIONS CLASS 70R Eccentric CLASS 70R 4.2 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. table 2. The section is designed for the flexure requirement at mid-span. The live load combinations may be changed based on the carriageway width as per IRC 6-2010. The shear force and bending moment for each of these load cases are determined at a distance. 3.25leff from the support based on the moments at that section. These section properties are used in creating a STAAD Pro grillage model for analysis. 15m CLASS A CLASS A 2. CLASS 70R ON INNER GIRDER CLASS 70R 5.65 9.465m CLASS 70R + 1 CLASS A 10m CLASS A CLASS 70R 4.0 1m 3 CLASS A 6.65m 19 CLASS A . 2. Loads are listed separately for the inner and outer girder. The stresses in concrete and steel are checked if they exceed the permissible limits. 3. The design of girders are carried as a T flange. 3.3 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.3. 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. 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. which is used for carrying out the design. ‘d’. The SIDL along with live load case is considered in the service stage and design is carried out. away from the support and at the mid-span for design purposes. 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. 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. 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.2. 20 .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.2 LOAD SUMMARY The load analysis is summarized for the section at effective depth. 5 LL. Dead load is not considered. 21 . the concrete is of different age and shrinkage occurs in the various components non-uniformly.3DL +1. as these are the only loads on the deck slab. 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. 304.7. 3. This generates a stress known as Differential Shrinkage Stress.1. The maximum shear force due to live load and SIDL are considered for the design as 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.Shear reinforcement is also determined at these 2 sections as per IRC 21-2000 Cl.5 DIFFERENTIAL SHRINKAGE STRESS As the various components of the superstructure are cast at different times. 4.3. The loads to be considered on the diaphragm are taken for the critical condition. from which the top and bottom reinforcements are designed. 7. ediff – Differential Shrinkage Strain Ecf – 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. The superstructure is jacked up from time to time.6 DIAPHRAGM DESIGN G2 G3 G1 G4 Jacking Point Fig 8 : BMD of Diaphragm from STAAD Pro The diaphragm beam is also modelled on STAAD to obtain the maximum sagging and hogging moments. The structure is closed down for vehicle usage 22 .43 3.It is calculated as per BS 5400-4 1990 Cl.5 Mcs = ediff x Ecf x Acf x acent Where. for replacement of the bearings which may wear off with use. which is often during jacking. 304. 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.7. crash barrier. 23 .during such maintenance and so live loads can be ignored.1. The loads considered to be acting on the diaphragm during jacking are the self-weight of girder. deck slab. ANALYSIS AND DESIGN OF BOX CULVERTS A culvert is a structure that allows water to flow under a road. Typically embedded so as to be surrounded by soil. or similar obstruction. Box Culverts are cross-drainage structures built beneath roadways which are box shaped as the name suggests.4. a culvert may be made from a pipe. Fig 9: Plan and sectional elevation of a Box Culvert 24 . They are less than or equal to 6m in span along the longitudinal direction of the road. railroad. reinforced concrete or any other material. restrained with spring supports.F. The parapet wall is of 0. x qa Where. k = ½ x Fs x (Distance between adjacent supports) 4. bottom slab and side walls are calculated separately as a Uniformly Distributed Load applied on the respective members. Clear height 3. The dead load for top slab.1 DETAILS OF THE STRUCTURE The basic design data required for analysis of the structure is as follows: 1. Dimension of Box Culvert 4.3 LOAD CALCULATIONS 4. Fs = 40 x S. S.F. The Super Imposed Dead Load (SIDL) includes wearing coat.3m 25 . Soil Properties 4. 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. Depth of fill and wearing coat 5. Clear span 2. 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. Bowles. fill and parapet wall.1 DEAD LOAD The dead loads are calculated by considering 1m of the box section.2 MODELLING OF THE STRUCTURE The box culvert in modelled as a 2-D member for a 1m strip. Width of carriage way 6. The concrete density is generally taken as 25kN/m3. is the safety factor qa is the Safe Bearing Capacity of the soil. who states that the Modulus of sub-grade reaction is given by. The stiffness.3.4. depending upon the b / lo ratio. beff = α x (1 – a/lo) + bl α – a constant having values as per the table in Cl. as per Cl 305.16. as per Cl. 214. The calculation of load dispersion in the direction across traffic. IRC 21200-. Surcharge Live Load is considered to be equivalent to 1.2010. 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.3.2 IRC 21-2000.2 LIVE LOAD For calculation of load dispersion along the traffic direction. Water pressure acting horizontally inside and outside will balance each other and is therefore ignored.3. 305. The pressures at top and bottom slab level are computed and applied on the side walls. The effective width. lo – the effective span 26 . 4.2. IRC 21-2000.16. As the parapet wall is constructed at the sides of the carriage-way. a – the distance of the center of gravity of the concentrated load from the nearer support. the parapet load is given throughout the span of the top slab. where b is the width of the slab. For the High Flood Level (HFL) condition.16. 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. Earth pressure is considered for the at rest condition.2m of earth fill as per Cl.1 IRC 6.width generally and height is provided as required which is including the height of fill. The unit weight of soil fill is taken as 20kN/m3 and the load is applied horizontally on the side walls. 305. 4 5 6 7 8 9 10 1 2 3 Fig 10: Critical sections of a Box Culvert 27 . the dimension of the tyre or track contact area over the road surface of the slab in a direction at right angles to the span plus twice the thickness of the wearing coat or surface finish above the structural slab. (Impact factor need not be considered for bottom slab and side wall as they are buried in the soil) The critical section for bending moment are taken at half the thickness of the slab from the corner nodes which are the equivalent of the inner face of the box culvert and at the center of the slab. The shear force and bending moment values at critical sections are tabulated after considering reduction due to longitudinal effect and impact factor. The critical section for Shear Force is taken at a distance. load due to both tracks or wheels are considered. overlapping of load dispersion occurs and net effective width is considered by taking the load dispersion due to both wheels without overlapping and for calculation of load intensity. The load intensity hence calculated is applied as a UDL per meter width on the top slab of the STAAD model.. effective depth.e. If the effective width is greater than the distance between wheels or tracks of the vehicle. The tracked and wheeled vehicles (including bogie load) of each class are separately analyzed for maximum value of bending moment by placing the vehicle at the center of span and for maximum shear force by placing the vehicle at the edge of the span.bl – breadth of the concentration area of the load i.‘d’. The critical load case hence obtained is considered for design. away from the face of the support as shown in the following figure. 3.3 LOAD COMBINATIONS The critical load combinations considered for design are as follows: 1.Critical Section for Shear Force for bottom slab 5 .2 IRC 6-2010 from the load intensity value. DL+SIDL+EP+LLS-L 3. 211. DL+SIDL+EP+LLS-L+LL 6.9 . DL+SIDL+EP 2.Critical Section for Bending Moment for top slab 7.6 .Critical Section for Shear Force for side wall The braking force is also calculated as per Cl.1.Critical Section for Shear Force for top slab 8.3 – Critical Section for Bending Moment for bottom slab 4. DL+SIDL+EP+LLS-BOTH+LL+BR-L 11. DL+SIDL+EP+LLS-R 4. DL+SIDL+EP+LLS-BOTH+LL 8. DL+SIDL+EP+LLS-L+LL+BR-L 9. 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. and half of the value so obtained are applied on each edge of the top slab in the STAAD model. DL+SIDL+EP+LLS-R+LL+BR-R 10. DL+SIDL+EP+LLS-BOTH 5. 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 28 .10 .Critical Section for Bending Moment for side wall 2 . DL+SIDL+EP+LLS-R+LL 7. If not section dimensions need to be revised. in case of floods. The design for flexure is done as per Working Stress Design Methodology. The combinations for HFL are as follows: 1. 4. DL+SIDL+SEP+WP+LLS-L 3. DL+SIDL+SEP+WP 2. DL+SIDL+SEP+WP+LLS-R+LL 7. 7 and 10 as shown in the figure above. dreq = (M/Qb)1/2 29 . DL+SIDL+SEP+WP+LLS-BOTH 5. 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. bottom slab and side wall are calculated by deducting the clear cover and depth of stirrup and diameter of the reinforcement bar. 6. The effective depth required is calculated as per the following procedure and the depth is checked if safe or not.1 DESIGN FOR FLEXURE The effective depth for the top slab.4 DESIGN OF BOX SECTION The critical case is taken for maximum shear force and maximum bending moment condition at the critical sections 1. 4. DL+SIDL+SEP+WP+LLS-R 4.The above load combinations are for Low Flood Level. DL+SIDL+SEP+WP+LLS-L+LL+BR-L 9. 4. 3. Effective depth required. DL+SIDL+SEP+WP+LLS-BOTH+LL 8. DL+SIDL+SEP+WP+LLS-L+LL 6. the High Flood Level (HFL) is considered where Submerged Earth Pressure and water pressure are additional forces instead of Dry Earth Pressure. The area of steel required is calculated as per the following formula and adequate steel is provided and spacing of bars are computed. 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 30 . The steel provided has to be greater than the minimum steel required that is 0.where dreq.12% of the gross area of section.3LL.2DL + 0. Ast req = M/(σst jd) The area of distribution steel is considered by considering the load combination 0. Area of steel required.Effective depth required M – Bending Moment at the section Q = (1/2) x j x k σcbc j = 1 – (k/3) k = (280/(3 σcbc)) / (280/(3 σcbc) + σst) σcbc & σst are the permissible flexural strength in steel and concrete respectively. 4.τc x b x d S – Spacing of the stirrups σs – Permissible tensile stress in shear reinforcement d – effective depth 31 . and the shear reinforcement is computed for the unbalanced shear force. τv = 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. 8 & 9.7 IRC 21-2000): Design Shear Stress. Vertical Shear Reinforcement.4. The permissible shear stress. 304. Asw = Vs x S / (σs x d) Asw – Total Cross-sectional area of stirrup legs Vs = V .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. τc is determined based on the percentage of steel provided as given in table 12B IRC 21-2000. 5. The design shear stress is computed as follows (Cl. IRC-78-2000. 