40m预应力混凝土T梁计算报告

40m预应力混凝土T梁计算报告规范标准：公桥规JTGD60-2004公桥规JTGD62-20042009年2月2日一) 预制梁自重a. 按跨中截面计算主梁的恒载集度g=0.7987X25=19.97KN/mb. 由于马蹄提高形成四个横置的三棱柱，折算成恒载集度为：g=4X(0.79-0.31)X4.37X0.09X25/39.94=0.47KN/mc. 由于腹板加厚所增加的重量折算成恒载集度为：g=2X(1.1014-0.7859)X(0.47+1.05)X25/39.94=0.6KN/md. 主梁中横隔梁的体积：g=0.8384X0.25X25X2X9/39.94=2.34KN/Me. 预制梁恒载集度为：g19.97+0.47+0.6+2.34=23.38KN/m二) 现浇段自重a. 现浇接头恒载集度为：g=0.25X(0.07+0.07)X2X9X25/39.94+0.2X2X0.15X25=1.9KN/m三) 二期恒载a. 铺装层恒载集度为：8cm混凝土铺装：0.08X9X25=18KN/m5cm沥青混凝土铺装：0.05X9X23=10.35KN/m若将桥面铺装分摊给五片主梁，则g=(10.35+18)/5=5.67KN/mb. 防撞栏恒载集度为：g=0.5X25/10=1.25KN/mc. 中梁二期恒载集度：g3=1.25+5.67=6.92KN/m(三)恒载内力如图1-2所示，设X为计算截面距左支座距离，并令a=X/L图1-2主梁弯矩和剪力的计算公式分别为：M以=0.5XaX（1-a）L2g;Q侦=0.5X（1-2a）Lg恒载内力计算见表1-3中梁恒载内力1-3跨中a=0.5四分点a=0.25变化点a=0.13897支点a=0.0预制梁自重弯矩KN/m4445.12253333.84192127.566120剪力KN0227.955329.194375455.91现浇段自重弯矩KN/m361.2375270.92813172.8988720剪力KN018.52526.75232337.05二期恒载弯矩KN/m1315.665986.74875629.7158920剪力KN067.4797.4347764134.94E弯矩KN/m5852.04754389.03562800.961730剪力KN0312.2925450.987845624.585二.活载内力计算（一）冲击系数和车道折减系数按“规范”4.3.2.5，对本设计而言f=nX.闽/m/2L2=n,3.45x1010x0.3788*107/30.92x103/9.8=2.005HZ所以，u=0.1767Xlnf-0.0157=0.11,冲击系数（1+U）=1.11按“规范”4.3.2.4，当车道多于两车道时，需进行车道折减，本设计按两车道设计，所以计算荷载内力时不需进行车道折减。（二）计算主梁的荷载横向分布系数mC1.计算几何特性（1）主梁抗弯惯矩I=0.4482m4主梁的比拟单宽抗弯惯矩:J?=O.4482/2.0=0.2241m4/m横隔梁抗弯惯矩l=4Xb=4X2.0=8.0mc/l=2.3/8.0=0.288查表c/l=0.288时，人/c=0.65得：人=2.3X0.65=1.5m2x1.5x0.15x些+0.25x1.8x0.9求横隔梁截面重心位置a=2=0.49my2x1.5x0.15+0.25x1.8故横隔梁的抗弯惯矩为：I=2X1.5X0.153/12+2X1.5X0.15X(0.49-0.075)2+0.25X1.83/12+0.28X1.8X(0.9-0.49)2=0.2846m4横隔梁比拟单宽抗弯惯矩：J=I/a=0.2846/4.85=58.6X10-3m4/m主梁与横隔梁的抗扭惯矩对于主梁梁肋：主梁翼板的平均厚度h1=0.16cmb/t=1.84/0.24=7.6查表得c=0.305It=cbt3=0.305X1.82X0.243=7.6X10-3m4对于横隔梁梁肋：b/t=(1.8-0.15)/0.25=6.6查表得c=0.301I=cbt3=0.301X1.65X0.253=7.76X10-3m4最后得ITaTT_0.183IJ/I,+千=1.9X10-3+3.88X10-3+3.8X10-32.计算参数。和以=9.58X10-3m4/m50.22413940.0586=0.179a=Gp、)=性x9.58x10-3=0.01792EyJ-J2E、0.2241x0.0586则、，履=0.143.计算各主梁横向影响线坐标已知0=0.172,从G-M法图表中可查得系数K1和、的值，如表1-4用内插法求实际梁位处的K1和值.