FinalNATIONAL ENGINEERING SERVICES PAKISTAN & PARTENERS LLC.Job No.Project: AZADI CHOWK FLYOVERBy: Subject: DESIGN OF RCC BOX GIRDERChk: Girder/ElementLoad CaseNegative Moment -MuMaximum Shear VuMoment Against Vu Date: January, 2014Entire BridgeStr I 156208INPUT DATAStr I 175555Str I 55154Str I Group7137Span of Box Girder,L=27000mm1st InteriorStrength 1Total Width of Box Girder =8600mmStrength 2Total Depth of Box Girder,h =1600mmService 1Effective Depth,d=1350mm2nd InteriorStrength 1Top Flange Thickness, hf =250mmStrength 2Bottom Flange Thickness,bf =200mmService 1Web Width, bw =300mm600for Shear3rd InteriorStrength 1No. of Cells =2no.Strength 2C/C Distance B/W Cells =2950mmService 1Cantilever/Overhang=1050mmLeft ExteriorStrength 1fc'=28MpaStrength 2fy=414MpaService 1Right ExteriorStrength 1FLEXURE DESIGNStrength 2Service 1(a)Determine Effective Compression Flange Width.For Interior GirderEffective Compression Flange Width Should be Smallest of the FollowingAASHTO LRFD 5.1.1btop=1/4xSpan Length=6750mmbtop=12hf+bw=3300mmbtop=Average Spacing of Adjacent Beam2950mm

btop=2950mmFor Exterior GirderEffective Compression Flange Width Should be Smallest of the Followingbtop=1/8xSpan Length=6750mmbtop=6hf+1/2xbw=1650mmbtop=Width of Overhang1200mm

btop=1200mm

btop=1/2xbtop of interior girder+btop btop=2675(b)Required Flexural Reinforcementmin>0.03fc'/fyAASHTO LRFD 5.1.10.0020289855For Interior GirderAg(inerior girder)=1732500mm2Asmin(interior girder)=3515mm25.45in2For Exterior GirderAg(exterior girder)=1608750mm2Asmin(exterior girder)=3264mm25.06in2

(c)Moment Calculation

For Interior GirderFOR INTERNAL GIRDERMoment Due to Selfweight of Girder,Ms=371Ton.m3639510000N.mmMOMENTS FROM SAP(T-M)+ve-veSHEARMoment Due to Wearing Surface,Mw=35Ton.m343350000N.mmSTRLGROUP918945220Moment Due to Superimposed Dead/Barrier,Mb=55Ton.m539550000N.mmEEGROUP7561075189Live Load Moment, MLL=150Ton.m1471500000N.mmSERGROUP654675155Mu=1.25x(Ms+Mb)+1.5xMw+1.75*MLLFOR INTERNAL GIRDER847.5Ton.m107510545750000N.mm10545.75KN.mSHEAR FROM SAP(T-M)SHEARMOMENTMu=xMnSTRLGROUP220936Mn=942Ton.m=9237750000N.mm9237.75KN.mEEGROUP1891068a=1xcSERGROUP155675c=Depth of N.A from Top1=0.85-0.05((fc'-28)/7))0.85Assume Section is Rectangular,a=Asxfy/0.85xfc'xbtop129.73mmSECTION IS RECTANGULARMn=Asxfyx(d-a/2)Putting Value of "a"in Mn We Find Equation,As=z/2*(1-sqrt(1-4*Mu/*fy*d*z))Where,z=1.7*fc'*btop*d/fy457891.304347826mm2

As(Exterior Girder)=22024.681411631mm234.1383244647in2##Provided As(Exterior Girder)=22000mm2111034.10in22227No. of Bars134.0909090909109.2592592593SpacingFor Exterior GirderFOR EXTERNAL GIRDERMoment Due to Self Weight of Girder,Ms=267Ton.m2619270000N.mmMOMENTS FROM SAP(T-M)+ve-veSHEARMoment Due to Wearing Surface,Mw=22Ton.m215820000N.mmSTRLGROUP649635160Moment Due to Superimposed Dead,Mb=38Ton.m372780000N.mmEEGROUP528700136Live Load Moment, MLL=150Ton.m1471500000N.mmSERGROUP462470106Mu=1.25x(Ms+Mb)+1.5xMw+1.75*MLLFOR EXTERNAL GIRDER676.75Ton.m7006867000000N.mm6867KN.mSHEAR FROM SAP(T-M)SHEARMOMENTMu=xMnSTRLGROUP160648Mn=752Ton.m=7376575000N.mm7376.575KN.mEEGROUP136693Assume Section is Rectangular,SERGROUP106465a=Asxfy/0.85xfc'xbtop110.55mmSECTION IS RECTANGULARMn=Asxfyx(d-a/2)Putting Value of "a"in Mn We Find Equation,As=z/2*(1-sqrt(1-4*Mu/*fy*d*z))Where,z=1.7*fc'*btop*d/fy415206.52173913mm2