1996. page 387-396. Standard Specifications and Code of Practice for Road Bridges.K. by Joseph E. Section III – Cement Concrete (Plain and Reinforced) (3rd Revision) 3. IRC 21-2000.Foundations and Substructures. Raina. Standard Specifications and Code of Practice for Road Bridges Section II – Loads and Stresses (5th Revision) 2.REFERENCES 1. Standard Specifications and Code of Practice for Road Bridges. Section VII. 5. V. Design and Economics. 32 . Dr. 5th edition. IRC 6-2010.Bowles. Foundation Analysis and Design. Concrete Bridge Practice: Analysis. 4. McGraw-Hill. Design of a RCC section subject to combined Axial Thrust and Biaxial Bending. .3 6.....2.. SEISMIC COEFFICIENT…………………………………………………………. 6..2 3 DEAD LOAD REACTION DUE TO DEAD LOAD……………………………………………....1 Superstructure………………………………………………………………..1.1 DETAILS OF SUBSTRUCTURE PERMISSIBLE STRESSES……………………………………………………….6.. 6. 13 13 14 5.….1 3..ANNEXURE 1 : SAMPLE DESIGN OF SUB-STRUCTURE CONTENTS 1 2 1 1.…………………………………………………...………………………………………………………. 4 4 5 6 4 4..... 5..4 6....5 6...7..6....2 ..6 6...…………………………………………………..1 Class 70R……………………………..1 Pier cap……………. SIDL…………………………………………...1 6... 10 10 11 11 11 11 11 12 12 12 12 12 12 12 LOAD CASES FORCES AND MOMENTS FOR FOOTING TOP………………………………… SEISMIC COMBINATIONS FOR FOOTING TOP…………………………….1 LONGITUDINAL FORCES FRICTIONAL FORCE……………………………………………………………… 7 7 5 5....1..7...2 Sub-structure………………………………………………………………….. 3 3 3.2 Class 70R + Class A………. 2 2...1 WIND FORCE DEAD LOAD…………………………………………………………………….…………………...……………………………………… DIRT WALL……………………. LIVE LOAD…………………………………………………………………. 5. LIVE LOAD 6..……………………………………………………… 6..... 6. SUB-STRUCTURE…………...1 Longitudinal Direction…………………………………………………….2 6. 8 9 9 9 9 SEISMIC FORCES SELF-WEIGHT CALCULATION OF PIER………………………………………...3 3-Class A……….. 3-CLASS A…………………………………………………………………………....……………………………………….2 Pier………. 3 REACTION DUE TO SIDL……………………………………………………….2 6 6...7... DEAD LOAD OF SUPERSTRUCTURE……………………….2 3.1 7..1 2.. CLASS 70R + 1 CLASS A………………………………………………………. 6.7 7 7...…………………………………………………………..3 LIVE LOAD CLASS 70R……………………………………………………………………….…………………………………………………………………….. ... NET PRESSURE…………………………………………………………………....4 13.5 13.3 13.1 8. FOOTING BOTTOM………………………………………………………………..4 SEISMIC COMBINATIONS FOR FOOTING BOTTOM…………………………..1 9.1 13. BOTTOM OF FOOTING…………………………………………………………. 15 15 8 8.. FOOTING SHEAR…………………………………………………………………. DESIGN AT CRITICAL SECTIONS…………………………………………….. 16 16 20 9 9..6 FOOTING DESIGN SECTIONAL PROPERTIES………………………………………………………. 32 32 33 34 37 38 43 ....3 7. WIND LOAD FOR FOOTING BOTTOM…………………………………………...2 LOAD COMBINATIONS PIER BOTTOM…………………………………………………………………. 24 24 25 10 DESIGN OF FREE-END PIER 26 11 MATERIAL STRESSES 27 12 PIER CAP DESIGN 28 13 13.. EARTHFILL………………………………………………………………………… FOOTING CORNER STRESSES…………………………………………………....2 13....2 LOAD SUMMARY BOTTOM OF PIER………………………………………………………………….7. 1. DETAILS OF SUBSTRUCTURE Grade of Concrete Grade of Steel Density of concrete Overall span of RCC Girder Effective Span Size of Pier Transverse Direction Longitudinal Direction (Thickness) Equivalent width of pier in transverse direction Depth of pier cap Thickness of dirt wall Spacing between bearings Eccentricity between C/L OF Pier & Bearings Height of Crash barrier Thickness of wearing coat Thickness of deck slab Depth of RCC Girder Thickness of bearing Minimum height of pedestal % camber Average thickness of bearing pedestal Total width of deck slab Depth of founding level from GL Depth of footing GL to footing top level FRL at pier location Existing ground level Average bearing Top level Pier cap top level Footing top level Founding level Height of pier from GL to pier cap top Height from bearing level to footing top Height of pier (i.e.. Footing top to pier cap top) 35.00 500.00 25.00 20.00 19.00 MPa MPa kN/m3 m m 3.00 1.00 2.79 1.50 0.30 3.00 0.11 1.15 0.06 0.23 1.50 0.07 0.20 2.50 0.31 12.00 2.00 1.00 1.00 621.59 613.64 619.67 619.30 612.64 611.64 5.65 7.03 6.65 m m m m m m m m m m m m m % m m m m m m m m m m m m m m 2 2.79 m 4 0.23 m 0.29 m Cross-sectional Area of Pier (A) Least moment of inertia (I) Least radius of gyration rmin = √(I/A) 1 Note 3 Table 13 IRC 21-2000 lef=1.75l 11.65 Slenderness Ratio ( lef/rmin) 40.34 <50 Hence, Short pier Stress Reduction factor (only for long column) (1.5-lef/(100*rmin) 1.00 1.1 PERMISSIBLE STRESSES (Stress increase as per IRC 21-2000) Permissible flexural compressive stress in concrete σcbc Normal Wind Seismic Normal Wind Seismic Normal Wind Seismic Permissible flexural tensile stress in steel σst Permissible compressive stress in steel σst 11.70 15.56 17.55 240.00 319.20 360.00 205.00 272.65 307.50 MPa Table 9 MPa MPa MPa Table 10 MPa MPa MPa Table 10 MPa MPa 2 440.00 kN/m Safe Bearing Capacity of Soil 2 2. DEAD LOAD 2.1 REACTION DUE TO DEAD LOAD (Girder+Diaphragm+Deck Slab) Width of pier cap 1.40 m Values from STAAD Model Reaction on Bearings Bearing Reaction (kN) Trans. ecc. Long. ecc. Trans. Moment B1 357.00 4.50 0.11 1606.50 B2 379.00 1.50 0.11 568.50 B3 379.00 -1.50 0.11 -568.50 B4 357.00 -4.50 0.11 -1606.50 1472.00 0.00 Long. Moment 39.27 41.69 41.69 39.27 161.92 2.2 REACTION DUE TO SIDL (Wearing coat+crash barrier) Values from STAAD Model Bearing B1 B2 B3 B4 Reaction on Bearings Reaction (kN) Trans. ecc. Long. ecc. Trans. Moment 174.00 4.50 0.11 783.00 31.00 1.50 0.11 46.50 31.00 -1.50 0.11 -46.50 174.00 -4.50 0.11 -783.00 410.00 0.00 Total reaction due to dead load = Long. Moment 19.14 3.41 3.41 19.14 45.10 1882.00 kN 3 13 1.45 1.20 2.37 3.52 A1 = A2 = Total Reaction due to Class 70R = 2.1 CLASS 70R 80 120 120 170 170 170 170 A2 A1 6.00 kN 0.96 743.05 1.37 256.81 kNm 4 .73 kN 2197.27 kN 743.79 Maximum Reaction = Transverse Moment = Longitudinal Moment = 6.98 1. LIVE LOAD 3.58 3.73 kN 1000.3.72 kNm 81.00 2. 00 kN 1100.30 7.50 142.20 2.36 kNM 5 357.79 6.0 3.47 kNm 35.95 2.16 kN 554.0 5.80 kN 981.2 A1 = A2 = 4.29 kNm 3.2 CLASS 70R + 1 CLASS A 27 27 114 114 68 68 68 68 A1 1.2 1.10 Maximum Reaction = Total Reaction due to Class A = 10% reduction for longitudnal effect as per IRC 6-2010 Cl.16 kN 1.00 2.3.50 70R A 0.3 3.1 A2 3.96 Transverse Moment = Longitudinal Moment = 1090.53 kNm 39.84 kN 357.45 1.89 kN . 205 Reaction = Transverse Moment = Longitudinal Moment = Total Reaction = 990.0 3. 8628 kNm 10% reduction due to longitudnal effect Maximum Reaction = Transverse Moment = Longitudinal Moment = 964.2 4.2 2.3 1.3 1.3 3-CLASS A 0.07652 kNm 6 .48 kN 803.75 Reaction due to 1 Class A vehicle = Maximum Reaction = Transverse Moment = Longitudinal Moment = 357.75 0.61 kNm 117.3 2.332 kN 723.249 kNm 106.3.45 0 2.25 2.16 1071.4 6 0. 64 3 DL+SIDL+3 Class A 142.Coefficient of friction at movable bearing = 0.73 kN Class 70R + Class A 990. LONGITUDINAL FORCES 4. Horizontal Force = μ(Rg + Rq) kN Description of traffic load 1 DL+SIDL+Class 70R 131.00 kN Rq .05 Rg .Reaction at free end due to live load Class 70R 743. 211.1 FRICTIONAL FORCE As per Cl.No.33 kN S.32 Free pier will have no braking forces acting on pier Bearing Deformation only needs to be calculated for elastomeric bearing 7 .5.29 2 DL+SIDL+Class 70R + 1 Class A 143. following values of horizontal force have been considered.4.Reaction at free end due to dead load = 1882.80 kN 3 Class A 964. μ .1 OF IRC 6-2010. 00 4.4 of IRC 6-2010. A1 Width of cross-section.40 CD for structures supported by 2 or more beams = = = 2. 209.09 CD for structures supported by single beam = 1.93 29. Horizontal wind pressure For basic wind speed of 42.09 2.5 m/s 8.5 of IRC 6-2010) FL = P z x A3 x G x C D A3 -Area in plan in m2 G .00 94. Vertical wind force . Horizontal wind pressure. FT ( Cl.Lift Coefficient = 0.Solid Area in m2 G . 209.44 m Gust factor (G) for spans upto 150m Transverse force on superstructure due to wind.Gust factor CD . of the force from bearing level 8 m m 2 m m 2 .3.36 kN = = 23.1.59 kN 1.Drag Coefficient Longitudinal wind force FL for superstructure shall be taken as 25% of the transverse wind force as per Cl. b b/d = = = = = 10. l Depth of superstructure resisting wind.7 N/m 769. FL C.3. FT Longitudinal force on superstructure due to wind. d Area of deck resisting wind. 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 Height of the superstructure Height from GL to bottom of superstructure 42.3 of IRC 6-2010) FT = P z x A1 x G x C D A1 .Gust factor CL .5m/s.31 12.G.92 m For height of 9m & for basic wind speed of 33m/s. Pz 2 463.1076 N/m Transverse wind force .1 DEAD LOAD 5. FT ( Cl. 209.85 m 5.75 5.3.00 2.5.1 Superstructure Length of superstructure resisting wind. 44 kN 5. FL Width of superstructure Area in plan. FL = 138.30 Lever arm (from top of footing to C.50 CD is multiplied by 0.50 1.60 Gust factor.80 m/s 10.85 18.00 m 2 120.2 Live Load (Cl.00 h/b = 5. (1-1. G = 2. h/b = 40.65 t/b = 3. 209. b = 1.65 As per note 4 of IRC 6-2010 page 30. where r is the radius of rounded pier corner. Cl.5 = 0.1.Vertical Wind Load. 0.82 m = 7.22 Longitudinal force on substructure due to wind = 1.5m/s.20 As per IRC 6-2010.5m/s Horizontal wind pressure Total length of superstructure exposed to wind force Height of exposed area of live load (excluding height of crash barrier) for calculating wind force Area of live load resisting wind CD value as per Cl. CD value should be multiplied with maximum of (1-1.95m & for basic wind speed 33m/s Horizontal wind pressure For height of 10.50 For pier with r = 0.6 of IRC 6-2010 Gust factor (G) for spans upto 150m Transverse wind force due to live load Longitudinal wind force C.81 m .3 IRC 6-2010) Height of deck from GL For basic wind speed of 42. of force from bearing level m 2 kN kN = 3.00 34. t = 3.00 m = = = = = = = 9 m m m 1.00 N/m = = 2 784.5m.5 for piers with rounded corners.00 Height of pier exposed to wind.00 m Vertical Wind Load.3.00 Dimension of pier in transverse direction. of exposed area) for wind force acting on substructure 5.00 Solid area of projected elevation.64 m = = 35.5r/b) or 0.71 m m2 kN kN 3. 209. A3 = = 12.2 Sub-structure = Dimension of pier in longitudinal direction.G.00 From table 5 of IRC 6-2010. Hourly mean speed of wind at deck level Height of live load from ground level For height of 10. 209.3.65 Transverse force on substructure due to wind = 5.83 8.4 Note 1.65 m = 2 473.20 2. A1 = 5.25 CD multiplication factor = 0. h = 5.53 N/m 10.95m & for basic wind speed 42.G.5r/b) = 0. CD = 1. 4 3.1 2.36 m 2 = 13.15 m 2 = 2. of pier cap from top Self weight of pier cap = 4.3685 m = 359.G.4 1 1 1.G.213 kN 2 = 0. SEISMIC FORCES 6.2 2 Area of pier cap above section 1-1 Area of pier cap between section 1-1 & 2-2 Total area of pier cap per unit width Volume of pier cap C.G. of pier cap between 1-1 & 2-2 from top C.77 m = 231 kN = 127.05 kNm Calculation of Seismic Coefficient Zone Factor Response Reduction Factor (table 5) = = 10 0.16 m 3 = 18.84386 m = 0.1 2 2 4.424 m = 0. of pier cap above 1-1 from top C.79 m 3 = 14.6 kN Height of straight portion of pier Area of pier Volume of pier Self weight of straight portion of pier C/s area of dirt wall Weight if dirt wall Longitudinal moment due to dirt wall over piercap = 5.1 SELF-WEIGHT CALCULATION OF PIER 12 1.2 m = 0.5 .60902 m = 460.6.4 0.8 m 2 = 8. 