对于1号梁:、25一一一一K=K3+(KBB-K3)X差=0.2KB+0.8K,4B4B4B对于2号梁:K)1B44BK=K+(1B475X=0.6125K+0.4K1B2对于3号梁:现将1、2、3号梁的横向影响线坐标值列表计算于下梁位荷载位置B3B/4B/2B/400-B/40-B/20-3B/40-B校核K000.960.9811.031.041.0310.980.968.02B/41.711.541.321.191.010.880.620.420.348.005B/23.092.11.721.351.010.610.26-0.15-0.528.185B3/43.372.72.11.571.010.42-0.14-0.65-1.388.005B3.83.22.481.721.050.26-0.52-1.18-1.97.96K100.960.9711.031.041.0310.970.968B/41.021.031.041.051.010.990.950.940.937.985B/21.11.091.081.0210.960.940.920.98.01B3/41.21.151.11.031.010.930.910.880.868.04B1.381.221.131.020.980.920.880.820.88.06梁号梁位荷载位置B3B/4B/2B/40-B/4-B/2-3B/4-B1K11.2361.1641.1061.0281.0040.9280.9040.8680.848*K03.4562.82.1761.61.0180.388-0.216-0.756-1.484K1-K0-2.22-1.636-1.07-0.572-0.0140.541.121.6242.332(k1-k0)-0.3108-0.22904-0.1498-0.08008-0.001960.07560.15680.227360.32648Ka=K0*(K1-K0)3.14522.570962.02621.519921.016040.4636-0.0592-0.52864-1.15752气=Ka/50.629040.5141920.405240.3039840.2032080.09272-0.01184-0.10573-0.23152K11.0681.0661.0641.0321.0040.9720.9440.9280.912K02.5381.8761.561.2861.010.7180.4040.078-0.176K1-K0-1.47-0.81-0.496-0.254-0.0060.2540.540.851.088如(K1-K0)-0.2058-0.1134-0.06944-0.03556-0.000840.035560.07560.1190.15232Ka=K0+加(k1-K0)2.33221.76261.490561.250441.009160.753560.47960.197-0.02368气=Ka/50.466440.352520.2981120.2500880.2018320.1507120.095920.0394-0.004743K10.960.9711.031.041.0310.970.96K00.960.9811.031.041.0310.980.96K1-K00-0.0100000-0.010Ja(K；-K0)0-0.001400000-0.00140Ka=K0+%M(K1-K0)0.960.978611.031.041.0310.97860.96气广Ka/50.1920.195720.20.2060.2080.2060.20.195720.1924.计算荷载分布系数1-3号梁的横向影响线和最不利布载如图2-4车辆荷载：图1-4中梁：mc=0.5X(0.3688+0.30+0.2357+0.1634)=0.53支点截面的荷载横向分布系数m0如图1-5所示，按杠杆原理法绘制荷载横向分布影响线支点的横向分布系数可计算如下：中梁：mo=0.5X（0.9+0.48）=0.693）横向分布系数汇总见表1-6表1-6梁号mmc（变化点处）m中梁0.530.600.693.计算荷载内力在活载内力计算中，对于横向分布系数的取值作如下考虑：计算主梁活载弯矩时，采用全跨统一的横向分布系数m，由于跨中和四分点的剪力影响线的较大坐标位于桥跨中部，故也按不变的m来计算。求支点和变化点截面活载剪力时，由于主要荷载集中在支点附近应考虑支承条件的影响，即从桥支点到L/4之间，横向分布系数用m0和mc内插，其余区段均取m。值，见图1-6和图1-7（经过内插取集中荷载P广237KN）图1-61)计算跨中截面最大弯矩和最大剪力采用以下公式：M=(1+u)Zm(qQ+Py)=(1+u)Zm(ql2+Lpl)+qX0.5Xmaxckc84k9.75X0.16X1.63X2Q=(1+u)Zm(qQ+1.2Py)=(1+u)Zm(1ql+1.2Py)+qX0.5X表1-7maxkc8k9.75X0.16X0.083式中：u车辆冲击系数E车道折减系数mc主梁荷载横向分布系数y沿桥跨纵向与荷载位置对应的内力影响线最大值Q影响线为正的处的面积跨中内力计算表弯矩剪力2534.34KNm106.8KN2）计算四分点截面最大弯矩和最大剪力M=(1+u)Zm(qQ+P尸)=(1+u)Zm(7.875X39X7.3125X0.5+237X7.3125)+7.875X0.5X9.75X0.16X(2.44+0.73)Q=(1+u)Zm(qQ+1.2Py)=(1+u)Zm(7.875X0.5X29.25X0.75+1.2X237X0.75)+7.875X0.5X9.75X0.16X0.075弯就帔图1-7表1-8四分点内力计算表弯矩剪力1701.8KNm176.8KN1) 