1017_19.08m 9.4.14

TitleCONSULTANTSP R A G A T I C O N S U L T A N T S404, M. G. R. ESTATESBESIDE MODEL HOUSE,PUNJAGUTTA, HYDERABAD - 500082TEL : 66668787, FAX : 66669761CLIENTSOUTH CENTRAL RAILWAY SECUNDERABADGOVERNMENT OF INDIACONTRACTORSPROJECTGUNTAKAL DIVISION RAICHUR - GUNTAKAL SECTION BRIDGE NO.1017 AT km 536/2-537/5TITLEDESIGN OF SUPERSTRUCTURE FOR 19.08M PSC SPAN9-4-14DN NO. : PC/TUN/PSC/SUP/002HARIC H ADATESS. NO.MODIFICATIONSPREPAREDCHECKEDPAGESAPPROVEDNOS :1TO88CHIEF CONSULTANT

IndexDESIGN OF SUPERSTRUCTURESI. NO.CONTENTSPAGE NO.1INTRODUCTION12SECTION PROPERTIES2 - 53CALCULATION OF LOADS ON THE STRUCTURE6 - 104STAAD ANALYSIS11 - 165CALCULATION OF PRESTRESSING FORCE IN THE CALBES17 - 316TABULATION OF BENDING MOMENTS327PSC DESIGN33 - 438CHECK FOR ULTIMATE MOMENT449CALCULATION OF CABLE ELONGATIONS45 - 4610TABULATION OF SHEAR FORCES47 - 4811SHEAR DESIGN49 - 5612DESIGN OF SHEAR CONNECTORS57 - 5813REINFORCEMENT DETAILS OF GIRDER5914DESIGN OF DECK SLAB60 - 7515DESIGN OF DIAPHRAGM76 - 8016TABULATION OF SUPPORT REACTIONS8117DESIGN OF BEARNGS82-8518DEFLECTIONS86 - 8719DESIGN OF PIER CAP88

INTINTRODUCTIONSOUTH CENTRAL RAILWAYBRIDGE NO: 1017 AT KM:536/2- 537/5, PROPOSED AS 34 x 19.08 + 2 x 19.38 m PSC GIRDERS FOR PROPOSED TRACK OVER TUNGABHADRA RIVER1. GENERALThe span consists of two precast prestressed concrete girders with a deck slab of 220mm thick.220A footpath of 0.9m width is provided on one side only. The girders are connected by 5nos. of crossgirders out of which 2 nos. end cross girders and 3 nos. intermediate cross girders.2. STRENGTH OF CONCRETEThe grade of concrete for the main girders, deck slab and cross girders shall be M40 while the samefor other components will be M25.3. PRESTRESSINGEach girder is prestressed with 6 cables, 5 Nos. each consisiting of 12 starands of 12.7 mm dia and1 cable consisting of 9 strands of 12.7 mm dia.4. BEARINGSElastomeric bearings of size 600 x 380 x 65 designed as per UIC code 772-R will be provided.5. SEQUENCE OF CONSTRUCTIONThe girders are cast at the casting bed and when the concrete attains a strength of 25 Mpa (i.e M25)or 7 days which ever is earlier, 1st stage of prestressing is carried out and when the concrete attains fulldesign strength i.e 40Mpa or 28 days which ever is earlier, 2nd stage of prestressing is done. The ductholes are grouted. Then girders are launched on to the bed blocks. Deck slab and diaphragm gaps are castthen, footpath, wearing coat and hand railing are added.DESIGN DATAc/c of piers=21.180mc/c of Bearings=19.080mClear span=18.600mOverall length of girders=19.980m1.3Overall length of deck slab=21.14m0.65No. of longitudinal girders=2nos.No. of End Cross girders=2nos.21.13No. of Intermediate Cross girders=3nos.Overall Width of deck=5.700mTransverse Spacing of Longitudinal girders =2.500mDepth of Longitudinal girder=2.200mUnit weight of Concrete=25kN/m3Unit weight of Wearing Coat=24kN/m3Grade of concrete=M40Grade of steel=Fe415CALCULATION OF LOADING1) Self Weight of Precast Girder1. Self weight of Precast girderCL10501050200200150641700013001300350193675071250030007507502200Girder at mid spanGirder over supports2200Wt.of running section at middle =1.133x25=28.3kN/mAdditional Wt.of end block = (1.720-1.133) x25=14.7kN/mWt.intermediate diaphragm= (1.050x1.900-0.908)x0.350x25=9.5kNWt.of end diaphragm = (1.050x1.900-1.495) x0.350x25=4.4kN4.4kN9.5kN10001500749043.028.3450444051005.14514.7304.4495402) Deck Slab and In Situ portion of Diaphragms2.Deck Slab and insitu portion of diaphragms:Wt. of Deck slab =0.220x5.700x25=31.35kN/mWt. Of Deck slab =0.20x5.65x25=28.3kN/mThe eccentricity of the deck slab with respect to the centre line of girders is equal to0.450m.Load on girder A =28.3x (1.2+0) /2.4=28.3x0.000Load on heavily loaded girder A =31.4x (1.25+0.450)=0.0t/m2.5Load on girder B =28.3-0.0=0.0t/m=21.3kN/mLoad on girder B =31.35-21.32=10.03kN/mWt. of Diaphragms = (2.2-0.3) x (3.3-1.05Wt.of Diaphragms = (0.9-0.2) x (2.4-) x0.35x250.75) x0.32x25+=37.4kN-7.2=30.2kN3) Super Imposed Dead Load(0.38+0.7) / 2 x1.425xLoad of track and ballast =60kN/m0.32x25Wearing coat =0.0625x4.5x24=6.8kN/m=9.2+6.2Kerbs =2x0.2x0.8x25=8.0kN/mBallast retainer =0.200x0.8x25=4.0kN/mFoot Path = (0.9-0.15) x0.1x25=1.9kN/m=15.4kNRailing =0.9x0.15x25=3.4kN/m3. Super Imposed Dead Load :Total =84.0kN/mDue to ballast =6.0x0.000=0.00t/mS.no.LoadPEcc.Girder AGirder BTriangular Load =0.00-0.00=0.00t/m1Ballast60-0.15026.433.62Wear.coat6.8-0.1503.03.8Due to wearing coat3Kerbs8.02.77512.9-4.9=0.05x4.5x2.5x0.0004Ballast ret.4.000-2.336-1.75.7=0.00t/m6Footpath1.92.7753.0-1.1=0.05x4.5x2.5x0.0007Railing3.43.2256.041-2.7=0.00t/mTotal =49.634.4Triangular Load =0.00-0.00=0.00t/m4) Live loadg30Kerbs =2x0.2x0.8x2.5Load on19.08m span to 25T axle standard of loadingx0.000x2=0.00t/mPage - 81 Bridge Rules-2008=2011.4kN=2x0.2x0.8x2.510.04510.045CDA with 300mm ballast cushion= [0.15+ (8)6.83062.8126(6+19.08)205.9376201.9196x (2-0.3] x0.5=0.3910.9GIRDER A191978.28Load on girder A with an eccentricity of-0.150m and misalignment of0.100202065.5and hence a net eccentricity of-0.050mLoad on girder A19.081985.2576=2011.4x1.391x (1.25+-0.050)2.5=1342.8kNLoad per metre =1342.8=70.4kN/m19.08GIRDER BLoad on girder B with an eccentricity of0.150m and misalignment of0.100and hence a net eccentricity of0.250mLoad on girder B=2011x1.391x (1.25+0.250)2.5=1678.5kNLoad per metre =1678.5=88.0kN/m19.085) Foot path live load2.5x2x0.000=0.000t/mGIRDER ATriangular Load =0.000-0.000=0.000t/mLive Load on footpath =0.9x5.0=4.5kN/mRailing =0.9x0.15x2.5x2Eccentricity =2.775mx0.000Hence, load on girder A =4.5x (1.25+2.775)=0.00t/m2.5=7.2kN/mGIRDER BSince ve load on this due to footpath live load, ignore it.6. Load due to centrifugal force:According to clause 2.5.2(b) of IRS Bridge Rules,Centrifugal force =W x V2127 RRadius of curvature for 1o curve =1000000mCentrifugal force =W x V2=1346x1302127 R127x1000000=0.2kNForce per meter =0.2=0.0kN/m19.08Load per meter on outer girder =0.0x1.83=0.0kN/m1.702Load per meter on inner girder =-0.0kN/mLOAD DISTRIBUTION BETWEEN GIRDERSS.NOType of LoadTotal Load (kN/m)Load on girder A (kN/m)Load on girder B (kN/m)1Selfwt. Of girder28.328.328.32Deck slab31.421.310.03Ballast & Track60.026.433.64Wearing coat6.83.03.85Kerbs8.012.9-4.96Footpath slab1.93.0-1.17Railing3.46.0-2.78Ballast retainer4.0-1.75.79Live Load158.370.488.010Footpath LL4.57.2-2.511Centrifugal force-0.00.0Total176.8160.7

&CPragati Consultants&C&P

ENDPROPERTIES OF COMPOSITE SECTION AT THE END OF PRECAST GIRDER3300105022020064150150220019362200750TypeWidthDepthNo'sA (m2)Yt (m)A.YtA.Yt2I-selfa1.0500.200010.21000.10000.02100.00210.0007b0.15000.064320.00960.22140.00210.00050.00000c0.75002.000011.50001.20001.80002.16000.5000Total1.71961.82312.16260.5007Yt=1.8231=1.060m1.7196Yb=2.200-1.060=1.140mI-xx=2.1626+0.5007-1.71961.06022=0.7304m4Zt=0.7304=0.6890m31.0602Zb=0.7304=0.6408m31.1398PROPERTIES OF COMPOSITE SECTIONTypeWidthDepthNo'sA (m2)Yt (m)A.YtA.Yt2I-self13.3000.220010.72600.11000.07990.00880.00292NET TOTAL11.71961.28022.20152.81830.7304COMPOSITE TOTAL2.44562.28132.82710.7333Yts=2.2813/2.4456=0.9328mYt=0.9328-0.2200=0.7128mYb=2.2000-0.7128=1.4872mI-xx=2.8271+0.7333-2.44560.93282=1.4324m4Zts=1.4324=1.5355m30.9328Zt=1.4324=2.0095m30.7128Zb=1.4324=0.9631m31.4872

&CPragati Consultants&C&Pbbcaxx

MidPROPERTIES OF COMPOSITE SECTION AT THE MID SPAN33001050220200150350350220013002200350200200250300750TypeWidthDepthNo'sA (m2)Yt (m)A.YtA.Yt2I-selfa1.0500.200010.21000.10000.02100.00210.0007b0.35000.150020.05250.25000.01310.00330.00007c0.35001.700010.59501.05000.62480.65600.1433d0.20000.250020.05001.81670.09080.16500.00021000e0.75000.300010.22502.05000.46130.94560.0017Total1.13251.21101.77190.1459Yt=1.2110=1.069m1.1325Yb=2.200-1.069=1.131mI=1.7719+0.1459-1.13251.06932=0.6230m4Zt=0.6230=0.5827m31.0693Zb=0.6230=0.5510m31.1307PROPERTIES OF COMPOSITE SECTIONTypeWidthDepthNo'sA (m2)Yt (m)A.YtA.Yt2I-self13.3000.220010.72600.11000.07990.00880.00292NET TOTAL11.13251.28931.46011.88250.6230COMPOSITE TOTAL1.85851.54001.89130.6259Yts=1.5400/1.8585=0.8286mYt=0.8286-0.2200=0.6086mYb=2.2000-0.6086=1.5914mI=1.8913+0.6259-1.85850.82862=1.2412m4Zts=1.2412=1.4979m30.8286Zt=1.2412=2.0394m30.6086Zb=1.2412=0.7799m31.5914

