7.29 预应力伸长量计算

一、 计算依据

根据《公路工程桥梁设计手册》、《公路桥涵施工技术规范》及《深圳市松白路光明新区段改造工程光侨立交高架桥》(图号2007Y023-SS00QL0102QL)施工设计图。二、 理论伸长值

ΔL=PP•L/AP•EP

PP—预应力钢材平均张拉力（N）；式中：

L—预应力钢材长度（mm）；AP—预应力钢材截面积（mm2）;EP—预应力钢材弹性模量（N/ mm2）；PP=P[1-e-（kx+μθ）]/kx+μθ

P—预应力钢材张拉端张拉力（N）;式中：

x—从张拉端至计算截面的孔道长度（m）;

θ—从张拉端至计算截面曲线孔道部分切线的夹角之和（rad）;k—孔道每米局部偏差对摩擦的影响系数,此处取k=0.0015;μ—预应力筋与孔道壁的磨擦系数, 此处取μ=0.25；三、 光侨立交高架桥预制梁预应力筋伸长量计算

由《桥规》附表G-8可知: K值取 K=0.0015; μ值取μ=0.25；钢绞线设计参数: AP=139mm2；EP=1.95×105MPa；

设计预应力钢束标准抗拉强度fpk=1860MPa,设计锚下控制应力δcon=0.73fpk=1357.8MPa， 预应力张拉按照3个行程控制：

初应力：δ0=δcon×10﹪=135.78MPa第二行程：δcon×20﹪=271.56MPa控制应力：δcon=1357.8MPa

（1）、中跨预制梁N1钢束初应力时伸长值δcon×10﹪=18.873(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN18.87318.873418.8056对应张拉力对应张拉力对应张拉力

18.873(KN)37.747(KN)188.734(KN)

μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN18.873418.805618.8056KN18.873418.839518.8056N/mm2195000195000195000mm2139139139mmrad10660007330.024440.00150.251290100029400张拉力20﹪时伸长值δcon×20﹪=37.774(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN37.74737.746837.6111μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN37.746837.611137.6111KN37.746837.679037.6111N/mm2195000195000195000mm2139139139mmrad10660007330.024440.00150.251290100029400第1页

光侨立交高架桥箱梁预应力张拉理论伸长量计算表

张拉力100﹪时伸长值δcon×100﹪=188.734(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN188.734188.7342188.0556钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN188.7342188.0556188.0556KN188.7342188.3949188.0556N/mm2195000195000195000mm2139139139μmmrad10660007330.024440.00150.251290100029400（2）、中跨预制梁N2钢束初应力时伸长值δcon×10﹪=18.873(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN18.87318.873418.5046μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN18.873418.504618.5046KN18.873418.6018.5046N/mm2195000195000195000mm2139139139mmrad130700045810.13090.00150.25883600029448张拉力20﹪时伸长值δcon×20﹪=37.774(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN37.74737.746837.0093μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN37.746837.009337.0093KN37.746837.378137.0093N/mm2195000195000195000mm2139139139mmrad130700045810.13090.00150.25883600029448张拉力100﹪时伸长值δcon×100﹪=188.734(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN188.734188.7342185.04μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN188.7342185.04185.04KN188.7342186.03185.04N/mm2195000195000195000mm2139139139mmrad130700045810.13090.00150.25883600029448（3）、中跨预制梁N3钢束初应力时伸长值δcon×10﹪=18.873(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN18.87318.873418.5316μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN18.873418.531618.5316KN18.873418.702518.5316N/mm2195000195000195000mm2139139139mmrad3215000520.112830.00150.255875000294第2页