计算变化点截面最大弯矩和最大剪力M=(1+u)Zm(qQ+Py)=(1+u)Zm(7.875X39X4.67X0.5+237X4.67)+7.875X0.5X9.75X0.16X(2.76+0.45)Q=(1+u)Zm(qQ+1.2Py)=(1+u)Zm(7.875X0.5X33.58X0.86+1.2X237X0.86)+7.875X(0.5X9.75X0.16X0.083+0.5X0.03X弯矩剪力1094.9KNm211.8KN4.26X0.82)4.67图1-8变化点内力计算表表1-92) 计算支点截面最大剪力0+1.2Q=(1+u)Zm(qQ+1.2P尸)=(1+u)Zm(7.875X0.5X39X1.X237X1)+7.875X0.5X9.75X0.16X(0.92+0.083)3.QB3图1-9支点内力计算表表1-10剪力264.5KN5）.内力组合序号荷载类别跨中截面四分点截面变化点截面支点截面MmaxQmaxMmaxQmaxMmaxQmaxMmaxQmaxKN/mKNKN/mKNKN/mKNKN/mKN(1)预制梁自重4445.1203333.84227.962127.57329.190455.91(2)现浇段自重361.230270.9318.53172.9026.75037.05(3)二期恒载1315.660986.7467.47629.7197.430134.94(4)(1)+(2)+(3)6122.0204591.51313.962930.18453.370627.9(5)汽车荷载2534.34106.81701.8176.81094.9211.80264.5(6)基本组合10894.50149.527892.33624.275049.07840.5701123.78(7)短期组合7720.2567.355664.72425.453620.66586.940794.70(8)长期组合7035.2938.495204.77377.673324.74529.700723.22（1）基本组合（用于承载能力极限状态计算）其中（5）按“规范”4.1.6进行基本组合（用于承载能力极限状态计算），S=&.S.+YS+6&.S.二1.2X（4）+1.4X（5）i=1i=2其中（6）按“规范”4.1.7.1进行短期组合（用于正常使用极限状态计算），S=&S.+&中S广（4）+0.7X（5）/1.11i=1jT其中（7）按“规范”4.1.7.2进行长期组合（用于长期使用极限状态计算），S=&S.+&中2S*二（4）+0.4X（5）/1.11i=1jT承载能力极限状态计算跨中截面正截面承载能力计算12x3+274=15.75cmh=h-a=200-15.75=184.25cmb=24cm,上翼缘板厚度为15cm,若考虑承托影响，其平均厚度为h=15+6X36/(200-24)=16.22cm上翼缘有效宽度取下列数值中较小者：(1)bfWS=200cm(2)bfWL/3=3900/3=1300cm(3)bWb+12h=24+12X16.2=218.4cm取b=200cmfff首先按公式fdA=1260X5004=6305040N,f刁-bf-hf=22.4X162.2X2000=7266560所以是第一类梯形截面，应按宽度为bf的矩形截面计算其承载力.计算砼的受压区高度x:1. X=fdA/fdbf=1260X5004/22.4X2000=140.7mmW0.4X1842.5=737哑将X=140.7哑代入下式计算截面承载力M广fdbfxX(1842.5-140.7/2)/106=22.4X2000X140.7X1722.15/106=10857.5KN.mV10894.5KN.m斜截面抗剪承载力计算选取支点h/2和边截面点处进行斜截面抗剪承载力复核.(1)距支点h/2截面斜截面抗剪承载力计算首先，进行截面抗剪强度上下限复核：I0.5X10-3。fbhWyVW0.51X10-3vfcukbh2td00d，0汗为验算截面处剪力组合设计值,按内插法距支点h/2=1000mm处的七为5.32V=1123.78-1123.78-840.57x1.0=1070.55KNd0.5X10-3a2孔岛0=0.5X10-3X1.25X1.83X418.6X1722.15=824.6KNb=460-460-2405.32x1.0=418.6mm0.51X10fcukbh=0.51X10-3X7.07X418.6X1722.15=2600KN，0计算结果表明，截面尺寸满足要求，但需要配置抗剪箍筋斜截面抗剪承载力按下式计算：V为设计剪力，比值应按x=-+0.6mh重新补插，得d2Vd=1035.50KN(m=1.637)vcs为砼和箍筋共同的抗剪承载力V=aaa0.45x10-3bhJ(2+0.6p).