PRE-STRESS

INVESTIGATE-REC BEAMINVESTIGATE RECTANGULAR PRE-STRESS BEAMMetric to SIFind the safe Live LoadGIRDER-1Given Data :kg/cum.N/cum.Wt.conc. =150.00pcf2400.0023545.0fc' =5000.00psi34.48Mpafpu =250000.00psi1723.75MpaL =51.25ft15.63mWdl =631.40#/ft9212.23N/mloads from slab, FFb =17.72in.450.00mmh =35.43in.900.00mmAps =3.03sq.in.1953.69sq.mm.b =450.00mm0.45mh =900.00mm0.90md =731.00mmSolution :b0.85fc'a/2aCd =hN.A.T =ApsfpsPp =Aps/bdPp =0.00594For Bonded beamfps =fpu ((1-(.5Pp*fpu)/fc'))fps =1468Mpawp =Pp*fps/fc'wp =0.253> 0.30OKC = T0.85Fc' ab =Aps fpsa =217.47a/2 =108.733(d-a/2) =622.267Mn =Aps fps (d-a/2)Mn =1784440184.69N-mmMn =1784.4401846935KN-mMu =OmnMu =1606.00KN-mWbdl =9535.70N/mdead load from beam aloneTot Wdl =10.16710KN/mD.L. =10.16710KN/mWu =1.4DL + 1.7LLMu =(Wu*L^2)/8Wu =8Mu/L^2Wu =52.63KN/mL.L. =22.58KN/m(Safe Live Load it could carry)Tot. unfactored Load =34.74KN/mCheck deflection:Allow. Def =L/300y all. =-52.08mmEc =4730 ( fc' )MpaEc =163066.75MpaI =1/12(bh^3)mm^4I =27337281300.66mm^4Def.,dl + ll,y1 =(5wl^4)/(384EI)y1 =-6.05mmDef.,pres, y2 =(ML^2)/(8EI)y2 =12.216mmNet def. y =y2-y1y =18.26mmOK

L-GIRDER2DESIGN OF LEDGER PRE-STRESS BEAMMetric to SIGIRDER-1Given Data :kg/cum.N/cum.Wt.conc. =150.00pcf2400.0023545.0Wll =1394.00#/ft20338.69N/mfc' =5000.00psi34.48Mpafc'i =4000.00psi27.58Mpa175500fsi =175500.00psi1210.07Mpafse =150400.00psi1037.01Mpafpu =250600.00psi1727.89MpaL =51.25ft15.63mWdl =1435.00#/ft20936.89N/mloads from slab, FFSolution :Approximate depth, h=L /25625.00mmsay900mmTry :b =400mm0.40mh =900mm0.90mhN.A.tf =200mm0.20m y1yfb =150mm0.15mtf y2b + fbWdl =9182.56N/mdead load from beamTot Wdl =10617.56N/my1 =450y2 =100Moment due to Dead Load:M =(Wdl*L^2)/8M =324022N-mLocate Neutral axis dist. : yA1 =b*h360000.00sq.mmA2 =tf*fb30000.00sq.mmAtot =(b*h)+(tf*fb)390000.00sq.mmy =423.08mmLocate Neutral axis dist. : xx1=b+(fb/2) =475x1 =b/2 =200x =221.15mmEstimate prestressed Steel, Aps: by assuming a =h-ya =476.92mmWll =20338.69N/mTotal W =Wll + WdlW =29521.26N/mfcTotal MomentCMT =900917.24N-m900917237.100031N-mmMTak-ftTa =MTT = MT/aToT =1889020.01NT =Aps*fseAps =T/fseAps =1821.61sq. mm.Area of TendonRecomputing Ac:T = AcfcAc = 2T / ( fc+0 )fc = 0.45fc'T = Ac*((fc+0)/2)Ac =243528.48sq.mm.Assumed Section Area,Ac =360000.00sq.mm.(furnished)greater than thoerytical therefore OKUse Section: b =400.00mmh =900.00mmT =Aps * fsiT =2204275.35NTa =Mdla = Mdl / Tha =147.0mmeKbae =Kb + aTKb =(1/6)hKb =150e =297.00mmCheck stress at mid-span at transfer:bFi =Aps * fsiFi =2204275.35NfT =(Fi/bh)(1-(6e/h))hfT =-6.00Mpaefb =(Fi/bh)(1+(6e/h))Fifb =18.25MpaDead Load Stress:fdl =(6Mdl) / (bh^2)Allowable stress, fc all. = 0.6fc'Ifdl =6.00Mpafc all. =16.55MpaStress diagram:Tranferdead load6.00-6.000+=-6.0018.2512.25MpaLess than allow. SafeCheck stress with service loads after losses have occurred in tendon.Fe =Aps * fse400Fe =1889020.01fT =(Fe/bh)(1-(6e/h))-5.14900fT =(Fe/bh)(1+(6e/h))e15.64FeStress Due to Total loads:f =(6MT) / (bh^2)Allowable stress, fc all. = 0.45fc'f =16.68Mpafc all. =15.51MpaStress diagram:Tranferdead loadLess than allow. Safe-5.1416.6811.54+=15.64-16.68(1.05)MpaCompute Ultimate Moment: due to Udl + UllbMu =( Wu*L^2 )/8Wu =1.4dl + 1.7lladNAWu =47431.37N/mVu =83.31k3.25k/fteMu =1447490.44N-m1067.34k-ftPp =Aps / bda =476.92mme =297.00mmPp =0.00588d =773.92mmwp =(Pp * fps)/fc'fpu =1727.887Mpafpu/2 =863.9435MpaLess than fse =1037.008Mpafps =fpu*(1- 0.5(Pp*fpu/fc'))fps =1473Mpabwp =(Pp * fps)/fc'wp =0.251aC = 0.85fc' abless