&CPragati Consultants&C&Pdebbcadxx

load_calSOUTH CENTRAL RAILWAYBRIDGE NO: 1017 AT KM:536/2- 537/5, PROPOSED AS 36 x 19.15 m PSC GIRDERS FOR PROPOSED TRACK OVER TUNGABHADRA RIVER1. GENERALThe span consists of two precast prestressed concrete girders with a deck slab of 220mm thick.220A footpath of 0.9m width is provided on one side only. The girders are connected by 5nos. of crossgirders out of which 2 nos. end cross girders and 3 nos. intermediate cross girders.2. STRENGTH OF CONCRETEThe grade of concrete for the main girders, deck slab and cross girders shall be M40 while the samefor other components will be M25.3. PRESTRESSINGEach girder is prestressed with 6 cables, 5 Nos. each consisiting of 12 starands of 12.7 mm dia and1 cable consisting of 9 strands of 12.7 mm dia.4. BEARINGSElastomeric bearings of size 600 x 380 x 65 designed as per UIC code 772-R will be provided.5. SEQUENCE OF CONSTRUCTIONThe girders are cast at the casting bed and when the concrete attains a strength of 25 Mpa (i.e M25)or 7 days which ever is earlier, 1st stage of prestressing is carried out and when the concrete attains fulldesign strength i.e 40Mpa or 28 days which ever is earlier, 2nd stage of prestressing is done. The ductholes are grouted. Then girders are launched on to the bed blocks. Deck slab and diaphragm gaps are castthen, footpath, wearing coat and hand railing are added.DESIGN DATAc/c of piers=21.180mc/c of Bearings=19.080mClear span=18.600mOverall length of girders=19.980m1.3Overall length of deck slab=21.14m0.65No. of longitudinal girders=2nos.No. of End Cross girders=2nos.21.13No. of Intermediate Cross girders=3nos.Overall Width of deck=5.700mTransverse Spacing of Longitudinal girders =2.500mDepth of Longitudinal girder=2.200mUnit weight of Concrete=25kN/m3Unit weight of Wearing Coat=24kN/m3Grade of concrete=M40Grade of steel=Fe415CALCULATION OF LOADING1) Self Weight of Precast Girder1. Self weight of Precast girderCL10501050200200150641700013001300350193675071250030007507502200Girder at mid spanGirder over supports2200Wt.of running section at middle =1.133x25=28.3kN/mAdditional Wt.of end block = (1.720-1.133) x25=14.7kN/mWt.intermediate diaphragm= (1.050x1.900-0.908)x0.350x25=9.5kNWt.of end diaphragm = (1.050x1.900-1.495) x0.350x25=4.4kN4.4kN9.5kN10001500749043.028.3450444051005.14514.7304.4495402) Deck Slab and In Situ portion of Diaphragms2.Deck Slab and insitu portion of diaphragms:Wt. of Deck slab =0.220x5.700x25=31.35kN/mWt. Of Deck slab =0.20x5.65x25=28.3kN/mThe eccentricity of the deck slab with respect to the centre line of girders is equal to0.450m.Load on girder A =28.3x (1.2+0) /2.4=28.3x0.000Load on heavily loaded girder A =31.4x (1.25+0.450)=0.0t/m2.5Load on girder B =28.3-0.0=0.0t/m=21.3kN/mLoad on girder B =31.35-21.32=10.03kN/mWt. of Diaphragms = (2.2-0.3) x (3.3-1.05Wt.of Diaphragms = (0.9-0.2) x (2.4-) x0.35x250.75) x0.32x25+=37.4kN-7.2=30.2kN3) Super Imposed Dead Load(0.38+0.7) / 2 x1.425xLoad of track and ballast =60kN/m0.32x25Wearing coat =0.0625x4.5x24=6.8kN/m=9.2+6.2Kerbs =2x0.2x0.8x25=8.0kN/mBallast retainer =0.200x0.8x25=4.0kN/mFoot Path = (0.9-0.15) x0.1x25=1.9kN/m=15.4kNRailing =0.9x0.15x25=3.4kN/m3. Super Imposed Dead Load :Total =84.0kN/mDue to ballast =6.0x0.000=0.00t/mS.no.LoadPEcc.Girder AGirder BTriangular Load =0.00-0.00=0.00t/m1Ballast60-0.15026.433.62Wear.coat6.8-0.1503.03.8Due to wearing coat3Kerbs8.02.77512.9-4.9=0.05x4.5x2.5x0.0004Ballast ret.4.000-2.336-1.75.7=0.00t/m6Footpath1.92.7753.0-1.1=0.05x4.5x2.5x0.0007Railing3.43.2256.041-2.7=0.00t/mTotal =49.634.4Triangular Load =0.00-0.00=0.00t/m4) Live loadg30Kerbs =2x0.2x0.8x2.5Load on19.08m span to 25T axle standard of loadingx0.000x2=0.00t/mPage - 81 Bridge Rules-2008=2011.4kN=2x0.2x0.8x2.510.04510.045CDA with 300mm ballast cushion= [0.15+ (8)6.83062.8126(6+19.08)205.9376201.9196x (2-0.3] x0.5=0.3910.9GIRDER A191978.28Load on girder A with an eccentricity of-0.150m and misalignment of0.100202065.5and hence a net eccentricity of-0.050mLoad on girder A19.081985.2576=2011.4x1.391x (1.25+-0.050)2.5=1342.8kNLoad per metre =1342.8=70.4kN/m19.08GIRDER BLoad on girder B with an eccentricity of0.150m and misalignment of0.100and hence a net eccentricity of0.250mLoad on girder B=2011x1.391x (1.25+0.250)2.5=1678.5kNLoad per metre =1678.5=88.0kN/m19.085) Foot path live load2.5x2x0.000=0.000t/mGIRDER ATriangular Load =0.000-0.000=0.000t/mLive Load on footpath =0.9x5.0=4.5kN/mRailing =0.9x0.15x2.5x2Eccentricity =2.775mx0.000Hence, load on girder A =4.5x (1.25+2.775)=0.00t/m2.5=7.2kN/mGIRDER BSince ve load on this due to footpath live load, ignore it.6. Load due to centrifugal force:According to clause 2.5.2(b) of IRS Bridge Rules,Centrifugal force =W x V2127 RRadius of curvature for 1o curve =1000000mCentrifugal force =W x V2=1346x1302127 R127x1000000=0.2kNForce per meter =0.2=0.0kN/m19.08Load per meter on outer girder =0.0x1.83=0.0kN/m1.702Load per meter on inner girder =-0.0kN/mLOAD DISTRIBUTION BETWEEN GIRDERSS.NOType of LoadTotal Load (kN/m)Load on girder A (kN/m)Load on girder B (kN/m)1Selfwt. Of girder28.328.328.32Deck slab31.421.310.03Ballast & Track60.026.433.64Wearing coat6.83.03.85Kerbs8.012.9-4.96Footpath slab1.93.0-1.17Railing3.46.0-2.78Ballast retainer4.0-1.75.79Live Load158.370.488.010Footpath LL4.57.2-2.511Centrifugal force-0.00.0Total176.8160.7


STAAD***************************************************** ** STAAD.Pro ** Version 2007 Build 04 ** Proprietary Program of ** Research Engineers, Intl. ** Date= APR 9, 2014 ** Time= 17:31: 5 ** ** USER ID: PRAGATI *****************************************************1. STAAD PLANE BRIDGE NO.356INPUT FILE: Tungabadra_girder 19.08m 9.4.14.STD2. START JOB INFORMATION3. ENGINEER DATE 05-MAY-094. END JOB INFORMATION5. INPUT WIDTH 796. UNIT METER KN7. JOINT COORDINATES8. 1 0 0 0; 2 0.45 0 0; 3 19.53 0 0; 4 19.98 0 09. MEMBER INCIDENCES10. 1 1 2; 2 2 3; 3 3 411. MEMBER PROPERTY INDIAN12. 1 TO 3 PRIS AX 1.1325 IZ 0.62313. DEFINE MATERIAL START14. ISOTROPIC MATERIAL115. E 3.16E+00716. POISSON 0.217. DENSITY 2518. END DEFINE MATERIAL19. CONSTANTS20. MATERIAL MATERIAL1 ALL21. SUPPORTS22. 2 3 PINNED23. LOAD 1 SELF WEIGHT OF GIRDER24. MEMBER LOAD25. 1 TO 3 UNI GY -28.326. 1 3 UNI GY -14.727. 2 UNI GY -14.7 0 1.228. 2 UNI GY -14.7 17.88 19.0829. 2 TRAP GY -14.7 0 1.2 330. 2 TRAP GY 0 -14.7 16.08 17.8831. JOINT LOAD32. 2 3 FY -4.433. MEMBER LOAD34. 2 CON GY -9.5 4.9235. 2 CON GY -9.5 9.5436. 2 CON GY -9.5 14.1637. LOAD 2 DECK SLAB AND INSITU PORTION OF DIAPHRAGMS38. MEMBER LOAD39. 1 TO 3 UNI GY -21.340. 2 CON GY -30.2 4.9241. 2 CON GY -30.2 9.5442. 2 CON GY -30.2 14.1643. JOINT LOAD44. 2 3 FY -30.245. LOAD 3 SUPER IMPOSED DEAD LOAD46. MEMBER LOAD47. *DUE TO BALLAST & TRACK48. 1 TO 3 UNI GY -26.449. *DUE TO WEARING COAT50. 1 TO 3 UNI GY -351. *DUE TO KERBS52. 1 TO 3 UNI GY -12.953. *DUE TO FOOTPATH SLAB54. 1 TO 3 UNI GY -355. *DUE TO RAILING56. 1 TO 3 UNI GY -6.0457. *BALLAST RETAINER58. 1 TO 3 UNI GY 1.759. LOAD 4 LIVE LOAD WITH CDA60. MEMBER LOAD61. 2 UNI GY -70.462. LOAD 5 FOOTPATH LIVE LOAD63. MEMBER LOAD64. 2 UNI GY -765. PERFORM ANALYSIS66. PRINT SUPPORT REACTIONSUPPORT REACTIONSUPPORT REACTIONS -UNIT KN METE STRUCTURE TYPE = PLANEJOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z2 1 0.00 338.85 0.00 0.00 0.00 0.002 0.00 288.29 0.00 0.00 0.00 0.003 0.00 495.90 0.00 0.00 0.00 0.004 0.00 671.62 0.00 0.00 0.00 0.005 0.00 66.78 0.00 0.00 0.00 0.003 1 0.00 338.85 0.00 0.00 0.00 0.002 0.00 288.29 0.00 0.00 0.00 0.003 0.00 495.90 0.00 0.00 0.00 0.004 0.00 671.62 0.00 0.00 0.00 0.005 0.00 66.78 0.00 0.00 0.00 0.0067. LOAD LIST 168. PRINT FORCE ENVELOPE NSECTION 8 LIST 2MEMBER FORCE ENVELOPEALL UNITS ARE KN METEMEMB DISTANCE FY LD MZ LD FZ LD MY LD2 0.00 MAX 315.10 1 4.35 1 0.00 1 0.00 1MIN 315.10 1 4.35 1 0.00 1 0.00 12.38 MAX 218.43 1 -627.13 1 0.00 1 0.00 1MIN 218.43 1 -627.13 1 0.00 1 0.00 14.77 MAX 149.24 1 -1063.88 1 0.00 1 0.00 1MIN 149.24 1 -1063.88 1 0.00 1 0.00 17.15 MAX 72.25 1 -1318.10 1 0.00 1 0.00 1MIN 72.25 1 -1318.10 1 0.00 1 0.00 19.54 MAX 4.75 1 -1409.91 1 0.00 1 0.00 1MIN 4.75 1 -1409.91 1 0.00 1 0.00 111.93 MAX -72.25 1 -1318.10 1 0.00 1 0.00 1MIN -72.25 1 -1318.10 1 0.00 1 0.00 114.31 MAX -149.24 1 -1063.88 1 0.00 1 0.00 1MIN -149.24 1 -1063.88 1 0.00 1 0.00 116.69 MAX -218.21 1 -627.13 1 0.00 1 0.00 1MIN -218.21 1 -627.13 1 0.00 1 0.00 119.08 MAX -315.10 1 4.35 1 0.00 1 0.00 1MIN -315.10 1 4.35 1 0.00 1 0.00 169. LOAD LIST 270. PRINT FORCE ENVELOPE NSECTION 8 LIST 2MEMBER FORCE ENVELOPEALL UNITS ARE KN METEMEMB DISTANCE FY LD MZ LD FZ LD MY LD2 0.00 MAX 248.50 2 2.16 2 0.00 2 0.00 2MIN 248.50 2 2.16 2 0.00 2 0.00 22.38 MAX 197.70 2 -529.94 2 0.00 2 0.00 2MIN 197.70 2 -529.94 2 0.00 2 0.00 24.77 MAX 146.90 2 -940.88 2 0.00 2 0.00 2MIN 146.90 2 -940.88 2 0.00 2 0.00 27.15 MAX 65.90 2 -1163.16 2 0.00 2 0.00 2MIN 65.90 2 -1163.16 2 0.00 2 0.00 29.54 MAX 15.10 2 -1259.75 2 0.00 2 0.00 2MIN 15.10 2 -1259.75 2 0.00 2 0.00 211.93 MAX -65.90 2 -1163.16 2 0.00 2 0.00 2MIN -65.90 2 -1163.16 2 0.00 2 0.00 214.31 MAX -146.90 2 -940.88 2 0.00 2 0.00 2MIN -146.90 2 -940.88 2 0.00 2 0.00 216.69 MAX -197.70 2 -529.94 2 0.00 2 0.00 2MIN -197.70 2 -529.94 2 0.00 2 0.00 219.08 MAX -248.50 2 2.16 2 0.00 2 0.00 2MIN -248.50 2 2.16 2 0.00 2 0.00 271. LOAD LIST 372. PRINT FORCE ENVELOPE NSECTION 8 LIST 2MEMBER FORCE ENVELOPEALL UNITS ARE KN METEMEMB DISTANCE FY LD MZ LD FZ LD MY LD2 0.00 MAX 473.57 3 5.03 3 0.00 3 0.00 3MIN 473.57 3 5.03 3 0.00 3 0.00 32.38 MAX 355.17 3 -983.25 3 0.00 3 0.00 3MIN 355.17 3 -983.25 3 0.00 3 0.00 34.77 MAX 236.78 3 -1689.15 3 0.00 3 0.00 3MIN 236.78 3 -1689.15 3 0.00 3 0.00 37.15 MAX 118.39 3 -2112.70 3 0.00 3 0.00 3MIN 118.39 3 -2112.70 3 0.00 3 0.00 39.54 MAX 0.00 3 -2253.88 3 0.00 3 0.00 3MIN 0.00 3 -2253.88 3 0.00 3 0.00 311.93 MAX -118.39 3 -2112.70 3 0.00 3 0.00 3MIN -118.39 3 -2112.70 3 0.00 3 0.00 314.31 MAX -236.78 3 -1689.15 3 0.00 3 0.00 3MIN -236.78 3 -1689.15 3 0.00 3 0.00 316.69 MAX -355.17 3 -983.25 3 0.00 3 0.00 3MIN -355.17 3 -983.25 3 0.00 3 0.00 319.08 MAX -473.57 3 5.03 3 0.00 3 0.00 3MIN -473.57 3 5.03 3 0.00 3 0.00 373. LOAD LIST 474. PRINT FORCE ENVELOPE NSECTION 8 LIST 2MEMBER FORCE ENVELOPEALL UNITS ARE KN METEMEMB DISTANCE FY LD MZ LD FZ LD MY LD2 0.00 MAX 671.62 4 0.00 4 0.00 4 0.00 4MIN 671.62 4 0.00 4 0.00 4 0.00 42.38 MAX 503.71 4 -1401.58 4 0.00 4 0.00 4MIN 503.71 4 -1401.58 4 0.00 4 0.00 44.77 MAX 335.81 4 -2402.71 4 0.00 4 0.00 4MIN 335.81 4 -2402.71 4 0.00 4 0.00 47.15 MAX 167.90 4 -3003.38 4 0.00 4 0.00 4MIN 167.90 4 -3003.38 4 0.00 4 0.00 49.54 MAX 0.00 4 -3203.61 4 0.00 4 0.00 4MIN 0.00 4 -3203.61 4 0.00 4 0.00 411.93 MAX -167.90 4 -3003.38 4 0.00 4 0.00 4MIN -167.90 4 -3003.38 4 0.00 4 0.00 414.31 MAX -335.81 4 -2402.71 4 0.00 4 0.00 4MIN -335.81 4 -2402.71 4 0.00 4 0.00 416.69 MAX -503.71 4 -1401.58 4 0.00 4 0.00 4MIN -503.71 4 -1401.58 4 0.00 4 0.00 419.08 MAX -671.62 4 0.00 4 0.00 4 0.00 4MIN -671.62 4 0.00 4 0.00 4 0.00 475. LOAD LIST 576. PRINT FORCE ENVELOPE NSECTION 8 LIST 2MEMBER FORCE ENVELOPEALL UNITS ARE KN METEMEMB DISTANCE FY LD MZ LD FZ LD MY LD2 0.00 MAX 66.78 5 0.00 5 0.00 5 0.00 5MIN 66.78 5 0.00 5 0.00 5 0.00 52.38 MAX 50.08 5 -139.36 5 0.00 5 0.00 5MIN 50.08 5 -139.36 5 0.00 5 0.00 54.77 MAX 33.39 5 -238.91 5 0.00 5 0.00 5MIN 33.39 5 -238.91 5 0.00 5 0.00 57.15 MAX 16.69 5 -298.63 5 0.00 5 0.00 5MIN 16.69 5 -298.63 5 0.00 5 0.00 59.54 MAX 0.00 5 -318.54 5 0.00 5 0.00 5MIN 0.00 5 -318.54 5 0.00 5 0.00 511.93 MAX -16.69 5 -298.63 5 0.00 5 0.00 5MIN -16.69 5 -298.63 5 0.00 5 0.00 514.31 MAX -33.39 5 -238.91 5 0.00 5 0.00 5MIN -33.39 5 -238.91 5 0.00 5 0.00 516.69 MAX -50.08 5 -139.36 5 0.00 5 0.00 5MIN -50.08 5 -139.36 5 0.00 5 0.00 519.08 MAX -66.78 5 0.00 5 0.00 5 0.00 5MIN -66.78 5 0.00 5 0.00 5 0.00 577. FINISHNODE NUMBERSBEAM NUMBERS