厂pfcs1230*cu,ksvsv气一一异号弯矩影响系数，取1.0a2预应力提高系数，取1.25a3受压翼缘的影响系数，取1.1bT梁截面腹板宽度360.75mmh0斜截面受压端正截面的有效高度1842.5mmP斜截面内纵向受拉钢筋的配筋百分率P=100P,P=Apb/bh0取P=0.75p箍筋配筋率，p=131.1/360.75X100=0.003634匕$=1.0x1.25x1.1x360.75x1842.5xJ(2+0.6x0.75)应x0.36%x280x0.45X10-3=1642.3KNVpb与斜截面相交的预应力弯起钢筋抗剪承载力设计值(KN)V=0.75x10-3fASin。=0.75x10-3x1260x0.14x5004=662.0KNV=V+Vb=662.0+1642.3=2304.3KN说明截面抗剪承载力是足够的(2)变截面点处斜截面抗剪承载力的计算首先进行抗剪强度上、下限的复核：0.5X10-3afbhWyVW0.51X10-3匕左bh2td00d，0其中，V816.58,b=240哑，h。仍取1842.5哑0.5X10-3a2ftdbh0=0.5X10-3X1.25X1.83X240X1842.5=505.7KN0.51X10-3、fcukbh=0.51X10-3X7.07X240X1842.5=1594.4KN,0计算结果表明，截面尺寸满足要求，但需要配置抗剪箍筋斜截面抗剪承载力按下式计算：YVdW_=aaa0.45x10-3bh、(2+0.6p)、：pfcs1230Vcu,ksv睥式中，P斜截面内纵向受拉钢筋的配筋百分率P=100p,p=A。/bh。取P=1.13p箍筋配筋率，p=131.1/240X125=0.00437Vcs=1.0x1.25x1.1x240x1842.5xJ(2+0.6x1.13)750x0.437%x280x0.45X10-3=1317.04KN=0.75x10-3fASind=0.75x10-3x1260x0.14x2502=331KNV=V+Vb=331.0+1317.04=1648.04KN四. 说明截面抗剪承载力是足够的预应力损失计算1. 摩阻损失。11按“公预规”第6.2.2条规定，预应力钢束与管道壁之间的摩擦损失计算公式为:c=b1-e-（R0bkx）式中：c张拉控制应力，c=0.75X1860=1395MPaU摩擦系数，取u=0.25k局部偏差影响系数，取k=0.0015各截面摩擦损失见下表截面-一钢束号1234支点x(m)0.110.170.130.41。（弧度）0.000.000.000.00。(MPa)110.220.350.280.85变截面x(m)5.625.695.655.73。（弧度）0.01570.03660.07850.1396。(MPa)1117.1324.4538.6559.37L/4截面x(m)9.729.799.759.82。（弧度）0.05590.07850.13440.1396。(MPa)1139.2847.0465.6867.55跨中x(m)19.7119.7719.7419.81。（弧度）0.13960.13960.13960.1396。(MPa)1187.0987.2187.1487.282. 锚具变形损失。12反摩擦影响长度1fb。1f=%EAZ-E/Ac,Ac=_I式中：。张拉端锚下控制应力；Al锚具变形值,OVM夹片锚无顶压时取6mm;。1扣除沿途管道摩擦损失后锚固端预拉应力；1张拉端到锚固端之间的距离，本例中取19737mm.当1fW1时，离张拉端x处由锚具变形、钢筋回缩和接缝压缩引起的、考虑反摩擦后的预应力损失Ac为，XAc=Ac,Ac=2Ac1xldff当1fWx时,表示该截面不受反摩擦的影响.锚具变形损失的计算见下两表反摩擦影响长度计算表钢束号1234。n(MPa)13951395139513950=00(MPa)1307.911307.791307.861307.72。d=(o0Oii)/L(MPa)0.00441240.0044186560.0044152770.0044223331(mm)16283.80116272.2585616278.4846416265.49159锚具变形损失计算表截面J、-钢束号1234总计(MPa)支点x(mm)1.10170.00130.00410.00568.83o(MPa)143.70143.80143.75143.86oi2(MPa)143.69142.30142.60140.24变截面x(mm)5620.005690.005650.005730.00374.66o(MPa)143.70143.80143.75143.86oi2(MPa)94.1193.5293.8693.18L/4截面x(mm)9723.009786.009752.009822.00229.84o(MPa)143.70143.80143.75143.86。