than0.30dT =Aps * fpsNAApsd-(a/2)T =2683389.25NT = Aps * fps603.28kC =Ta/2 =114.46mme =297.00mm0.85fc' ab =Td =773.92mmb =400.00mmsolve for a =T/(0.85fc' * b)a =228.93mmCompute Ultimate Moment: due to Prestress Load400Mn =0.85fc' ab (d-a/2)h-y =476.92Mn =C*(d-a/2)d =773.92NAh =900Mn =1769576725.9N-mmApse =297.00Mn =1769576.73N-mMu =O MnMu =1592619.05N-mGreater than Mu dl+ll therefore OK1174.36k-ftCheck deflection:Allow. Def =L/300tf =200y all. =52.08mmfb =150.00b =400.00Ec =4730 ( fc' )Mpad1 =476.92Ec =99031495.894408Mpad2 =423.08I =1/3((bd1^3)+(bd2^3)-(fbd3^3)mm^4d3 =223.08I =24005894401.46mm^4Def.,dl + ll,y1 =(5wl^4)/(384EI)y1 =9.64mmDef.,pres, y2 =(ML^2)/(8EI)y2 =0.020mmNet def. y =y2-y1y =9.62mmOKStirruppsfc' =5000.00Wu =47431.37n/m3.250k/ftb =15.75Vu =83.31h =35.43d =30.47QVc =67.08d/2 (in) =15.23d/2 (m) =0.39@ X < = d Vu =75.06@ X > d Vu =8.25Vs =88.30Vs =9.71S(in) =2.73S(in) =61.24S(m) =0.07S(m) =1.56*LEDGER DESIGN*0.200.30Mu =1.25Wu =0.10for 12mm dia. use :0.43Vu =2.55Ku =200.00for 16mm dia. use :0.24F =0.0063for 20mm dia. use :0.15b(m.)=0.30b(in.)=11.81for 25mm dia. use :0.10d(m.)=0.06d(in.)=2.52for 32mm dia. use :0.06h(m.)=0.12h(in.)=4.90QVc =7.28d/2 (in) =3.31d/2 (m) =0.08use h(m) =0.20use h(in) =7.87@ X < = d Vu =2.49d' (in) =1.25use d(in) =6.62Vs =2.94S(in) =17.87Fa =0.04S(m) =0.45Kua =29.05@ X > d Vu =(4.73)au =2.58Vs =(5.57)As =0.07sq.inS(in) =(9.42)Asmin =0.186sq.inS(m) =(0.24)use 10mm Top bar @ 0.15moc

L-GIRDERDESIGN OF LEDGER PRE-STRESS BEAMMetric to SIGIRDER-1Given Data :kg/cum.N/cum.Wt.conc. =150.00pcf2400.0023545.0Wll =1394.00#/ft20338.69N/mfc' =5000.00psi34.48Mpafc'i =4000.00psi27.58Mpa175500fsi =175500.00psi1210.07Mpafse =150400.00psi1037.01Mpafpu =250600.00psi1727.89MpaL =47.98ft14.63mWdl =1435.00#/ft20936.89N/mloads from slab, FFSolution :Approximate depth, h=L /25585.08mmsay900mmTry :b =400mm0.40mh =900mm0.90mhN.A.tf =200mm0.20m y1yfb =150mm0.15mtf y2b + fbWdl =9182.56N/mdead load from beamTot Wdl =10617.56N/my1 =450y2 =100Moment due to Dead Load:M =(Wdl*L^2)/8M =283952N-mLocate Neutral axis dist. : yA1 =b*h360000.00sq.mmA2 =tf*fb30000.00sq.mmAtot =(b*h)+(tf*fb)390000.00sq.mmy =423.08mmLocate Neutral axis dist. : xx1=b+(fb/2) =475x1 =b/2 =200x =221.15mmEstimate prestressed Steel, Aps: by assuming a =h-ya =476.92mmWll =20338.69N/mTotal W =Wll + WdlW =29521.26N/mfcTotal MomentCMT =789505.88N-m789505876.699702N-mmMTak-ftTa =MTT = MT/aToT =1655415.55NT =Aps*fseAps =T/fseAps =1596.34sq. mm.Area of TendonRecomputing Ac:T = AcfcAc = 2T / ( fc+0 )fc = 0.45fc'T = Ac*((fc+0)/2)Ac =213412.69sq.mm.Assumed Section Area,Ac =360000.00sq.mm.(furnished)greater than thoerytical therefore OKUse Section: b =400.00mmh =900.00mmT =Aps * fsiT =1931685.03NTa =Mdla = Mdl / Tha =147.0mmeKbae =Kb + aTKb =(1/6)hKb =150e =297.00mmCheck stress at mid-span at transfer:bFi =Aps * fsiFi =1931685.03NfT =(Fi/bh)(1-(6e/h))hfT =-5.26Mpaefb =(Fi/bh)(1+(6e/h))Fifb =15.99MpaDead Load Stress:fdl =(6Mdl) / (bh^2)Allowable stress, fc all. = 0.6fc'Ifdl =5.26Mpafc all. =16.55MpaStress diagram:Tranferdead load5.26-5.260+=-5.2615.9910.73MpaLess than allow. SafeCheck stress with service loads after losses have occurred in tendon.Fe =Aps * fse400Fe =1655415.55fT =(Fe/bh)(1-(6e/h))-4.51900fT =(Fe/bh)(1+(6e/h))e13.70FeStress Due to Total loads:f =(6MT) / (bh^2)Allowable stress, fc all. = 0.45fc'f =14.62Mpafc all. =15.51MpaStress diagram:Tranferdead loadLess than allow. Safe-4.5114.6210.11+=13.70-14.62(0.92)MpaCompute Ultimate Moment: due to Udl + UllbMu =( Wu*L^2 )/8Wu =1.4dl + 1.7lladNAWu =47431.37N/mVu =77.99k3.25k/fteMu =1268487.45N-m935.35k-ftPp =Aps / bda =476.92mme =297.00mmPp =0.00516d =773.92mmwp =(Pp * fps)/fc'fpu =1727.887Mpafpu/2 =863.9435MpaLess than fse =1037.008Mpafps =fpu*(1- 0.5(Pp*fpu/fc'))fps =1505Mpabwp =(Pp * fps)/fc'wp =0.225aC = 0.85fc' abless than0.30dT =Aps * fpsNAApsd-(a/2)T =2401849.17NT = Aps * fps539.98kC =Ta/2 =102.45mme =297.00mm0.85fc' ab =Td =773.92mmb =400.00mmsolve for a =T/(0.85fc' * b)a =204.91mmCompute Ultimate Moment: due to Prestress Load400Mn =0.85fc' ab (d-a/2)h-y =476.92Mn =C*(d-a/2)d =773.92NAh =900Mn =1612758623.4N-mmApse =297.00Mn =1612758.62N-mMu =O MnMu =1451482.76N-mGreater than Mu dl+ll therefore OK1070.28k-ftCheck deflection:Allow. Def =L/300tf =200y all. =48.76mmfb =150.00b =400.00Ec =4730 ( fc' )Mpad1 =476.92Ec =99031495.894408Mpad2 =423.08I =1/3((bd1^3)+(bd2^3)-(fbd3^3)mm^4d3 =223.08I =24005894401.46mm^4Def.,dl + ll,y1 =(5wl^4)/(384EI)y1 =7.40mmDef.,pres, y2 =(ML^2)/(8EI)y2 =0.016mmNet def. y =y2-y1y =7.38mmOKStirruppsfc' =5000.00Wu =47431.37n/m3.250k/ftb =15.75Vu =77.99h =35.43d =30.47QVc =67.08d/2 (in) =15.23d/2 (m) =0.39@ X < = d Vu =69.74@ X > d Vu =8.25Vs =82.04Vs =9.71S(in) =2.94S(in) =56.90S(m) =0.07S(m) =1.45*LEDGER DESIGN*0.200.30Mu =1.25Wu =0.10for 12mm dia. use :0.43Vu =2.55Ku =200.00for 16mm dia. use :0.24F =0.0063for 20mm dia. use :0.15b(m.)=0.30b(in.)=11.81for 25mm dia. use :0.10d(m.)=0.06d(in.)=2.52for 32mm dia. use :0.06h(m.)=0.12h(in.)=4.90QVc =7.28d/2 (in) =3.31d/2 (m) =0.08use h(m) =0.20use h(in) =7.87@ X < = d Vu =2.49d' (in) =1.25use d(in) =6.62Vs =2.94S(in) =17.87Fa =0.04S(m) =0.45Kua =29.05@ X > d Vu =(4.73)au =2.58Vs =(5.57)As =0.07sq.inS(in) =(9.42)Asmin =0.186sq.inS(m) =(0.24)use 10mm Top bar @ 0.15moc

slabDESIGN OF PRE-STRESS SLABMetric to SIGIRDER-1Given Data :kg/cum.N/cum.Wt.conc. =150.00pcf2400.0023545.0Wll =99.97#/ft1458.58N/mfc' =5000.00psi34.48Mpafc'i =4000.00psi27.58Mpafsi =175500.00psi1210.07Mpafse =150400.00psi1037.01Mpafpu =250600.00psi1727.89MpaL =14.76ft4.50mWdl =124.97#/ft1823.33N/mloads from slab, FFSolution :Approximate depth, h=L /25180.00mmsay180mmTry :b =300mm0.30mh =180mm0.18mhWdl =1271.43N/mdead load from beam aloneTot Wdl =1396.40N/mbMoment due to Dead Load:M =(Wdl*L^2)/8M =3535N-mEstimate prestressed Steel, Aps: by assuming a =0.3ha =54mmWll =1458.58N/mTotal W =Wll + WdlW =2,730.01N/mfcTotal MomentCMT =6910.34N-m6910339.63127604N-mmMTak-ftTa =MTT = MT/aToT =127969.25NT =Aps*fseAps =T/fseAps =123.40sq. mm.Area of TendonRecomputing Ac:T = AcfcAc = 2T / ( fc+0 )fc = 0.45fc'T = Ac*((fc+0)/2)Ac =16497.53sq.mm.Assumed Section Area,Ac =54000.00sq.mm.(furnished)greater than thoerytical therefore OKUse Section: b =300.00mmh =180.00mmT =Aps * fsiT =149325.82NTa =Mdla = Mdl / Tha =23.7mmeKbae =Kb + aTKb =(1/6)hKb =30e =54mmCheck stress at mid-span at transfer:bFi =Aps * fsiFi =149325.82NfT =(Fi/bh)(1-(6e/h))hfT =-2.18Mpaefb =(Fi/bh)(1+(6e/h))Fifb =7.71MpaDead Load Stress:fdl =(6Mdl) / (bh^2)Allowable stress, fc all. = 0.6fc'Ifdl =2.18Mpafc all. =16.55MpaStress diagram:Tranferdead load2.18-2.180+=-2.187.715.53MpaLess than allow. SafeCheck stress with service loads after losses have occurred in tendon.Fe =Aps * fse300Fe =127969.25fT =(Fe/bh)(1-(6e/h))-1.87180fT =(Fe/bh)(1+(6e/h))e6.61FeStress Due to Total loads:f =(6MT) / (bh^2)Allowable stress, fc all. = 0.45fc'f =4.27Mpafc all. =15.51MpaStress diagram:Tranferdead loadLess than allow. Safe-1.874.272.40+=6.61-4.272.34MpaCompute Ultimate Moment: due to Udl + UllbMu =( Wu*L^2 )/8Wu =1.4dl + 1.7llh/2dNAWu =4259.59N/mVu =2.15k0.29k/fteMu =10782.08N-m7.95k-ftPp =Aps / bdh/2 =90mme =54mmPp =0.00286d =144mmwp =(Pp * fps)/fc'fpu =1727.887Mpafpu/2 =863.9435MpaLess than fse =1037.008Mpafps =fpu*(1- 0.5(Pp*fpu/fc'))fps =1604Mpabwp =(Pp * fps)/fc'wp =0.133aC = 0.85fc' abless than0.30dT =Aps * fpsNAApsd-(a/2)T =197926.68NT = Aps * fps44.50kC =Ta/2 =11.26mme =53.67mm0.85fc' ab =Td =143.67mmb =300.00mmsolve for a =T/(0.85fc' * b)a =22.51mmCompute Ultimate Moment: due to Prestress Load300Mn =0.85fc' ab (d-a/2)h/2 =90Mn =C*(d-a/2)d =143.67Mn =26208159.9N-mmApse =53.67Mn =26208.16N-mMu =O MnMu =23587.34N-mGreater than Mu dl+ll therefore OK17.39k-ftCheck deflection:Allow. Def =L/300y all. =15.00mmEc =4730 ( fc' )MpaEc =8624366.5797381MpaI =1/12(bh^3)mm^4I =145800000mm^4Def.,dl + ll,y1 =(5wl^4)/(384EI)y1 =11.59mmDef.,pres, y2 =(ML^2)/(8EI)y2 =0.047mmNet def. y =y2-y1y =11.54mmOK1

I-GIRDERDESIGN OF I-SECTION PRE-STRESS BEAMMetric to SII-BEAMGiven Data :kg/cum.N/cum.Wt.conc. =150.00pcf2400.0023545.0Wll =1394.00#/ft20338.69N/mfc' =5000.00psi34.48Mpafc'i =4000.00psi27.58Mpa175500fsi =175500.00psi1210.07Mpafse =150400.00psi1037.01Mpafpu =250000.00psi1723.75MpaL =62.73ft19.13mWdl =631.40#/ft9212.23N/mloads from slab, FFSolution :Approximate depth, h=L /25765.00mm0.45say1000mm0.20Try :b =450mm0.45mh =1000mm1.00mh0.60Wdl =7063.51dead load from beam alone0.20Tot Wdl =7694.91N/m0.20bMoment due to Dead Load:M =(Wdl*L^2)/8M =351817N-mEstimate prestressed Steel, Aps: by assuming a =0.5ha =500mmWll =20338.69N/mTotal W =Wll + WdlW =27,402.20N/mfcTotal MomentCMT =1252848.00N-m1252848004.15355N-mmMTak-ftTa =MTT = MT/aToT =2505696.01NT =Aps*fseAps =T/fseAps =2416.27sq. mm.Area of TendonRecomputing Ac:T = AcfcAc = 2T / ( fc+0 )fc = 0.45fc'T = Ac*((fc+0)/2)Ac =323029.06sq.mm.Assumed Section Area,Ac =449999.85sq.mm.(furnished)greater than thoerytical therefore OKUse Section: b =450.00mmh =1,000.00mmT =Aps * fsiT =2923867.35NTa =Mdla = Mdl / Tha =120.3mmeKbae =Kb + aTKb =(1/6)hKb =167e =287mmCheck stress at mid-span at transfer:bFi =Aps * fsiFi =2923867.35NfT =(Fi/bh)(1-(6e/h))hfT =-4.69Mpaefb =(Fi/bh)(1+(6e/h))Fifb =17.69MpaDead Load Stress:fdl =(6Mdl) / (bh^2)Allowable stress, fc all. = 0.6fc'Ifdl =4.69Mpafc all. =16.55MpaStress diagram:Tranferdead load4.69-4.690+=-4.6917.6912.99MpaLess than allow. SafeCheck stress with service loads after losses have occurred in tendon.Fe =Aps * fse450Fe =2505696.01fT =(Fe/bh)(1-(6e/h))-4.021000fT =(Fe/bh)(1+(6e/h))e15.16FeStress Due to Total loads:f =(6MT) / (bh^2)Allowable stress, fc all. = 0.45fc'f =16.70Mpafc all. =15.51MpaStress diagram:Tranferdead loadLess than allow. Safe-4.0216.7012.68+=15.16-16.70(1.55)MpaCompute Ultimate Moment: due to Udl + UllbMu =( Wu*L^2 )/8Wu =1.4dl + 1.7llh/2dNAWu =44464.69N/mVu =95.59k3.05k/fteMu =2032957.03N-m1499.05k-ftPp =Aps / bd-((b-wt)*(d-Ft))h/2 =500mmb-wt =250.00sq.mme =287mmd-Ft =586.99sq.mmd =787mmPp =0.011650.79mwp =(Pp * fps)/fc'fpu =1723.75Mpafpu/2 =861.875MpaLess than fse =1037.008Mpafps =fpu*(1- 0.5(Pp*fpu/fc'))fps =1222Mpabwp =(Pp * fps)/fc'wp =0.413aC = 0.85fc' abless than0.30dT =Aps * fpsNAd-(a/2)T =2951940.24NT = Aps * fps663.66kC =Ta/2 =201.47mme =286.99mm0.85fc' ab =Td =786.99mmb =450.00mmsolve for a =T/(0.85fc' * b)a =402.94mmCompute Ultimate Moment: due to Prestress Load450Mn =0.85fc' ab (d-a/2)h/2 =500Mn =C*(d-a/2)d =786.99Mn =1728421863.2N-mmApse =286.99Mn =1728421.86N-mMu =O MnMu =1555579.68N-mGreater than Mu dl+ll therefore OK1147.04k-ftCheck deflection:Allow. Def =L/300y all. =63.75mmEc =4730 ( fc' )Mpah^2 =1000000Ec =43573858.1935395Mpab*Ft =90000I =(h^2/12)(6bFt+hwt)mm^4h*wt =200000I =24166666666.6667mm^4Def.,dl + ll,y1 =(5wl^4)/(384EI)y1 =45.33mmDef.,pres, y2 =(ML^2)/(8EI)y2 =0.068mmNet def. y =y2-y1y =45.26mmOK