00 20% Live load = 198.06 6.5 Time Period. F = 3EI/L = 555792 Dead load from superstructure (DL+SIDL) = 1882.86 7.65 3 Stiffness of pier.06 Seimic force due to permanent load of superstructure acts the the C.00 13. E Height of pier above foundation.5 Transverse Seismic Coefficient = 0.2325 = 30172 = 6.5 D= Dead load from super structure in kN F. T=2(D/1000F)0.6 0 1.2 m 6.8098 Young's Modulus of Elasticity .3247 sec 2. of section about its C.95 kN kN kN m = = = = = 231. of section about its C.5 0.108 kN kN kN m m ..4 SIDL Total Load Seismic force in Transverse Direction Seismic force in Longitudinal Direction CG of SIDL from bearing top 6.I.2 Transverse direction M.5 Sa/g (fig 13 IRC -2-2010) Longitudinal Seismic Coefficient = 0.16 D = 2080.32 kN = 0 kN = 1.00 = = = 4 m Mpa m kN/m kN 0.2.Stiffness in kN/mm Time Period. F = 3EI/L3 Dead load from superstructure (DL+SIDL).G.Importance Factor = 1.G.12236 Sa/g (fig 13 IRC -2-2010) = 2. of the superstructure 6. L Stiffness of pier. I = 1.2 6.G.3 DEAD LOAD OF SUPERSTRUCTURE Total Load Seismic force in Transverse Direction Seismic force in Longitudinal Direction CG of superstructure from bearing top m4 Mpa m kN/m kN kN kN sec = 1472.2. T=2(D/1000F)0. L = 6.709 2.00 24. E = 30172 Height of pier above foundation..86 13.2 SEISMIC COEFFICIENT 6.5 DIRT WALL Total Load Seismic force in Transverse Direction Seismic force in Longitudinal Direction CG of dirt wall from top of footing Height of Dirt wall 11 = = = = 410. T=2(D/1000F) = 0. D Time Period.65 = 71401 = 1882. I Young's Modulus of Elasticity .00 kN = 88.1 Longitudinal Direction M.I.16 0. 98 m .2m above FRL C.05 kN kN kN m m 964.7.7 LIVE LOAD Only 20% Live load is considered for seismic case 6.2 Pier Height from GL to pier cap bottom Total Load Seismic force in Transverse Direction Seismic force in Longitudinal Direction CG of pier cap from top of footing = 4.15 m = 289.636 0.6.7.3887 kN = 17.33 kN 11.61 6.1 Pier cap Total Load Seismic force in Transverse Direction Seismic force in Longitudinal Direction CG of pier cap from top of pier cap CG of pier cap from top of footing = = = = = 6.3 3-Class A Total Load Seismic force in Transverse Direction Seismic force in Longitudinal Direction = = = Horizontal seismic force acts at 1.81 kN = 17.6 SUB-STRUCTURE 6. of live load from bearing top = 12 460.80 kN = 11.572 kN 0 kN 2.8896 kN = 0 kN 6.3887 kN = 3.2 Class 70R + Class A Total Load Seismic force in Transverse Direction Seismic force in Longitudinal Direction = 990.7.60 27.0775 m 6.1 Class 70R Total Load Seismic force in Transverse Direction Seismic force in Longitudinal Direction = 743.92476 kN = 0 kN 6.636 27.6.73 kN = 8.G.6. 1 On superstructure 5.1 5.82 3.39 4.64 142.20 5 Wind Load 5.03 m HT (kN) eL (m) eT (m) ML (kNm) 1472.83 8.03 922.44 Net force on superstructure -138.04 377.33 MT (kNm) 81.3 4.1 4.82 13 199.1.1 FORCES AND MOMENTS FOR FOOTING TOP The elevation difference between top of bearing to top of S.1 3.1 Frictional Force DL+SIDL+Class 70R DL+SIDL+Class 70R + Class A DL+SIDL+3 Class A 131.00 460.35 294.1 1.19 1.03 1009.00 161.7.59 8.1.32 7.4 Dead Load Self weight of superstructure Weight of dirt wall+approach slab Weight of pier cap Weight of pier 2 SIDL 3 3.05 410.76 94.2 1.68 143.47 10.29 7. LOAD CASES 7. Description of loads 1.1.36 981.83 8.83 32.72 35.00 45.44 5.No.2 4.03 7.3 1.10 743.71 94.73 990.80 964.94 .36 34.47 106.60 359.1.92 231.30 129.10 1176.21 -127.3 Live Load Class 70R Class 70R + Class A 3 Class A P (kN) HL (kN) 7.50 1000.47 10.98 19.25 4 Longitudinal Forces 4.1.2 3.34 799.30 5.08 723.81 2197.2 Wind over permanent load Wind over live load -138.2 On substructure 23.22 3. 1.2 70R) L+0.01 10.71 6.01 10.5 Pier 6.67 180.1 T+0.33 119.80 98.23 8.1 Longitudinal Seismic Case Dead load on 6.3L (DL+SIDL+ Class 2.6.09 53.71 6.00 10.33 17.67 183.3 Dirt Wall 6.2 Class 70R + Class A 6.00 17.89 11.6 Live Load 6.86 27.4 A) P (kN) HL (kN) ML HT (kN) (kNm) MT (kNm) 58.00 0.00 0.92 11.No.4 A) 2 Transverse Seismic Case 2.88 54.54 327.3L (DL+SIDL) T+0.88 55.70 220.2.1 superstructure 6.1 Class 70R 6.4 Pier Cap 6.85 167.88 55.23 1364.2.00 115.11 327.85 167.1.2 SIDL 6.98 7.2 Transverse Seismic Case Dead load on 6.45 417.86 106.6.83 14 .50 58.57 10.08 0.88 51.1 L+0.3L (DL+SIDL+ Class 2.30 58.73 98.69 98.2.23 1394.1.23 1390.08 726.51 0.01 89.98 7.23 1275.3 3 Class A 88.01 327.51 8.6.1 Class 70R 6.00 13.20 58.39 8.01 17.05 3. Description of loads Longitudinal Seismic 1 Case 1.1 superstructure 6.3T (DL+SIDL) L+0.45 409.2 Class 70R + Class A 6.3 70R+ Class A) L+0.67 171.6.4 Pier Cap 6.1.00 0.00 106.64 17.2.6.1.00 0.1.1.39 8.2 SEISMIC COMBINATIONS FOR FOOTING TOP S.60 13.1.6 Seismic Loads 6.38 98.1.05 3.01 0.67 183.2.3 70R+ Class A) T+0.00 6.2.23 8.3L (DL+SIDL+ 3 Class 2.01 10.3T (DL+SIDL+ 3 Class 1.45 382.00 0.6 Live Load 6.2 SIDL 6.3T (DL+SIDL+ Class 1.3 3 Class A 0.2 70R) T+0.2.64 17.25 17.82 7.00 0.2.5 Pier 6.22 327.09 53.3T (DL+SIDL+ Class 1.45 418.3 Dirt Wall 6.6.01 10.32 24.2.86 27. 01 0.83 9.2.98 8.55 21.40 88.1. Description of loads P (kN) Longitudinal Seismic 1 Case 1.1.05 4.2 Wind over permanent load Wind over live load -138.40 412.23 9.00 7.6.46 11.1 Class 70R 7.01 122.87 1808.47 11.23 9.13 22.1 On superstructure 5.88 243.6 Live Load 7.2.82 163.40 30.2.1.76 144.91 579.58 6.44 5.2.1 superstructure 7.74 9.33 34.1.00 150.33 22.89 482.1.82 150.00 0.08 214.2 70R) L+0.62 144.6 Live Load 7.3T (DL+SIDL+ 3 Class 1.71 94.47 11.87 1967.24 7.61 68.71 7.00 0.3L (DL+SIDL+ 3 Class 2.01 11.3L (DL+SIDL+ Class 2.1 5.2.6.82 4.55 21.1.01 11.3 70R+ Class A) T+0.1.22 4.30 129.3T (DL+SIDL+ Class 1.05 893.22 144.2 70R) T+0.35 103.For Footing bottom .87 1972.3T (DL+SIDL+ Class 1.3 70R+ Class A) L+0.08 225.83 32.16 .1.55 73.98 8.3 Dirt Wall 7.2.29 25.2 Class 70R + Class A 7.4 A) 2 Transverse Seismic Case 2.3 Dirt Wall 7.62 159.19 1.88 243.01 11.08 229.6.2 On substructure 23.86 14.40 88.63 11.33 22.1 L+0.77 482.91 590.00 0.33 34.64 73.91 144.1 superstructure 7.4 WIND LOAD FOR FOOTING BOTTOM 5 Wind Load 5.01 11.00 11.1.75 17.40 1305.59 8.1.6.6.No.18 326.51 22.63 0.2 Class 70R + Class A 7.91 591.87 1931.3 3 Class A 0.1.2.4 Pier Cap 7.6.08 1018.2.3L (DL+SIDL) T+0. depths are increased by 1m and seismic forces are increased by 7 Seismic Loads 7.61 67.61 68.00 0.2.44 Net force on superstructure -138.91 542.4 A) HL (kN) ML HT (kN) (kNm) MT (kNm) 73.43 482.83 9.2 Transverse Seismic Case Dead load on 7.08 0.77 306.2 SIDL 7.3 SEISMIC COMBINATIONS FOR FOOTING BOTTOM S.30 5.2 SIDL 7.3 3 Class A 110.00 17.71 7.3L (DL+SIDL+ Class 2.05 4.00 0.00 0.75 7.74 9.1 T+0.16 14.40 73.5 Pier 7.3T (DL+SIDL) L+0.4 Pier Cap 7.61 64.1 Class 70R 7.5 Pier 7.08 229.77 482.1 Longitudinal Seismic Case Dead load on 7.82 15 223.36 34. 72 8.87 45.73 3676.10 81.68 1084.Class 70R Longitudinal Frictional Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522.36 1009.00 16 34.Class 70R+Class A Longitudinal Frictional Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522. Description of loads 1 Dead Load 2 SIDL Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522.81 410.03 0. 1 2 3 4 Description of loads Dead Load SIDL LL .47 981. 1 2 3 4 Description of loads Dead Load SIDL LL .No.87 45.1.29 7.33 3897.81 922.32 7.87 45.1.81 34.No.14 142.64 7.10 35.10 106. LOAD COMBINATIONS 8.25 .20 1186.25 723.8.61 143.81 410.3 DL+SIDL+LL Class 70R+Class A+Longitudinal Forces S.81 410.4 DL+SIDL+LL 3 Class A+Longitudinal Forces S.83 981.00 34.80 3923.08 1000.47 8. 1 2 3 4 Description of loads Dead Load SIDL LL .No.32 142.1.72 2197.1 DL+SIDL (Without Live Load) S.25 723.2 DL+SIDL+LL Class 70R+Longitudinal Forces S.50 1124.1.No.1 PIER BOTTOM 8.46 2197.10 79.00 964.00 34.97 8.29 131.00 743.03 0.3 Class A Longitudinal Frictional Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522.03 0.54 131.64 143.00 2932.81 410.00 990.87 45. 87 45.98 1423.87 45.30 177.39 19.94 2177.41 Negative because wind is assumed to act upwards for critical condition 34.58 .81 410.22 134.80 8.17 34.54 2197.No.22 134.8.03 32.73 Longitudinal Frictional Force 131.30 1. 1 2 3 4 5 5.89 134.1.25 1176.39 19.87 45.82 3.08 1000.1.00 990.No.36 1009.30 1.30 129.7 DL+SIDL+LL 3 Class A+Longitudinal Forces+Wind Load S. 1 2 3 4 5 5.No.94 1919.1.10 4.98 1383.44 3758.41 3.33 142.72 1176.19 On substructure 1.39 19.64 -138.82 294.98 1485.10 106.Class 70R 743.22 3.10 4.1 5.91 981.44 3785.2 Description of loads Dead Load SIDL LL .10 4.03 32.1 5.82 Total 3538.30 175.41 17 3.29 7.94 3394.33 723.20 7.19 5.10 35.00 964.81 922.30 5.82 3.2 Description of loads P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) Dead Load 2522.2 Description of loads Dead Load SIDL LL .00 LL .71 34.80 143.03 Wind Load On superstructure -138.47 1176.6 DL+SIDL+LL Class 70R +Class A+Longitudinal Forces+Wind Load S.44 32.Class 70R+Class A Longitudinal Frictional Force Wind Load On superstructure On substructure Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522.05 8.1 5.32 -138.10 81.68 3.50 7.24 129.81 SIDL 410.5 DL+SIDL+LL Class 70R+Longitudinal S.82 294.82 294.3 Class A Longitudinal Frictional Force Wind Load On superstructure On substructure Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522.92 129.19 5. 1 2 3 4 5 5.81 410.10 164. 88 202.00 198.11 34.81 410.32 58.87 45.03 55.88 51.75 3081.54 327.Class 70R Longitudinal Frictional Force Longitudinal Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522.54 51.No.83 144. 1 2 3 4 5 Description of loads Dead Load SIDL LL .Class 70R+Class A Longitudinal Frictional Force Longitudinal Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522.00 148.45 407.36 922.1.81 HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 34.22 1000.8 DL+SIDL+Longitudinal Seismic Case (Without Live Load) S.01 18 34.87 45.97 143.46 439.81 410.00 3 Longitudinal Seismic Force Total 2932.84 8.22 34.No.10 16.29 58.16 3130.10 21.87 45.81 410.17 7.54 409.10 58.50 8.81 410.01 55.65 417.68 142.03 54.68 327.No.1.1.3 Class A Longitudinal Frictional Force Longitudinal Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522.00 192.20 327.07 1009.90 . Description of loads P (kN) 1 Dead Load 2 SIDL 2522.03 55.11 DL+SIDL+20% LL 3 Class A+Longitudinal Forces+Longitudinal Seismic Forces S.45 1423.20 614.45 1428.99 196.88 58.56 131.50 8.20 7.10 DL+SIDL+20% LL Class 70R+Class A+Longitudinal Forces+Longitudinal Seismic Forces S.88 190.50 382.29 418.22 54.25 561. 1 2 3 4 5 Description of loads Dead Load SIDL LL .11 55.No.9 DL+SIDL+20% LL Class 70R+Longitudinal Forces+Longitudinal Seismic Forces S.64 58.30 848.1.10 7.42 382.50 327.87 3125.45 1346.52 7. 1 2 3 4 5 Description of loads Dead Load SIDL LL .88 201.87 45.8. 1 2 3 4 5 Description of loads Dead Load SIDL LL .98 7.80 171.00 192.81 410.65 1390.25 439.30 8.1.81 410.87 45.83 1535.29 17.00 8.69 34.1.33 1803.69 183.10 98.36 922.20 98.No.12 DL+SIDL+Transverse Seismic Case (Without Live Load) S.80 1275.62 144.00 198.78 196.1.38 183.16 3130.10 21. 1 2 3 4 5 Description of loads Dead Load SIDL LL .48 .14 DL+SIDL+20% LL Class 70R+Class A+Longitudinal Forces+Transverse Seismic Forces S.No.07 1009.23 178.23 1117.50 98.23 1194.00 2932.67 161.10 16.1.No.81 410.10 7.13 DL+SIDL+20% LL Class 70R+Longitudinal Forces+Transverse Seismic Forces S.38 19 34.No.67 148.01 1590.67 159.Class 70R Longitudinal Frictional Force Transverse Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522.97 143.81 410.87 45.22 1000.3 Class A Longitudinal Frictional Force Transverse Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522.8.31 7.67 17.95 7.87 45.00 148.23 1199.64 17.03 180.81 17. Description of loads 1 Dead Load 2 SIDL 3 Transverse Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522.Class 70R+Class A Longitudinal Frictional Force Transverse Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 2522.32 17.87 3125.87 45. 