As(Exterior Girder)=14132.8733190123mm221.9059974565in2Provided As(Exterior Girder)=17000mm21110111026.35in21721157.3529411765127.380952381(a)Max Reinforcement CheckNo. of BarsSpacingFor Interior Girderc=a/1c=Depth of N.A from Top1=0.85-0.05((fc'-28)/7))0.85c=152.6177769213mmc/d=0.11< 0.6OKAASHTO LRFD 5.3.2.1For Exterior Girderc=a/1c=Depth of N.A from Top1=0.85-0.05((fc'-28)/7))0.85c=130.06mmc/d=0.10< 0.6OKAASHTO LRFD 5.3.2.1

SHEAR DESIGN FOR INTERIOR GIRDER

(a)Check Critical Section for Shear

As=22000.00mm2btop=2950mm2a=Asfy/0.85fc'b129.73mmCritical Distance from Face of Support "dv" is Largest of Following(i)de-a/21285.14mm(ii)0.9de1215mm(iii)0.72h1152mmso,dv=1285.14mmCritical Section is at Distance dv from Face of Support i.e Distance B/W Centerline and Critical Section=2085.14mm0.077L

(b)Determine Mu and Vu at Critical SectionMu=954.00Ton.m9358740000N.mm9358.74KN.mVu=278.00Ton2727180N2727.18KNv=Vu/vxbvxdv4.72N/mm2v/fc'=0.17300.00OK

(d)Determine Maximum Spacing RequiredVuMu/dvxf+(Vu/v-0.5Vs)xcotAsxfy=7038000NMu/dvxf+(Vu/v-0.5Vs)xcot=4696182.11NOK

CRACK CONTROL CHECK FOR INTERIOR GIRDER

(a)Check if the Section is CrackedService Load Moments=611Ton.m5993910000N.mm5993.91KN.mModulus of Rupture, fr=0.63*(fc')1/23.33N/mm20.8xfr=2.67N/mm2btop=2950mmIg=636610174264mm4y'=717mmWhere, y' is the Distance from Most Compressed Concrete Fiber to N.AS= Ig/(h-y')720962824.761042mm3fc=M+ve/S8.31N/mm2SECTION IS CRACKED(b)Calculate Tensile Stress of ReinforcementAssuming N.A is Located in the Web, Thus Finding it's Location "x"WithAs'=0mm2d'=0mmn=Es/Ec=7.871=Asxfy/0.85xfc'xbtopx=sqrt(B2+C)-B356.16mm>hfOK

B=1/bw(hfx(b-bw)+nxAs+(n-1)xAs')2785.78C=2/bw(hf2/2x(b-bw)+nxdxAs+(n-1)xd'xAs')2111186.78Icr=214475110797.627mm4fs=n*M+ve*(d-x)/Icr218.71N/mm2the allowable stress can be obtained by putting Z=30000 for moderate exposure and dc=50mmfsa=Z/(dc*A)1/3352.85N/mm2OK

CRACK CONTROL CHECK FOR EXTERIOR GIRDER

(a)Check if the Section is CrackedService Load Moments=477Ton.m4679370000N.mm4679.37KN.mModulus of Rupture, fr=0.63*(fc')1/23.33N/mm20.8xfr=2.67N/mm2bbot=1600mmIg=377775853628mm4y'=493mmWhere, y' is the Distance from Most Compressed Concrete Fiber to N.AS= Ig/(h-y')341260933.719964mm3fc=M+ve/S13.71N/mm2SECTION IS CRACKED(b)Calculate Tensile Stress of ReinforcementAssuming N.A is Located in the Web, Thus Finding it's Location "x"WithAs'=0mm2d'=0mmn=Es/Ec=7.871=Asxfy/0.85xfc'xbtopx=sqrt(B2+C)-B328mm0.03fc'/fyAASHTO LRFD 5.1.10.0025For Interior GirderAg(inerior girder)=1972500mm2Asmin(interior girder)=4931.25mm27.64in2For Exterior GirderAg(exterior girder)=1686142mm2Asmin(exterior girder)=4215.355mm26.53in2

(c)Moment Calculation

For Interior GirderMoment Due to Selfweight of Girder,Ms=375Ton.m3678750000N.mmMoment Due to Wearing Surface,Mw=105Ton.m1030050000N.mmMoment Due to Superimposed Dead/Barrier,Mb=37.5Ton.m367875000N.mmLive Load Moment, MLL=302Ton.m2962620000N.mm