GIRDER-2bDESIGN OF RECTANGULAR PRE-STRESS BEAMMetric to SIGIRDER-2Given Data :kg/cum.N/cum.Wt.conc. =150.00pcf2400.0023545.0Wll =1394.00#/ft20338.69N/mfc' =5000.00psi34.48Mpafc'i =4000.00psi27.58Mpa175500fsi =175500.00psi1210.07Mpafse =150400.00psi1037.01Mpafpu =250000.00psi1723.75MpaL =51.25ft15.63mWdl =631.40#/ft9212.23N/mloads from slab, FFSolution :Approximate depth, h=L /25625.00mmsay900mmTry :b =450mm0.45mh =900mm0.90mhWdl =9535.74N/mdead load from beam aloneTot Wdl =10167.14N/mbMoment due to Dead Load:M =(Wdl*L^2)/8M =310276N-mEstimate prestressed Steel, Aps: by assuming a =0.5ha =450mmWll =20338.69N/mTotal W =Wll + WdlW =29,874.43N/mfcTotal MomentCMT =911695.30N-m911695296.381898N-mmMTak-ftTa =MTT = MT/aToT =2025989.55NT =Aps*fseAps =T/fseAps =1953.69sq. mm.Area of TendonRecomputing Ac:T = AcfcAc = 2T / ( fc+0 )fc = 0.45fc'T = Ac*((fc+0)/2)Ac =261186.31sq.mm.Assumed Section Area,Ac =405000.00sq.mm.(furnished)greater than thoerytical therefore OKUse Section: b =450.00mmh =900.00mmT =Aps * fsiT =2364103.49NTa =Mdla = Mdl / Tha =131.2mmeKbae =Kb + aTKb =(1/6)hKb =150e =281mmCheck stress at mid-span at transfer:bFi =Aps * fsiFi =2364103.49NfT =(Fi/bh)(1-(6e/h))hfT =-5.11Mpaefb =(Fi/bh)(1+(6e/h))Fifb =16.78MpaDead Load Stress:fdl =(6Mdl) / (bh^2)Allowable stress, fc all. = 0.6fc'Ifdl =5.11Mpafc all. =16.55MpaStress diagram:Tranferdead load5.11-5.110+=-5.1116.7811.67MpaLess than allow. SafeCheck stress with service loads after losses have occurred in tendon.Fe =Aps * fse450Fe =2025989.55fT =(Fe/bh)(1-(6e/h))-4.38900fT =(Fe/bh)(1+(6e/h))e14.38FeStress Due to Total loads:f =(6MT) / (bh^2)Allowable stress, fc all. = 0.45fc'f =15.01Mpafc all. =15.51MpaStress diagram:Tranferdead loadLess than allow. Safe-4.3815.0110.63+=14.38-15.01(0.63)MpaCompute Ultimate Moment: due to Udl + UllbMu =( Wu*L^2 )/8Wu =1.4dl + 1.7llh/2dNAWu =47925.81N/mVu =84.18k3.28k/fteMu =1462579.72N-m1078.47k-ftPp =Aps / bdh/2 =450mme =281mmPp =0.00594d =731mmwp =(Pp * fps)/fc'fpu =1723.75Mpafpu/2 =861.875MpaLess than fse =1037.008Mpafps =fpu*(1- 0.5(Pp*fpu/fc'))fps =1468Mpabwp =(Pp * fps)/fc'wp =0.253aC = 0.85fc' abless than0.30dT =Aps * fpsNAApsd-(a/2)T =2867807.92NT = Aps * fps644.74kC =Ta/2 =108.74mme =281.24mm0.85fc' ab =Td =731.24mmb =450.00mmsolve for a =T/(0.85fc' * b)a =217.48mmCompute Ultimate Moment: due to Prestress Load450Mn =0.85fc' ab (d-a/2)h/2 =450Mn =C*(d-a/2)d =731.24Mn =1785227904.6N-mmApse =281.24Mn =1785227.90N-mMu =O MnMu =1606705.11N-mGreater than Mu dl+ll therefore OK1184.74k-ftCheck deflection:Allow. Def =L/300y all. =52.08mmEc =4730 ( fc' )MpaEc =43573858.1935395MpaI =1/12(bh^3)mm^4I =27337500000mm^4Def.,dl + ll,y1 =(5wl^4)/(384EI)y1 =19.46mmDef.,pres, y2 =(ML^2)/(8EI)y2 =0.041mmNet def. y =y2-y1y =19.42mmOK