1 2 3 4 5 Description of loads Dead Load SIDL LL .00 1275.68 98.20 171.73 34.56 131.54 1364.15 DL+SIDL+20% LL 3 Class A+Longitudinal Forces+Transverse Seismic Forces S.73 180.68 142.03 183.88 8.75 3081.67 34.03 183.29 1394. 00 MT (kNm) 34.10 35.29 131.52 1328.75 2197.80 143.2.10 81.00 743.81 MT (kNm) 34.81 410.54 8.29 3676.00 964.81 410.64 3923.64 143.00 2932.8.32 20 8.2 FOOTING BOTTOM It may be noted that Seismic loads are increased by 25% in seismic cases for 8.No. Description of loads 1 Dead Load 2 SIDL 3 LL .32 142.2 DL+SIDL+LL Class 70R+Longitudinal Forces S.No.00 MT (kNm) 34.25 1142.1 DL+SIDL (Without Live Load) S.87 45.36 981.No.81 410.10 79.03 0.47 8.14 1268.87 45.14 142.08 723.87 45.97 8.47 981.2. Description of loads 1 Dead Load 2 SIDL Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 2522.03 0.72 1053. Description of loads 1 Dead Load 2 SIDL 3 LL .03 0. Description of loads 1 Dead Load 2 SIDL 3 LL .61 8.81 410.56 723.00 990.73 131.3 DL+SIDL+LL Class 70R+Class A+Longitudinal Forces S.87 45.2.97 1215.10 106.47 1153.33 3897.Class 70R+Class A Longitudinal Frictional 4 Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 2522.4 DL+SIDL+LL 3 Class A+Longitudinal Forces S.Class 70R Longitudinal Frictional 4 Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 2522.72 8.25 .81 2197.No.3 Class A Longitudinal Frictional 4 Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 2522.2.00 MT (kNm) 34. 1 On superstructure 5. Description of loads 1 Dead Load 2 SIDL 3 LL .No.7 DL+SIDL+LL 3 Class A+Longitudinal Forces+Wind Load S.19 5.44 3785.82 MT (kNm) 981.00 964.81 410.00 990.00 3 LL .73 Longitudinal Frictional 4 Force 131.Class 70R 743.No.25 1305.03 129.82 Total 3538.19 5.8.97 4.22 134.44 3758.2.5 DL+SIDL+LL Class 70R+Longitudinal Forces+Wind Load S.30 1.22 4.10 106.89 134.25 1142.41 Negative because wind is assumed to act upwards for critical condition 34.81 2 SIDL 410.Class 70R+Class A Longitudinal Frictional 4 Force 5 Wind Load 5.21 8.1 On superstructure 5.81 MT (kNm) 2197.41 4.19 5.10 35.81 410.22 134.44 32.16 2053.87 45.1 On superstructure -138.08 142.2.87 45.16 3528.29 1661.41 4.82 MT (kNm) 723.16 1305.29 8.82 326.58 25.52 4.30 177.40 6.36 143.64 -138.87 45.30 129.40 6.33 34.40 6.17 32.82 326.16 2312.30 1.47 1153.29 1548.71 32.72 1053.2 On substructure Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 2522.32 -138.2 On substructure Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 2522.30 5.03 129.80 34.6 DL+SIDL+LL Class 70R +Class A+Longitudinal Forces+Wind Load S.14 4.2.43 1305.46 8.30 175.03 5 Wind Load 5.58 25.82 326.24 8.99 .58 25.2 On substructure 1.29 1601.10 164.92 21 8.10 81. Description of loads P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 1 Dead Load 2522.3 Class A Longitudinal Frictional 4 Force 5 Wind Load 5. Description of loads 1 Dead Load 2 SIDL 3 LL .No. 81 410.98 .10 591.56 MT (kNm) 73.77 67.97 482.87 45.81 410.89 68.81 410.68 73.00 198.89 MT (kNm) 196.87 45. Description of loads 1 Dead Load 2 SIDL 3 LL .64 3130.94 8.55 8.36 131.03 68.61 217.91 1723.No.43 482. Description of loads P (kN) 1 Dead Load 2 SIDL 2522.43 64.54 1053.10 16.62 590.21 579. Description of loads 1 Dead Load 2 SIDL 3 LL .22 142.2.87 45.Class 70R Longitudinal Frictional 4 Force 5 Longitudinal Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 2522.32 3125.2.00 3 Longitudinal Seismic Force Total 2932.75 34.3 Class A Longitudinal Frictional 4 Force 5 Longitudinal Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 2522.81 410.77 68.9 DL+SIDL+20% LL Class 70R+Longitudinal Forces+Longitudinal Seismic Forces S.8.2.91 1726.07 143.91 1633.87 34.25 8.03 67.97 73.61 204.8 DL+SIDL+Longitudinal Seismic Case (Without Live Load) S.52 482.92 22 8.89 8.00 192.Class 70R+Class A Longitudinal Frictional 4 Force 5 Longitudinal Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 2522. Description of loads 1 Dead Load 2 SIDL 3 LL .00 148.No.10 DL+SIDL+20% LL Class 70R+Class A+Longitudinal Forces+Longitudinal Seismic Forces S.29 1153.No.55 542.91 562.77 439.16 34.65 1142.11 DL+SIDL+20% LL 3 Class A+Longitudinal Forces+Longitudinal Seismic Forces S.40 1018.10 21.No.10 7.61 64.10 73.14 482.81 HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 34.93 8.64 787.29 3081.77 MT (kNm) 144.61 73.2.88 542.03 68.33 734.87 45.61 215. 91 MT (kNm) 439.87 34.87 45.08 165.75 34.2.87 45.84 1808.97 22.00 148.13 2168. Description of loads 1 Dead Load 2 SIDL 3 LL .00 3 Transverse Seismic Force Total 2932.64 3130.No.58 1967.81 410.13 DL+SIDL+20% LL Class 70R+Longitudinal Forces+Transverse Seismic Forces S.87 45.12 DL+SIDL+Transverse Seismic Case (Without Live Load) S.10 7.51 8.62 229.40 23 8.76 214.17 1931.72 8.10 22.29 1153. Description of loads 1 Dead Load 2 SIDL 3 LL .62 MT (kNm) 196.08 214.87 1295.No. Description of loads 1 Dead Load 2 SIDL 3 LL .03 229.15 DL+SIDL+20% LL 3 Class A+Longitudinal Forces+Transverse Seismic Forces S.No.42 8.81 410.51 1808.32 3125.10 21.97 144.06 1972.87 45.33 2370.2.87 1388.29 3081.40 .22 142.87 8.65 1142.03 229.16 34.2.56 22.14 144. Description of loads P (kN) 1 Dead Load 2 SIDL 2522.10 16.03 225.22 229.8.76 144.2.87 1385.00 198.52 144.36 131.37 8.54 1053.00 192.68 22.81 410.75 2112.3 Class A Longitudinal Frictional 4 Force 5 Transverse Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 2522.91 225.08 22.No.22 MT (kNm) 144.Class 70R+Class A Longitudinal Frictional 4 Force 5 Transverse Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 2522.81 410.07 143.14 DL+SIDL+20% LL Class 70R+Class A+Longitudinal Forces+Transverse Seismic Forces S.87 224.08 153.81 HL (kN) HT (kN) eL (m) eT (m) ML (kNm) MT (kNm) 34.Class 70R Longitudinal Frictional 4 Force 5 Transverse Seismic Force Total P (kN) HL (kN) HT (kN) eL (m) eT (m) ML (kNm) 2522.08 164. 00 1084.17 54.80 178.56 148.10 164.50 3081.61 143.24 134.50 3125.17 177.91 2177.41 1485.No.81 17.92 134. LOAD SUMMARY 9.98 183.46 2197.32 0.84 3130.71 175.11 1423.00 79.31 183.83 561.67 171.00 1186.05 3785.25 3538.14 142.48 5 6 7 8 9 10 11 12 13 14 15 DL+SIDL+LL Class 70R+Longitudinal Forces+Wind Load DL+SIDL+LL Class 70R +Class A+Longitudinal Forces+Wind Load DL+SIDL+LL 3 Class A+Longitudinal Forces+Wind Load DL+SIDL+Longitudinal Seismic Case (Without Live Load) DL+SIDL+20% LL Class 70R+Longitudinal Forces+Longitudinal Seismic Forces DL+SIDL+20% LL Class 70R+Class A+Longitudinal Forces+Longitudinal Seismic Forces DL+SIDL+20% LL 3 Class A+Longitudinal Forces+Longitudinal Seismic Forces DL+SIDL+Transverse Seismic Case (Without Live Load) DL+SIDL+20% LL Class 70R+Longitudinal Forces+Transverse Seismic Forces DL+SIDL+20% LL Class 70R+Class A+Longitudinal Forces+Transverse Seismic Forces DL+SIDL+20% LL 3 Class A+Longitudinal Forces+Transverse Seismic Forces 24 NORMAL HT (kN) WIND HL (kN) SEISMIC LONGITUDINAL P (kN) 2932.41 1423.33 1919.68 201.90 2932.01 1428.81 SEISMIC TRANSVERSE S.00 3081.83 981. Description of Load Combination 1 DL+SIDL (Without Live Load) .22 1346.69 1194.62 1535.80 3758.20 55.9.97 202.46 848.81 58.00 1124.30 3125.88 3130.52 55.68 159.47 4 DL+SIDL+LL 3 Class A+Longitudinal Forces 3897.73 1117.78 1590.56 190.54 407.42 382.64 0.00 0.1 BOTTOM OF PIER ML (kNm) MT (kNm) 0.25 1803.58 2932.38 1199.54 3394.97 0.88 51.97 161.41 1383.99 614.20 1275.25 723.95 180.54 131.89 134.00 2 DL+SIDL+LL Class 70R+Longitudinal Forces 3676.29 0.72 3 DL+SIDL+LL Class 70R+Class A+Longitudinal Forces 3923. 40 5 6 7 8 9 10 11 12 13 14 15 DL+SIDL+LL Class 70R+Longitudinal Forces+Wind Load DL+SIDL+LL Class 70R +Class A+Longitudinal Forces+Wind Load DL+SIDL+LL 3 Class A+Longitudinal Forces+Wind Load DL+SIDL+Longitudinal Forces+Longitudinal Seismic Case (Without Live Load) DL+SIDL+20% LL Class 70R+Longitudinal Forces+Longitudinal Seismic Forces DL+SIDL+20% LL Class 70R+Class A+Longitudinal Forces+Longitudinal Seismic Forces DL+SIDL+20% LL 3 Class A+Longitudinal Forces+Longitudinal Seismic Forces DL+SIDL+Longitudinal Forces+Transverse Seismic Case (Without Live Load) DL+SIDL+20% LL Class 70R+Longitudinal Forces+Transverse Seismic Forces DL+SIDL+20% LL Class 70R+Class A+Longitudinal Forces+Transverse Seismic Forces DL+SIDL+20% LL 3 Class A+Longitudinal Forces+Transverse Seismic Forces 25 NORMAL HL (kN) WIND P (kN) SEISMIC LONGITUDINAL Description of Load Combination SEISMIC TRANSVERSE S.06 2168. .64 0.68 215.94 3130.17 2370.71 175.89 67.54 131.42 3125.89 134.21 3758.91 1295.75 2197.37 225.24 134.32 0.25 3538.88 542.46 3785.92 134.77 1726.41 1601.00 0.89 1723.81 0.43 3528.25 2053.92 68.99 2932.72 3 DL+SIDL+LL Class 70R+Class A+Longitudinal Forces 3923.43 562.17 177.14 142.10 787.9.61 143.56 153.77 1633.00 2 DL+SIDL+LL Class 70R+Longitudinal Forces 3676.00 1215.16 2312.22 1388.55 3081.81 22.56 723.56 204.29 0.2 BOTTOM OF FOOTING HT (kN) ML (kNm) MT (kNm) 1 DL+SIDL+Longitudinal Forces (Without Live Load) 2932.98 2932.97 165.97 0.00 1268.68 164.47 4 DL+SIDL+LL 3 Class A+Longitudinal Forces 3897.21 1018.No.40 229.00 1328.25 68.41 1548.81 73.41 1661.10 164.51 3081.93 3125.97 217.84 1808.62 1385.61 64.87 3130.76 224.08 214.72 229.47 981.00 79.62 734.58 2112. 00 Mpa Permissible flexural compressive stress in concrete σcbc Permissible flexural tensile stress in steel σst Permissible compressive stress in steel σst Normal Wind Seismic Normal Wind Seismic Normal Wind Seismic 11.65 307.371579 mm2 10 Grade of Concrete 35.00 272.20 360.81265 mm2 8370 mm2 SAFE 26 .00 205.1 m No.79 m2 8846.79 m 1.724913 mm Percentage of Steel Area of concrete to resist axial load only 0.10.55 240.58 mm2 Minimum Area of steel Area of steel required 2682.990877 mm2 No. of bars along tranverse direction (on one side) Bar Diameter Area of steel along transverse direction 16 Nos.00 319. DESIGN OF FREE-END PIER Length of section along tranverse direction Length of section along longitudinal direction 2. of bars along longitudinal direction (on one side) Bar Diameter Area of steel along longitudinal direction IRC 21-2000 Table 9 Note 1 Modular Ratio 6 Nos.317086914 % 335351.70 15. 16 mm 3216.56 17.00 m Effective Cover End Spacing 60 mm 0. 16 mm 1206.50 MPa MPa MPa MPa MPa MPa MPa MPa MPa Area of Concrete Area of steel 2. 78 1590.00 2.80 0.46 848. ZTT 1.60 6.56 1346.96 15 3125.15 21.97 1194.00 1206.76 4 3897.71 1485.29 0.99 614.00 0.74 53.36 0.No.46 2197.00 1.43 3.G.71 53.37 1335.62 1535.47E+06 4.38 0.18 5. transverse steel from NA Area of steel along longitudinal direction on one face Distance to C.51 7.25 5.14 0.72 0.54 3394.17 1423.74 14 3130.90E+08 Section Modulus in the longitudinal direction.33 1919.91 9 3081.10 29.28 5.39 0.48 51.) kNm kNm ex (m) WIND P (kN) m(bd^3/12+MT/ZT-ML/ZL) (bd^3/12+MT/ZT+ML/ZL) LONGITUDINAL SEISMIC S.40 0.81 178.32 2 3676.81 407.29 0.44 0.98 3 3923.38 0.97 0.84 0.11.60 52.74 72.48 0.13 13 3081.03 0.45 0.97 1423.83 561.68 1428.88 0.25 1803.19 5.33 59.00 65.30 0.70 53.46 0.14 1186.90 0.47 51.13 3.91 2177.20 1275.61 1124.05 0.45 50. mm2 mm3 TRANSVERSE SEISMIC STEEL TENSION CONCRETE COMP m m mm mm2 mm mm2 mm mm2 .25 0.58 7.06 0.20 5.50 0.00 8846.59 5.96 7.62 27 NORMAL Mx (Trans.30 0.79 60 3216.10 1383.38 0.49 5.50 0.42 382.83 12 2932.54 1084.99 440.83 981.67 7 3758.81 79.76 8 2932.30 32.G.08 66.15 11 3125.35E+09 mm3 ey (m) σ concrete σ steel (Mpa) tension (Mpa) 1 2932.25 723.85 5 3538.51 5.) My (Long.56 1117.00 0. of longitudinal steel from NA Total Area of Steel = Modular Ratio Effective Area = Section Modulus in transverse direction.09 10 3130.00 2.47 0.58 0.68 53. ZLL 1.68 1199. MATERIAL STRESSES Longitudinal Direction (Thickness) Equivalent width of pier in transverse direction Effective Cover Area of steel along transverse direction on one face Distance to C.89 6 3785.72 10. 