pre_stressPRESTRESSIt is proposed to use 5 nos. of 12T13 and 1 no. of 9T13 low relaxation cables.Area of each strand=98.7mm2Area of each cable=12x98.7=1184.4mm2Ultimate Tensile Stress=183.71Kg/mm2 for 12.7mm strand.Ultimate Force in 12 T 13 =183.71x1184.4=217586.124Kg183.71=2176kNUltimate Force in 9 T 13 =183.71x888.3=163189.593Kg=1631.9kNUsing Corrugated HDPE for the cables with the following properties:m = 0.17, k = 0.0020/mAll the cables are stressed from both endsInitial Jacking Force in the cables =0.765x2176=1664.5kN----- for 12 T13=0.765x1631.9=1248.4kN----- for 9 T13


cable 1&2Cable 1 & 2( 12T 13 )CL of cable0.0850.1700.0851.0001.0001.0000.000102900.1809.8406.840length of the cable=9.840mheight of the cable at the starting point =0.180mlength of the vert. curve=2.000mstarting point of the curve=6.840mending point of the curve=8.840mvertical drop in the curve=0.085mtheta (q)=4.858degreestheta (q) in radians =0.08483y= ax2a =0.02120dist (m) from centreordinates (m)angle(deg)for analysissection no.0.0000.000L/210.0000.1800.0000.0003L/822.3850.1800.0000.000L/434.7700.1800.0000.000L/847.1550.1820.7650.0007.155D57.5400.1901.7000.000SUPPORT69.5400.3244.8580.000JACKEND79.8400.3504.8580.0000.3000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.000


cable3Cable 3( 12T 13 )CL of cable0.1850.5200.3351.0001.8501.8500.0000.1809.8405.1405.140length of the cable=9.840m4.700height of the cable at the starting point =0.180m9.840length of the vert. curve=3.700mstarting point of the curve=5.140mending point of the curve=8.840mvertical drop in the curve=0.335mtheta (q)=10.340degreestheta (q) in radians =0.18054y= ax2a =0.02451dist (m) from centreordinates (m)angle(deg)for analysissection no0.0000.000L/210.0000.1800.0000.0003L/822.3850.1800.0000.000L/434.7700.1800.0000.0004.77L/847.1550.2805.6400.000D57.5400.3216.7090.000SUPPORT69.5400.64310.3400.000JACKEND79.8400.7010.3400.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.000


cable 4Cable 4( 12 T 13 )CL of cable0.1620.6204300.4581.0002.8502.8500.0006200.4309.8403.1409.840length of the cable=9.840mheight of the cable at the starting point =0.430mlength of the vert. curve=5.700mstarting point of the curve=3.140mending point of the curve=8.840mvertical drop in the curve=0.458mtheta (q)=9.148degreestheta (q) in radians =0.15973y= ax2a =0.01408dist (m) from centreordinates (m)angle(deg)for analysissection no0.0000.000L/210.0000.4300.0000.0003L/822.3850.4300.0000.000L/434.7700.4672.6290.0004.845L/847.1550.6576.4520.000D57.5400.7037.0650.000SUPPORT69.5401.0009.1480.000JACKEND79.8401.0499.1480.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.000


cable 5Cable 5( 12 T 13 )CL of cable0.1180.5704300.4527801.0003.8503.8500.000570S0.7809.8401.1409.840length of the cable=9.840mheight of the cable at the starting point =0.780mlength of the vert. curve=7.700mstarting point of the curve=1.140mending point of the curve=8.840mvertical drop in the curve=0.452mtheta (q)=6.703degreestheta (q) in radians =0.11704y= ax2a =0.00762dist (m) from centreordinates (m)angle(deg)for analysissection no0.0000.000L/210.0000.7800.0000.0003L/822.3850.7921.0870.000L/434.7700.8803.1670.0004.845L/847.1551.0565.2390.000D57.5401.0925.5720.000SUPPORT69.5401.3146.7030.000JACKEND79.8401.3496.7030.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.000


cable 6Cable 6( 9 T 13 )CL of cable0.1460.7700.6241.0004.2954.2950.0001.0809.8400.2509.840length of the cable=9.840mheight of the cable at the starting point =1.080mlength of the vert. curve=8.590mstarting point of the curve=0.250mending point of the curve=8.840mvertical drop in the curve=0.624mtheta (q)=8.274degreestheta (q) in radians =0.14447y= ax2a =0.00845dist (m) from centreordinates (m)angle(deg)for analysissection no0.0000.000L/210.0001.0800.0000.0003L/822.3851.1192.0670.000L/434.7701.2534.3680.0004.845L/847.1551.4836.6560.000D57.5401.5297.0240.000SUPPORT69.5401.8058.2740.000JACKEND79.8401.8498.2740.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.00000.0000.0000.000


cable_distCable 1 & 2851708510001000100068409840a)q =4.858degrees=0.0848radiansL1 =1.004ma1 =0b)vertical curveP0 = lo2/ 2h0 =23.53mcurved length S2 isS2 =2.002mL2 =3.006a2 =0.0848radiansc)L3 =9.846ma3 =0.0848radiansCable 32179218552033510001850185051409840a)q =10.340degrees =0.1805radiansL1 =1.017ma1 =0b)vertical curveP0 = lo2/ 2h0 =20.43mcurved length S2 isS2 =3.720mL2 =4.737a2 =0.180radiansc)L3 =9.877ma3 =0.180radiansCable 416262045810002850285031409840a)q =9.148degrees =0.160radiansL1 =1.013ma1 =0b)vertical curveP0 = lo2/2h0 =35.47mcurved length s2 iss2 =5.724ml2 =6.737a2 =0.160radiansc)l3 =9.877ma3 =0.160radiansCABLE 511857045210003850385011409840a)q =6.703degrees =0.117radiansL1 =1.007ma1 =0b)vertical curveP0 = lo2/2h0=65.59mcurved length s2 iss2 =7.718ml2 =8.725a2 =0.117radiansc)l3 =9.865ma3 =0.117radiansCABLE 61467706241000429542952509840a)s2 =8.274degrees =0.144radiansl2 =1.011ma2 =0b)vertical curveP0 = lo2/2h0=59.13mcurved length s2 iss2 =8.620ml2 =9.631a2 =0.144radiansc)l3 =9.881ma3 =0.144radians


cab_forcesCALCULATION OF CABLE FORCESK =0.002m =0.17Cable noCable Length (L)Total angle change (a)(KL + ma)123a1a2a31231 & 21.0043.0069.8460.0000.0850.0850.0020.0200.03431.0174.7379.8770.0000.1800.1800.0020.0400.05041.0136.7379.8770.0000.1600.1600.0020.0410.04751.0078.7259.8650.0000.1170.1170.0020.0370.04061.0119.6319.8810.0000.1440.1440.0020.0440.044cable noe(KL + ma)Force at jack endForce at points1231231 & 21.00201.02061.03471664.531661.201630.881608.720.7031556.031.00201.04101.05171664.531661.151599.021582.671686.141.00201.04151.04801664.531661.161598.281588.2751.00201.03801.04041664.531661.191603.531599.88152961.00201.04481.04531664.531661.171593.181592.39slip = (sx x dx)/Es = (Px x dx)/(A x Es) = Area/(A x Es)Area =0.006x (98.7x12) x1950001000=1385.7kN-m for12T 13Area =0.006x (98.7x9) x1950001000=1039.3kN-m for9T 13