GIRDER-1bDESIGN OF RECTANGULAR PRE-STRESS BEAMMetric to SIGIRDER-1Given Data :kg/cum.N/cum.Wt.conc. =150.00pcf2400.0023545.0Wll =1394.00#/ft20338.69N/mfc' =5000.00psi34.48Mpafc'i =4000.00psi27.58Mpa175500fsi =175500.00psi1210.07Mpafse =150400.00psi1037.01Mpafpu =250000.00psi1723.75MpaL =47.98ft14.63mWdl =1435.00#/ft20936.89N/mloads from slab, FFSolution :Approximate depth, h=L /25585.08mmsay900mmTry :b =450mm0.45mh =900mm0.90mhWdl =9535.74N/mdead load from beam aloneTot Wdl =10970.74N/mbMoment due to Dead Load:M =(Wdl*L^2)/8M =293397N-mEstimate prestressed Steel, Aps: by assuming a =0.5ha =450mmWll =20338.69N/mTotal W =Wll + WdlW =29,874.43N/mfcTotal MomentCMT =798951.07N-m798951074.096349N-mmMTak-ftTa =MTT = MT/aToT =1775446.83NT =Aps*fseAps =T/fseAps =1712.09sq. mm.Area of TendonRecomputing Ac:T = AcfcAc = 2T / ( fc+0 )fc = 0.45fc'T = Ac*((fc+0)/2)Ac =228886.87sq.mm.Assumed Section Area,Ac =405000.00sq.mm.(furnished)greater than thoerytical therefore OKUse Section: b =450.00mmh =900.00mmT =Aps * fsiT =2071748.13NTa =Mdla = Mdl / Tha =141.6mmeKbae =Kb + aTKb =(1/6)hKb =150e =292mmCheck stress at mid-span at transfer:bFi =Aps * fsiFi =2071748.13NfT =(Fi/bh)(1-(6e/h))hfT =-4.83Mpaefb =(Fi/bh)(1+(6e/h))Fifb =15.06MpaDead Load Stress:fdl =(6Mdl) / (bh^2)Allowable stress, fc all. = 0.6fc'Ifdl =4.83Mpafc all. =16.55MpaStress diagram:Tranferdead load4.83-4.830+=-4.8315.0610.23MpaLess than allow. SafeCheck stress with service loads after losses have occurred in tendon.Fe =Aps * fse450Fe =1775446.83fT =(Fe/bh)(1-(6e/h))-4.14900fT =(Fe/bh)(1+(6e/h))e12.91FeStress Due to Total loads:f =(6MT) / (bh^2)Allowable stress, fc all. = 0.45fc'f =13.15Mpafc all. =15.51MpaStress diagram:Tranferdead loadLess than allow. Safe-4.1413.159.01+=12.91-13.15(0.24)MpaCompute Ultimate Moment: due to Udl + UllbMu =( Wu*L^2 )/8Wu =1.4dl + 1.7llh/2dNAWu =47925.81N/mVu =78.80k3.28k/fteMu =1281710.73N-m945.10k-ftPp =Aps / bdh/2 =450mme =292mmPp =0.00513d =742mmwp =(Pp * fps)/fc'fpu =1723.75Mpafpu/2 =861.875MpaLess than fse =1037.008Mpafps =fpu*(1- 0.5(Pp*fpu/fc'))fps =1503Mpabwp =(Pp * fps)/fc'wp =0.224aC = 0.85fc' abless than0.30dT =Aps * fpsNAApsd-(a/2)T =2572702.43NT = Aps * fps578.40kC =Ta/2 =97.55mme =291.62mm0.85fc' ab =Td =741.62mmb =450.00mmsolve for a =T/(0.85fc' * b)a =195.10mmCompute Ultimate Moment: due to Prestress Load450Mn =0.85fc' ab (d-a/2)h/2 =450Mn =C*(d-a/2)d =741.62Mn =1656998068.6N-mmApse =291.62Mn =1656998.07N-mMu =O MnMu =1491298.26N-mGreater than Mu dl+ll therefore OK1099.64k-ftCheck deflection:Allow. Def =L/300y all. =48.76mmEc =4730 ( fc' )MpaEc =99031495.894408MpaI =1/12(bh^3)mm^4I =27337500000mm^4Def.,dl + ll,y1 =(5wl^4)/(384EI)y1 =6.58mmDef.,pres, y2 =(ML^2)/(8EI)y2 =0.015mmNet def. y =y2-y1y =6.56mmOK

GIRDER-1DESIGN OF RECTANGULAR PRE-STRESS BEAMMetric to SIGIRDER-1Given Data :kg/cum.N/cum.Wt.conc. =150.00pcf2400.0023545.0Wll =836.40#/ft12203.22N/mfc' =5000.00psi34.48Mpafc'i =4000.00psi27.58Mpa175500fsi =175500.00psi1210.07Mpafse =150400.00psi1037.01Mpafpu =250000.00psi1723.75MpaL =57.16ft17.43mWdl =464.94#/ft6783.55N/mloads from slab, FFSolution :Approximate depth, h=L /25697.07mmsay800mmTry :b =450mm0.45mh =800mm0.80mhWdl =8476.21N/mdead load from beam aloneTot Wdl =8941.15N/mbMoment due to Dead Load:M =(Wdl*L^2)/8M =339422N-mEstimate prestressed Steel, Aps: by assuming a =0.5ha =400mmWll =12203.22N/mTotal W =Wll + WdlW =20,679.43N/mfcTotal MomentCMT =785028.23N-m785028229.816039N-mmMTak-ftTa =MTT = MT/aToT =1962570.57NT =Aps*fseAps =T/fseAps =1892.53sq. mm.Area of TendonRecomputing Ac:T = AcfcAc = 2T / ( fc+0 )fc = 0.45fc'T = Ac*((fc+0)/2)Ac =253010.47sq.mm.Assumed Section Area,Ac =360000.00sq.mm.