巧(MPa)57.9057.3257.6356.99跨中x(mm)19708.0019771.0019737.0019808.000.00o(MPa)143.70143.80143.75143.86。巧(MPa)0.000.000.000.00分批张拉损失o14先扣除上述两项预应力损失。+。2后，预应力钢筋的合力Np为:3pPpeAp，pe=on-1-/2后张法预应力构件，由混凝土弹性压缩引起的预应力损失的简化算法公式:b=mzlaa142eppc截面-.钢束号1234总计(MPa)支点Np1565111.711566685.821566400.291568641.9154.01。(MPa)-0.151.261.703.56。(MPa)13.5013.5013.5013.50变化点Np1605990.051597561.501579375.911554295.1797.41。(MPa)2.372.333.083.72。i4(MPa)24.3524.3524.3524.35L/4截面Np1623579.521614586.031590879.241589347.4691.87。(MPa)2.932.212.722.72。i4(MPa)22.4223.1523.1523.15跨中Np1636198.641636044.021636127.461635953.2381.78。p(MPa)2.562.282.282.28。(MPa)19.9220.6220.6220.623. 钢筋松弛引起的预应力损失。15bb二中&(0.52f-0.26)bPk式中：中一一张拉系数，一次张拉时，中=1.0&钢筋松弛系数，11级松弛(低松弛)，&=0.3bp传力锚固时的钢筋应力，对后张法构件bp=bb1b12b14截面钢束号。p(MPa)。i5(MPa)12341234支点1237.581238.841238.611240.4131.9332.0932.0632.29变化点1259.411252.681238.141218.0934.8033.9032.0029.43L/4截面1275.411267.491248.541247.3136.9535.8833.3633.20跨中1288.001287.171287.231287.0938.6738.5638.5738.554. 混凝土收缩、徐变损失。16混凝土收缩和徐变引起的应力损失b根据“公预规”6.2.7,由混凝土收缩徐变引起的构件受拉区预应力钢筋的预应力损失，可按下列公式计算：.9Epcs(%)b=16(t)Eppc-,()/1+15ppps式中:A+APASp=_+1psi2e=+psA+Ai2=I/A设混凝土的传力锚固龄期及加载龄期均为28天，计算时间=8,桥梁所处环境的年平均相对湿度为75%,以跨中截面计算其理论厚度h:h=2Ac/u=2X0.7935X1000/8.15=194.7哑查表得M(t,t0)=0.22X1036(t,t)=1.66混凝土收缩、徐变损失的计算表截面e(mm)PPpsNe(N)M(KN.M)。(MPa)。(MPa)。PC(MPa)。l6(MPa)支点252.800.00571.166199267.230.005.710.005.7179.02变截面732.300.00722.106215366.722800.9615.474.5510.91106.434/L802.500.00712.356303465.124389.0322.799.3713.42121.58跨中805.200.00712.386442010.445852.0427.4313.7713.67122.986.预应力损失组合上述各项预应力损失组合情况列于下表截面。二。+。+。(MPa)。二。+。(MPa)1234平均1234平均支点157.42156.16156.39154.59156.14110.95111.11111.08111.31111.11变化点135.59142.32156.86176.91152.92145.42144.52142.62140.05143.15L/4截面119.59127.51146.46147.69135.31163.50162.43159.91159.75161.39跨中107.00107.83107.77107.91107.63168.30168.19168.20168.18168.22正常使用极限状态计算1.全预应力混凝土构件抗裂性验算(1)正截面抗裂性验算正截面抗裂性验算以截面受拉边的正应力控制。在荷载短期效应组合作用下应满足:ost0.85opcW0。