slipCable 1 &2CL1664.52.421661.21630.90.32.3012.68664039545.07309750647.45955461749.84601172841608.7SDL/8L/43L/8L/21454.81492.01482.61494.11501.91509.61509.58168884421487.41457.11453.81.0042.0026.8409.8469.841.000610948Area = { [210.77+204.09] x1.0042+ [204.09+143.45] x2.0022+143.45+99.14] x6.8402=208.18+347.96+829.66=1385.8~1385.8kN-m1 =Average stress during stressing=1{ (1664.5+1661.20) x1.0049.8462+ (1661.2+1630.88) x2.0022+ (1630.9+1608.72) x6.8402=1629.52kN2 =Average stress after anchoring=1{ (1453.8+1457.1) x1.0049.8462+ (1457.1+1487.4) x2.0022+ (1487.4+1509.6) x6.842=1488.78kNCable 3CL1664.51661.21599.00.32.30866963142.69512085245.08911088327.48310091419.8771582.7SDL/8L/43L/8L/21422.21446.21452.61487.91495.51503.11503.1028674781486.71424.61421.21.0173.7205.1409.8779.841.003769405Area = { [243.30+236.53] x1.0172+ [236.53+112.27] x3.7202+112.27+79.56] x5.1402=243.99+648.80+493.01=1385.8~1385.8kN-m1 =Average stress during stressing=1{ (1664.5+1661.15) x1.0179.8772+ (1661.2+1599.02) x3.7202+ (1599.0+1582.67) x5.1402=1613.04kN2 =Average stress after anchoring=1{ (1421.2+1424.6) x1.0179.8772+ (1424.6+1486.7) x3.7202+ (1486.7+1503.1) x5.142=1472.73kNCable 4CL1664.51661.21598.30.32.30875978542.69522609735.08930961387.48339313049.8771588.3SDL/8L/43L/8L/21439.21455.81460.11486.41506.91514.51514.49451390221504.51441.61438.21.0135.7243.1409.8776.7379.84Area = { [226.30+219.56] x1.0131.00380860232+ [219.56+93.79] x5.7242+93.79+73.78] x3.1402=225.84+896.88+263.08=1385.8~1385.8kN-m1 =Average stress during stressing=1{ (1664.5+1661.16) x1.0139.8772+ (1661.2+1598.28) x5.7242+ (1598.3+1588.27) x3.1402=1621.53kN2 =Average stress after anchoring=1{ (1438.2+1441.6) x1.0139.8772+ (1441.6+1504.5) x5.7242+ (1504.5+1514.5) x3.142=1481.23kNCable 5CL1664.51661.21603.50.32.30574770892.69170982545.08266994967.47363007389.8651599.9SDL/8L/43L/8L/21459.81471.91474.81492.61510.51523.51523.49678246371519.81462.21458.81.0077.7181.1409.8659.84Area = { [205.69+198.99] x1.0071.00249900398.7252+ [198.99+83.69] x7.7182+83.69+76.38] x1.1402=203.75+1090.81+91.24=1385.8~1385.8kN-m1 =Average stress during stressing=1{ (1664.5+1661.19) x1.0079.8652+ (1661.2+1603.53) x7.7182+ (1603.5+1599.88) x1.1402=1631.93kN2 =Average stress after anchoring=1{ (1458.8+1462.2) x1.0079.8652+ (1462.2+1519.8) x7.7182+ (1519.8+1523.5) x1.142=1491.45kNCable 6CL1664.51661.21593.20.32.30951932612.69611277855.09098390577.48585503299.8811592.4SDL/8L/43L/8L/21456.11468.71471.81490.71509.61527.31527.27373510431526.51458.51455.11.0118.6200.2509.8819.6319.84Area = { [209.41+202.68] x1.0111.00413883742+ [202.68+66.71] x8.6202+66.71+65.11] x0.2502=208.23+1161.09+16.48=1385.8~1385.8kN-m1 =Average stress during stressing=1{ (1664.5+1661.17) x1.0119.8812+ (1661.2+1593.18) x8.6202+ (1593.2+1592.39) x0.2502=1629.96kN2 =Average stress after anchoring=1{ (1455.1+1458.5) x1.0119.8812+ (1458.5+1526.5) x8.6202+ (1526.5+1527.3) x0.252=1489.70kN


bm_tableFrom STAAD AnalysisTabulation of Bending Moments ( in KN-m)S.NoLoadingBM @ L/2BM @ 3L/8BM @ L/4BM @ L/8BM @ Supp.1Self wt.1409.91318.11064.0627.0-4.42Deck Slab1260.01163.0941.0530.0-2.23SIDL2254.02113.01689.0983.0-5.04FPLL318.5298.6239.0139.40.08446.25Live Load3203.73003.02402.71401.60.06Centrifugal Force0.00.00.00.00.08641.8Tabulation of Bending Moments after applying partial load factors as per IRS CodeS.NoLoadingBM @ L/2BM @ 3L/8BM @ L/4BM @ L/8BM @ Supp.2.461Self wt.x1.01409.91318.11064.0627.0-4.42Deck Slab x 1.01260.01163.0941.0530.0-2.23SIDL x 1.22704.82535.62026.81179.6-6.04FPLL x 1.0318.5298.6239.0139.40.09217.35Live Load x 1.13524.13303.32643.01541.80.06Centrg.Forcex1.00.00.00.00.00.09431.3


DESIGNCHECKING OF STRESSES AT VARIOUS SECTIONS:UTS of cables = (98.7x1837) x12=2176kN1664.443242Grade of concrete =M40SectionSupportL/8L/43L/8L/25L/83L/47L/8SupportGross Sectional Properties of girderA(m2)1.71961.13251.13251.13251.13251.13251.13251.13251.7196Yt(m)1.06021.06931.06931.06931.06931.06931.06931.06931.0602Yb(m)1.13981.13071.13071.13071.13071.13071.13071.13071.13980.15D(m)2.20002.20002.20002.20002.20002.20002.20002.20002.2000SZt(m3)0.68900.58270.58270.58270.58270.58270.58270.58270.68901292.3Zb(m3)-0.6408-0.5510-0.5510-0.5510-0.5510-0.5510-0.5510-0.5510-0.6408Composite Sectional Properties of girderA(m2)2.44561.85851.85851.85851.85851.85851.85851.85852.4456Yts(m)0.93280.82860.82860.82860.82860.82860.82860.82860.9328Yt(m)0.71280.60860.60860.60860.60860.60860.60860.60860.7128Yb(m)1.48721.59141.59141.59141.59141.59141.59141.59141.4872D(m)2.42002.42002.42002.42002.42002.42002.42002.42002.4200Zts(m3)1.53551.49791.49791.49791.49791.49791.49791.49791.5355Zt(m3)2.00952.03942.03942.03942.03942.03942.03942.03942.0095Zb(m3)-0.9631-0.7799-0.7799-0.7799-0.7799-0.7799-0.7799-0.7799-0.9631BM due to self wt. of girder with partial safety factor of1.0BM-4.4627.01064.01318.11409.91318.11064.0627.0-4.4BM due to self wt. of deck slab with partial safety factor of1.0BM-2.2530.0941.01163.01260.01163.0941.0530.0-2.2BM due to SIDL with partial safety factor of1.2BM-6.01179.62026.82535.62704.82535.62026.81179.6-6.0BM due to Live Load with partial fos of1.1BM0.01541.82643.03303.33524.13303.32643.01541.80.0BM due to FPLL with partial fos1.0BM0.0139.4239.0298.6318.5298.6239.0139.40.0Total Live load ( Live load + Footpath live load )BM0.01681.22882.03601.93842.63601.92882.01681.20.09217.3BM due to Centrifugal ForceBM0.00.00.00.00.00.00.00.00.0Prestressing forces and momentsCABLESectionSupportL/8L/43L/8L/25L/83L/47L/8Support1 &2P1454.81482.61494.11501.91509.61501.91494.11482.61454.80.15(12 T 13)q4.8580.7650.0000.0000.0000.0000.0000.7654.858Sy0.3240.1820.1800.1800.1800.1800.1800.1820.3241394.52.0psin q123.219.80.00.00.00.00.019.8123.2nos.pcos q1449.51482.51494.11501.91509.61501.91494.11482.51449.5e=y-yb-0.816-0.949-0.951-0.951-0.951-0.951-0.951-0.949-0.816M = Pcosq x e-1182.1-1406.3-1420.5-1427.8-1435.2-1427.8-1420.5-1406.3-1182.13P1422.21452.61487.91495.51503.11495.51487.91452.61422.2(12 T 13)q10.3405.6400.0000.0000.0000.0000.0005.64010.3400.15y0.6430.2800.1800.1800.1800.1800.1800.2800.643S1.0psin q255.3142.80.00.00.00.00.0142.8255.31346.1nos.pcos q1399.11445.61487.91495.51503.11495.51487.91445.61399.1e=y-yb-0.497-0.851-0.951-0.951-0.951-0.951-0.951-0.851-0.497M = Pcosq x e-694.8-1230.5-1414.5-1421.8-1429.0-1421.8-1414.5-1230.5-694.84P1439.21460.11486.41506.91514.51506.91486.41460.11439.2(12 T 13)q9.1486.4522.6290.0000.0000.0002.6296.4529.148y1.0000.6570.4670.4300.4300.4300.4670.6571.0001.0psin q228.8164.168.20.00.00.068.2164.1228.8nos.pcos q1420.91450.81484.81506.91514.51506.91484.81450.81420.9e=y-yb-0.140-0.474-0.663-0.701-0.701-0.701-0.663-0.474-0.140M = Pcosq x e-198.3-687.3-984.9-1055.9-1061.2-1055.9-984.9-687.3-198.35P1459.81474.81492.61510.51523.51510.51492.61474.81459.8(12 T 13)q6.7035.2393.1671.0870.0001.0873.1675.2396.703y1.3141.0560.8800.7920.7800.7920.8801.0561.314691.0psin q170.4134.782.528.70.028.782.5134.7170.42.76nos.pcos q1449.91468.61490.41510.21523.51510.21490.41468.61449.9e=y-yb0.174-0.075-0.250-0.339-0.351-0.339-0.250-0.0750.174M = Pcosq x e252.8-110.1-373.0-511.8-534.3-511.8-373.0-110.1252.86P1456.11471.81490.71509.61527.31509.61490.71471.81456.1(9 T 13)q8.2746.6564.3682.0670.0002.0674.3686.6568.274y1.8051.4831.2531.1191.0801.1191.2531.4831.8050.75psin q209.5170.6113.554.40.054.4113.5170.6209.5nos.pcos q1441.01461.91486.31508.61527.31508.61486.31461.91441.0e=y-yb0.6660.3520.122-0.012-0.051-0.0120.1220.3520.666M = Pcosq x e959.0514.9181.2-18.4-77.5-18.4181.2514.9959.0CALCULATION OF STRESSESFirst stage PrestressingCable - 1, 2 & 5cg of cables0.6540.4730.4130.3840.3800.3840.4130.4730.654S Pcosq4348.94433.54478.64513.94542.74513.94478.64433.54348.9SM-2111.4-2922.6-3214.0-3367.5-3404.7-3367.5-3214.0-2922.6-2111.4692.76st-536-1101-1562-1794-1832-1794-1562-1101-536sb582492199788100981019010098978892195824Stresses due to self weight of girderst-61076182622622420226218261076-6sb7-1138-1931-2392-2559-2392-1931-11387Net stresses due to self weight of girder + I stage prestressst-542-25265468588468265-25-542sb583180817857770576327705785780815831Stress at cg level393563376430644264156442643063373935Average stress at c.g. of cables =5856kN/m2Calculation of prestressing losses due to 1st stage of prestressingLoss due to Elastic Shortening of concrete at transferAverage stress at c.g of cables =5856kN/m2Average stress for elastic shortening =5856=2928kN/m22Es =195000.00MpaEc =25000Mpa (for M25 Concrete)Assuming M40 concrete becomes M25 in 7 days after casting.Loss due to elastic shortening =2928x195000=22839kN/m225000=0.023kN/mm2Area of cross section of I stage cables =3.000x1184.4=3553.2mm2Loss of force in the cable =3553x0.023=81.1kNAverage force in first stage cables =4455kN% of loss=81.1x100=1.82%4455Loss of Stress in cables due to Elastic Shorteningst102028333333282010sb-106-168-178-184-186-184-178-168-106Net stresses at transfer of first stage prestressst-532-5293501621501293-5-532sb572579137678752174467521767879135725Stress at cg level386462106290629662676296629062103864Average stress at c.g. of cables =5732kN/m2Max Comp Stress =7913kN/m2 -1250kN/m2(for M25 Concrete at transfer)Loss in 1st stage Prestressing between 7 days and 28 daysLoss of Prestress due to Relaxation of steelRelaxation loss shall be taken as 2.5% if the average force is 70% of the UTS and 0% if the average force is50% of the UTS with a linear variation in between.Average force in the cables after anchoring=3.0x1485=1485kN3.0% of UTS=1485x100=68.2%2176% loss of prestresing force at 1000 hrs=0.0+ (2.5-0) x (68.2-50)(70-50)=2.28%% loss for 504 hrs ( 28 - 7 = 21 days) =504x2.28=1.15%1000Loss of force in I stage cables =1.15x4455=51.2kN100Loss Due to Shrinkage and creep of concrete.ShrinkageTaking the concrete at the time of prestressing be 7 days old, the residual shrinkage strain from 7 days to 28 days= (3.5-1.9) x1.0E-04=1.6E-04Modulus of elasticity of steel =1.95E+05MpaShrinkage stress =1.60E-04x1.95E+05=31.2MpaCreepCreep Strain of Concrete = (2.2-1.6) x4.3E-05=2.58E-05per MpaAverage stress in concrete at the c.g of the cables =5732kN/m2=5.732MpaHence Creep Strain =2.58E-05x5.732=1.48E-04Stress loss due to creep of concrete =1.48E-04x2E+05=28.8MpaTotal stress loss due to shrinkage & creep of concrete =31.2+28.8=60.0MpaLoss of force in the cable =60.0x (3.000x1184.4) =213324N=213.3kN% Loss of force=213.3x100=4.79%4455Total loss of Prestressing force from 7 days to 28 days =4.79+1.15=5.94%Loss of Stress in cables due to creep, shrinkage, and relaxation of steel from 7 days to 28 daysst326593107109107936532sb-346-547-581-600-605-600-581-547-346Net stresses at 28 days ( before second stage prestress )st-5006038660873060838660-500sb537973667097692268416922709773665379Stress at cg level363057945836582057855820583657943630Second stage Prestressing3,4 & 6( done after 28 days of casting of girder )SPcosq3900.83992.84087.44133.84163.14133.84087.43992.83900.8SM-173.8-1531.7-2263.5-2491.5-2548.4-2491.5-2263.5-1531.7-173.8cg of cables1.0900.7450.5770.5270.5160.5270.5770.7451.090Stresses due to IInd stage prestressingst2016897-276-626-698-626-2768972016sb254063067717817283018172771763062540Stress at cg level228044745621606561896065562144742280Average stress at c.g. of cables =4785kN/m2Loss due to Elastic Shortening of concrete in II stage cablesAverage stress at c.g of cables=4785kN/m2Average stress for elastic shortening =4785=2393kN/m22Es =195000.00MpaEc =31623Mpa( for M40 concrete )Loss due to elastic shortening =2393x195000=14754kN/m231623=0.0148kN/mm2area of cross section of II stage cables =1184.4x2.750=3257.1Sq.mmLoss of force in the cable =3257.1x0.0148=48.1kNAverage force in II stage cables =4044kN% of loss =48.1x100=1.19%4044Loss of Stress in II stage cables due to Elastic Shorteningst-24-1137873-11-24sb-30-75-92-97-99-97-92-75-30Loss in I stage cables due to Elastic Shortening during stressing of II stage cables.Loss due to elastic shortening =4785x195000=29509kN/m231623=0.0295kN/mm2Area of cross section of I stage cables =3.000x1184.4=3553.2mm2Loss of force in the cable =3553.2x0.0295=104.9kNAverage force in I stage cables =4455kN% of loss=104.9x100=2.35%4455Loss of Stress in I stage cablesst132637424342372613sb-137-217-230-238-240-238-230-217-137Net stresses at transfer of II stage prestresingst15049721503183311509721504sb7751133791449214759148031475914492133797751cg of cables0.8630.6030.4920.4520.4450.4520.4920.6030.863Stress at cg level53029977112871173111824117311128799775302Average stress at c.g of cables =9824Max Comp Stress =14803kN/m216000kN/m2( for M40 concrete at 28 days )Max.tensile Stress =31kN/m2-1000kN/m2Stresses due to self weight of deck slabst-391016151996216319961615910-3sb3-962-1708-2111-2287-2111-1708-9623Stresses due to Differencial Shrinkagests-1068-887-887-887-887-887-887-887-1068st202021972197219721972197219721972020sb-1099-946-946-946-946-946-946-946-1099Stresses due to SDL acting on transformed sectionsts-478713531693180616931353787-4st-3578994124313261243994578-3sb6-1512-2599-3251-3468-3251-2599-15126Net stressessts-1072-100466805918805466-100-1072st351846584956546857705468495646583518sb666299599240845181038451924099596662Stress at cg level554186388370789476737894837086385541Average stress at c.g of cables =7617kN/m2Max Comp Stress =9959kN/m20kN/m2Balance Loss of Prestress due to 1st stage prestressing( between 28 days to a days )Total loss of prestress due to relaxation in I stage cables ( taking the ultimate loss to be 3 times the 1000 hrs loss )=2x2.28=4.56%Balance loss of prestress due to relaxation of steel from 28 days to a ==4.56-1.15=3.41%Loss of force in I st stage cables =3.41x4455=152.0kN100Loss Due to Shrinkage and creep of concrete.ShrinkageShrinkage strain =1.90E-04Modulus of elasticity of steel =195000MpaShrinkage stress =1.90E-04x195000=37.1MpaCreepCreep Strain of Concrete =1.6x4.3E-05=6.88E-05per MpaAverage stress at the c.g of the cable =7617kN/m2=7.617MpaHence, Creep Strain =6.88E-05x7.617=5.24E-04Stress loss due to creep of concrete =5.24E-04x2.0E+05=102.2MpaTotal stress loss due to shrinkage & creep of concrete =37.1+102.2=139.2MpaLoss of force in I stage cables =139.2x3.000x1184.4=494768N=494.8kNAverage force in I stage cables after anchoring =4455kN% Loss of force =494.8x100=11.11%4455Balance Loss of prestress =3.41+11.11=14.52%Loss of force in I stage cables =152.0+494.8=646.8kNcg of cables =0.6540.4730.4130.3840.3800.3840.4130.4730.654S P-646.8-646.8-646.8-646.8-646.8-646.8-646.8-646.8-646.8e = y - yb-0.833-1.118-1.178-1.207-1.211-1.207-1.178-1.118-0.833SM538.7723.1761.8780.9783.5780.9761.8723.1538.7Loss of Stresses in I stage cables due to balance loss of prestressing forcests8613516117317517316113586st47263536352674sb-824-1275-1325-1349-1353-1349-1325-1275-824Net stressessts-98535626979109397962635-985st352146644982550358065503498246643521sb583886847915710267507102791586845838Stress at cg level514978197364682365876823736478195149Average stress at c.g of cables =6766kN/m2Max. Comp Stress =8684kN/m20kN/m2Loss of Prestress in 2nd stage cables( between 28 days to a days )Loss of Prestress due to Relaxation of steelAverage force in II stage cables after anchoring =4044kNNo. of cables in II stage =2.75Average force per cable =4044=1470kN2.75% of UTS=1470x100=67.6%2176% loss of prestresing force at 1000 hrs=0.0+ (2.5-0) x (67.6-50)(70-50)=2.20%% loss at a =2x2.20=4.40%Loss of force in II stage =4.40x4044=177.7kN100Loss Due to Shrinkage and creep of concreteShrinkageshrinkage strain =1.90E-04Modulus of elasticity of steel=2.0E+05MpaShrinkage stress =1.90E-04x2.0E+05=37.1MpaCreepCreep Strain of Concrete =1.6x4.3E-05=6.88E-05per MpaAverage stress at the c.g of the cable =7617kN/m2=7.617MpaHence Creep Strain=6.88E-05x7.617=5.24E-04Stress loss due to creep of concrete =5.24E-04x2.0E+05=102.2MpaTotal stress loss due to shrinkage & creep of concrete =37.1+102.2=139.2MpaLoss of force in the cable =139.2x2.75x1184.4=453538N=453.5kN% Loss of force=453.5x100=11.22%4044Balance Loss of prestress =4.40+11.22=15.61%Loss of force in II stage cables =177.7+139.2=317.0kNcg of cables1.0900.7450.5770.5270.5160.5270.5770.7451.090S P-317.0-317.0-317.0-317.0-317.0-317.0-317.0-317.0-317.0e = y - yb-0.397-0.846-1.014-1.065-1.075-1.065-1.014-0.846-0.397S M125.9268.3321.5337.4340.8337.4321.5268.3125.9Loss of Stresses in II stage cables due to balance loss of prestressing forcests-48944555755449-48st-67-39-13-5-3-5-13-39-67sb-260-515-583-603-607-603-583-515-260Net stressessts-10334367010331150103367043-1033st345446254969549858025498496946253454sb557781697332649961436499733281695577Max. Comp Stress =8169kN/m2-1600kN/m2Train Load + Footpath Live Loadsts011221924240525652405192411220st0824141317661884176614138240sb0-2156-3695-4618-4927-4618-3695-21560Net stresses at serviceability limit state:sts-10331166259434383716343825941166-1033st345454506382726476867264638254503454sb557760143637188112161881363760145577Max Comp Stress =7686kN/m20.0kN/m2