(furnished)greater than thoerytical therefore OKUse Section: b =450.00mmh =800.00mmT =Aps * fsiT =2290100.64NTa =Mdla = Mdl / Tha =148.2mmeKbae =Kb + aTKb =(1/6)hKb =133e =282mmCheck stress at mid-span at transfer:bFi =Aps * fsiFi =2290100.64NfT =(Fi/bh)(1-(6e/h))hfT =-7.07Mpaefb =(Fi/bh)(1+(6e/h))Fifb =19.79MpaDead Load Stress:fdl =(6Mdl) / (bh^2)Allowable stress, fc all. = 0.6fc'Ifdl =7.07Mpafc all. =16.55MpaStress diagram:Tranferdead load7.07-7.070+=-7.0719.7912.72MpaLess than allow. SafeCheck stress with service loads after losses have occurred in tendon.Fe =Aps * fse450Fe =1962570.57fT =(Fe/bh)(1-(6e/h))-6.06800fT =(Fe/bh)(1+(6e/h))e16.96FeStress Due to Total loads:f =(6MT) / (bh^2)Allowable stress, fc all. = 0.45fc'f =16.35Mpafc all. =15.51MpaStress diagram:Tranferdead loadLess than allow. Safe-6.0616.3510.29+=16.96-16.350.61MpaCompute Ultimate Moment: due to Udl + UllbMu =( Wu*L^2 )/8Wu =1.4dl + 1.7llh/2dNAWu =32612.16N/mVu =63.89k2.24k/fteMu =1238016.33N-m912.88k-ftPp =Aps / bdh/2 =400mme =282mmPp =0.00617d =682mmwp =(Pp * fps)/fc'fpu =1723.75Mpafpu/2 =861.875MpaLess than fse =1037.008Mpafps =fpu*(1- 0.5(Pp*fpu/fc'))fps =1458Mpabwp =(Pp * fps)/fc'wp =0.261aC = 0.85fc' abless than0.30dT =Aps * fpsNAApsd-(a/2)T =2758991.07NT = Aps * fps620.28kC =Ta/2 =104.61mme =281.55mm0.85fc' ab =Td =681.55mmb =450.00mmsolve for a =T/(0.85fc' * b)a =209.23mmCompute Ultimate Moment: due to Prestress Load450Mn =0.85fc' ab (d-a/2)h/2 =400Mn =C*(d-a/2)d =681.55Mn =1591753981.8N-mmApse =281.55Mn =1591753.98N-mMu =O MnMu =1432578.58N-mGreater than Mu dl+ll therefore OK1056.35k-ftCheck deflection:Allow. Def =L/300y all. =58.09mmEc =4730 ( fc' )MpaEc =32086204.6697882MpaI =1/12(bh^3)mm^4I =19200000000mm^4Def.,dl + ll,y1 =(5wl^4)/(384EI)y1 =40.31mmDef.,pres, y2 =(ML^2)/(8EI)y2 =0.088mmNet def. y =y2-y1y =40.22mmOK

GIRDER-2DESIGN OF RECTANGULAR PRE-STRESS BEAMMetric to SIGIRDER-2Given Data :kg/cum.N/cum.Wt.conc. =150.00pcf2400.0023545.0Wll =836.40#/ft12203.22N/mfc' =5000.00psi34.48Mpafc'i =4000.00psi27.58Mpa175500fsi =175500.00psi1210.07Mpafse =150400.00psi1037.01Mpafpu =250000.00psi1723.75MpaL =62.73ft19.13mWdl =464.94#/ft6783.55N/mloads from slab, FFSolution :Approximate depth, h=L /25765.00mmsay800mmTry :b =450mm0.45mh =800mm0.80mhWdl =8476.21N/mdead load from beam aloneTot Wdl =8941.15N/mbMoment due to Dead Load:M =(Wdl*L^2)/8M =408796N-mEstimate prestressed Steel, Aps: by assuming a =0.5ha =400mmWll =12203.22N/mTotal W =Wll + WdlW =20,679.43N/mfcTotal MomentCMT =945477.96N-m945477959.404179N-mmMTak-ftTa =MTT = MT/aToT =2363694.90NT =Aps*fseAps =T/fseAps =2279.34sq. mm.Area of TendonRecomputing Ac:T = AcfcAc = 2T / ( fc+0 )fc = 0.45fc'T = Ac*((fc+0)/2)Ac =304722.57sq.mm.Assumed Section Area,Ac =360000.00sq.mm.(furnished)greater than thoerytical therefore OKUse Section: b =450.00mmh =800.00mmT =Aps * fsiT =2758167.92NTa =Mdla = Mdl / Tha =148.2mmeKbae =Kb + aTKb =(1/6)hKb =133e =282mmCheck stress at mid-span at transfer:bFi =Aps * fsiFi =2758167.92NfT =(Fi/bh)(1-(6e/h))hfT =-8.52Mpaefb =(Fi/bh)(1+(6e/h))Fifb =23.84MpaDead Load Stress:fdl =(6Mdl) / (bh^2)Allowable stress, fc all. = 0.6fc'Ifdl =8.52Mpafc all. =16.55MpaStress diagram:Tranferdead load8.52-8.520+=-8.5223.8415.32MpaLess than allow. SafeCheck stress with service loads after losses have occurred in tendon.Fe =Aps * fse450Fe =2363694.90fT =(Fe/bh)(1-(6e/h))-7.30800fT =(Fe/bh)(1+(6e/h))e20.43FeStress Due to Total loads:f =(6MT) / (bh^2)Allowable stress, fc all. = 0.45fc'f =19.70Mpafc all. =15.51MpaStress diagram:Tranferdead loadLess than allow. Safe-7.3019.7012.40+=20.43-19.700.73MpaCompute Ultimate Moment: due to Udl + UllbMu =( Wu*L^2 )/8Wu =1.4dl + 1.7llh/2dNAWu =32612.16N/mVu =70.11k2.24k/fteMu =1491051.04N-m1099.46k-ftPp =Aps / bdh/2 =400mme =282mmPp =0.00743d =682mmwp =(Pp * fps)/fc'fpu =1723.75Mpafpu/2 =861.875MpaLess than fse =1037.008Mpafps =fpu*(1- 0.5(Pp*fpu/fc'))fps =1403Mpabwp =(Pp * fps)/fc'wp =0.303aC = 0.85fc' abless than0.30dT =Aps * fpsNAApsd-(a/2)T =3199010.26NT = Aps * fps719.20kC =Ta/2 =121.30mme =281.55mm0.85fc' ab =Td =681.55mmb =450.00mmsolve for a =T/(0.85fc' * b)a =242.59mmCompute Ultimate Moment: due to Prestress Load450Mn =0.85fc' ab (d-a/2)h/2 =400Mn =C*(d-a/2)d =681.55Mn =1792242741.6N-mmApse =281.55Mn =1792242.74N-mMu =O MnMu =1613018.47N-mGreater than Mu dl+ll therefore OK1189.40k-ftCheck deflection:Allow. Def =L/300y all. =63.75mmEc =4730 ( fc' )MpaEc =32086204.6697882MpaI =1/12(bh^3)mm^4I =19200000000mm^4Def.,dl + ll,y1 =(5wl^4)/(384EI)y1 =58.47mmDef.,pres, y2 =(ML^2)/(8EI)y2 =0.120mmNet def. y =y2-y1y =58.35mmOK

case-3DESIGN OF RECTANGULAR PRE-STRESS BEAMMetric to SIGIRDER-11.0m DepthGiven Data :kg/cum.N/cum.Wt.conc. =150.00pcf2400.0023545.0Wll =1284.60#/ft18742.53N/mfc' =5000.00psi34.48Mpafc'i =4000.00psi27.58Mpafsi =175500.00psi1210.07Mpafse =150400.00psi1037.01Mpafpu =250600.00psi1727.89MpaL =62.25ft18.98mWdl =568.26#/ft8291.01N/mloads from slab, FFSolution :Approximate depth, h=L /25759.15mmsay1000mmTry :b =450mm0.45mh =1000mm1.00mhWdl =10595.26N/mdead load from beam aloneTot Wdl =11163.52N/mbMoment due to Dead Load:M =(Wdl*L^2)/8M =502623N-mEstimate prestressed Steel, Aps: by assuming a =0.5ha =500mmWll =18742.53N/mTotal W =Wll + WdlW =29,337.79N/mfcTotal MomentCMT =1320895.57N-m1320895568.74595N-mmMTak-ftTa =MTT = MT/aToT =2641791.14NT =Aps*fseAps =T/fseAps =2547.51sq. mm.Area of TendonRecomputing Ac:T = AcfcAc = 2T / ( fc+0 )fc = 0.45fc'T = Ac*((fc+0)/2)Ac =340574.15sq.mm.Assumed Section Area,Ac =450000.00sq.mm.(furnished)greater than thoerytical therefore OKUse Section: b =450.00mmh =1,000.00mmT =Aps * fsiT =3082675.16NTa =Mdla = Mdl / Tha =163.0mmeKbae =Kb + aTKb =(1/6)hKb =167e =330mmCheck stress at mid-span at transfer:bFi =Aps * fsiFi =3082675.16NfT =(Fi/bh)(1-(6e/h))hfT =-6.70Mpaefb =(Fi/bh)(1+(6e/h))Fifb =20.40MpaDead Load Stress:fdl =(6Mdl) / (bh^2)Allowable stress, fc all. = 0.6fc'Ifdl =6.70Mpafc all. =16.55MpaStress diagram:Tranferdead load6.70-6.700+=-6.7020.4013.70MpaLess than allow. SafeCheck stress with service loads after losses have occurred in tendon.Fe =Aps * fse450Fe =2641791.14fT =(Fe/bh)(1-(6e/h))-5.741000fT =(Fe/bh)(1+(6e/h))e17.48FeStress Due to Total loads:f =(6MT) / (bh^2)Allowable stress, fc all. = 0.45fc'f =17.61Mpafc all. =15.51MpaStress diagram:Tranferdead loadLess than allow. Safe-5.7417.6111.87+=17.48-17.61(0.13)MpaCompute Ultimate Moment: due to Udl + UllbMu =( Wu*L^2 )/8Wu =1.4dl + 1.7llh/2dNAWu =46695.67N/mVu =99.62k3.20k/fteMu =2102411.13N-m1550.26k-ftPp =Aps / bdh/2 =500mme =330mmPp =0.00682d =830mmwp =(Pp * fps)/fc'fpu =1727.887Mpafpu/2 =863.9435MpaLess than fse =1037.008Mpafps =fpu*(1- 0.5(Pp*fpu/fc'))fps =1432Mpabwp =(Pp * fps)/fc'wp =0.283aC = 0.85fc' abless than0.30dT =Aps * fpsNAApsd-(a/2)T =3649172.92NT = Aps * fps820.41kC =Ta/2 =138.37mme =329.71mm0.85fc' ab =Td =829.71mmb =450.00mmsolve for a =T/(0.85fc' * b)a =276.73mmCompute Ultimate Moment: due to Prestress Load450Mn =0.85fc' ab (d-a/2)h/2 =500Mn =C*(d-a/2)d =829.71Mn =2522850337.7N-mmApse =329.71Mn =2522850.34N-mMu =O MnMu =2270565.30N-mGreater than Mu dl+ll therefore OK1674.25k-ftCheck deflection:Allow. Def =L/300y all. =63.26mmEc =4730 ( fc' )MpaEc =39216472.3741856MpaI =1/12(bh^3)mm^4I =37500000000mm^4Def.,dl + ll,y1 =(5wl^4)/(384EI)y1 =33.70mmDef.,pres, y2 =(ML^2)/(8EI)y2 =0.070mmNet def. y =y2-y1y =33.63mmOK