79 28 Torsion (kNm) 39.32 36.00 174.17 (Cl.19 Loads @ distance 'd' from the face of pier considering impact factor S.00 875.32 647.00 285.23 593.00 205.00 343 297 285.No. 208) For Class A and combination For Class 70R 1.70 B1 1.96 22.27 81.87 71.00 337.00 343.27 19.99 Torsion (kNm) 80.4025 m 1.40 Impact Factor (As per IRC-6-2010 Cl. 208.16 744.14 38.4 Fig 5) Loads @ face of pier considering impact factor S. 1 2 3 3.2) 1.4025 B2 3.105 1.4 1.55 96.1 14.36 1071.50 266. PIER CAP DESIGN Effective depth.No.79 296.2 3.16 569.82 1123.04 0.No. Description 1 2 3 4 5 Dead Load SIDL Class 70R Class 70R + Class A 3 Class A Shear Force (kN) 357.00 174.81 .5 Depth @ 'd' away from face of pier 0.3 Bending Moment (kNm) 607.00 1.1 3.19 Bending Moment (kNm) 1148.4 m 0.24 683.14 44.17 (Cl.28 543.3 Dead Load SIDL Live Load Class 70R Class 70R + Class A 3 Class A Reaction of Bearing (kN) B1 B2 357.00 379. d = Width of pier cap 1. Description 1 2 3 4 5 Dead Load SIDL Class 70R Class 70R + Class A 3 Class A Shear Force (kN) 736.20 1.20 4.53 1295.30 405.00 297.40 Results from STAAD after 10% reduction due to longitudinal effect for 3 lanes traffic for live load Description S. 208.00 31.12. 65 1.30 204.92 88.No.20 m kNm kN m 3442.11 S.71 Torsion SF (kN) BM (kNm) 102.70 104.32 211.70 kN 98.50 m 157.67 kN Torsion 199. BM (kNm) 112. SF (kN) 117.54 3541.71 3391.G.38 174. m kNm kN m kNm 1.55 1034.66 Eq.70 199.7 29 at distance 'd' away from pier face Eq.62 1034.32 1727.87 199.19 1817.06 kN 172.43 225.No.22 102.34 3442.85 319.06 105. BM (kNm) 243.38 3 DL+SIDL+3 Class A 174.77 kN C. of pier cap section from Bending Moment due to self weight Shear due to dirt wall Lever arm of shear force due to Bending Moment due to dirt wall 1.05 .78 2 DL+SIDL+Class 70R +Class A 185.40 3638.55 108.Bending Moment and Shear Force due to self weight of cantilever portion of pier cap Depth of pier cap Shear due to pier cap Increase shear by 10% for bearing at pier face 1.55 988.32 976.83 Eq.63 Calculation of Equivalent Shear force and bending moment due to torsion at pier face Load Combination S.70 Eq.6T/b Eq.65 2.73 95.78 at distance 'd' away from pier face SF (kN) BM (kNm) 5065.33 131.40 5065.89 212.60 98.32 1817.66 61.87 Torsion 102. SF (kN) 228.22 Eq.73 95. BM = T(1+D/b)/1.20 110.56 1704.20 3187.63 96.20 m 89.71 at pier face Load Combination 1 DL+SIDL+Class 70R DL+SIDL+Class 70R 2 +Class A 3 DL+SIDL+3 Class A Maximum at distance d away 1.78 185.55 96. SF = 1. Torsion 1 DL+SIDL+Class 70R 199. 73 1402.86 2 DL+SIDL+Class 70R +Class A2158.26 3604.89 3954.31 0.60 3 DL+SIDL+3 Class A 2049. b Design Shear Force at column face Maximum Bending Moment Effective Depth Required.69 1098.53 1929.88 1833. D Width of pier cap.00 MPa k j Q 0.No.00 11.21 Maximum 2305.24 1929. d 40.69 1929.86 1312. of Provided Reinforcement Side face reinforcement (0.00 mm 28.69 Grade of Concrete Grade of Steel Modular Ratio Permissible flexural compressive stress in concrete σcbc Normal 35.89 3954.32 mm2 25.90 1. dreq Depth provided.00 1st layer 14 Nos.00 MPa 500.60 3668.45 1808.86 Load Combination at distance 'd' away SF (kN) BM (kNm) 1151. at pier face SF (kN) BM (kNm) 1 DL+SIDL+Class 70R 2305.70 MPa Permissible flexural tensile stress in steel σst Normal 240.00 1500. of 13744.00 mm 10. of bars required 25 mm dia bars 25 mm dia bars Provide 12 mm dia bars along each side face 10 Nos.00 2305.00 30 .05%) Diameter of bars No. of bars required mm m m kN kNm mm mm 13117.26 1085.47 1050.Total Shear Force and Bending Moments S. of 2nd layer 14 Nos.00 mm2 12.50 Design for flexure Ast req Diameter of bar No.00 MPa Permissible compressive stress in steel σst Normal 205.89 3954.64 Clear Cover Total Depth.00 1400.00 MPa 10. 3 Maximum Torsion Average effective width.67 kN 788.41 804.00 480. Aswt 31 kNm mm mm mm2 OK .4.35 MPa 1618.185 SAFE < 199.65 Effective depth Design Shear Stress.30 Mpa 1402. b1 Average effective depth.19 mm2 Shear force for which reinforcement is required Area of shear reinforcement required Provide 4 legged 16 mm dia stirrups Asv Spacing Required Provide Fe415 grade 804.248 Transverse Reinforcement As per IRC 21-2000 Cl 304.2. τc 0.25 mm2 142. τc max 2.3 SAFE 0. d1 Torsional transverse reinforcement required. τv % reinforcement Table 12B IRC 21-2000 Shear stress in concrete.17 < 2.7.50 mm 1.00 813.85 mm mm dia 16 stirrups @ 4 legged Area of shear reinforcement provided 140 mm > 804.25 mm2 788.78 1263.Design for shear At the face of pier Table 12A IRC 21-2000 For M35 concrete. of footing normal to traffic direction (from left) Area of footing section Volume of footing 2.3 2 0.2 1.1 SECTIONAL PROPERTIES Area of pier Footing dimension along transverse direction Footing dimension along longitudinal direction Area Section Modulus.75 m 5.2 1.05 m2 27.91 m 2.3 P3 1.13.15 Traffic Direction 3.15 P4 P1 1. ZL Section Modulus.G.G.4 Ground Level 0.50 30. FOOTING DESIGN P2 3 1.38 kN Load due to soil above footing(upto GL) 598.50 5.73 m3 27. ZT 2.73 m3 C.79 5.1 1.78 m3 Weight of footing 694. of footing along traffic direction (from left) C.70 kN 32 .00 3.25 m2 27.7 13. 40 m 3306.95 m Weight of soil retained by RE wall Eccentricity of wt of soil on footing along longitudinal direction Moment due to soil above GL 2361.08 1295.23 1661.71 2197.99 8 2932.62 2375.55 9 3081.38 2053.61 7578.06 2029.81 6587.14 7551.47 1239.10 2367.82 734.67 1328.02 723.20 1726.11 0.21 7 3758.08 1633.14 1268.54 7331.10 7192.56 1322.94 10 3130.40 m 7.33 224.45 kN 1.49 1723.84 1037.76 2168.97 6785.49 1385.97 6785.72 3 3923.56 6736.78 2112.78 2312.97 893.02 542.93 11 3125.13.2 EARTHFILL Distance between pier and RE wall Height of soil retained by RE wall 0.68 6780.25 1772.43 981.81 6587.17 1981.51 13 3081.68 6780.43 1847.88 2370.46 6 3785.80 787.21 2319.98 12 2932.92 1018.25 5 3538.33 79.47 4 3897.81 6587.87 14 3130.70 1601.06 1215.56 6736.03 kNm Eccentricity of pier from centre of footing 1 2932.07 3528.88 1376.16 1689.85 m .42 15 3125.40 33 NORMAL ML (Mx) kNm MT (Mx) kNm WIND Ml (kNm) LONGITUDINAL SEISMIC Pbottom (kN) TRANSVERSE SEISMIC Ptop (kN) S.33 562.00 2 3676.17 7439.71 7413.20 1388.75 1396.No.98 1808.63 1548.58 2037. 0. 71 OK 34 .40 5 298.97 2 271.41 43.45 373.65 14 229.46 371.21 170.72 213.62 223.3 FOOTING CORNER STRESSES Footing Corner Stresses P1 (kN/m ) P2 (kN/m2) P3 (kN/m2) P4 (kN/m2) 185.91 383.97 249.00 371.97 111.00 431.31 375.27 269.98 3 241.63 43.71 148. Pressure (kN/m2) Min.00 379.98 320.63 6 268.49 390.55 115.65 65.00 343.34 110.31 72.65 379.55 249.29 338.26 7 255.13.57 247.95 283.47 221.12 11 164.27 OK Transverse Seismic 550. Pressure (kN/m2) Normal 440.91 177.39 101.91 219.88 271.83 74.42 13 236.06 8 187.55 185.72 OK Wind 550.71 15 226.42 259.60 343.24 323.22 107.24 112.32 12 245.76 102.09 10 167.31 336.09 102.81 WIND 1 NORMAL 2 TRANSVERSE LONGITUDINAL SEISMIC SEISMIC Load Case Summary of Base Pressure at bottom of footing 2 SBC (kN/m ) Max.82 330.61 4 228.71 208.91 OK Longitudinal Seismic 550.95 9 175.98 112.05 175.82 286.51 281.71 65.11 189.14 431.07 234. 96 P4 P41 1.00 5.5 9.5 P14 3.355 .P2 P23 PF P3 P32 PB P21 PA PE P34 PC 1.4 35 1.355 PG 2.1 PH 1.79 P12 P43 PD P1 5. 56 350.46 277.23 239.58 227.28 14 190.53 343.18 359.26 292.71 106.51 222.20 188.29 112.31 192.13 202.28 172.29 324.86 220.06 277.60 4 215.05 257.58 107.26 313.55 12 213.84 146.51 332.70 170.06 158.86 233.13 281.02 3 223.52 327.63 246.01 287.83 368.92 346.18 338.45 155.21 204.72 143.04 258.24 337.25 157.54 239.31 261.Footing Corner Stresses P23 (kN/m2) P32 (kN/m2) P34 (kN/m2) P43 (kN/m2) P41 (kN/m2)P14 (kN/m2) 1 185.83 15 189.45 311.38 196.08 7 218.86 2 232.69 243.85 291.31 184.70 324.69 296.78 337.66 120.61 119.00 143.30 142.34 124.97 233.57 249.39 309.43 182.58 349.41 147.82 295.01 208.12 294.37 323.51 206.64 9 157.36 287.55 185.77 169.37 271.96 284.09 310.01 157.65 263.50 187.27 317.47 264.55 299.93 397.91 125.72 373.75 13 194.79 5 235.77 187.98 300.78 111.84 337.28 301.81 237.77 237.82 252.17 307.50 270.33 328.27 336.07 10 153.27 250.60 11 151.97 249.55 221.57 221.71 261.98 336.31 170.56 257.50 6 227.18 151.92 222.27 8 178.41 346.11 288.73 229.67 36 NORMAL P21 (kN/m2) WIND P12 (kN/m2) TRANSVERSE LONGITUDINA SEISMIC L SEISMIC Load Case .57 179. 24 108.42 88.05 263.18 179.98 4 212.30 220.13 305.11 245.37 125.07 186.93 254.50 221.66 230.29 37 NORMAL PC (kN/m2) WIND PB (kN/m2) TRANSVERSE LONGITUDINA SEISMIC L SEISMIC 2 Load Case PA (kN/m ) .09 199.84 95.43 3 213.53 14 190.37 212.52 251.50 130.64 342.71 5 203.02 142.26 138.58 128.75 217.29 221.15 223.13 159.08 kN 30.89 138.88 141.15 8 181.55 266.27 169.10 137.55 254.01 159.93 193.86 6 210.81 13 189.25 m2 42.82 229.03 136.45 194.19 252.71 225.83 175.60 242.71 181.39 170.77 282.45 164.70 239.98 96.73 163.40 224.88 280.64 209.58 121.37 267.31 108.07 234.30 167.12 175.Pressure at 4 corners due to footing and soil PD (kN/m2) PE (kN/m2) PF (kN/m2) PG (kN/m2) PH (kN/m2) 1 179.44 167.64 264.97 2 206.96 236.46 189.01 198.75 142.38 12 179.95 223.47 220.39 15 190.13.41 287.22 184.75 kN/m2 Net pressure = Pressure due to load and moment .89 233.02 190.97 294.39 208.74 233.73 259.57 96.4 NET PRESSURE Self weight of footing + soil Area of base at footing Pressure at 4 corners of footing 1293.90 127.81 149.94 125.02 223.38 11 192.79 224.92 249.24 296.33 165.04 107.99 254.23 135.40 148.96 193.78 141.90 217.48 227.81 184.54 10 192.57 247.33 239.38 184.95 160.42 7 210.22 195.56 215.00 266.49 142.47 256.97 207.45 251.46 116.49 195.37 261.58 161.92 9 190. 00 0.79 Traffic Direction 3 3 PD 0.45 1.901 m 2 1 P2 b P3 PF d d 0.45 1.36 PB 4 0.1 1 1.901 0.355 .13.901 PG 2.5 c 0.917 m 0.2 0.917 3.917 2 38 b 1.901 PA PE PC 4 0.901 c P1 P4 PH a 2.5 DESIGN AT CRITICAL SECTIONS Effective cover Diameter of reinforcement along traffic direction Diameter of reinforcement across traffic direction Effective depth along traffic direction Effective depth across traffic direction a 75 mm 16 mm 16 mm 0.4 0. 21 j 0.92 199.47 2446.53 2 311.47 7 159.61 405.87 6 232.91 Q 1.00 1809.49 k 0.85 301.25 303.80 10 742.94 275.37 97.52 195.68 .Moment at 1-1 due to earth retained by RE wall 38.13 259.93 13 556.73 5 77.32 285.68 k 0.56 857.60 12 124.18 2749.50 Maximum Ast WIND 1 NORMAL Ast Required (mm2) LONGITUDINAL SEISMIC Depth Required (mm) TRANSVERSE SEISMIC Moment Load Case about 1-1 (kNm) -751.05 11 752.81 123.03 9 757.17 3 620.76 1060.47 8 325.06 168.42 261.57 2416.87 590.87 4 548.94 15 551.76 193.74 257.92 Q 1.28 j 0.80 139.93 Q 1.72 3111.76 1792.63 k 0.21 j 0.68 259.29 1561.37 kNm 3111.87 mm2 39 k 0.62 68.93 Q 1.70 14 541.53 304.54 1761.23 j 0.54 2463. 