预制梁板张拉伸说长量计算

东阳至永康高速公路 公路建设项目钢 绞线 伸 长 量 计 算 书浙江省交通工程建设集团有限公司东永高速公路第1合同段项目经理部二0一一年十二月钢绞线伸长量计算说明一、计算原则 1、根据桥涵施工技术规范（JTJ041-2000）标准； 2、 根据桥梁、涵洞通用图设计图纸要求。二、计算公式与参数及说明1、已知参数：j15.24mm钢绞线：Ep=1.88105MPa；Ap=140mm；k=0.0015;=0.25,见检测附件；每根钢绞线的张拉控制力为195.3KN，根据锚板和千斤顶的机械参数以及张拉预留长度，则张拉端长度取L=50cm。2、计算公式：1）、Pp=P(1-e-(kx+)/（kx+）的P是预应力筋张拉端的张拉力，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）；x从张拉端至计算截面的孔道长度（m）；从张拉端至计算截面的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，k=0.0015；预应力筋与孔道壁的摩擦系数，=0.25。2）、P=conAgnb1000con预应力筋张拉端的控制应力(Nmm2)；Ag每根预应力筋的截面面积(mm2)；n同时张拉预应力筋根数；b超张拉系数，不超张拉时为1；P预应力筋张拉端的张拉力。3）、Ps=Pe-(kx+)这里Ps经过长度L后预应力筋的终点处张拉力（N）；P预应力筋的起点处张拉力（N）。4）、L= PpL/（Ap Ep） L理论伸长值(m)； L预应力筋相应的长度（m）； Ap钢绞线的截面积（mm2）;Ep 预应力筋的弹性模量（Mpa）。 5）、L=0L/ EpL初张拉伸长量（m）0张拉初应力（Mpa）；L从张拉端至计算孔道截面之间的距离（m）。3、张拉伸长量控制及读数计算方法： 4、各种规格梁板理论伸长量计算如下：A、30米T梁边跨钢绞线理论伸长量计算1、已知参数：钢绞线：Ep=1.88105MPa；Ap=140mm2；k=0.0015;=0.25N1钢绞线布置大样图N1（非连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.50002011.6 2011.6 5003.82 BC4.21500.00632250.9936974451998.9 2005.2 421532.11 CD9.7740.122173048 0.0452042620.9558022281910.6 1954.4 977472.58 DE0.76800.0011520.9988486631908.4 1909.5 7685.57 L伸长量（mm）114.08 N1（连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.50002011.6 2011.6 5003.82 BC4.21500.00632250.9936974451998.9 2005.2 421532.11 CD9.7740.122173048 0.0452042620.9558022281910.6 1954.4 977472.58 DE0.69800.0010470.9989535481908.6 1909.6 6985.06 L伸长量（mm）113.58 L1=L+L=114.08+113.58228mm N2钢绞线布置大样图N2（非连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.50001810.4 1810.4 5003.82 BC2.35700.00353550.9964707431804.0 1807.2 235717.98 CD5.2360.174532925 0.0514872310.9498157781713.5 1758.4 523638.87 DE7.17100.01075650.9893011441695.2 1704.3 717151.59 L伸长量（mm）112.27 N2（连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.50001810.4 1810.4 5003.82 BC2.35700.00353550.9964707431804.0 1807.2 235717.98 CD5.2360.174532925 0.0514872310.9498157781713.5 1758.4 523638.87 DE7.10100.01065150.9894050261695.4 1704.4 710151.09 L伸长量（mm）111.76 L2=L+L=112.27+111.76224mmN3钢绞线布置大样图N3（非连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.50001810.4 1810.4 5003.82 BC1.98100.00297150.9970329111805.1 1807.7 198115.12 CD3.6650.122173048 0.0360407620.9646009741741.2 1772.9 366527.43 DE9.0800.013620.9864723331717.6 1729.4 908066.29 L伸长量（mm）112.66 N3（连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.50001810.4 1810.4 5003.82 BC1.98100.00297150.9970329111805.1 1807.7 198115.12 CD3.6650.122173048 0.0360407620.9646009741741.2 1772.9 366527.43 DE9.0100.0135150.9865759181717.8 1729.4 901065.78 L伸长量（mm）112.15 L3=L+L=112.66+112.15225mmB、30米T梁中跨钢绞线理论伸长量计算1、已知参数：钢绞线：Ep=1.88105MPa；Ap=140mm2；k=0.0015;=0.25（N1、N2、N3）钢绞线布置大样图N1分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.50001810.4 1810.4 5003.82 BC4.21500.00632250.9936974451799.0 1804.7 421532.11 CD9.7740.122173048 0.0452042620.9558022281719.5 1759.0 977472.58 DE0.69800.0010470.9989535481717.7 1718.6 6985.06 L伸长量（mm）113.58 L1=2L=2*113.58227mmN2分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.50001609.3 1609.3 5003.82 BC2.35700.00353550.9964707431603.6 1606.4 235717.98 CD5.2360.174532925 0.0514872310.9498157781523.1 1563.0 523638.87 DE7.10100.01065150.9894050261507.0 1515.0 710151.09 L伸长量（mm）111.76 L2=2L=2*111.76224mmN3分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.50001609.3 