为在荷载短期荷载效应组合作用下,截面受拉边的应力：b=Jy+My+Mg2K+0亦/(1+四)ystJnixJn2xJ0x跨中截面：其中J、y、J、y、J、y分别为阶段1、阶段2、阶段3、截面惯性矩和截N1N1xN2N200x面重心至受拉边缘的距离，可由上面表查得：J0/y0=369832450哑3J/y=304859690哑3J/y=358549690哑3N1N1xN2N2x4445.12361.231315.06+0.7x2534.34/1.11b=+代入公式得:st0.30490.35850.3698=14.5+1.0+7.88=23.38MPabpc为截面下缘有效预压应力:b=土+NZnypcAJnxNp=(1395-107.63-168.22)X50.04=5600.23KNe=y=1054.5mm,5600.235600.23x1.0545、，bpc=0+林)/1000=22.27MPa23.38-22.27X0.85=4.45MPaN0,不满足要求.若按部分预应力混凝土A类梁计算:23.38-22.27=1.05MPaW0.7f尸.85MPa四分点截面:J/y=309268170哑3J/y=353363430哑3N1N1xN2N2xJ0/yo=364689690哑3代入公式得:3333.84270.93986.74+0.7x1701.8/1.11b=+st0.30920.35340.3647=17.2MPabpc为截面下缘有效预压应力:b=L+，ypcAJnxNp=(1395-135.31-161.39)X50.04=5495.89KNe=y=946.3mm,5495.895495.89x0.9463、，b疽(1+0.3647)/100=20.442MPa17.19-20.442X0.85=-0.19MPaW0,满足要求.变化点截面:J/y=317641170哑3J/y=3436335900哑3N1N1xN2N2xJ0/y0=354954020哑3代入公式得:2127.57172.9629.71+0.7x1094.9/1.11b=+st0.31760.34360.3550=10.92MPabpc为截面下缘有效预压应力:b=土+fypcAJnxN=(1395-152.92-143.15)X50.04=5499.05KNpe=y=704.9哑,5499.055499.05x0.7049、，b=(08891+八c)/10000.3550=17.10MPa10.92-17.10X0.85=-3.62MPaW0,满足要求.综上，截面下缘需配置一定抗拉主筋。(2)斜截面抗裂性验算斜截面抗裂性验算以主拉应力控制，一般取变截面点分别计算截面上梗肋、形心轴和下梗肋处在荷载短期效应组合作用下的主拉应力，应满足a卬0.6f的要求。a卬为荷载短期效应组合作用下的主拉应力a=fc+t2tp2l2a=a干j,My干2k+k5）ycxpcJn1Jn2J0VVV+0.7V/（1+旦）aAsin0ST=G1PKS+G1mKS+Q1KSPPPnLJbntJbn2Jb0Jbn1n20n1上述公式中车辆荷载产生的内力值，按最大剪力布置荷载，即取最大剪力对应的弯矩值。下图为计算点的位置示意图。各计算点的部分截面几何性质按上面表取用，下表中，A1为阴影部分的面积，S1为阴影部分的面积对截面形心轴的面积矩，yxi为阴影部分的形心到截面形心轴的距离,d为计算点到截面形心轴的距离。计算点几何性质计算点受力阶段Ai（X106）yxi（mm）D（mm）S1（X109mm3）上梗肋处阶段10.2188678.3590.30.1484阶段20.2188713.9625.90.1562阶段30.3560648.6558.60.2309阶段10.4304198.629.70.0855阶段20.4390178.665.30.0784阶段30.4900198.60.00.0973阶段10.1710999.7779.70.1709阶段20.1920964.1744.10.1851阶段30.19201029.4809.40.1976形心位置下梗肋处变截面处有效预应力:b=bbb川=1395152.92143.15=1098.93N=。A=1098.93X5.004=5499.05KNe=y=704.9预应力弯起角度分别为：1. 01=6.85。02=5703=4.56。04=0。(未弯起)a)上梗肋处b=(5499.05/0.8892-5499.05X0.7049X0.59/0.4335)/1000=0.91MPa八，172.9(629.71+0.7x1094.9/1.11)b=0.91+37853x0.6+397?&x0.63+433.?x0.56=6.0MPa329.19x0.148426.75x0.1562(97.43+0.7x211.8/1.11)x0.2309T=+378.53x0.24397.26x0.24433.52x0.24x5004xsin4.2775。x0.15378530x0.24=0.37MPab=竺-J(竺)2+0.372=-0.022MPatp22b)形心轴处b=(5499.05/0.8892+5499.05X0.7049X0.297/0.4335)/1000=8.92MPa172.9(629.71+0.7x1094.9/1.11)八b=8.92-37853x0.297397x0.65343352x0=7.18MPa_329.19x0.085526.75x0.0784(97.43+0.7x211.8/1.11)x0.0973T378.53x0.24+397.26x0.24+433.52x0.24x5004xsin4.2775。