59 7 1376.71 397.68 k 0.00 12 1110.68 4372.44 4985.93 Q 1.42 8 1165.30 6657.59 399.98 13 1289.42 377.73 3790.24 399.42 9 1344.94 409.09 10 1360.72 6 1367.28 399.28 j 0.86 368.42 3 1319.49 k 0.17 4425.15 408.99 5 1349.21 j 0.56 Maximum Ast WIND 1 NORMAL Ast Required (mm2) LONGITUDINAL SEISMIC Depth Required (mm) TRANSVERSE SEISMIC Moment Load Case about 2-2 (kNm) 6657.65 14 1306.93 Q 1.1087.14 6521.48 364.52 5086.63 k 0.53 403.92 401.86 11 1361.23 j 0.24 5054.55 410.91 Q 1.42 15 1306.99 mm2 40 k 0.99 6614.30 406.21 j 0.79 3612.36 4194.92 Q 1.68 .90 4248.96 4249.80 408.88 5449.96 2 1301.82 4 1328.27 405.22 4427. 60 12 1197.91 3 1244.93 Q 1.40 3876.09 3979.60 4 1204.35 11 1116.21 420.96 441.13 5 1590.32 3162.21 j 0.89 15 1313.18 335.96 14 1322.67 6 1441.23 j 0.28 j 0.44 3635.21 j 0.50 371.16 7 1400.30 383.06 2 1394.01 2797.92 Q 1.63 k 0.85 369.68 .06 3610.61 375.95 3292.93 Q 1.87 353.91 390.06 4095.89 402.66 405.78 3069.86 4520.66 413.54 9 1150.17 13 1343.75 8 1017.60 414.79 401.34 4520.37 10 1125.98 3750.49 k 0.10 2856.68 k 0.59 3692.67 mm2 Maximum Ast TRANSVERSE SEISMIC LONGITUDINAL SEISMIC WIND NORMAL 1 41 k 0.83 382.22 4342.91 Q 1.21 3093.Moment Load Case about 3-3 (kNm) Depth Required (mm) Ast Required (mm2) 917. 36 4397.67 4434.36 347.17 340.62 11 893.64 3291.78 5 517.21 j 0.60 3878.86 269.34 2586.47 775.91 Q 1.27 3088.10 6 7 737.18 335.99 16 160 mm 6911.77 298.28 j 0.55 8 852.1 917.92 1.06 259.7) Minimum reinforcement Reinforcement required along traffic direction Diameter of bar Provide 16 mm diameter bars @ Reinforcement provided Reinforcement required across traffic direction Diameter of bar Provide 16 mm diameter bars @ Reinforcement provided 6600 6657.24 3330.21 j 0.03 294.49 WIND Depth Required (mm) k 0.54 15 670.97 NORMAL Ast Required (mm2) k 0.19 10 885.50 5019.49 13 622.11 2 725.50 mm2 mm2 c/c mm2 mm2 mm c/c mm2 42 SAFE SAFE PROVIDE MINIMUM REINFORCEMENT SAFE .12% of cross-sectional area (As per IRC 78-2000 Cl.09 3701.19 984.48 301.92 267.68 k 0.68 TRANSVERSE LONGITUDINA SEISMIC L SEISMIC Moment Load Case about 4-4 (kNm) Maximum Ast 5019.74 12 647.93 Q 1.16 310.74 303.93 Q 1. 707.80 3 4 946.12 4826.78 mm2 Minimum Area of reinforcement = 0.10 4678.23 j Q 0.63 k 0.37 4173.69 14 662.49 3214.45 287.05 240.33 3688.2.08 5019.55 4234.03 9 840.40 264.68 309.78 16 160 mm 6911. 30 15 166.34 0.63 -254.13.05 m2 4.35 254.73 -151.14 kN/m Moment(a-a) x tanβ / da-a tanβ = 0.51 0.33 SAFE 242.22 -46. kNm a-a.30 9 162.83 m Moment about a-a due to soil 433.14 SAFE 0.83 0.72 0.55 -16.12 5.13 SAFE 0.64 653.Stress b.96 -150.75 SAFE 254.73 5. kN/m2 b.56 m2 Permissible Shear Stress is obtained from Table 12B of IRC 21-2000 -73.48 -129.30 SAFE 251.61 681.74 0.30 12 167.57 SAFE 245.15 SAFE 0.88 0.74 661.20 3 198.15 SAFE 0. Mpa TRANSVERSE SEISMIC Stress at Load BM about SF along section aCase a-a.11 SAFE 206.20 2 189.74 662.30 -82.12 SAFE 0.31 SAFE 254.30 SAFE SAFE 43 WIND 168.15 SAFE 0.20 4 197.70 -250.81 662.28 -26.14 SAFE 0.27 -179.66 SAFE 217.12 SAFE 0.84 SAFE 202.30 10 163.79 -103.15 SAFE 0.15 SAFE 0.30 11 163.34 -176.61 694.07 SAFE 251.10 692.27 6 190.39 666.39 653.57 0.80 SAFE 243. kN (τv).63 -56.29 -85.75 SAFE 240.15 SAFE 0.17 586.15 0. kN a.81 556.30 14 166.94 SAFE 256.20 SAFE 243.39 0.57 -257.20 5 181.21 -182. kN/m2 .10 Effective depth at section a-a 0.27 8 164.64 -100.96 272.71 kNm Area resisting shear at a distance 'd' away from the face of the pier along traffic direction (section c-c & d-d) across traffic direction (section a-a & b-b) 5.30 13 165.15 0.63 97.20 -130.15 SAFE 0.68 -151.00 683.07 -24.96 689.6 FOOTING SHEAR Weight of soil retained by RE wall beyond section a-a per meter Reduction in shear along section a-a due to flaring depth 347.24 -130.17 692.73 0.14 -63.15 SAFE 0.27 245.48 0.37 152.along b.15 SAFE 0.47 0.37 544.09 0.33 125.27 7 189.38 LONGITUDINAL SEISMIC 1 NORMAL Permissi ble Shear Stress (τc) Mpa Stress at Shear SF section b.05 0.19 SAFE 247.98 0. 99 0.12 SAFE 187.13 SAFE 153.56 0.0.84 611.34 686.181.90 645.30 10 222.01 645.87 0.56 0.16 x (fck)0.20 0.89 325.20 4 238.34 0.26 311.25 m2 7.13 SAFE 123.52 0.32 321.30 12 237.14 0.41 466.88 0.08 0.45 418.06 SAFE 0.92 487.06 SAFE 0.08 SAFE 0.09 SAFE 0.12 SAFE 194.66 0.51 622.09 SAFE 0.11 SAFE 168.07 m2 Punching shear.52 0.27 0. Aps 0.63 0.24 299.30 11 221.05 SAFE 0.87 447.12 SAFE 176.along d.10 642.09 SAFE 0.27 6 285.11 SAFE 128.30 678.12 SAFE 166.20 3 246.34 0.61 0. τcp = Vp/Aps Grade of concrete Allowable Punching Shear .10 355. kN (τv) Mpa c.61 376.44 0.30 14 261.50 0.13 SAFE 132.16 561.64 457.09 SAFE 0.97 0.Stress d.13 SAFE 131.07 SAFE 0. P .51 0.55 532.14 SAFE 146. kN (τv).10 0.96 719.88 424.14 SAFE 102.27 8 201. Mpa LONGITUDINAL SEISMIC Stress at Shear SF section d. Mpa TRANSVERSE SEISMIC Stress at Shear Load SF along section cStress Case c-c.10 SAFE 0.49 0. kN/m2 30.08 SAFE 0.26 0.30 13 266.20 2 276.86 m 8.06 SAFE 0.10 SAFE 181.27 0.06 SAFE 0.71 0. Vp = Net Load.50 0.39 443.01 0.(P1+P2+P3+P4)/4 x Area effective in carrying punching shear Punching Shear Stress.12 SAFE 175.5 35.81 613.64 485.07 SAFE 0.48 238.00 Mpa 44 .47 615.78 349.13 656.11 m2 23. kN/m2 d.06 0.13 609.14 m2 Average depth at d/2 away from pier Area resisting punching shear.30 Area of footing at base Area available at d/2 away from face of pier Area effective in carrying punching shear WIND 1 NORMAL Permissi ble Shear Stress (τc).30 15 260.95 0.27 7 277.07 SAFE 0.84 0.20 5 314.13 SAFE 143.30 9 227. 73 0.20 1.42 SAFE 12 1547.0.05 0.42 SAFE 15 1592.8) Minimum area of reinforcement = Along traffic direction Across traffic direction = = Spacing Calculation & Actual provided area of reinforcement 45 250 mm2/m in each direction 1375 mm2 1375 mm2 .21 1.51 0.44 0.21 0.42 SAFE 14 1594.42 SAFE 11 1592.2.03 0.21 0.49 0.95 SAFE 5 1689.44 0.19 1.49 TRANSVERSE SEISMIC 1 NORMAL Allowable Load Punching Shear τ .26 SAFE 7 1741.19 1.20 1.20 1.80 0.20 1.22 0.22 1.69 0.19 LONGITUDINAL SEISMIC 1547.42 SAFE WIND 0. Mpa Reinforcement at top of footing As per IRC 78-2000 Cl.95 SAFE 2 1722.42 SAFE 10 1594.22 1.20 1.20 1.26 SAFE 6 1747.25 0.05 0. kN cp Stress.80 0.95 SAFE 3 1780.49 0.42 SAFE 13 1582. MPa Case Shear.22 0.42 SAFE 9 1582. 707.26 SAFE 8 1547.95 SAFE 4 1774. GIRDER DESIGN 8 3.. LOAD CALCULATION 5 2.5 2.4 1.1 CONSTRUCTION STAGE…………………………………………………………………. SHEAR DESIGN 16 5..ANNEXURE 2 : SAMPLE DESIGN OF SUPER-STRUCTURE CONTENTS DETAILS OF THE STRUCTURE 1 1.1 DEAD LOAD…………………………………………………………………………....8 3.…….2 MID-SPAN…………………………………………………………………………………. DIFFERENTIAL SHRINKAGE STRESSES 18 7..…26 .2 1. SECTION PROPERTIES 2 1....6 2..2 SIDL……………………………………………………………………………………..1 NEAR SUPPORT…………………………………………………………………………..…….3 1..……7 3.3 LIVE LOADS……………………………………………………………………………….5 LOAD COMBINATIONS……………………………………………………………….4 2.…21 STAAD Input file for Diaphragm Design………………………………………………….....5 2.3 INTERMEDIATE SECTION………………………………………………………………...5 2.2 SERVICE STAGE………………………………………………………………………….4 DIAPHRAGM……………………………………………………………………………….4 ANALYSIS RESULTS……………………………………………………………………….10 4...... DIAPHRAGM DESIGN 19 STAAD Input file for Girder Design………………………………………………………. SHEAR CONNECTOR DESIGN 17 6.. 34 m Height of pier from GL to pier cap top 7.DETAILS OF SUPERSTRUCTURE Grade of Concrete 35.64 m Pier cap top level 621.00 kN/m Overall span of RCC Girder 18.00 m Effective Span 17.00 m Thickness of wearing coat 0.50 m % camber 2.00 MPa Density of concrete 3 25.50 m Spacing between bearings 3.00 MPa Grade of Steel 500.00 m FRL at pier location 621.70 m 1 .59 m Existing ground level 613.06 m Depth of RCC Girder 1.50 % Total width of deck slab 12. 73 1. from top Distance of N.666667 2.80E+12 2.37 767.11E+09 1.G.70E+10 2.13 0. from top of girder 1.61 1.00 40.41 m Moment of inertia about y-y axis 4 0.G.00E+00 7.51E+04 0.00E+00 2. SECTION PROPERTIES 1.00E+00 0.37 Moment of Inertia Ztop slab Ztop girder 4 0.A. from bottom Distance of N.26 m Zbottom 3 0.57E+10 3.10E+08 1615 1. (mm) 767.00E+00 0. Girder Slab Total Area (mm2) 924375 690000 1614375 230.98E+10 m2 mm mm mm 4 0.23 m Moment of inertia Ztop Zbottom Composite Section at support Thickness of deck slab Actual Width of deck slab Effective width of deck slab Grade of concrete in deck slab Grade of concrete in girder S.57E+09 1.47 m 3 0.00 3000.00 40.G.63 Ibase (mm4) 6.00E+00 Area C.21E+07 1875 1341.52E+06 0 0 0.98E+10 5.04E+09 mm mm mm Mpa Mpa Ibase (mm4) 7. 1 2 3 4 5 Total A x CG (mm3) Area (mm2) C.No.00 3000.1 NEAR SUPPORT 750 2 150 25 2 3 3 75 1500 1 0 5 5 0 0 4 4 600 600 S. from bottom 0.38E+09 0.92 767. of composite section from bottom Distance of N.1.63 732.53E+12 m2 m m m m m Total Area Total depth of section C.79E+11 3.10E+08 Iself (mm4) 1.47E+11 .A.99E+08 0. (mm) 900000 750 6.No.00 A x CG (mm3) C. from top of slab Distance of N.00E+00 0.00E+00 0 0 0.18 m 3 0.82E+09 Iself (mm4) 1.63 7.18E+11 5.24E+11 Iyy (mm4) 2.A.75E+11 4.24 m 4 0.A.69E+11 4.60 1. from bottom Distance of N.75E+08 22500 1425 3.13 0.G.22E+07 6.00E+00 924375 7.A.24E+11 1.55 m 2 Iyy (mm4) 2.78 m 3 1. 24E+07 125 9.No. from bottom 0.2 MID-SPAN 750 2 150 75 2 3 3 225 1500 1 150 5 5 4 4 150 250 300 600 S.A.72E+08 1615 1.20 0.31E+12 m2 m m m m m Total Area Total depth of section C.04E+09 mm mm mm Mpa Mpa Ibase (mm4) 5.21 4 0.38E+11 1.59E+09 Iself (mm4) 1. 1 2 3 4 5 Total Area (mm2) 450000 67500 16875 75000 22500 631875 A x CG (mm3) C. Girder Slab Total Area (mm2) 631875 690000 1321875 230.08E+11 Iyy (mm4) 3.1.11E+09 1.94E+09 9.00 A x CG (mm3) C.G.74 747.41E+10 m2 mm mm mm 4 0.26 Ibase (mm4) 3.36 m Zbottom 3 0.26 4.55E+11 3.G.30 Moment of Inertia Ztop slab Ztop girder 4 0.27E+08 5.00 3000.A.53 1.20 0. of composite section from bottom Distance of N. from bottom Distance of N.No.41 m 3 m 0.34 m Moment of inertia about y-y axis 4 0. from top Distance of N.38E+06 300 6.00 3000.56E+09 2.A. (mm) 750 3.32E+11 . from top of girder 1.75E+06 4.38E+09 4.21 m Moment of inertia Ztop Zbottom Composite Section at mid-span Thickness of deck slab Actual Width of deck slab Effective width of deck slab Grade of concrete in deck slab Grade of concrete in girder S.18E+11 5.G.77 3 1.81E+07 Area C.A.32 1.96E+10 1. from bottom Distance of N.02E+08 3.38E+08 1425 9.73 1.08E+11 1.G. from top of slab Distance of N.26 752. (mm) 747.91E+08 2.44E+10 1.27E+06 3.16 m 3 m 0.72E+08 Iself (mm4) 8.05E+09 5.62E+07 1325 2.37E+11 2.94E+09 9.53 m 3 Iyy (mm4) 1.00 40.00 40.A.63 747.80E+12 2.28E+08 1.41E+10 5. 32E+11 4 0.G.38E+08 Iself (mm4) 1.15 m 3 0.4 DIAPHRAGM 400 1480 including slab depth S.11 m 3 0. 1 Area (mm2) 592000 3 A x CG (mm ) C.54 m Total Area Moment of Inertia Moment of inertia about y-y axis 1.47 m 4 0.08E+11 Ibase (mm4) 4.1.15 m Moment of Inertia Ztop Zbottom 4 .44 m 4 0.00 4.3 INTERMEDIATE SECTION 3 1.No. (mm) 740. 25 kN/m 2.30 m m m m2 2.3 LIVE LOADS Class 70R .80 kN/m 17.2 SIDL SIDL due to wearing coat on girder SIDL due to crash barrier 6.00 0. LOAD CALCULATION Thickness of deck slab Distance between bearings Thickness of wearing coat Cross-sectional area of crash barrier 0.465 Class 70R + Class A 10 Class 70R Class A 4.on 2nd girder Class 70R 5.15 Class A Class A Class A 2.01 Class 70R .11 kN/m 15.65 5 .2.50 kN/m 2.23 3.10 0.Maximum Eccentricity Class 70R 4.65 9.60 kN/m 7.01 3 Class A 6.1 DEAD LOAD Dead load of girder at the support Dead load of girder at midspan Dead load due to deck slab 23. 