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1、40m预应力混凝土 T梁上拱度计算(一)一、截面几何特性计算1、L /2截面几何特性计算管道自身惯性矩从略(含L/4、3L/8、端部)计算结果见下表：截面编 号截面积A (m2)截面重 心距梁 底 d(m)截面对梁 底面积矩Ad(m3)小块截面 重心距全 截面重心 距离Y(m)小块截面 对全截面 重心之惯 性矩AY2(m4)截面本 身惯性 矩 I(m4)总惯性矩I+ AY2 (m4)123456789砼 截 面11.70+0.16=0.2722.420.658241.02090.2834880.00058020.6*0.09=0.0542.310.124740.91090.0448060.00
2、002430.20*1.99=0.3981.3450.535310.05410.0011650.13134340.20*0.25=0.050.433330.021670.965770.0466360.00017450.60*0.35=0.210.1750.036751.22410.3146680.0021440.9841.39911.376710.6907550.1342650.82502净 截 面0.9841.39911.376710.031240.0009600.82502管 道-n*0.082/4=-0.025130.207-0.0052021.22334-0.037609净 截 面0.
3、958871.430341.37151-0.0366490.7883712、 L/4 截面净截面0.9841.39911.376710.0275690.0007100.82502管 道-0.025130.3739-0.0093961.052064-0.027815净截面0.958871.4259641.367374-0.0271050.7979153、L/8截面用cad查询(计入管道自身惯性矩)结果:净截面1.3700管 道-0.025130.7498净截面1.34490267791.4097130.905898893、3L/8 截面净截面0.9841.39911.376710.0304930
4、.0009150.82502管 道-0.025130.2353-0.0059161.194193-0.035838净截面0.958871.4295931.370794-0.0349230.7900974、端部截面几何特性计算计算结果见下表截截面积A (m2)截面重截面对梁小块截面小块截截面本总惯性矩面心距梁底面积矩重心距全面对全身惯性I+ AY2 (m4)编底 d(m)Ad(m3)截面重心截面重矩 I(m4)号距离Y(m)心之惯 性矩AY2(m4)123456789砼11.7*0.16=0.22.420.658241.0337650.290670.00058截7280面20.4*0.06=0.
5、02.320.055680.9337650.020920.00000246530.6*2.34=1.41.171.642680.2162350.065640.6406404851.700001.386232.35660.377250.641231.01848252净1.700001.386232.35660.0005750.000001.01848截50562面管-0.025131.348-0.0338750.03881-0.00003道785净1.674871.386812.322725-0.000031.018445截73面二、有效预应力值的计算1、张拉控制应力cr =0.75*1860=
6、1395Mpacon2、摩擦损失平均弯起角0 = (7330/60000*2+11782/75000+1679刀120000+12597/90000) /5=0.136271radl=(39304*2+39358+39390+39432) /5/2=19679mmo =o 1-e-(p0 +k x)=1395*1- e(0.25*0.13627+0.0015*19.679)=85.9 Mpal1 con3、锚具变形、钢筋回缩和接缝压缩引起的预应力损失O2=(y A l)Ep / 1=1.95*105*6/19679=59.5 Mpa4、砼弹性压缩损失o =aAo13 EPpca =1.95*1
7、05/3.45*104=5.7EP计算截面取在 l/4 跨度，先张拉钢筋重心处，由于后张拉一根钢筋产生的砼法向应力一根钢束预加应力为(按中跨每束8 根钢绞束)cosa = (cos0。*2+cos9.00078。+cos8.01998。+cos8.01950。)/5=0.99363nN =(1395-85.9-59.5)*140*8*0.99363=1390637N=1390.637kNy钢束重心距梁底373. 9mme=1425.964-373.9=1052.1mmW =0.797915/1.0521=0.758402m30 o pc 二手 + 器=1390637/(958870) + (
8、1390637*1052.1)/(7.58402*108) =1.93 Mpal3=a ep工A。pC=5.7*1.93*(5-l)/2=22.0Mpa5、钢束有效预应力o =o -o -o -o =1395-85.9-59.5-22.0=1227.6 Mpay con l1 l2 l3二、上拱度计算预应力 T 型梁在预加应力作用下，在纵轴线方向由于受到编心压力的作用而产生 上拱度。1、计算采用虚位移公式f MIMp/ (EJ) dx2、传力锚固时各截面弯矩Mp的计算(1) 钢绞束预应力合力预应力合力=1227.6*140*8*5=6874560N=6874.560kN(2) 各截面钢束重心距
9、梁底L/2 截面：a2=0.207m3L/8 截面： a=0.2353mL/4 截面： a=0.3739mL/8 截面： a=0.7498 m端部截面： a=1.348m(3) 各截面平均起弯角L/2 截面 cosa =cos0。=1nL/4 截面cosa = (cos0。*2+cos9.00078。+cos8.01998。+cos8.01950。)/5=0.99363nL/8 截面cosa n=(cos(12597/60000*180。/n )*2* + cos9.00078。+cos8.01998。+cos8.01950。) /5=0.984843L/8 截面cosa =(cos0。 *2
10、* + cos0。 +cos8.01998。 +cos8.01950。) /5=0.99609n端部截面 cosa =0.98484(同 L/8)n(4)各截面弯矩计算如下表截面位置Ny至净截面重心距离(m)预应力合力(kN)cosa n预应力弯矩(kN.m)L/21.43034-0.207=1.223346874.56018409.93L/81.42959-0.2353=1.194296874.5600.996098178.1L/41.42596-0.3739=1.052066874.5600.993637186.4L/81.409713-0.7498=0.6599136874.5600.9
11、84844467.8端部1.38681-1.348=0.038816874.5600.98484262.83、用图乘法计算积分6 = J MIMpd蛊/(El) =Ew |*y/(EI) 用图乘法计算积分I MLMpdx =工3 i*yi单位力矩图Ml和预应力力矩图Mp如下(L=39.92m)3 *y =5.0*4.375*0.5*(2/3*4467.8+1/3*262.8)=33535.8113 *y=5.0*4.375*0.5*(2/3*4467.8+1/3*7186.4)22+5.0*7.5*0.5*(2/3*7186.4+1/3*4467.8)= 176531.93 *y =5.0*7
12、.5*0.5*(1/3*8178.1+2/3*7186.4)33+5.0*9.375*0.5*(1/3*7186.4+2/3*8178.1)= 324869.73 *y =5. 0*9. 375*0. 5*(1/3*8409. 9+2/3*8178. 1) 44+5.0*10.0*0.5*(1/3*8178.1+2/3*8409.9)=401801.0工3 i*yi=936738.4 kN-m3二工3 *yi /(EI)=93 6 7 38 . 4/ (3 . 45*107*0.78 8 371) =0 . 034m=34mm 1i4、自重产生的垂度q=25*52.32/40=32.7kN/m=32.7N/mm =5*32.7*400004/(384*3.45*104*0.788371*1012) =40mm25、扣除自重垂度后的上拱度 =2*A =2*34-40=28mm1- 22011-09-23截面特性计算简图如下：78g土32L/4