x0.09378530x0.24=0.13MPa。=坐-丫718)?+0.132=-0.002MPatp22b)下梗肋处q=(5499.05/0.8892+5499.05X0.7049X0.78/0.4335)/1000=13.3MPa2127.57172.9(629.71+0.7x1094.9/1.11)MO1q=13.3x0.78x74-x0.81-378.53397.26433.52=6.37MPa329.19x0.170926.75x0.1851(97.43+0.7x211.8/1.11)x0.1976T378.53x0.24+397.26x0.24+433.52x0.24-x5004xsin4.278。x0.17378530x0.24=0.27MPa。=637(6)2+0.272=-0.01MPatp22综上，形心轴处主拉应力最大,q二一0.002W0.7f广1.86MPa变形计算(1)预制现浇阶段的挠度计算主梁砼浇筑，预应力筋束张拉B0=0.95EJ=0.95X3.45X104X0.3661X1012=1.2X1016N哑2此时由预制T梁自重产生的挠度值f=5xL、=5x392x4445.12x1012=587G48xBGK48x1.2x1016.0预加力引起的反拱MMf=-j-p-dx=2p1BB00其中W为跨中截面作用单位力P=1时所产生的M图在半跨范围内的面积:My121LLL2W=xx=峋224162Mp为半跨范围M1图的重心（距支点L/3处）所对应的预加力引起的弯矩图纵坐标conM=Ne，其中N=（。-。）A，其中q近似取L/4截面损失值pPppconIpIN=(q-Qi)A=(1395-135.31)X50.04=6303.49KNep为距支点L/3处预应力的偏心距e=yx一a=1193.9-187.75=1006.15哑M=6303.5X103X1006.15=6341.3X106N哑q392x6341.3x1012f=121016=100.46mm现浇阶段(1)B0=0.95EJ=0.95X3.45X104X0.4108X1012=1.35X1016N哑2此时由现浇段恒重产生的挠度值q5392x361.23x1012。f二x13510=4.28哑即此时由预加力引起的反拱度减少了4.28哑二期恒载阶段B0=0.95EJ=0.95X3.45X104X0.4482X1012=1.47X1016N哑2此时由二期恒载恒重产生的挠度值q_5392x1315.66x1012一c/48x1.35x1016-.mm即此时由预加力引起的反拱度减少了14.2哑汽车荷载作用后Bo=0.95EJ=0.95X3.45X104X0.4482X1012=1.47X1016N哑2此时由汽车荷载产生的挠度值f=兰X392XgXI012=175g481.47x1016即此时由预加力引起的反拱度减少了17.2哑最后由预应力引起的反拱度为6.08哑使用阶段的挠度计算使用阶段的挠度值，按短期荷载效应组合计算，并考虑挠度长期影响系数气,对C50砼,气=1.425，刚度Bo=1.47X1016N哑2f=兰x392X7720.25X1012=83.20哑S481.47X1016自重产生的挠度值按等效均布荷载作用情况计算f=Ax392X6122.02X1012=66.0哑g481.47x1016消除自重产生的挠度，并考虑挠度长期影响系数，使用阶段挠度值为:f气(f-f)=1.425X(83.2-66.0)=24.51WL/600=65哑计算结果表明，使用阶段的挠度值满足规范要求.5.预加力引起的反拱计算及预拱度设置。B/0.95EJ=0.95X3.45X104X0.3661X1012=1.2X1016N哑2MMmpf=-Jl_pdx=2p100其中W为跨中截面作用单位力P=1时所产生的M图在半跨范围内的面积:M_121LLL2W=xx=岭224162M为半跨范围图的重心(距支点L/3处)所对应的预加力引起的弯矩图纵坐标M=Ne，其中N=(b-b-b)A，其中b近似取L/4截面损失值pPppconIIIpIN=(b七)-A=(1395110.42-164.76)X5.004=5603.57KN为距支点L/3处预应力的偏心距pe=y-a=1193.9-187.75=1006.15哑M=5603.57X103X1006.15=5637.2X106N哑二89.31mmf=2x392X5637.2xlgx1016x16此时考虑反拱长期增长系数门0=2.02.0Xf=178.63哑1.425X83.2=118.56哑故可不设预拱度。五. 持久状况应力验算按持久状况设计的预应力砼受弯构件，尚应计算其使用阶段正截面砼的法向应力,受拉钢筋的拉应力以及斜截面的主压应力。作用时取其标准值，不计分项系数,汽车荷载应考虑冲击系数。