Mu=1.25x(Ms+Mb)+1.5xMw+1.75*MLL1201.63Ton.m=11787941250N.mm11787.94KN.mMu=xMnMn=1335.14Ton.m=13097712500N.mm13097.71KN.ma=1xcc=Depth of N.A from Top1=0.85-0.05((fc'-28)/7))0.8Assume Section is Rectangular,a=Asxfy/0.85xfc'xbtop111.09mmSECTION IS RECTANGULARMn=Asxfyx(d-a/2)Putting Value of "a"in Mn We Find Equation,As=z/2*(1-sqrt(1-4*Mu/*fy*d*z))Where,z=1.7*fc'*btop*d/fy621119.791666667mm2

As(Exterior Girder)=22509.6965791272mm234.8900994778in2Provided As(Exterior Girder)=24000mm237.2000744001in224-#11

For Exterior GirderFor Exterior GirderMoment Due to Self Weight of Girder,Ms=285Ton.m2795850000N.mmMoment Due to Self Weight of Girder,Ms=285Ton.m2795850000N.mmMoment Due to Wearing Surface,Mw=80Ton.m784800000N.mmMoment Due to Wearing Surface,Mw=80Ton.m784800000N.mmMoment Due to Superimposed Dead,Mb=30Ton.m294300000N.mmMoment Due to Superimposed Dead,Mb=30Ton.m294300000N.mmLive Load Moment, MLL=238Ton.m2334780000N.mmLive Load Moment, MLL=238Ton.m2334780000N.mm

Mu=1.25x(Ms+Mb)+1.5xMw+1.75*MLLMu=1.25x(Ms+Mb)+1.5xMw+1.75*MLL930.25Ton.m=9125752500N.mm9125.7525KN.m930.25Ton.m=9125752500N.mm9125.7525KN.mMu=xMnMu=xMnMn=1033.6111111111Ton.m=10139725000N.mm10139.725KN.mMn=1033.61Ton.m=10139725000N.mm10139.725KN.mAssume Section is Rectangular,Assume Section is Rectangular,a=Asxfy/0.85xfc'xbtop78.80mmSECTION IS RECTANGULARa=Asxfy/0.85xfc'xbtop38892.70mmSECTION IS RECTANGULARMn=Asxfyx(d-a/2)Mn=Asxfyx(d-a/2)Putting Value of "a"in Mn We Find Equation,Putting Value of "a"in Mn We Find Equation,As=z/2*(1-sqrt(1-4*Mu/*fy*d*z))As=z/2*(1-sqrt(1-4*Mu/*fy*d*z))Where,z=1.7*fc'*btop*d/fy656757.81mm2Where,z=1.7*fc'*btop*d/fy1330.5838579125mm2

As(Exterior Girder)=17247.52mm2As(Exterior Girder)=ERROR:#NUM!mm226.73in2ERROR:#NUM!in2Provided As(Exterior Girder)=18000mm2Provided As(Exterior Girder)=18000mm227.90in218-#1127.9000558001in218-#11(a)Max Reinforcement Check

For Interior Girderc=a/1c=Depth of N.A from Top1=0.85-0.05((fc'-28)/7))0.8c=138.8621022179mmc/d=0.0965997233< 0.6OKAASHTO LRFD 5.3.2.1

For Exterior Girderc=a/1c=Depth of N.A from Top1=0.85-0.05((fc'-28)/7))0.8c=98.50mmc/d=0.07< 0.6OKAASHTO LRFD 5.3.2.1

SHEAR DESIGN FOR INTERIOR GIRDER

(a)Check Critical Section for Shear

As=24000.00mm2btop=3050mm2a=Asfy/0.85fc'b111.09mmCritical Distance from Face of Support "dv" is Largest of Following(i)de-a/21381.96mm(ii)0.9de1293.75mm(iii)0.72h1080mmso,dv=1381.96mmCritical Section is at Distance dv from Face of Support i.e Distance B/W Centerline and Critical Section=2181.96mm0.095L

(b)Determine Mu and Vu at Critical SectionMu=114.00Ton.m1118293879.38071N.mm1118.2938793807KN.mVu=232.14Ton2277301.79984592N2277.3017998459KNv=Vu/vxbvxdv4.58N/mm2v/fc'=0.13Mu/dvxf+(Vu/v-0.5Vs)xcotAsxfy=7560000NMu/dvxf+(Vu/v-0.5Vs)xcot=4320603.44812714NOK