diff.shrinkDifferential Shrinkage( as per clause 17.4.3.4 )The girder is assumed to be 30 to 60 days old when the Deck Slab is laid.Thickness of deck slab =220mmEffective width of deck slab =2050+1250=3300mmArea=3300x220=726000mm2For M40 Concrete, Ec =31.6kN/mm2Force,F =0.43x31.6x726000x2.5x1.00E-04=2468kNAT SUPPORTEccentricity =0.933-0.22=0.823m2sts =-2468+2467.8+2467.8x0.8230.72602.44561.5355=-1068kN/m2st =2468+2467.8x0.8232.44562.0094683748=2020kN/m2sb =2468+2467.8x0.8232.4456428571-0.9631351215=-1099kN/m2AT L/8Eccentricity =0.8286-0.22=0.719m2sts =-2468+2468+2468x0.7190.7261.8591.4979151747=-887kN/m2st =2468+2468x0.7191.85852.0393823128=2197kN/m2sb =2468+2468x0.7191.8585-0.7799366497=-946kN/m2AT L/4Eccentricity =0.829-0.22=0.719m2sts =-2468+2468+2468x0.7190.7261.85851.4979151747=-887kN/m2st =2468+2468x0.719=2197kN/m21.85852.039sb =2468+2468x0.7191.8585-0.780=-946kN/m2AT 3L/8Eccentricity =0.829-0.22=0.719m2sts =-2468+2468+2468x0.7190.7261.85851.4979151747=-887kN/m2st =2468+2468x0.7191.85852.0393823128=2197kN/m2sb =2468+2468x0.7191.8585-0.7799366497=-946kN/m2At MidSpan:Eccentricity =0.8286-0.22=0.719m2sts =-2468+2468+2468x0.7190.7261.85851.4979151747=-887kN/m2st =2468+2468x0.7191.85852.0393823128=2197kN/m2sb =2468+2468x0.7191.8585-0.7799366497=-946kN/m2


ultimate_momentCHECK FOR ULTIMATE LIMIT STATEThe Ultimate BM = 1.4 DL + 2.0 SDL + 1.5 FPLL + 2.0 LL + 1.0 CF=1.4x2669.9+2x2254.0+1.5x318.5+2x3203.7=15131.1kN-mReferring to clause 16.4.3.2 of IRS Concrete Bridge code : 1997,Ultimate Moment of Resistance, Mu = Fpb Aps (d 0.5x)Fpb =0.87x1900=1653.0MpaAps =5.750x12x98.7=6810mm2d =2200-157=2043mmAssuming the neutral axis lies within the flange,Fpu Aps =1900x6810=0.0275Fck b.d40x5750x2043Referring to table 25 of IRS concrete bridge code : 1997(Fpb / 0.87 Fpu ) = 1.0x/d =0.109+ (0.217-0.109) x-0.02250.05=0.060Hence x =0.060x2043=124mm 15131.1kN-mHence, O.K.Hence, the girder is safe for ultimate limit state.