64 68.10 698.2 4.56 1063.86 717.48 6 Impact Factor Included Impact factor and longitudinal effect included Impact Factor Included Impact factor and longitudinal effect included .25m from support) 253.2 3.55 162.31 1005.25m from from support) support) Bending Moment (kNm) At midspan 0.25 25.90 310.19 1322.79 435.53 112.34 199.1 4.89 113.1 3.No.62 173.31 1261.36 113.56 4 4.44 95.25 3 3.70 146.34 943.5m (4.89 1440.3 4.86 180. 2.90 178.46 256.81 73.44 601.55 18.1 3.23 1223.01 223.02 681.27 295.00 976.44 424.12 1084.14 963.23 338.92 1768.36 591.2 3.4 Live Load (Maximum SF) 70R eccentric Load Case 20 70R on girder 2 Load Case 60 70R + 1 Class A Load Case 100 3 Class A Load Case 145 237.13 1054.65 74. Load Case 1 DL of girder+deck slab+diaphragm 2 SIDL (Crash Barrier+Wearing Coat) Shear Force daway 0.36 187.83 153.18 147.44 926.82 1080.1875 Effective Length of span 17 m The live load results are including increase for impact factor and 10% reduction for longitudinal effect for 3 lane configuration Summary of Forces for Outer Girder S.20 146. Load Case 1 DL of girder+deck slab+diaphragm 2 SIDL (Crash Barrier+Wearing Coat) Shear Force (kN) daway 0.20 704.42 222.3 3.58 179.25 leff (4.11 228.12 993.2 4.25m from from support) support) Bending Moment (kNm) At midspan 0.32 1512.22 185.93 3 3.4 Live Load (Maximum BM) 70R eccentric Load Case 15 70R on girder 2 Load Case 55 70R + 1 Class A Load Case 95 3 Class A Load Case 144 244.4 Live Load (Maximum SF) 70R eccentric Load Case 20 70R on girder 2 Load Case 60 70R + 1 Class A Load Case 100 3 Class A Load Case 145 213.29 1020.45 166.4 ANALYSIS RESULTS Live load results from STAAD Impact Factor for Class 70R 1.60 923.25 leff (1.07 1270.49 1063.STAAD grillage model is prepared with the vehicle postions as shown above.03 1262.80 Impact Factor Included Impact factor and longitudinal effect included Impact Factor Included Impact factor and longitudinal effect included Summary of Forces for Inner Girder S.00 127.39 1036.78 102.37 100.50 1311.13 50.4 Live Load (Maximum BM) 70R eccentric Load Case 15 70R on girder 2 Load Case 55 70R + 1 Class A Load Case 95 3 Class A Load Case 144 276.24 119.No.1 4.04 116.21 4 4.01 933.71 1326.185 Impact Factor for Class A and combinations 1.3 3.75 966.70 939.32 815.25 leff (4.76 446.25m from support) 252.25 leff (1.58 110.3 4.38 111.5m (4. 76 1525.26 1146.49 Combo 5 Combo 6 Combo 7 Combo 8 2 + 4.20 118.4 333.72 142.14 1087.92 1594.1 2 + 3.85 2104.1 2 + 3.25 203.45 1116.25 1921.5m (4.85 170.46 Combo 5 Combo 6 Combo 7 Combo 8 2 + 4.4 262.40 118.71 343.15 286.14 214.25m from from support) support) Bending Moment (kNm) At midspan 0.85 1479.2 2 + 4.06 307.93 248.06 1921.56 1655.19 1192.64 1464.No.16 785.70 1216.14 248.63 1386.82 198. Load Case Shear Force daway 0.54 1026.60 297.94 1914. 7 .03 1145.57 1671.3 2 + 4.14 1628.51 193.25 1262.54 217.85 1372.59 1054.31 274.45 815.39 2104.2.25 leff (4.24 134.69 1037.No.5m (4.31 253.25 leff (1.87 1531.73 Maximum 396.56 1372.35 1370.43 181.37 871.75 187.2 2 + 4.49 274.1 2 + 4.25 leff (1.48 1334.43 1173.73 Maximum 335.47 320.92 131.3 2 + 3.27 792.2 2 + 3.4 396.3 2 + 3.5 LOAD COMBINATIONS Load Combinations for Outer Girder S.56 130.16 1207. Load Case Shear Force daway 0.25m from support) Combo 1 Combo 2 Combo 3 Combo 4 2 + 3.3 2 + 4.19 1531.21 165.65 178.1 2 + 4.25 leff (4.10 335.25m from support) Combo 1 Combo 2 Combo 3 Combo 4 2 + 3.2 2 + 3.28 247.37 Load Combinations for Inner Girder S.62 247.25m from from support) support) Bending Moment (kNm) At midspan 0.4 270.70 195.59 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.79 1164. 00 0.1 CONSTRUCTION STAGE Design of girder for construction stage (Dead Load alone) bf σc σ c' kd Neutral Axis D d bw σst/m Width of the web.00 1368.00 1270.00 40.36 8 .00 1500.00 32.00 12063. Df Overall depth of the section.00 750.00 132.00 5.00 5.00 mm mm mm mm mm mm kNm mm at Nos. mm from bottom of girder mm mm2 MPa 13.00 MPa 10. D Clear Cover Effective depth Moment to be resisted by the section. mm from bottom of girder mm at Nos.33 MPa 240.72 40.00 150. of bars Effective cover provided Area of steel provided Grade of concrete adopted Permissible compressive stress in bending Permissible tensile stress in reinforcement Modular Ratio.00 5.3. bw Width of the flange. m Factor for critical neutral axis 300.00 68. of bars Diameter of main bar No. of bars Diameter of main bar No.36 32. GIRDER DESIGN 3. mm from bottom of girder mm at Nos. bf Depth of the flange.00 196.00 32. Me Diameter of main bar No.00 132. 5 x σc x kd) x (d .kd/3)) . for kd<Df (bf x kd) x (kd/2) = m x Ast x (d .84 Mpa Top of Girder 6.σc 8. kd 521.Df)/3)) 1. kd 608.Df/2) + (bw x kd) x kd/2 = m x Ast x (d .Df) x (d .27E+09 = 2.38 As neutral axis depth (kd) < Depth of flange.1.21E+05 kd Bending Moment .(kd .66E+08 σc .83E+08 σc where σc' = (σc x (kd . neutral axis lies in the web For kd >Df ((bf .kd) Solving Neutral Axis depth.kd) 6.00 Revised Neutral axis depth.bw) x Df) x (kd .Check for neutral axis If neutral axis lies within the range.44 Stresses for given moment 1.27E+09 = 1.84 MPa 9 . M = (bf x (0.5 x σc' x (kd .70E+08 = 0.((bf . k 0.76 mm Neutral Axis depth factor.Df)/kd) Actual stress in concrete.bw) x (0.00 kd^2 = 1.65E+08 150.28E+07 x 1.94 Mpa Actual stress in bottom most steel layer.94 MPa 93.75E+04 x kd .69 mm Neutral Axis depth factor.88E+05 kd .06E+06 + 150.00 kd^2 + 1.Df .5. σc 6. σst = (D-d1'-kd) x σc x m/kd 93. k 0. Curtailment Design of girder for construction stage (DL alone) bf σc σ c' kd Neutral Axis D d bw σst/m Width of the web, bw Width of the flange, bf Depth of the flange, Df Overall depth of the section, D Clear Cover Effective depth Moment to be resisted by the section, Me Diameter of main bar No. of bars Diameter of main bar No. of bars Diameter of main bar No. of bars Effective cover provided Area of steel provided Grade of concrete adopted Permissible compressive stress in bending Permissible tensile stress in reinforcement Modular Ratio, m Factor for critical neutral axis 300.00 750.00 150.00 1500.00 40.00 1400.00 966.76 32.00 5.00 68.00 32.00 5.00 132.00 32.00 0.00 196.00 100.00 8042.48 40.00 mm mm mm mm mm mm kNm mm at Nos. mm from bottom of girder mm at Nos. mm from bottom of girder mm at Nos. mm from bottom of girder mm mm2 MPa 13.33 MPa 240.00 MPa 10.00 0.36 10 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 451.11 mm Neutral Axis depth factor, k 0.32 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 = 1.13E+08 150.00 kd^2 + 1.48E+05 kd - 1.18E+08 = 0.00 Revised Neutral axis depth, kd 520.58 mm Neutral Axis depth factor, k 0.37 Stresses for given moment 8.04E+04 kd 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)) 9.67E+08 = 2.39E+08 σc - σc 6.69E+07 x 9.67E+08 = 1.73E+08 σc where σc' = (σc x (kd - Df)/kd) Actual stress in concrete, σc 5.60 Mpa Actual stress in bottom most steel layer σst = (D-d1'-kd) x σc x m/kd 98.08 Mpa Top of Girder 5.6 MPa 98.08 MPa 11 3.2 SERVICE STAGE Design of Composite girder for Service stage bf σc σc ' kd Neutral Axis D d bw σst/m Width of the web, bw Width of the flange, bf Depth of the flange, Df Overall depth of the section, D Clear Cover Effective depth Moment to be resisted by the section, Me Diameter of main bar No. of bars Diameter of main bar No. of bars Diameter of main bar No. of bars Effective cover provided Area of steel provided Grade of concrete adopted Permissible compressive stress in bending Permissible tensile stress in reinforcement Modular Ratio, m Factor for critical neutral axis 300.00 3000.00 230.00 1730.00 40.00 1598.00 2104.19 32.00 5.00 68.00 32.00 5.00 132.00 32.00 5.00 196.00 132.00 12063.72 40.00 mm mm mm mm mm mm kNm mm at Nos. mm from bottom of girder mm at Nos. mm from bottom of girder mm at Nos. mm from bottom of girder mm mm2 MPa 13.33 MPa 240.00 MPa 10.00 0.36 12 00 Revised Neutral axis depth.2. for kd<Df (bf x kd) x (kd/2) = m x Ast x (d .14E+07 + 150.5 x σc x kd) x (d .06 Mpa Top of Girder 3.86E+08 σc where σc' = (σc x (kd .20 As neutral axis depth (kd) < Depth of flange.21 Stresses for given moment 1.bw) x Df) x (kd . σst 215.00 kd^2 + 7.5 x σc' x (kd .10E+09 = 7.42E+05 kd .07 Mpa Actual stress in bottom most steel layer σst = (D-d1'-kd) x σc x m/kd 122.06 MPa Final Stresses Actual stess in concrete at top of girder flange.Check for neutral axis If neutral axis lies within the range.53 mm Neutral Axis depth factor.93E+08 150.07 MPa 122. kd 333. k 0. kd 320.kd/3)) .bw) x (0. M = (bf x (0.Df)/kd) Actual stress in concrete.Df/2) + (bw x kd) x kd/2 = m x Ast x (d .90 MPa Actual stress within permissible limit 13 .44E+08 σc .7.80E+07 x 2.kd) 6. neutral axis lies in the web For kd >Df ((bf . σc 3.21E+05 x kd .64E+08 = 0.kd) Solving Neutral Axis depth.21E+05 kd Bending Moment .((bf .71 mm Neutral Axis depth factor. k 0.89 Mpa Actual Stress in bottom most steel layer.Df)/3)) 2.Df .Df) x (d .(kd .σc 5.00 kd^2 = 1. σc 7.10E+09 = 6. Curtailment Design of Composite girder for Service stage bf σc σ c' kd Neutral Axis D d bw σst/m Width of the web.33 MPa 240.00 8042. bw Width of the flange. Df Overall depth of the section. of bars Effective cover provided Area of steel provided Grade of concrete adopted Permissible compressive stress in bending Permissible tensile stress in reinforcement Modular Ratio.37 32.00 100.00 MPa 10.00 5.00 1531.00 mm mm mm mm mm mm kNm mm at Nos.00 230. mm from bottom of girder mm at Nos.00 0.00 132.00 40. D Clear Cover Effective depth Moment to be resisted by the section.00 5.00 196. of bars Diameter of main bar No.00 68.00 32.36 14 .00 1630.48 40. mm from bottom of girder mm at Nos.00 0. m Factor for critical neutral axis 300.00 1730. bf Depth of the flange. of bars Diameter of main bar No. Me Diameter of main bar No.00 3000.00 32. mm from bottom of girder mm mm2 MPa 13. 5 x σc' x (kd .30E+08 σc .Df)/kd) Actual stress in concrete.Df) x (d .53E+09 = 6. σc 2.kd/3)) .Df/2) + (bw x kd) x kd/2 = m x Ast x (d . k 0. σc 5.kd) Solving Neutral Axis depth.((bf .Df)/3)) 1.7.00 Final Stresses (Curtailment design) Actual stess in concrete at top of girder flange.04E+04 kd Bending Moment .31E+08 150. neutral axis lies in the web For kd >Df ((bf .00 Revised Neutral axis depth.17 Stresses for given moment 8.03E+08 = 0. M = (bf x (0.2.21E+05 x kd .53E+09 = 6. for kd<Df (bf x kd) x (kd/2) = m x Ast x (d .99 Mpa Actual Stress in bottom most steel layer. k 0.01E+05 kd .kd) 6.35 Mpa Top of Girder 2.00 kd^2 + 7.48 MPa 126.43 MPa Actual stress within permissible limit Adding stress due to differential shrinkage Final stress in steel 226.35MPa Modular Ratio 10.79 Mpa 15 .79 mm Neutral Axis depth factor.17E+08 σc where σc' = (σc x (kd .17 As neutral axis depth (kd) < Depth of flange.bw) x Df) x (kd .26E+07 x 1.00 kd^2 = 1.bw) x (0. kd 270.03 mm Neutral Axis depth factor.Check for neutral axis If neutral axis lies within the range. σst 224.(kd .14E+07 + 150.48 Mpa Actual stress in bottom most steel layer σst = (D-d1'-kd) x σc x m/kd 126.5 x σc x kd) x (d .Df . kd 272.σc 1. 