光侨立交高架桥箱梁预应力张拉理论伸长量计算表

张拉力20﹪时伸长值δcon×20﹪=37.774(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN37.74737.746837.0631钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN37.746837.063137.0631KN37.746837.405037.0631N/mm2195000195000195000mm2139139139μmmrad3215000520.112830.00150.255875000294张拉力100﹪时伸长值δcon×100﹪=188.734(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN188.734188.7342185.3156μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN188.7342185.3156185.3156KN188.7342187.0249185.3156N/mm2195000195000195000mm2139139139mmrad3215000520.112830.00150.255875000294（4）、中跨预制梁N4钢束初应力时伸长值δcon×10﹪=18.873(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN18.87318.873418.00μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN18.873418.0018.00KN18.873418.706718.00N/mm2195000195000195000mm2139139139mmrad532000063100.105170.00150.25311100029482张拉力20﹪时伸长值δcon×20﹪=37.774(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN37.74737.746837.0799μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN37.746837.079937.0799KN37.746837.413437.0799N/mm2195000195000195000mm2139139139mmrad532000063100.105170.00150.25311100029482张拉力100﹪时伸长值δcon×100﹪=188.734(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN188.734188.7342185.3997μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN188.7342185.3997185.3997KN188.7342187.0669185.3997N/mm2195000195000195000mm2139139139mmrad532000063100.105170.00150.25311100029482第3页

光侨立交高架桥箱梁预应力张拉理论伸长量计算表

（5）、边跨预制梁N1钢束初应力时伸长值δcon×10﹪=18.873(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L3L4L5ΣLKN18.87318.873418.810018.873418.873mmradμ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN18.873418.810018.805618.805618.8734KN18.873418.841718.807818.839518.8734N/mm2195000195000195000195000195000mm2139139139139139110006850.022840.00150.25258300007330.024440.00150.25106500029502张拉力20﹪时伸长值δcon×20﹪=37.774(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L3L4L5ΣLKN37.74737.746837.615537.746837.747μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN37.746837.620037.611137.611137.7468KN37.746837.683437.613337.679037.7468N/mm2195000195000195000195000195000mm2139139139139139mmrad110006850.022840.00150.25258300007330.024440.00150.25106500029502张拉力100﹪时伸长值δcon×100﹪=188.734(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L3L4L5ΣLKN188.734188.7342188.0777188.7342188.734μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN188.7342188.0998188.0556188.0556188.7342KN188.7342188.4170188.0666188.3949188.7342N/mm2195000195000195000195000195000mm2139139139139139mmrad110006850.022840.00150.25258300007330.024440.00150.25106500029502（6）、边跨预制梁N2钢束初应力时伸长值δcon×10﹪=18.873(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L3L4L5ΣLKN18.87318.873418.509518.873418.873μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN18.873418.514418.504618.504618.8734KN18.873418.693918.507118.6018.8734N/mm2195000195000195000195000195000mm2139139139139139mmrad146800044580.127370.00150.251773000045820.13090.00150.251307000295第4页

光侨立交高架桥箱梁预应力张拉理论伸长量计算表

张拉力20﹪时伸长值δcon×20﹪=37.774(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L3L4L5ΣLKN37.74737.746837.019137.746837.747钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN37.746837.0237.009337.009337.7468KN37.746837.387937.014237.378037.7468N/mm2195000195000195000195000195000mm2139139139139139μmmrad146800044580.127370.00150.251773000045820.13090.00150.251307000295张拉力100﹪时伸长值δcon×100﹪=188.734(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L3L4L5ΣLKN188.734188.7342185.09188.7342188.734μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN188.7342185.1445185.0463185.0463188.7342KN188.7342186.9393185.0708186.02188.7342N/mm2195000195000195000195000195000mm2139139139139139mmrad146800044580.127370.00150.251773000045820.13090.00150.251307000295（7）、边跨预制梁N3钢束初应力时伸长值δcon×10﹪=18.873(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L3L4L5ΣLKN18.87318.873418.534318.873418.873μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN18.873418.537018.531618.531618.8734KN18.873418.705218.532918.702518.8734N/mm2195000195000195000195000195000mm2139139139139139mmrad336100055500.1110.00150.2511800000520.112830.00150.25321500029568张拉力20﹪时伸长值δcon×20﹪=37.774(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L3L4L5ΣLKN37.74737.746837.068637.746837.747μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN37.746837.074137.063137.063137.7468KN37.746837.410537.065937.405037.7468N/mm2195000195000195000195000195000mm2139139139139139mmrad336100055500.1110.00150.2511800000520.112830.00150.25321500029568第5页