(1)各截面砼法向正应力验算根据规范7.1.5受压区砼的最大压应力对于未开裂构件b+b=NkcptAn1二+MWns2+MQ1KWns1Wns20.5fck其中N=(bb)-A对于跨中截面：5600.235600.23x1.04354445.12361.231315.66+2534.34“+/10000.77860.45820.45820.48100.5687二11.46MPa0.5fk=16.2MPa对于四分点截面:0.4621竺售-5495.89x0.9295+333384+*+986.74+170L80.77860.46210.46210.47720.5643=8.47MPa0.5f=16.2MPa对于变化点截面：5499.055499.05x0.67522127.57172.9629.71+1094.9“+/10000.77860.46830.46830.47070.5568=7.13MPa0.5f广16.2MPa对于支点截面：5643.265643.26x0.0445II/10001.09050.5222=4.68MPa0.5f广16.2MPa(2)截面预应力钢筋拉应力验算根据规范7.1.5对于受拉区预应力钢筋的最大拉应力b=(b+ab)0.65f气,是按荷载效应标准值，对后张法构件不包括T梁预制自重计算预应力钢筋重心处砼的法向应力b=+MG2K+MQ1KktwOP跨中截面：361.23+1315.66+2534.34b=kt425.07=9.9MPab=1119.15+5.65X9.9=1175.09V0.65X1860=1209MPa四分点截面：270.93+986.74+1701.8b=kt468.2=6.32MPab=1098.3+5.65X6.32=1134.01V0.65X1860=1209MPa四分点截面：172.9+629.7+1094.9b=kt615.05=3.08MPab=1109.93+5.65X3.09=1127.34V0.65X1860=1209MPa支点截面：0+0+0c=kt5713.34=0MPac=1127.75+5.65X0=1127.75V0.65X1860=1209MPa(3)斜截面主应力验算一般取变截面点分别计算截面上梗肋、形心轴和下梗肋处在标准值效应组合作用下的主压应力,应满足c0.6f的要求。cpckccpccxk+i2气疽cpc干MG1PKJn1MG1mKJn2G2KJ0T=G1PKSkJbnt+G1mKSJn2bVG2K+VSJ0b0a)上梗肋处c=(5499.04/0.8892-5499.04X0.7049XO.59/O.4335)/1000=0.91MPa433.52c=0.91+217X0.6+冬X0.63+(629.71+尝x0.56cx378.53397.26=6.73MPa329.19x0.148426.75x0.1562(97.43+211.8)x0.2309T=+378.53x0.24397.26x0.24433.52x0.24x5004xsin4.2775。x0.15378530x0.24=0.57MPac=6.73+(623)2+0.572=6.78MPatp22b)形心轴处2127.57 c=(5499.04/0.8892+5499.04X0.7049X0.297/0.4335)/1000=8.92MPa172.9(629.71+1094.9)八c=8.9237853乂0.297-x0.65343352一乂0=6.97MPa_329.19x0.085526.75x0.0784(97.43+211.8)x0.0973T378.53x0.24+397.26x0.24+433.52x0.24x5004xsin4.2775。x0.09378530x0.24=0.22MPa。=竺7+,：(竺)2+0.222=6.98MPatp22b)下梗肋处2127.57 q=(5499.04/0.8892+5499.04X0.7049X0.78/0.4335)/1000=13.3MPa172.9(629.71+1094.9)MO1q=13.3x0.78x0.74_x0.81-378.53397.26433.52=5.37MPa丁_329.19x0.1709+26.75x0.1851+(97.43+211.8)x0.1976一378.53x0.24+397.26x0.24+433.52x0.24x5004xsin4.278。x0.17378530x0.24=0.46MPaQ=契+：(537)2+0.462=5.41MPatp22综上，上梗肋处主压应力最大，q=6.78W0.6fk=0.6X32.4=19.44MPa，斜截面主压应力满足要求。六. 短暂状态应力验算预应力砼结构按短暂状态设计时,应计算构件在制造、运输及安装等施工阶段,由预加力、构件自重及其它施工荷载引起的截面应力，对简支梁，以跨中截面上、下缘砼正应力控制。预制阶段：6441.2 (1)上缘砼应力Qt=曳-N%1+MG1pK0