40米T梁张拉伸长值计算2.doc

40米T梁后张法预应力钢绞线张拉伸长值的计算（一）后张法钢绞线理论伸长值计算 根据公路桥梁施工技术规范(JTJ 041-2000)中关于预应筋伸长值的计算按照以下公式：L=Pp*L/(Ap*Ep)；Pp=P(1e-(kx+)/(kx+)；式中：L各分段预应力筋的理论伸长值（mm）；Pp各分段预应力筋的平均张拉力，注意不等于各分段的起点力与终点力的平均值（N）；L预应力筋的分段长度（mm）；Ap预应力筋的截面面积（mm2）；Ep预应力筋的弹性模量（Mpa）；P预应力筋张拉端的张拉力，将钢绞线分段计算后，为每分段的起点张拉力，即为前段的终点张拉力（N）；从张拉端至计算截面曲线孔道部分切线的夹角之和，分段后为每分段中各曲线段的切线夹角和（rad）；x从张拉端至计算截面的孔道长度，整个分段计算时x等于L（m）；k孔道每束局部偏差对摩擦的影响系数（1/m），管道弯曲及直线部分全长均应考虑该影响；预应力筋与孔道壁之间的磨擦系数，只在管道弯曲部分考虑该系数的影响。1、正弯矩： YWC250C型千斤顶编号：801181# 对应压力表编号：09.9.15.486YWC250C型千斤顶编号：Z205# 对应压力表编号：09.9.15.505根据设计图纸说明及规范要求，已知以下参数（表1）：项目名称取值张拉控制应力k1395 Mpa钢绞线面积Ag140 mm2弹性模量Eg2.0105Mpa管道摩阻系数0.25管道偏差系数k0.0015张拉端的张拉力193.9KN根据钢绞线要素（见设计图Q02-3），钢绞线分段以T梁中间对称划分，一半为3段（端头ab段包括工作长度60），可以计算出各分段长度，根据公式计算出伸长量，采用计算一半钢绞线的伸长值然后乘以二的方法，见表2； 表2编号线段L（m）（rad）kx+e-(kx+)边跨N1束ab2.79700.00419550.9958bc7.330.122170.04153750.9593cd10.16500.01524750.9848边跨N2束ab1.69600.0025440.9975bc11.7820.157080.0569430.9446cd6.84100.01026150.9898边跨N3束ab2.79600.0041940.9958bc16.7970.139980.06019050.9416边跨N4束ab6.47600.0097140.9903bc12.5970.139980.05389050.9475中跨N1束ab2.79700.00419550.9958bc7.330.122170.04153750.9593cd10.08500.01512750.985中跨N2束ab1.69600.0025440.9975bc11.7820.157080.0569430.9446cd6.76100.01014150.9899中跨N3束ab2.79600.0041940.9958bc16.7970.139980.06019050.9416中跨N4束ab6.47600.0097140.9903bc12.5970.139980.05389050.9475根据以上参数可计算：1） 边跨N1束ab段：Pp=P(1e-(kx+)/(kx+)=193.9103(10.9958)/0.0041955=194108NL=Pp*L/(Ap*Ep)= 1941082.797/(2.0105140)=0.019M边跨N1束bc段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.9593)/ 0.0415375=189990NL=Pp*L/(Ap*Ep)= 1899907.33/(2.0105140)=0.049M边跨N1束cd段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.9848)/ 0.0152475=193296NL=Pp*L/(Ap*Ep)= 19329610.165/(2.0105140)=0.070M故边跨N1束两端伸长值为：L=(abbccd)2=(0.0190.0490.070)2=0.276M2） 边跨N2束ab段：Pp=P(1e-(kx+)/(kx+)=193.9103(10.9975)/ 0.002544=190546NL=Pp*L/(Ap*Ep)= 1905461.696/(2.0105140)=0.012M边跨N2束bc段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.9446)/ 0.056943=188645NL=Pp*L/(Ap*Ep)= 18864511.782/(2.0105140)=0.079M边跨N2束cd段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.9898)/ 0.0102615=192737NL=Pp*L/(Ap*Ep)= 1927376.841/(2.0105140)=0.047M故边跨N2束两端伸长值为：L =(abbccd)2=(0.0120.0790.047)2=0.276M3） 边跨N3束ab段：Pp=P(1e-(kx+)/(kx+)=193.9103(10.9958)/ 0.004194=194177NL=Pp*L/(Ap*Ep)= 1941772.796/(2.0105140)=0.019M边跨N3束bc段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.9416)/ 0.0601905=188132NL=Pp*L/(Ap*Ep)= 18813216.797/(2.0105140)=0.113M故边跨N3束两端伸长值为：L =(abbc)2=(0.0190.113)2=0.264M4） 边跨N4束ab段：Pp=P(1e-(kx+)/(kx+)=193.9103(10.9903)/ 0.009714=193620NL=Pp*L/(Ap*Ep)= 1936206.476/(2.0105140)=0.044M边跨N3束bc段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.9475)/ 0.0538905=188896NL=Pp*L/(Ap*Ep)= 18889612.597/(2.0105140)=0.085M故边跨N3束两端伸长值为：L =(abbc)2=(0.0440.085)2=0.258M5） 中跨N1束ab段：Pp=P(1e-(kx+)/(kx+)=193.9103(10.9958)/0.0041955=194108NL=Pp*L/(Ap*Ep)= 