&C&P&C&P

elongationsCALCULATION OF JACK GAUGE PRESSURE AND ELONGATION OF CABLES1) Jack gauge pressureFrom the literature of BBRV CONA CM200 jack is to be used for stressing 12 T 13 cables.Area of Piston of jack=482.24cm2Jack friction loss=4.0%Hence, Jack Gauge Pressure=Force in cable at jack end x 1.04Piston area=P ( t ) x 1000 x 1.04482.24=2.157P (t)Kg/cm22) Cable elongationsAll the cables are stressed fromboth ends. Cable lengths are for cable ends exactly flush with theanchorage faces. But for elongation, 750mm extra cable length from the face of the anchorage to thepoint of jack grips shall be considered in each stressing side.Hence, for a typical cable, length of the cable will beL =19692+750+75020292=21192mmArea of 12T13 cable =1184.4mm20.3E for strands =1.95E+05Mpas1 for 12T13 cable=Average stress in cable during stressing (N/mm2)=Average force in the cable during stressing (P) x 10001184.4(area of cable in mm2)=0.844P N/mm2Cable elongation at stressing end =s1xLE=0.844x P x L1.95E+05=4.33E-06P (kN) x L (mm)for 12 T 13 CablesJack gauge pressure and elongations at stressing end are tabulated for the cables.Initial jacking force in the 12T13 cables =1650.0kNJack gauge pressure for 12T13 cables =2.157x165.0=355.84Kg/cm2356Kg/cm2Area of 9T13 cable=888.3mm2E for strands=1.95E+05Mpas1 for 9T13 cable=Average stress in cable during stressing (N/mm2)=Average force in the cable during stressing (P) x 1000888.3(area of cable in mm2)=1.126PN/mm2Cable elongation at stressing end =s1xLE=1.126x P x L1.95E+05=5.77E-06P (kN) x L (mm)Initial jacking force in the 9 T 13 cables=1237.5kNJack gauge pressure for 9 T 13 cables=2.157x123.75=266.9Kg/cm2267Kg/cm2Elongation at stressing end for 12T13 cable=2.16E-06x P (kN) x L mmElongation at stressing end for 9T13 cable=2.89E-06x P (kN) x L mmCable noNo. of strandsJack gauge pressure (kg/cm2)Length of Cable (mm)Average force in cable during stressing (kN)cable elongation at stressing end (mm)1 & 212T13356211921590.273.02179222080312 T 13356212541565.872.021850412 T 13356212551578.8172.621852512 T 13356212291595.5673.32182869 T 13267212611194.273.321859


sf_tableTabulation of Shear Forces ( in kNs )S.NoLoadingDL/8L/43L/8L/21Self wt.223.0219.0149.372.34.82Deck Slab & diaph202.0198.0147.066.015.03SIDL364.4355.2237.0118.40.04FPLL51.450.134.017.00.05Live Load *514.1529.0403.2301.1202.66Centrifugal Force0.00.00.00.00.0*Shear Forces at different sections due to Live Loada) At Section 'D' from support7.188752.6516.880.4519.08m0.45Loaded Length = (19.08+0.45) -2.65=16.88mPage-81 Bridge Rules - 2008Total load for Shear =1905.40+ (1997.12-1905.40) x1.00.88=1986.1kNCDA = (0.15+8) x ( 2 -( 0.3 / 0.9 )] x 0.56+19.08)=0.391Max SF on girder A =1.391x1986.1x (8.44-0.4570.3819.08158.3=1.391x1986.1x0.419x0.444=514.1kNCorresponding BM =514.1x2.65=1362.4kNmb) At Section L/8Loaded Length = (19.08+0.45) -2.385=17.145mTotal load for Shear =1997.1+ (2088.9-1997.1) x1.000.15=2010.4kNMax SF on girder A =1.391x2010.4x (8.57-0.4570.3819.08158.3=1.391x2010.4x0.426x0.444=529.0kNCorresponding BM =529.0x2.385=1261.8kNmc) At Section L/4Loaded Length = (19.08+0.45) -4.770=14.760mTotal load for Shear =1740.59+ (1813.48-1740.59) x1.0000.760=1796.0kNMax SF on girder A =1.391x1796.0x (7.38-0.4570.3819.08158.3=1.391x1796.0x0.363x0.444=403.2kNCorresponding BM =403.2x4.770=1923.4kNmd) At Section 3L/8Loaded Length = (19.08+0.45) -7.155=12.375mTotal load for Shear =1589.22+ (1671-1589.22) x10.375=1619.8kNMax SF on girder A =1.391x1619.8x (6.19-0.4570.3819.08158.3=1.391x1619.8x0.301x0.444=301.1kNCorresponding BM =301.1x7.155=2154.3kNmd) At Section L/2Loaded Length = (19.08+0.45) -9.540=9.990mTotal load for Shear =1315.03+ (1377-1315.03) x0.50.490=1376.1kNMax SF on girder A =1.391x1376.1x (5.125 / 2-0.45) x 84.419.08158.3=1.391x1376.1x0.238x0.444=202.6kNCorresponding BM =202.6x9.540=1933.0kNm

&CPragati Consultants&C&P* )* )* )* )

ShearCALCULATION OF SHEAR STRESSESGrade of concrete = M40Grade of steel = fy415123456789DL/8L/43L/8L/25L/83/4 L7L /8DWeb thickness B (m)0.3500.3500.3500.3500.3500.3500.3500.3500.350Ap(m2)1.85851.85851.85851.85851.85851.85851.85851.85851.8585Yts(m)0.82860.82860.82860.82860.82860.82860.82860.82860.8286Yt(m)0.60860.60860.60860.60860.60860.60860.60860.60860.6086Yb(m)1.59141.59141.59141.59141.59141.59141.59141.59141.5914D(m)2.42002.42002.42002.42002.42002.42002.42002.42002.4200Zts(m3)1.49791.49791.49791.49791.49791.49791.49791.49791.4979Zt(m3)2.03942.03942.03942.03942.03942.03942.03942.03942.0394Zb(m3)-0.7799-0.7799-0.7799-0.7799-0.7799-0.7799-0.7799-0.7799-0.7799SHEAR FORCES IN kNS.NOLOADINGDL/8L/43L/8L/25L/83/4 L7L /8D1D.L + Deck Slab425.0417.0296.3138.319.8138.3296.3417.0425.02SDL364.4355.2237.0118.40.0118.4237.0355.2364.4DL + SDL789.4772.2533.3256.719.8256.7533.3772.2789.43FPLL51.450.134.017.00.017.034.050.151.44LL with impact514.1529.0403.2301.1202.6301.1403.2529.0514.15Centrg.Force x 1.00.00.00.00.00.00.00.00.00.0* According to IRS Concrete Bridge Code:1997CALCULATION OF ULTIMATE SHEAR FORCE (1.4 DL+2.0 SDL+1.5 FPLL+2.0LL) - For Max SF Case1DL x 1.4595.0583.8414.8193.627.7193.6414.8583.8595.02SDL x 2.0728.8710.4474.0236.80.0236.8474.0710.4728.83FPLL x 1.577.175.251.025.50.025.551.075.277.14LL x 2.01028.21058.1806.4602.2405.2602.2806.41058.11028.25Centrg.Force x 1.00.00.00.00.00.00.00.00.00.0Ult. Shear (V)2429.12427.41746.31058.1432.91058.11746.32427.42429.1Calculation of Corresponding Ultimate BM (1.4 DL + 2.0 SDL + 1.5 FPLL+2.0LL) - For Max SF Case1DL x 1.41567.01619.82807.03473.53737.93473.52807.01619.81567.02SDL x 2.01866.11966.03378.04226.04508.04226.03378.01966.01866.13FP LL x 1.5198.5209.1358.5447.9477.8447.9358.5209.1198.54LL x 2.02724.82523.53846.74308.53866.04308.53846.72523.52724.85Centrg.Force x 1.00.00.00.00.00.00.00.00.00.0Ult BM6356.46318.410390.212456.012589.712456.010390.26318.46356.4CALCULATION OF ULTIMATE BM (1.4 DL + 2.0 SDL + 1.5 FPLL+2.0LL) - for Max Bending Moment CaseBM CaseS.NoLoadingBM @ L/2BM @ 3L/8BM @ L/4BM @ L/8BM @ SupBM @ D1DL x 1.41567.01619.82807.03473.53737.93473.52807.01619.81567.01Self wt.183.5172.7138.481.2-1.573.32SDL x 2.01866.11966.03378.04226.04508.04226.03378.01966.01866.12Deck Slab239.6226.5179.5102.2-1.492.03FP LL x 1.5198.5209.1358.5447.9477.8447.9358.5209.1198.53SIDL576.0539.7431.0249.8-3.9225.24LL x 2.0744.42803.24805.46006.06407.46006.04805.42803.2744.44FPLL83.278.062.436.40.032.95Centrg.Force x 1.00.00.00.00.00.00.00.00.00.05Live Load3203.73003.02402.71401.60.0388.2Ult BM4376.06598.111348.914153.515131.114153.511348.96598.14376.06CF133.4125.099.857.8-0.952.1CALCULATION OF Corresponding Ultimate SF (1.4 DL + 2.0 SDL + 1.5 FPLL+2.0 LL) - For Max BM Case1DL x 1.4595.0583.8414.8193.627.7193.6414.8583.8595.02SDL x 2.0728.8710.4474.0236.80.0236.8474.0710.4728.83FPLL x 1.577.175.251.025.50.025.551.075.277.14LL x 2.0620.3598.2398.8199.40.0199.4398.8598.2620.35Centrg.Force x 1.00.00.00.00.00.00.00.00.00.0Ult SF2021.211967.491338.62655.3227.65655.321338.621967.492021.21calculation of relief of shear due to prestressingCABLESECTION123456789DL/8L/43L/8L/25L/83/4 L7L /8D1 &2P1492.01482.61494.11501.91509.61501.91494.11482.61492.0149.1150.5152.7154.5156.4(12 T 13)q1.7000.7650.0000.0000.0000.0000.0000.7651.7y0.1900.1820.1800.1800.1800.1800.1800.1820.22.000psin q44.2619.7980.0000.0000.0000.0000.00019.79844.3nos.pcos q1491.291482.51494.11501.91509.61501.91494.11482.51491.3e=y-yb-1.401-0.9-1.0-1.0-1.0-1.0-1.0-0.9-1.4M = Pcosq x e-2089.3-1406.3-1420.5-1427.8-1435.2-1427.8-1420.5-1406.3-2089.33P1446.21452.61487.91495.51503.11495.51487.91452.61446.2(12 T 13)q6.7095.60.00.00.00.00.05.66.7y0.3210.30.20.20.20.20.20.30.31.000psin q168.95142.80.00.00.00.00.0142.8169.0nos.pcos q1436.291445.61487.91495.51503.11495.51487.91445.61436.3e=y-yb-1.270-0.9-1.0-1.0-1.0-1.0-1.0-0.9-1.3M = Pcosq.e-1824.4-1230.5-1414.5-1421.8-1429.0-1421.8-1414.5-1230.5-1824.44P1455.81460.11486.41506.91514.51506.91486.41460.11455.8(12 T 13)q7.16.52.60.00.00.02.66.57.1y0.70.70.50.40.40.40.50.70.71psin q179.05164.168.20.00.00.068.2164.1179.1pcos q1444.781450.81484.81506.91514.51506.91484.81450.81444.8e=y-yb-0.889-0.5-0.7-0.7-0.7-0.7-0.7-0.5-0.9M = Pcosq.e-1284.0-687.3-984.9-1055.9-1061.2-1055.9-984.9-687.3-1284.05P1471.91474.81492.61510.51523.51510.51492.61474.81471.9(12 T 13)q5.65.23.21.10.01.13.25.25.6y1.11.10.90.80.80.80.91.11.11psin q142.93134.782.528.70.028.782.5134.7142.9nos.pcos q1464.941468.61490.41510.21523.51510.21490.41468.61464.9e=y-yb-0.499-0.1-0.3-0.3-0.4-0.3-0.3-0.1-0.5M = Pcosq.e-731.3-110.1-373.0-511.8-534.3-511.8-373.0-110.1-731.36P1468.71471.81490.71509.61527.31509.61490.71471.81468.7(9 T 13)q7.06.74.42.10.02.14.46.77.0y1.51.51.31.11.11.11.31.51.50.75psin q179.60170.6113.554.40.054.4113.5170.6179.6nos.pcos q1457.711461.91486.31508.61527.31508.61486.31461.91457.7e=y-yb-0.0620.40.1-0.0-0.1-0.00.10.4-0.1M = Pcosq.e-90.8514.9181.2-18.4-77.5-18.4181.2514.9-90.8 P cosq8366.98389.58559.88641.38699.28641.38559.88389.58366.9 M-6003.0-4043.1-4255.5-4277.5-4299.4-4277.5-4255.5-4043.1-6003.0no. of cables at section5.7505.7505.7505.7505.7505.7505.7505.7505.750relief due to prestress after15.61% loss Psinq714.2609.1235.869.50.069.5235.8609.1714.20.844x Psinq602.7514.0199.058.60.058.6199.0514.0602.7 Pcosq8366.98389.58559.88641.38699.28641.38559.88389.58366.90.844x Pcosq7060.77079.87223.57292.37341.17292.37223.57079.87060.70.844x M-5065.9-3411.9-3591.2-3609.7-3628.2-3609.7-3591.2-3411.9-5065.9Stresses due to prestress after15.61% losssts4171532148915141528151414891532417st131568716957703170817031695768716037sb10294818484918552860285528491818410294e-0.717-0.482-0.497-0.495-0.494-0.495-0.497-0.482-0.717y0.1880.1750.1570.1570.1570.1570.1570.1750.188a) d = D - y2.2322.2452.2632.2632.2632.2632.2632.2452.232b) d = 0.8*D1.9361.9361.9361.9361.9361.9361.9361.9361.936d = max of a & b2.2322.2452.2632.2632.2632.2632.2632.2452.232Max.allowable ult SF3144.13162.43188.83188.83188.83188.83188.83162.43144.1(as per cl 16.4.4.5 of IRS Bridge code - 1997)[4700*(B-(2/3)*0.075]dult SF2429.12427.41746.31058.1432.91058.11746.32427.42429.1From 6)UncrackedUncrackedCrackedCrackedCrackedCrackedCrackedUncrackedUncrackedrelief due to Prestress714.2609.10.00.00.00.00.0609.1714.2net ult SF1714.91818.31746.31058.1432.91058.11746.31818.31714.9OKOKOKOKOKOKOKOKOKHence web thickNesses provided are adequate.calculation of shear reinforcementUncracked sectionWeb thickNess (b) (m)0.3500.3500.3500.3500.3500.3500.3500.3500.350D (m)2.4202.4202.4202.4202.4202.4202.4202.4202.420ft (kN/m2)151815181518151815181518151815181518(as per cl 16.4.4.2 of IRS Bridge code - 1997)fcp (kN/m2) = Pcosq/A379938093887392439503924388738093799Vco =0.67 * b * D * sqrt(ft2 + 0.87* fcp* ft)(as per cl 16.4.4.2 of IRS Bridge code - 1997)1) Vco153515371548155315561553154815371535Cracked sectionMaximum SF caseWeb thickness (b) (m)0.3500.3500.3500.3500.3500.3500.350.350.35db (m)2.2322.2452.2632.2632.2632.2632.2632.2452.232fpt (kN/m2)959680898392845485048454839280899963ult Vu (kN)2429.12427.41746.31058.1432.91058.11746.32427.42429.1Corresponding ult Mu (kNm)6356.46318.410390.212456.012589.712456.010390.26318.46356.40.037*b*d*sqrt(fck)182.8183.8185.4185.4185.4185.4185.4183.8182.8Mcr (kN/m2)833673147519756175957561751973148586(0.37sqrt(fck)+0.87 fpt)*(I/Y)(Mcr*Vu)/Mu3186281012646422616421264281032812)Vcr(kN) -336829941449828447828144929943464(0.037*b*d*sqrt(fck)+ Mcr/Mu*Vu)Maximum BM caseWeb thickness (b) (m)0.3500.350.350.350.350.350.350.350.35db (m)2.2322.2452.2632.2632.2632.2632.2632.2452.232fpt (kN/m2)959680898392845485048454839280899963Corresponding ult Vu (kN)2021.21967.51338.6655.327.7655.31338.61967.52021.2ult Mu (kNm)4376.06598.111348.914153.515131.114153.511348.96598.14376.00.037*b*d*sqrt(fck)182.8183.8185.4185.4185.4185.4185.4183.8182.8Mcr (kN/m2)833673147519756175957561751973148586(0.37sqrt(fck)+0.87 fpt)*(I/Y)(Mcr*Vu)/Mu3850218188735014350887218139663)Vcr (kN)4033236510725351995351072236541484)Min Vcr(kN)494497501501501501501497494(0.1 bd sqrt(fck))5)Min Vc153515371072535199535107215371535(Min of 1, 2, & 3)6)Check whether section is cracked or uncrackedCrackedCrackedCrackedCrackedCrackedCrackedCrackedCrackedCrackedVc to be considered153515371072535501535107215371535(max of 4 & 5)Vu - Vc486431266120-473120266431486Providing2L Tor -10stirrups Asv =157mm2dt =2.420-0.04-0.005=2.375Sv (mm)2773135061123-2841123506313277(0.87*fy*d*Asv) / (V-Vc)Sv min (mm)405405405405405405405405405(0.87*fy*Asv) / (0.4*B*1000)Sv Provided4 L Tor 10 @ 1902 L Tor 10 @ 1904 L Tor 10 @ 190