CRACK CONTROL CHECK FOR INTERIOR GIRDER

(a)Check if the Section is CrackedService Load Moments=819.5Ton.m8039295000N.mm8039.295KN.mModulus of Rupture, fr=0.63*(fc')1/23.73N/mm20.8xfr=2.98N/mm2btop=3050mmIg=636610174264mm4y'=717mmWhere, y' is the Distance from Most Compressed Concrete Fiber to N.AS= Ig/(h-y')813039813.87484mm3fc=M+ve/S9.8879475061N/mm2SECTION IS CRACKED(b)Calculate Tensile Stress of ReinforcementAssuming N.A is Located in the Web, Thus Finding it's Location "x"WithAs'=0mm2d'=0mmn=Es/Ec=7.041=Asxfy/0.85xfc'xbtopx=sqrt(B2+C)-B360.54mm>hfOK

B=1/bw(hfx(b-bw)+nxAs+(n-1)xAs')2078.8271273643C=2/bw(hf2/2x(b-bw)+nxdxAs+(n-1)xd'xAs')1628971.74117224Icr=242503477095.354mm4fs=n*M+ve*(d-x)/Icr251.4524049455N/mm2the allowable stress can be obtained by putting Z=30000 for moderate exposure and dc=50mmfsa=Z/(dc*A)1/3348.9541658916N/mm2OK

CRACK CONTROL CHECK FOR EXTERIOR GIRDER

(a)Check if the Section is CrackedService Load Moments=633Ton.m6209730000N.mm6209.73KN.mModulus of Rupture, fr=0.63*(fc')1/23.73N/mm20.8xfr=2.98N/mm2bbot=1600mmIg=377775853628mm4y'=493mmWhere, y' is the Distance from Most Compressed Concrete Fiber to N.AS= Ig/(h-y')375149804.993049mm3fc=M+ve/S16.5526675407N/mm2SECTION IS CRACKED(b)Calculate Tensile Stress of ReinforcementAssuming N.A is Located in the Web, Thus Finding it's Location "x"WithAs'=0mm2d'=0mmn=Es/Ec=7.041=Asxfy/0.85xfc'xbtopx=sqrt(B2+C)-B302.7378092813mm ( Vu / v -0.5 Vs - Vp) x cot( Vu / v -0.5 Vs - Vp) x cot =1177727NOK(f) Side Reinforcement in the WebAsk0.001(de-760) 5.7.3.4-41.29mm2/mm of heightAskAs+APS/1200 5.7.3.4-415.4mm2/mm of heightAssume spacing at200c/cAsk=258mm20.40in2PROVIDE20@200mm c/cCURVE TENDON EFFECT(g) In-Plane Force EffectFu-in=Pu/R 5.10.4.3.1-1Factored tendon Force,Pu=35810424NRadius of Curvature of Tendon,R=1500000mmFu-in=23.873616N/mmShere Resistance of Concrete Cover against Pull-out by Deviation Fofces,Vr=VnWhere,Vn=0.9*(0.33*dc*fc'1/2)235.74N/mmOK, Provide min Reinforcement(h) Out-of-Plane Force EffectFu-out=Pu/R 5.10.4.3.1-1Factored tendon Force,Pu=35810424NRadius of Curvature of Tendon,R=1500000mmFu-out=7.5994321184N/mmShere Resistance of Concrete Cover against Pull-out by Deviation Fofces,Vr=VnWhere,Vn=0.9*(0.33*dc*fc'1/2)471.47N/mmOK, Provide min ReinforcementMaximum Spacing of Confinement Reinforcement "smax" is Smallest of Following(i)3 times dia of duct450.00mm5.10.4.3(ii)600mmso,smax=450.00mmPROVIDE12@450mm c/c

Sheet1

Flyover Girder/ElementLoad CasePositive Moment +MuNegative Moment -MuMaximum Shear VuMoment Against VuEntire Bridge SectionStr I Group206520704542620Left ExteriorStr I Group6226202047931st InteriorStr I Group8658912211457Right ExteriorStr I Group620617278954Note: All Forces are in Tons-m

Flyover Girder/ElementLoad CasePositive Moment +MuNegative Moment -MuMaximum Shear VuMoment Against VuEntire Bridge SectionEE I Group 32166222515533189Left ExteriorEE I Group 3249664321010441st InteriorEE I Group 3269710012221337Right ExteriorEE I Group 32495641226906Note: All Forces are in Tons-m

WAKWEB REINFORCEMENT REQUIREMENTMID SECTIONMcr524.8077774949T-MMID SPANIc FROM CAD0.7093M4Y0.844Sc0.8404028436M34273.710672056Fc'4ksiFr0.74ksi1.2Mcr3795.0550767858K-FT524.8077774949T-MSUPPORTSMAX.+VE Mu865T-MIc FROM CAD0.7159M4MAX.-VE Mu1001T-MY0.832Sc0.8604567308M34375.6909452735Fc'4ksiFr0.74ksi1.2Mcr3885.6135594029K-FT537.3308621496T-MSHRINIKAGE AND TEMPERATURE REINFORCEMENTFy60000PSIH8INB116IN537.3308621496T-MAs0.08107526880.11