1941082.797/(2.0105140)=0.019M中跨N1束bc段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.9593)/ 0.0415375=189990NL=Pp*L/(Ap*Ep)= 1899907.33/(2.0105140)=0.049M中跨N1束cd段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.985)/ 0.0151275=192266NL=Pp*L/(Ap*Ep)= 19226610.085/(2.0105140)=0.069M故中跨N1束两端伸长值为：L=(abbccd)2=(0.0190.0490.069)2=0.274M6） 中跨N2束ab段：Pp=P(1e-(kx+)/(kx+)=193.9103(10.9975)/ 0.002544=190546NL=Pp*L/(Ap*Ep)= 1905461.696/(2.0105140)=0.012M中跨N2束bc段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.9446)/ 0.056943=188645NL=Pp*L/(Ap*Ep)= 18864511.782/(2.0105140)=0.079M中跨N2束cd段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.9899)/ 0.0101415=193106NL=Pp*L/(Ap*Ep)= 1931066.761/(2.0105140)=0.046M故中跨N2束两端伸长值为：L =(abbccd)2=(0.0120.0790.046)2=0.274M7） 中跨N3束ab段：Pp=P(1e-(kx+)/(kx+)=193.9103(10.9958)/ 0.004194=194177NL=Pp*L/(Ap*Ep)= 1941772.796/(2.0105140)=0.019M中跨N3束bc段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.9416)/ 0.0601905=188132NL=Pp*L/(Ap*Ep)= 18813216.797/(2.0105140)=0.113M故中跨N3束两端伸长值为：L =(abbc)2=(0.0190.113)2=0.264M8） 中跨N4束ab段：Pp=P(1e-(kx+)/(kx+)=193.9103(10.9903)/ 0.009714=193620NL=Pp*L/(Ap*Ep)= 1936206.476/(2.0105140)=0.044M中跨N3束bc段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.9475)/ 0.0538905=188896NL=Pp*L/(Ap*Ep)= 18889612.597/(2.0105140)=0.085M故中跨N3束两端伸长值为：L =(abbc)2=(0.0440.085)2=0.258M编号线段L（m）（rad）kx+e-(kx+)T1ab1.79300.00268950.99731bc1.5870.078540.0220154540.97823cd8.36700.01255050.98753T2ab1.79300.00268950.99731bc1.5870.078540.0220154540.97823cd5.36700.00805050.99198T3ab1.79300.00268950.99731bc1.5870.078540.0220154540.97823cd2.36700.00355050.996452、负弯矩：YDC260Q-200型千斤顶编号：1636 对应压力表编号：09.09.15.1217YDC260Q-200型千斤顶编号：1637 对应压力表编号：09.09.15.1375根据设计图纸要求，计算时和正弯矩张拉伸长值的方法一样，划分为3段，分段计算后叠加乘二。T1束：ab段：Pp=P(1e-(kx+)/(kx+)=193.9103(10.99731)/ 0.0026895=193936NL=Pp*L/(Ap*Ep)= 1954031.793/(2.0105140)=0.012Mbc段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.97823)/ 0.0223245=189083NL=Pp*L/(Ap*Ep)= 1890831.587/(2.0105140)=0.011Mcd段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.98753)/ 0.0125505=192656NL=Pp*L/(Ap*Ep)= 1926568.367/(2.0105140)=0.057M故两端伸长值为：L =(abbccd)2=(0.0120.0110.057)2=0.16 MT2束：ab段：Pp=P(1e-(kx+)/(kx+)=193.9103(10.99731)/ 0.0026895=193936NL=Pp*L/(Ap*Ep)= 1954031.793/(2.0105140)=0.012Mbc段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.97823)/ 0.0223245=189083NL=Pp*L/(Ap*Ep)= 1890831.587/(2.0105140)=0.011Mcd段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.99198)/ 0.0080505=193165NL=Pp*L/(Ap*Ep)= 1931655.367/(2.0105140)=0.037M故两端伸长值为：L =(abbccd)2=(0.0120.0110.037)2=0.12 MT3束：ab段：Pp=P(1e-(kx+)/(kx+)=193.9103(10.99731)/ 0.0026895=193936NL=Pp*L/(Ap*Ep)= 1954031.793/(2.0105140)=0.012Mbc段: Pp=P(1e-(kx+)/(kx+)=193.9103(10.97823)/ 0.0223245=189083NL=Pp*L/(Ap*Ep)= 1890831.587/(2.0105140)