光侨立交高架桥箱梁预应力张拉理论伸长量计算表

张拉力100﹪时伸长值δcon×100﹪=188.734(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L3L4L5ΣLKN188.734188.7342185.3430188.7342188.734钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN188.7342185.3705185.3156185.3156188.7342KN188.7342187.0523185.3293187.0249188.7342N/mm2195000195000195000195000195000mm2139139139139139μmmrad336100055500.1110.00150.2511800000520.112830.00150.25321500029568（8）、边跨预制梁N4钢束初应力时伸长值δcon×10﹪=18.873(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L3L4L5ΣLKN18.87318.873418.1918.873418.873μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN18.873418.3818.0018.0018.8734KN18.873418.708618.0918.706718.8734N/mm2195000195000195000195000195000mm2139139139139139mmrad5600062370.103950.00150.25626000063100.105170.00150.25532000029583张拉力20﹪时伸长值δcon×20﹪=37.774(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L3L4L5ΣLKN37.74737.746837.083837.746837.747μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN37.746837.087637.079937.079937.7468KN37.746837.417237.081837.413437.7468N/mm2195000195000195000195000195000mm2139139139139139mmrad5600062370.103950.00150.25626000063100.105170.00150.25532000029583张拉力100﹪时伸长值δcon×100﹪=188.734(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L3L4L5ΣLKN188.734188.7342185.4188188.7342188.734μ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN188.7342185.4379185.3997185.3997188.7342KN188.7342187.0861185.4092187.0669188.7342N/mm2195000195000195000195000195000mm2139139139139139mmrad5600062370.103950.00150.25626000063100.105170.00150.25532000029583第6页

光侨立交高架桥箱梁预应力张拉理论伸长量计算表

（9）、负弯矩张拉T1钢束初应力时伸长值δcon×10﹪=18.873(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN18.87318.873418.7446mmradμ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN18.873418.744618.7446KN18.873418.809018.7446N/mm2195000195000195000mm21391391394590004190.052360.00150.25912200020000张拉力20﹪时伸长值δcon×20﹪=37.774(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN37.74737.746837.41mmradμ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN37.746837.4137.41KN37.746837.618037.41N/mm2195000195000195000mm21391391394590004190.052360.00150.25912200020000张拉力100﹪时伸长值δcon×100﹪=188.734(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN188.734188.7342187.4455mmradμ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN188.7342187.4455187.4455KN188.7342188.09187.4455N/mm2195000195000195000mm21391391394590004190.052360.00150.25912200020000（10）、负弯矩张拉T2钢束初应力时伸长值δcon×10﹪=18.873(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN18.87318.873418.7446mmradμ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN18.873418.744618.7446KN18.873418.809018.7446N/mm2195000195000195000mm21391391394590004190.052360.00150.2536220009000张拉力20﹪时伸长值δcon×20﹪=37.774(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN37.74737.746837.41mmradμ钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN37.746837.4137.41KN37.746837.618037.41N/mm2195000195000195000mm21391391394590004190.052360.00150.2536220009000第7页

光侨立交高架桥箱梁预应力张拉理论伸长量计算表

张拉力100﹪时伸长值δcon×100﹪=188.734(KN)张拉端张拉力每段孔道长P1参数Xθk单位L1L2L32ΣLKN188.734188.7342187.4455mmrad钢束末端张拉力平均张拉力弹性模量截面积P2PPEPAPKN188.7342187.4455187.4455KN188.7342188.09187.4455N/mm2195000195000195000mm2139139139μ4590004190.052360.00150.2536220009000注：

1、实际伸长值与理论伸长值之差应小于6﹪，否则应停止张拉，待查明原因并采取措施加以调整后，行张拉。

2、箱梁钢束平曲线部分因为曲线长度、弯起角很小，对钢束应力影响不大，故本计算中未计入孔道摩对应力的影响。

3、实际量测伸长值=(20%控制应力时量测的伸长值-10%控制应力时量测的伸长值)+20%～100%控制应力段量测的伸长值。

4、本计算根据1跟钢绞线进行受力与伸长值关系计算，实际张拉时，理论上一束钢绞线所受应力=表中根钢绞线理论应力×该束中钢绞线根数。

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