shear_connectorDESIGN OF SHEAR CONNECTORSShear forces developed in girder and insitu deck slab in kN.S.NOShear force due toD1/ 8 span1/ 4 span3/ 8 span1SIDL364.4355.2237.0118.42Vehicular LL on G1514.1529.0403.2301.13FPLL on G151.450.134.017.04Centrifugal Force0.00.00.00.02.0 x SIDL + 2.0 x LL + 1.0 x CF1859.81868.61348.4873.0Shear flow at interface of girder and deck slab in horizontal direction,t =Q A yIWhere,Q = Shear forceA = Area of insitu deck slab=2.250x0.220=0.495m2y =Distance from N.A of composite girder to centroid of deck slab.At Section 1 - 1Longitudinal shear force shall not exceed lesser of followinga) k1 x fck x LsWhere,k1 =constant depending on the concrete bond across the shear plane under consideration,taken as 0.09.fck =Characteristic cube strength of concrete.=40Ls =length of shear plane under consideration.b) 0.7 x Ae x fyWhere,Ae =area of fully anchored reinforcement per unit length crossing the shear plane underconsideration.fy =Characteristic strength of steel.at ' D' ,k1 x fck x Ls=0.09x40x1050=3780kN/m0.7 x Ae x fy=0.7x1820x415=528.8kN/mArea of reinforcement =Q / 0.7x fy=528.8x10000.7x415=1820mm2DescriptionShear ForceAnalogousyMoment ofShear flowArea ofQarea ofInertia, Iat planereinforcementdeck slab1 - 1k1 Fck Ls0.7 Ae fy( kN )( m2 )( m )( m4 )( kN/m )( mm2 / m )At ' D '1859.80.49500.8231.432528.818203780528.81.362At 1/8 Span1868.60.49500.7191.2412535.518433780535.51.1867At 1/4 Span1348.40.49500.7191.2412386.513303780386.51.1867At 3/8 Span873.00.49500.7191.2412250.28613780250.21.1867At Section 2 - 2Ls =Length of shear plane under consideration =220mmDescriptionShear ForceCantileveryMoment ofShear flowArea ofQarea ofInertia, Iat planereinforcementdeck slab1 - 1K1 Fck Ls0.7 Ae fy( kN )( m2 )( m )( m4 )( kN/m )( mm2 / m )At ' D '1859.80.14500.8231.4324154.9533792154.9At 1/8 Span1868.60.14500.7191.2412156.9540792156.9At 1/4 Span1348.40.14500.7191.2412113.2390792113.2At 3/8 Span873.00.14500.7191.241273.325279273.3Shear connectors between deck slab and girderSNo.DescriptionReinforcement required in mm2/mProposed reinforcement1At ' D '1820Provide 4-legged Tor-16 stirrups @190c/c(4232.8827332578mm2/m )2At 1/8 Span1843Provide 4-legged Tor-16 stirrups @190c/c(4232.8827332578mm2/m )3At 1/4 Span1330Provide 4-legged Tor-16 stirrups @190c/c(4232.8827332578mm2/m )4At 3/8 Span861Provide 4-legged Tor-16 stirrups @190c/c(4232.8827332578mm2/m )Minimum reinforcement in cantilever portion of deck slab for shear lag.SNo.DescriptionReinforcement required in mm2/mProposed minimum reinforcementin deck slab1At ' D '533Provide Tor-10 @ 200c/c + Tor-12 @200 c/c at top.Provide Tor-10 @ 200c/c at bottom.2At 1/8 Span540Provide Tor-10 @ 200c/c + Tor-12 @200 c/c at top.Provide Tor-10 @ 200c/c at bottom.3At 1/4 Span390Provide Tor-10 @ 200c/c + Tor-12 @200 c/c at top.Provide Tor-10 @ 200c/c at bottom.4At 3/8 Span252Provide Tor-10 @ 200c/c + Tor-12 @200 c/c at top.Provide Tor-10 @ 200c/c at bottom.


grdr_reftLONGITUDINAL REINFORCEMENT FOR PSC GIRDERSGrade of concrete=M40Grade of steel=Fe415As Per 15.3 of IRC18 - 2000 Minimum % of longitudinal reinforcement in PSC Girders are calculated.At End SectionCross Sectional area of PSC girder=1.720m2Min % of reinforcement=0.18x1.720x106100=3095.36mm2 /mProvided48no's Tor -10(3769.9111843078mm2 )At Mid Span SectionCross Sectional area of PSC girder=1.133m2Min % of reinforcement=0.18x1.1325x106100=2038.5mm2 /mProvided32no's Tor -10(2513.2741228718mm2 )


