20米、40米箱梁预应力筋伸长量计算

箱梁预应力筋伸长量计算书一、工程简况我分部桥梁上部结构采用20m、40m箱梁，结构体系为先简支后连续。箱梁预应力束采用公称直径s15.2预应力钢绞线，其公称面积Ap=140mm2，抗拉标准强度fpk=1860Mpa，弹性模量Ep=2.01105Mpa，技术标准符合GB/T5224-2014，配M15-3、M15-4和M15-5系列锚具，预应力管道采用波纹管。二、计算说明钢绞线理论伸长值LL（mm）可按式（1-1）计算：LL=PPLAPEP （1-1）式中：PP预应力筋的平均张拉力（N）,直线筋取张拉端的拉力；两端张拉的曲线筋，计算方法见式（1-2）；L预应力筋的长度（mm）；AP预应力筋的截面面积（mm）；EP预应力筋的弹性模量（N/mm）。预应力筋平均张拉力应按式（1-2）计算：PP=P（1-e-（kx+）kx+ （1-2）式中：PP预应力筋的平均张拉力（N）；P预应力筋张拉端的张拉力（N）；从张拉端至计算截面的孔道长度（m）；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0.0015；预应力筋与孔道壁的摩擦系数0.25。注：当预应力筋为直线时PP=P。1.锚下控制力:k=0.751860Mpa=1395Mpa；2.张拉控制力:P=kAp=1395140=195.3kN；3.弹性模量:Ep=2.01105Mpa；4.公称面积:Ap=140mm2。三、计算过程3.1 20米箱梁边跨（半跨）伸长值计算：N1筋：AB=20.927/2-0.65-BC-CD=20.927/2-0.65-2.128-2.8798=4.8057；BC=R*/180*=30*5.5/180*=2.8798；CD=2.128；=5.5/180*=0.09599rad。名称L(m)（rad）kx+1-e-（kx+）P(KN)LL(cm)AB4.805700.007208550.007183976.53.3BC2.87980.095990.02831720.027920969.52.0CD2.12800.0031920.003187942.41.49.81356.7N2筋：AB=20.938/2-0.65-BC-CD=20.938/2-0.65-3.582-2.8798=3.3572；BC=R*/180*=30*5.5/180*=2.8798；CD=3.582；=5.5/180*=0.09599rad。名称L(m)（rad）kx+1-e-（kx+）P(KN)LL(cm)AB3.357200.00503580.005023781.22.3BC2.87980.095990.02831720.027920777.32.0CD3.58200.0053730.005359755.62.49.8196.7N3筋：AB=20.801/2-0.65-BC-CD=20.801/2-0.65-0.7330-8.001=1.0165；BC=R*/180*=30*1.4/180*=0.7330；CD=8.001；=1.4/180*=0.0244rad。名称L(m)（rad）kx+1-e-（kx+）P(KN)LL(cm)AB1.016500.00152480.0015236781.20.7BC0.73300.02440.00720950.0071836780.00.5CD8.00100.01200150.0119298774.45.59.75056.73.2 20米箱梁中跨（半跨）伸长值计算：N1筋：AB=20.902/2-0.65-BC-CD=20.902/2-0.65-2.8798-0.537=6.3842；BC=R*/180*=30*5.5/180*=2.8798；CD=0.537；=5.5/180*=0.09599rad。名称L(m)（rad）kx+1-e-（kx+）P(KN)LL(cm)AB6.384200.0095760.009530781.24.4BC2.87980.095990.0283170.027920773.762.0CD0.537000.00080550.0008052752.150.39.8016.7N2筋：AB=20.936/2-0.65-BC-CD=20.902/2-0.65-2.8798-2.015=4.9232；BC=R*/180*=30*5.5/180*=2.8798；CD=2.015；=5.5/180*=0.09599rad。名称L(m)（rad）kx+1-e-（kx+）P(KN)LL(cm)AB4.923200.00738480.0073576781.23.4BC2.87980.095990.0283170.027920775.452.0CD2.01500.00302250.0030179753.801.39.8186.7N3筋：AB=20.701/2-0.65-BC-CD=20.701/2-0.65-2.8798-7.901=1.0665；BC=R*/180*=30*1.4/180*=0.733；CD=7.901；=1.4/180*=0.0244rad。名称L(m)（rad）kx+1-e-（kx+）P(KN)LL(cm)AB1.066500.0016000.0015987585.90.74BC0.73300.02440.00719950.0071736584.960.51CD7.90100.011850.01178580.775.449.70056.693.3 40米箱梁边跨（半跨）伸长值计算：N1筋：AB=40.970/2-0.65-BC-CD=40.970/2-0.65-3.8397-2.578=13.4173；BC=R*/180*=55*4/180*=3.8397；CD=2.578；=4/180*=0.0698rad。名称L(m)（rad）kx+1-e-（kx+）P(KN)LL(cm)AB13.417300.0201260.019925976.59.3BC3.83970.06980.0232100.022943957.02.6CD2.57800.0038670.003860935.11.719.83513.6N2筋：AB=40.960/2-0.65-BC-CD=40.960/2-0.65-3.8397-4.580=11.4103；BC=R*/180*=55*4/180*=3.8397；CD=4.580；=4/180*=0.0698rad。名称L(m)（rad）kx+1-e-（kx+）P(KN)LL(cm)AB11.410300.0171150.016969976.57.9BC3.83970.06980.0232100.022943959.92.6CD4.58000.0068700.006846937.93.119.8313.6N3筋：AB=40.950/2-0.65-BC-CD=40.950/2-0.65-3.8397-6.582=9.4033；BC=R*/180*=55*4/180*=3.8397；CD=6.582；=4/180*=0.0698rad。名称L(m)（rad）kx+1-e-（kx+）P(KN)LL(cm)AB9.403300.0141050.0140061171.86.5BC3.83970.06980.0232100.0229431155.42.6CD6.58200.0098730.0098241128.94.419.82513.5N4筋：AB=40.940/2-0.65-BC-CD=40.940/2-0.65-3.8397-8.584=7.3963；BC=R*/180*=55*4/180*=3.8397；CD=8.584；=4/180*=0.0698rad。名称L(m)（rad）kx+1-e-（kx+）P(KN)LL(cm)AB7.396300.0110940.0110331171.85.1BC3.83970.06980.0232100.0229431158.92.6CD8.58400.0128760.0127931132.35.819.8213.5N5筋：AB=40.930/2-0.65-BC-CD=40.930/2-0.65-3.8397-10.586=7.3963；BC=R*/180*=55*4/180*=3.8397；CD=10.586；=4/180*=0.0698rad。名称L(m)（rad）kx+1-e-（kx+）P(KN)LL(cm)AB5.389300.0080840.0080511171.83.7BC3.83970.06980.0232100.0229431162.42.6CD10.58600.0158790.0157541135.77.119.81513.4N6筋：AB=40.897/2-0.65-BC-CD=40.897/2-0.65-0.5236-15.528=3.7469；BC=R*/180*=30*1/180*=0.5236；CD=15.528；=1/180*=0.01745rad。名称L(m)（rad）kx+1-e-（kx+）P(KN)LL(cm)AB3.746900.0056200.0056041171.82.6BC0.52360.017450.0051480.0051351165.20.4CD15.52800.0232920.0230231159.210.719.798513.7四、箱梁理论伸长量汇总20米箱梁边跨理论伸长值计算汇总表位置边跨N1筋N2筋N3筋受力钢绞线长度19.627 m19.638 m19.501 m伸长值13.4 cm13.4 cm13.4 cm20