50 MPa Refer IRC 21-200 Table 12A .4. Asv.56 MPa Permissible Shear Stress. Asv.max 2.35 kN SAFE 83.00 MPa 578. SHEAR DESIGN Design for shear at distance 'd' away from the support of girder Shear at 'd' distance away from support Nominal shear stress.25 kN 0.min 2 Design for shear at distance 0.min 16 2 .96 Total Shear resistance at the section 544.19 mm 125.64 % 0.55 mm SAFE Minimum shear reinforcement. Vuc 2. τv 648.35 MPa Permissible Shear Stress. corresponding to M40 concrete Section is adequate Percentage Reinforcement at the section Design shear strength in concrete Shear in concrete.97 kN SAFE 41.51 MPa 249.39 kN 1.25m) from the support of girder Shear at 4. τv 274.09 mm SAFE Minimum shear reinforcement.19 250.60 MPa 287.52 % 0. τc. Vuc Provide 2 legged 12 mm dia stirrups @ 1.50 MPa Refer IRC 21-200 Table 12A .33 kN 865.64 kN Provide 2 legged 12 mm dia stirrups @ Asv Sv σsv Shear resistance of vertical stirrups Total Shear resistance at the section 125 mm spacing 2 226.25m distance away from support Nominal shear stress.25leff (4.00 mm 200.max 2. τc.00 200.00 294.39 kN 250 mm spacing mm2 mm MPa kN Asv Sv σsv Shear resistance of vertical stirrups 226. corresponding to M40 concrete Section is adequate Percentage Reinforcement at the section Design shear strength in concrete Shear in concrete. 91 mm 150.00 mm SAFE .5.11 kN 620.00 Mpa 98.78 kN 3000 230 C.( Distance between CG of compressive area and that of composite section) Design Shear = VAY / I Provide 2 legged Area of connector.5LL) 119.3DL + 1. of compressive area 321 C. As Permissible Shear Stress for fy Shear Capacity of connector.32 m 338.41 m Inertia of composite section Maximum shear due to SIDL ('d' away) Maximum shear due to live load ('d' away) Total shear (1. SHEAR CONNECTOR DESIGN 4 0. Ac CG of composite section Y.39 kN 290.55 mm 0.G. of composite section 1500 1274 300 Transformed compressive area of concrete flange.19 mm 435.G. C Spacing Required Provided 2 0.69 m 1273.23 kN/m 12 mm dia shear connectors @ 500 17 150 mm spacing 2 226.70 kN 310. Area of the effective concrete flange acent .Modulus of elasticity of the concrete flange Acf .3.00E-04 31622. DIFFERENTIAL SHRINKAGE STRESSES Sectional properties at mid span of composite section of girder and slab Grade of concrete Total Area Total Depth of section CG Distance of NA from top of slab Distance of NA from bottom Moment of inertia Ztop Zbottom 40.42 -0.25 kN Stress in compression flange Stress due to direct compression Stress at top due to flexural bending Stress at bottom due to flexural bending Tension negative Total stress at top due to differential shrinkage Total stress at bottom due to differential shrinkage -1.78 Mpa 2 0.6.69 m 0.5 Mcs = ediff x Ecf x Acf x acent ediff .Distance of the centroid of the concrete flange from the centroid of the concrete section Φ .4.00 1.Reduction coefficient to allow for creep 1.24 MPa .41 0.36 0.20 0.71 MPa 0.34 m 0.77 0.20 0.53 1.24 Mpa 0.95 Mpa Mpa Mpa Mpa -0.71 0.42 MPa -0.Differential Shrinkage Strain Ecf .32 1.95 MPa 18 -0.36 kNm 938.73 1.34 Mpa m2 m m m m m4 m3 m3 As per BS 5400-4 1990 Cl 7.43 Mcs Fcs 320.23 MPa (+) (-) + (+) + = (-) (-) -0.36 MPa -1.23 Mpa -0. 5m 1m 2m 3m 2m 1m 1.00 1891. b Effective depth required Clear cover Effective depth provided 400.23 50.70 kNm 568. Ag 1480.69 m k j Q Width of the section.00 0.00 Mpa 500.5m Design of Longitudinal Reinforcement for Diaphargm Overall depth of diaphragm Width of the diaphragm Gross Area.28 0.reqd Minimum steel to be provided Area of steel to be provided Diameter of the bar provided Cross-sectional area of the bar No.00 mm 400.00 Mpa σcbc 13. DIAPHRAGM DESIGN Girder+Deck Slab+Wearing Coat Crash Barrier Diaphragm 1.7.50 mm mm mm mm 1891.00 490.00 916.00 Mpa 240.33 1184.33 25.91 1.87 4 1963.00 1380.00 MPa σsv 200.50 SAFE mm2 mm2 mm2 mm mm2 Design of top reinforcement Ast.00 mm 592000.33 MPa 10.00 mm2 Moment obtained from STAAD model Design sagging moment Design Hogging Moment 294. of bars required Ast provided 19 mm2 .15 kNm Grade of concrete Grade of Steel IRC 21-2000 Table 9 &10 σst 40. 00 1184.00 mm 410.54 mm2 4.00 mm spacing 452.00 mm at 20 .37 SAFE mm2 mm2 mm2 mm mm2 mm2 Design of shear reinforcement for Diaphragm Maximum shear force at support Nominal Shear Stress As per IRC 21-2000 permissible shear stress from table 12B Maximum shear stress 910.34 mm 250 mm spacing on each face of diaphragm 10.00 bars of 592. Area of provided stirrups 4 LVS @ MPa % MPa kN 180.00 16.00 265.Design of bottom reinforcement Ast.00 mm 78.41 mm2 Provide 12 mm. of bars required Ast provided 981.00 201.00 mm2 10.43 Spacing of stirrups Shear stirrups required 180.36 0.28 755.50 OK 0.03 1184.05 kN 1.06 6 1206.65 Mpa % of reinforcement Permissible shear stress Shear to be carried by reinforcement 2.reqd Minimum steel to be provided Area of steel to be provided Diameter of the bar provided Cross-sectional area of the bar No.39 mm2 SAFE Design of Side reinforcement Provide side face reinforcement Diameter of bar to be provided Cross-sectional area of the bar No. of bars required in one direction Spacing of bars along web Provide 4. 19 2.5 0 10. 28 3. 65 9.5 0 10.5.5. 17 1. 4 0 0 7.5.5. 60 8.5 0 7.5 0 0. 5 0 0 10.5 0 10.5. 90 13.5 0 7.5. 96 14. 64 9.5 0 7. 87 13. 52 7.5 0 4.5 0 4.5. 41 5. 75 11. 20 2.5 0 12.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. 91 14.5. 84 12.5. 98 15.5.5 0 0.5 0 7.5.5.5 0 7. 47 6.5 0 7. 25 3.5.5.5 0 0. 61 9.5 0 12.5.5.5. 62 9. 93 14.5 0 12.5.5 0 10.5 0 12.5 0 1.5 0 12.5 0 10.5.5 0 10. 18 1.5 0 1.5 0 1.5 0 0. 16 1. 38 5.5. 70 10.5 0 4. 3 0 0 4. 67 10. 21 . 57 8.5 0 7.5. 68 10.5.5.5 0 4.5 0 12. 80 12.5 0 7.5.5.5.5.5 0 0. 48 6.5 0 1. 85 13. 53 7.5 0 12.5. 7 0.5 0 0. 13 1. 74 11. 8 0.5.5 0 12. 88 13.5. 76 11.5 0 7. 94 14. 2 0 0 1.5 0 0.5 0 0.5.5.5 0 10.5 0 10.5.5 0 10.5 0 7.5 0 4. 22 2.5 0 7.5. 86 13. 30 3.5 0 1.5.5 0 4.5.5. 29 3. 14 1. 33 4.5 0 10.5. 49 7.5 0 1.5 0 4. 58 8.5 0 10.5 0 0. 95 14.5. 89 13. 92 14.5 0 4. 11 0.5.5 0 12. 59 8.5 0 0.5.5 0 12.5 0 10.5. 23 2. 34 4.5 0 4. 44 6.5.5. 10 0. 46 6.5 0 1.5. 42 5.5 0 1.5 0 7.5 0 4.5 0 12. 43 6. 24 2. 81 12. 39 5. 71 10.5 0 0.5.5. 50 7. 27 3. 63 9. 21 2.5.5. 97 15.5 0 0.5.5. 26 3. 72 10.5 0 12.5 0 1.5 0 1.5 0 12.5 0 4.5.5. 6 0 0 12.5. 79 12.5. 77 11.5 0 10.5. 15 1. 32 4.5 0 4.5 0 12.5.5. 51 7.5 0 1.5 0 4.5 0 12.5 0 1. 40 5. 82 12.5 0 0. 54 7. 69 10.5. 35 4.5 0 1.5.5 0 7.5 0 1.5 0 0.5. 31 4. 55 8.5 0 7. 9 0. 83 12.5 0 0. 78 11.5.5 0 10. 37 5. 66 9.5 0 1. 45 6. 73 11. 56 8. 36 4.5 0 1.5.5 0 0.5 0 4.5 0 4.5. 12 0.5 0 10.5 0 7.5. 46 26 27. 95 50 56. 34 19 20. 56 31 32.5 0 4. 20 10 16. 91 51 52. 108 58 64. 117 18 0 4. 26 16 17. 111 61 62. 157 87 88. 128 68 74. 15 10 11. 72 37 43. 45 25 26. 164 89 95. 153 83 89.5 0 0. 63 33 39. 94 49 55. 32 17 23. 124 69 70. 16 11 12. 121 66 72. 162 87 93. 101 15. 60 35 36. 140 75 81. 38 23 24. 120 18 0 12. 6 1 7. 127 67 73. 37 22 23. 22 . 99 54 60. 64 34 40. 76 41 47.5 0 10. 143 78 84. 144 79 80. 126 71 72.5 0 10.5. 119 18 0 10. 58 33 34.5. 52 27 33. 57 32 33.5. 116 18 0 1.5. 68 38 39. 39 19 25. 78 43 44. 156 86 87. 103 16. 89 49 50. 112 62 63.5 0 7. 142 77 83. 92 52 53. 107 57 63.99 15. 2 2 3. 117 62 68. 13 8 9. 165 90 96. 114 64 65. 97 52 58. 41 21 27. 23 13 14. 93 53 54.5 0 4. 133 73 74. 88 48 54. 149 79 85. 50 25 31. 138 73 79. 102 15. 111 17.5 0 4. 123 68 69. 48 28 29. 116 61 67. 154 84 90. 22 12 18. 98 53 59. 82 47 48. 8 3 9. 139 74 80. 105 55 61. 148 83 84. 136 76 77. 109 17. 44 24 30. 61 31 37. 107 16. 132 72 78.5. 47 27 28. 104 59 60. 106 56 62. 80 45 46. 10 5 11. 115 65 66. 161 86 92. 145 80 81. 131 71 77. 3 3 4. 113 17. 17 7 13. 65 35 41. 108 16. 25 15 16. 113 63 64. 59 34 35. 67 37 38. 55 30 36.5 0 7.5. 135 75 76. 40 20 26. 49 29 30. 122 67 68. 118 18 0 7. 71 41 42. 102 57 58. 141 76 82. 35 20 21. 100 15. 28 13 19. 51 26 32. 106 16. 101 56 57. 96 51 57. 86 46 52. 134 74 75. 130 70 76.5 0 12. 90 50 51. 11 6 12. 74 39 45. 9 4 10. 7 2 8. 29 14 20. 21 11 17.5 0 10. 85 45 51.5. 109 59 65. 120 65 71. 84 44 50. 30 15 21. 110 60 66. 166 91 92. 5 5 6. 114 17. 104 16. 12 7 8. 19 9 15. 105 16. 33 18 24. 146 81 82. 62 32 38. 4 4 5. 167 92 93. 137 77 78.5. 151 81 87. 119 64 70. 75 40 46.5. 54 29 35. 77 42 48. 159 89 90. 36 21 22.5 0 12. 163 88 94. 69 39 40. 79 44 45. 168 93 94. 160 85 91.5 0 0.5. 152 82 88.5 0 1. 129 69 75.5 0 1. 87 47 53. 158 88 89.5.5.5 0 7. 100 55 56. 70 40 41. 125 70 71. 150 80 86. 115 18 0 0. 14 9 10. 83 43 49. 112 17. 147 82 83.5 0 12. 118 63 69. 66 36 42. 155 85 86. 43 23 29. 24 14 15. 18 8 14. 81 46 47.5. 27 17 18. 53 28 34. 42 22 28.5. MEMBER INCIDENCES 1 1 2.5. 73 38 44. 103 58 59. 31 16 22. 110 17. 614 IX 0. 174 94 100. 211 116 117. 205 110 116.01 IY 0. 201 111 112.01 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. 190 105 106. 194 104 110. 204 109 115. 209 114 120. 187 102 108.05 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. 178 98 99. 203 113 114. 185 100 106.41 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 1.01 IY 0. 175 95 101.169 94 95.01 ZD 0. 180 100 101. 186 101 107. 188 103 104. 172 92 98. 199 109 110. 181 101 102.547 IZ 0. 200 110 111.01 IY 0. 170 95 96. 196 106 112. 184 99 105. 173 93 99.23 ZD 1 23 . 213 118 119.32 IX 0. 192 107 108. DEFINE MATERIAL START ISOTROPIC CONCRETE E 2.438 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. 195 105 111. 176 96 102. 177 97 98. 189 104 105.539 IZ 0. 191 106 107. 171 91 97. 182 97 103.467 IX 0. 193 103 109.466 95 TO 98 106 TO 109 117 TO 120 PRIS AX 1.5616 ALPHA 1e-005 DAMP 0. 179 99 100.17185e+007 POISSON 0. 197 107 113.17 DENSITY 23. 212 117 118. 198 108 114.531 IZ 0. 206 111 117. 208 113 119. 202 112 113. 207 112 118. 183 98 104. 214 119 120. 210 115 116. 01 XINC 1 *0.37 WID 1.43 0 4.3 3 3 3 WID 1.37 3.93 TYPE 2 LOAD 13.2 4.65 XINC 1 TYPE 2 -18.52 2.13 1.86/2 LOAD GENERATION 40 TYPE 1 -13.15 XINC 1 TYPE 2 -18.43 0 5.43 0 4.45+1.3-0.01 XINC 1 *CLASS 70R (Girder 2) *4.06 1.5 13.93/2 LOAD GENERATION 40 TYPE 1 -13.5 57 57 34 34 34 34 DIST 1.465 XINC 1 *CLASS 70R + 1 CLASS A LOAD GENERATION 40 TYPE 1 -13.48 0 9.8 LOAD 1 LOADTYPE Traffic TITLE LIVE LOAD *CLASS 70R (Ecc) *0.1 3.48 0 2.2 1.98 1.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 3.79+0.5+1.2+2.5/2=10 TYPE 2 -18.5+2.45+7.65 XINC 1 24 .8 0 10 XINC 1 *3 CLASS A LOAD GENERATION 40 TYPE 2 -18.48 0 6. 25 *Diaphragm .5 LOAD 166 LOADTYPE Dead TITLE WEARING COAT+CRASH BARRIER MEMBER LOAD *Crash Barrier .LOAD 165 LOADTYPE Dead TITLE GIRDER+DECK SLAB+DIAPHRAGM MEMBER LOAD *Support girder .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 -7.4*(1.23 7 TO 10 18 TO 21 29 TO 32 40 TO 43 51 TO 54 62 TO 65 73 TO 76 84 TO 87 95 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*0.25*0.63 84 TO 87 95 TO 98 106 TO 109 117 TO 120 128 TO 131 UNI GY -15.5 *Wearing Coat of thickness 100mm .25*0.6 PERFORM ANALYSIS FINISH 25 .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*3*0.22*0.75 *Intermediate Section Girder .1*3 7 TO 10 18 TO 21 29 TO 32 40 TO 43 51 TO 54 62 TO 65 73 TO 76 84 TO 87 95 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 -6.23) 12 TO 16 199 TO 203 UNI GY -12.92+0.375 *Deck Slab .63)/2 51 TO 54 62 TO 65 73 TO 76 139 TO 142 150 TO 153 161 TO 164 UNI GY -19.25*0.48-0.25*(0. 5 7.5 0 0.48 ZD 0. DEFINE MATERIAL START ISOTROPIC CONCRETE E 2. 8 7 8.17185e+007 POISSON 0. 3 3 4. MEMBER INCIDENCES 2 2 3.17 DENSITY 23.5 0 0. 4 4.5 0 0. 5 5 6. 8 12 0 0.5 0 0.5 0 0. 7 9 2.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. 3 2. 6 6 7. 9 0 0 0. 7 10. 4 4 5.5 0 0.5616 ALPHA 1e-005 DAMP 0.05 END DEFINE MATERIAL MEMBER PROPERTY AMERICAN 2 TO 8 PRIS YD 1. 6 9.4 CONSTANTS MATERIAL CONCRETE ALL SUPPORTS 3 6 PINNED LOAD 1 LOADTYPE Dead TITLE DEAD LOAD 26 . 5 JOINT LOAD 2 4 5 7 FY -59.75 MEMBER LOAD 2 TO 6 UNI GY -12.5 JOINT LOAD 2 4 5 7 FY -333.4 PERFORM ANALYSIS FINISH 27 .JOINT LOAD 8 9 FY -67.