deck_slabDESIGN OF DECK SLAB :CL OF TRACK1509004500150220205025001150Effective span=2500mmDepth of slab =220mmTotal deck width =5700mmLoads:Dead LoadSelf Weight of Slab =0.220x25=5.5kN/m2Super Imposed Dead LoadWeight of Ballast =60.0/5.7=10.5kN/m2Wearing Coat =(( 0.075 + 0.025 )/2) x 24 x4.5=0.95kN/m25.7=11.47kN/m2Kerbs =2x (0.2x0.8) x25=8.0kN/mBallast Retainer =1x (0.200x0.800) x25=4.0kN/mFootpath slab = (0.750x0.100) x25=1.9kN/mParapet wall = (0.900x0.150) x25=3.4kN/mFPLLFootpath live load =5.0kN/m2i.e0.900x5.0=4.5kN/mLive Load:A) Live load with type I sleeper ( 2745 x 254 mm )case(a)Max. axle load =25t =250kNDispersion along the span =2.745+0.075+0.300=3.120mEffective width across the span =0.254+0.075+0.300+2.500x24=1.879mWheel spacing for 25t wheel =1.950m>1.879mHence, Effective width across the span =1.879mCDA = [0.15+8] x [ 2-0.3] x 0.56+2.50.9=1.091x0.833=0.909Intensity of load =250x1.909=81.42kN/m23.120x1.879case(b)Max. axle load =22.5t =225kNDispersion along the span =3.120mEffective width across the span =0.254+0.075+0.300+2.500x2=1.879m4Wheel spacing for 22.5t =1.650m30.61kNmd) MR of steel at servicebility =sst x Ast x j x d=311x1340x0.923x172=66.24kNm >30.61kNmHence, section is safe with Tor -16@150mm c/c ----- at TopCheck for min. % of reinforcement% of steel provided =1340x100=0.78% >0.20%1000x172Distribution ReinforcementAs per CL.15.9.4.2 of IRS Code of Pratice for plain, reinforced and prestressed concrete forGeneral Bridge Construction - 1997 )Ast =0.12x1000x172=206.4mm2/m100Hence provideTor -10@180mm c/c (436mm2/m) on top face.Check for bottom steelc) MR of concrete at servicebility =0.5 x fcb x n x j x b x d2 ==0.5x20x0.231x0.923x1000x1722=63.0kNm >36.70kNmd) MR of steel at servicebility =sst x Ast x j x d=311x2011x0.923x172=99.36kNm >36.70kNmHence, section is safe with Tor -16@200mm c/c+ Tor -16@200mm c/c ----- at bottom.Check for min. % of reiforcement% of steel provided =2011x100=1.17% >0.20%1000x172Distribution ReinforcementAs per CL.15.9.4.2 of IRS Code of Pratice for plain, reinforced and prestressed concrete forGeneral Bridge Construction - 1997 )Ast =0.12x1000x172=206.4mm2/m100Hence provideTor -10@180mm c/c (436mm2/m) on bottom face.Check for ultimate Shear at distance 'd' from support:Effective depth =220-40-16=172mm2due to dead Load =5.5x5.700-5.5x2.7472=0.6kNdue to SDL =64.69-11.5x2.747-9.9-3.4=19.9kNdue to Live Load =83.45x3.120-83.45x1.0146kN2due to FPLL =7.25-4.50=2.7kNAccording to Combination 1 as given in table 12 of IRS Concrete bridge code :1997,Ultimate SF =1.4x0.6+2.0x19.9+1.5x2.7+2.0x46.1=137.1kNUltimate shear stress in concrete, n =Vb x d=137.1x1000=0.80Mpa0.80MpaHence, the deck slab is safe in shear at ultimate limit state without shear reinforcement.DESIGN OF CANTILEVER PORTION(9.9+4.5)kN/m3.4kN/mX11.5+5.0kN/mY753501000525Y3501875BM at section X - Xdue to DL =5.5x1.8752=9.67kNm2due to SDL =11.47x1.8752+9.9x1.3502+3.4x1.8=39.62kNmdue to FPLL =4.5x1.350=6.08kNmdue to PQRS LOADINGBM at section X - X =85.6x0.311=26.62kNm/mA) Check for ultimate limit stateAccording to Combination 1 as given in table 12 of IRS Concrete bridge code :1997,Ultimate BM =1.4 x DL + 2.0 x SDL + 1.5 x FPLL + 2.0 x LL=1.4x9.67+2.0x39.62+1.5x6.08+2.0x0.00=101.89kNmAssuming a reinforcement of Tor -16@150mm c/c ----- at TopArea of steel, Ast =1340mm2d =450-40-16=402mm2Z = (1-1.1x415x1340) xd40x1000x402=0.962d>0.95dHence, Z =0.950x402=382mmUltimate Moment of Resistance according to clause 15.4.2.2.1 of IRS Concrete Bridge Code:1997,is lesser of the following :i) Ultimate MR of steel =0.87xfyxAstxz=0.87x415x1340x382=184.82kNmii)Ultimate MR of concrete =0.15xfckxbxd2=0.15x40x1000x4022=969.62kNmHence, Mu of section =184.82kNm>101.89kNmHence, the section is safe at ultimate limit state.B) Check for Serviceability Limit stateAccording to Combination 1 as given in table 12 of IRS Concrete bridge code :1997,BM at serviceability limit state =1.0 x DL + 1.2 x SDL + 1.0 x FPLL + 1.1 x LL=1.0x9.67+1.2x39.62+1.0x6.08+1.1x0.00=63.29kNmAccording to Combination 5 as given in table 12 of IRS Concrete bridge code :1997,BM at serviceability limit state =1.0 x DL +1.0 x SDL + 1.0 x derailment loads + 1.0 x PQRS Load=1.0x9.67+1.0x39.62+1.0x0.00+1.0x26.62=75.91kNmfor M40Concrete, As per table 11of IRC concrete bridge code - 1997fcb=40x0.5=20Mpasst=415x0.75=311Mpam=280=280=4.673xfcb3x201n=1 +sst=0.231m x fcbj =1-n/3 =0.923iii) MR of concrete at servicebility limit state =0.5 x fcb x n x j x b x d2=0.5x20x0.231x0.923x1000x4022=344.14kNm >75.91kNmiv) MR of steel at servicebility limit state =sst x Ast x j x d=311x1340x0.923x402=154.82kNm >75.91kNmHence, section is safe with Tor -16@150mm c/c ----- at Top.Check for min. % of reiforcement% of steel provided =1340x100=0.33% >0.20%1000x402BM at section Y - Ydue to DL =5.5x1.5252=6.40kNm2due to SDL =11.5x1.5252+11.5x1.0002+3.4x1.450=29.75kNmdue to FPLL =4.5x1.000=4.50kNmLength of PQRS loading beyond Y-Y =0.486+1.060-1.0522=0.491mBM due to PQRS loading =85.6x0.4912=10.32kNm2A) Check for ultimate limit stateAccording to Combination 1 as given in table 12 of IRS Concrete bridge code :1997,Ultimate BM =1.4 x DL + 2.0 x SDL + 1.5 x FPLL + 2.0 x LL=1.4x6.40+2.0x29.75+1.5x4.50+2.0x0.00=75.19kNmAssuming a reinforcement of Tor -16@150mm c/c ----- at TopArea of steel, Ast =1340mm2d =220-40-16=172mm2Z = (1-1.1x415x1340) xd40x1000x172=0.911d75.19kNmHence, the section is safe at ultimate limit state.B) Check for Serviceability Limit stateAccording to Combination 1 as given in table 12 of IRS Concrete bridge code :1997,BM at serviceability limit state =1.0 x DL + 1.2 x SDL + 1.0 x FPLL + 1.1 x LL=1.0x6.40+1.2x29.75+1.0x4.50+1.1x0.00=46.59kNmAccording to Combination 5 as given in table 12 of IRS Concrete bridge code :1997,BM at serviceability limit state =1.0 x DL +1.0 x SDL + 1.0 x derailment loads + 1.0 x PQRS Load=1.0x6.40+1.0x29.75+1.0x0.00+1.0x10.32=46.46kNmfor M40Concrete, As per table 11of IRC concrete bridge code - 1997fcb=40x0.5=20Mpasst=415x0.75=311Mpam=280=280=4.673xfcb3x201n=1 +sst=0.231m x fcbj =1-n/3 =0.923iii) MR of concrete at servicebility limit state =0.5 x fcb x n x j x b x d2=0.5x20x0.231x0.923x1000x1722=63.0kNm >46.59kNmiv) MR of steel at servicebility limit state =sst x Ast x j x d=311x1340x0.923x172=66.24kNm >46.59kNmHence, section is safe with Tor -16@150mm c/c ----- at TopCheck for min. % of reinforcement% of steel provided =1340x100=0.78% >0.20%1000x172DESIGN OF LONGITUDINAL CANTILEVER PORTION125X10.0+11.474 kN/mkNX127mm350865BM at section X - Xdue to DL =10.0x0.8652=3.74kNm2due to SDL =11.474x0.8652=4.29kNm2Live Load:A) Live load with type I sleeper ( 2745 x 254 mm )case(a)Max. axle load =25t =250kNMax. Wheel load =12.5t =125kNDispersion across the span =Effective width across the span =0.254+0.075+0.300+0.738x1.2=1.515mWheel spacing for 25t wheel =1.676m>1.515mHence, Effective width across the span =1.515mCDA = [0.15+8] x [ 2-0.3] x 0.56+0.7380.9=1.337x0.833=1.114Max. axle load =25t =250kNDispersion along the span =2.745+0.075+0.300=3.120mEffective width across the span =0.254+0.075+0.300+2.500x24=1.879mWheel spacing for 25t wheel =1.950m>1.879mHence, Effective width across the span =1.879mIntensity of load =125x2.114=174.50kN/m21.515LIVE LOAD BM.174.50x0.738=128.78kNmA) Check for ultimate limit stateAccording to Combination 1 as given in table 12 of IRS Concrete bridge code :1997,Ultimate BM =1.4 x DL + 2.0 x SDL + 1.5 x FPLL + 2.0 x LL=1.4x3.74+2.0x4.29+1.5x0.00+2.0x128.78=271.39kNmAssuming a reinforcement of Tor -16@100mm c/c ----- at Top+10@180mm c/c ----- at TopArea of steel, Ast =2447mm2d =400-40-16=352mm2Z = (1-1.1x415x2447) xd40x1000x352=0.921d271.39kNmHence, the section is safe at ultimate limit state.B) Check for Serviceability Limit stateAccording to Combination 1 as given in table 12 of IRS Concrete bridge code :1997,BM at serviceability limit state =1.0 x DL + 1.2 x SDL + 1.0 x FPLL + 1.1 x LL=1.0x3.74+1.2x4.29+1.0x0.00+1.1x128.78=150.55kNmAccording to Combination 5 as given in table 12 of IRS Concrete bridge code :1997,BM at serviceability limit state =1.0 x DL +1.0 x SDL + 1.0 x derailment loads + 1.0 x PQRS Load=1.0x3.74+1.0x4.29+1.0x0.00+1.0x128.78=136.82kNmfor M40Concrete, As per table 11of IRC concrete bridge code - 1997fcb=40x0.5=20Mpasst=415x0.75=311Mpam=280=280=4.673xfcb3x201n=1 +sst=0.231m x fcbj =1-n/3 =0.923iii) MR of concrete at servicebility limit state =0.5 x fcb x n x j x b x d2=0.5x20x0.231x0.923x1000x3522=263.85kNm >150.55kNmiv) MR of steel at servicebility limit state =sst x Ast x j x d=311x2447x0.923x352=247.47kNm >150.55kNmHence, section is safe with Tor -16@100mm c/c ----- at Top.Check for min. % of reiforcement% of steel provided =2447x100=0.70% >0.20%1000x352

&CPragati Consultants&C&P=wearing coat thicknessdepth of ballast cushionspan of deck slab = spacing of girders.wearing coat thicknessdepth of ballast cushionspan of deck slab = spacing of girders.wearing coat thicknessdepth of ballast cushionspan of deck slab = spacing of girders.

cross-girDESIGN OF CROSS GIRDERS1) CENTRAL CROSS GIRDERSpacing of cross girder =4.770mWidth, b =0.350mLoad calculationa) Dead loadSelf wt. Of deck slab =4.770x0.220x25=26.24kN/mSelf wt. Of cross girder =0.350x1.900x25=16.63kN/mTotal DL=42.86kN/mb) SDLdue to Ballast =6.0x4.770=11.45kN/m2.5Due to wearing coat =0.0625x24x4.770=7.16kN/mTotal SDL =18.60kN/mc) Live LoadAs per the note given in Appendix II of Bridge Rules, the live load on a cross girder will beequal to half the total load for bending in a length L, equal to twice the distance over centres ofcross girders.L =2x4.770=9.540mTotal load for BM =1089.4+ (1108.53-1089.4) x (9.540-9.500.5)=1090.9kNCDA = (0.15+8) x(6+9.540)(2-0.3) x0.50.9=0.554Span of the cross girder =2.5mUDL on cross girder =1090.9x1.554=339.06kN/m2.5x2Hence, Total Load = DL + SDL + LL=42.86+18.60+339.06=400.52kN/mMax. + ve BM =400.52x2.52=312.91kNm8Max. - ve BMdue to DL + SDL = (42.86+18.60) x2.0522=129.15kN/mdue to Kerbs, footpath slab, footpath live load, parapet wall= (1.45x4.770) x1.554+ (3.75x4.77) x (2.05-0.075)=46.08kN/mTherefore, Total - ve BM =129.15+46.08=175.23kN/mFor + ve BM,Ultimate BM =1.5x312.91=469.36kNmAssuming,4nos. Tor -20---- at bottom. (1885mm2+2nos. Tor -20)( Ast )min = 0.85 x b x d / fy =0.85x350x1850415=1326mm20.073dTherefore, Resisting Moment, Mu =0.87.fy.Ast.d(1- Ast.fy / b.d.fck)=0.87x415x1885x1850x(1-1885x415)350x1850x40=1221.02kNm>469.36kNmHence, safe.For - ve BM,Ultimate BM =1.5x175.23=262.84kNmAssuming,3nos. Tor -20---- at top. (1571mm2+2nos. Tor -20)( Ast )min = 0.85 x b x d / fy =0.85x350x1850415=1326mm20.061dTherefore, Resisting Moment, Mu =0.87.fy.Ast.d(1- Ast.fy / b.d.fck)=0.87x415x1571x1850x(1-1571x415)350x1850x40=1022.79kNm>262.84kNmHence, safe.Distribution of reinforcement,at Top 0.2D =0.2x1900=380mmAst =1571x0.5x (2.5-0.5)1.69=769mm2Provide5nos. Tor -20(1571mm2)Balance to be distributed in 0.6 D =0.6x1900=1140mmBalance steel to be provided =1571-769=802mm2Provide,10 nos. Tor-10 ( 785 mm2), distributed equally on each face.2) END CROSS GIRDERThe end cross girder is also designed for the same moments as the central crossgirder and it is also checked for lifting of super structure for future replacement of bearings.DL + SDL + FPLL on each bearing=627.0+496.0+67.0=1190.0kNsay1190kN1190kN1190kN2.5m1.251.25595595595595Max. + ve BM =595x1.25=371.88kNm>312.91kNm2Max. - ve BM =595x1.875+595x0.625-1190x1.25=0kNm1571mm2xu=0.87.fy.Ast / 0.36.fck.b.d =d=0.87x415x15710.36x40x350x1850=0.061( xu )lim for Fe415 =0.480>0.061dTherefore, Resisting Moment, Mu =0.87.fy.Ast.d(1- Ast.fy / b.d.fck)=0.87x415x1571x1850x(1-1571x415)350x1850x40=1022.79kNm>262.84kNmHence, safe.Distribution of reinforcement,at Top 0.2D =0.2x1850=370mmAst =1571x0.5x (2.5-0.5)1.69=769mm2Provide5nos. Tor -20(1571mm2)Balance to be distributed in 0.6 D =0.6x1850=1110mmBalance steel to be provided =1571-769=802mm2Provide,10 nos. Tor-10 ( 785 mm2), distributed equally on each face.Shear :As this is a deep beam shear does not govern. Hence provide minimum shear reinforcement.Provide 2L - Tor 10 @ 200 c/c.


Reactions TABULATION OF REACTIONSSUPPORTS216TotalNodeL/CForce-X kNForce-Y kNForce-Z kNMoment-X kNmMoment-Y kNmMoment-Z kNmDead Load ( kN )2103390000Self Wt.339339678.00202880000304960000Deck slab288.00288576.0040672000050670000SIDL496.00496992.003103390000202880000Total DL+SDL1123.0011232246.00304960000406720000Live load On Footpath67.0067134.0050670000Liveload672.006721344.00DL+SIDL+LL1862.001862.003724.00Max Load1862.001862.003724.001872.581872.58Min load1123.001123.002246.001121.871121.87


BearingDesign of Elastomeric Bearings- designed as per UIC code 772-R.Load on each bearing1)Self Weight of girder+ deck slab =627.0kNfrom STAAD analysis.2)Super Imposed Dead Load =496.0kN3)Foot Path Live Load =67.0kNNo. of internal elastomeric layers=4nos.Thickness of internal elastomeric layers=10mmNo. of M.S.plates=5nos.Thickness of M.S. plates=3mmCover at top and bottom of M.S. plates=5mmCover at sides=6mmLoaded Length (effective length) =19.08mTotal load for Shear =2181+ (2272-2181) x0.08=2188kN1.0CDA =0.15+8(6+19.08)=0.469x0.833=0.3914) Train Load == {1.391x2188x (1.25+0.10) }2.54=410.8kNTotal Load on each bearing =1600.8kN say1602kN116144Assuming a fully moulded neoprene bearing of dimensions,600x380x65mmPlan area of bearing, A = ab =588x368=216384mm2Effective plan area, A' = (588-1.730) x368=215747mm2Pc =Sustained

Documents

1017_19.08m 9.4.14