1609.3 5003.82 BC1.98100.00297150.9970329111604.5 1606.9 198115.12 CD3.6650.122173048 0.0360407620.9646009741547.7 1575.9 366527.43 DE9.0100.0135150.9865759181526.9 1537.3 901065.78 L伸长量（mm）112.15 L3=2L=2*112.15224mmC、25米小箱梁边跨钢绞线理论伸长量计算1、已知参数：钢绞线：Ep=1.88105MPa；Ap=140mm2；k=0.0015;=0.25N1钢绞线布置大样图N1（非连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.5000804.6 804.6 5003.82 BC6.2900.0094350.99060937797.1 800.9 629047.85 CD3.3770.087266463 0.0268821160.973475992775.9 786.5 337725.23 DE2.62300.00393450.99607323772.9 774.4 262319.29 L伸长量（mm）96.19 N1（连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.5000804.6 804.6 5003.82 BC8.1600.012240.987834604794.8 799.7 816061.99 CD3.2210.087266463 0.0266481160.973703812773.9 784.4 322124.00 DE0.77900.00116850.998832182773.0 773.5 7795.72 L伸长量（mm）95.53 L1=L+L=96.19+95.53192mm N2钢绞线布置大样图N2（非连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.5000804.6 804.6 5003.82 BC4.28500.00642750.993593112799.5 802.1 428532.64 CD3.7770.087266463 0.0274821160.972892082777.8 788.6 377728.29 DE4.22300.00633450.993685521772.9 775.4 422331.10 L伸长量（mm）95.86 N2（连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.5000804.6 804.6 5003.82 BC6.17500.00926250.990780265797.2 800.9 617546.98 CD3.5980.087266463 0.0272136160.973153339775.8 786.5 359826.88 DE2.40200.0036030.996403483773.0 774.4 240217.67 L伸长量（mm）95.34 L2=L+L=95.86+95.34191mmN3钢绞线布置大样图N3（非连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.5000804.6 804.6 5003.82 BC3.27500.00491250.995099547800.7 802.7 327524.97 CD3.1770.087266463 0.0265821160.973768079779.7 790.1 317723.84 DE5.82300.00873450.991303535772.9 776.3 582342.94 L伸长量（mm）95.57 N3（连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.5000804.6 804.6 5003.82 BC4.19500.00629250.993727256799.6 802.1 419531.96 CD3.9760.087266463 0.0277806160.972601717777.7 788.6 397629.78 DE4.02400.0060360.99398218773.0 775.3 402429.63 L伸长量（mm）95.20 L3=L+L=95.57+95.2191mmN4钢绞线布置大样图N4（非连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.5000804.6 804.6 5003.82 BC0.000100.000000150.99999985804.6 804.6 0.10.00 CD1.7980.024434610 0.0088056520.991233004797.6 801.1 179813.68 DE10.45700.01568550.984436877785.2 791.4 1045778.60 L伸长量（mm）96.11 N4（连续端）分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.5000804.6 804.6 5003.82 BC0.000100.000000150.99999985804.6 804.6 0.10.00 CD1.7970.024434610 0.0088041520.991234491797.6 801.1 179713.67 DE10.24800.0153720.984745546785.4 791.5 1024877.04 L伸长量（mm）94.54 L4=L+L=96.11+94.54191mmD、25米小箱梁中跨钢绞线理论伸长量计算1、已知参数：钢绞线：Ep=1.88105MPa；Ap=140mm2；k=0.0015;=0.25（N1、N2、N3）钢绞线布置大样图N1分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.5000804.6 804.6 5003.82 BC8.1600.012240.987834604794.8 799.7 816061.99 CD3.2210.087266463 0.0266481160.973703812773.9 784.4 322124.00 DE0.77900.00116850.998832182773.0 773.5 7795.72 L伸长量（mm）95.53 L1=2L=2*95.53191mmN2分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.5000804.6 804.6 5003.82 BC6.17500.00926250.990780265797.2 800.9 617546.98 CD3.5980.087266463 0.0272136160.973153339775.8 786.5 359826.88 DE2.40200.0036030.996403483773.0 774.4 240217.67 L伸长量（mm）95.34 L2=2*L=2*95.34191mmN3分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.5000603.5 603.5 5003.82 BC4.19500.00629250.993727256599.7 601.6 419531.96 CD3.9760.087266463 0.0277806160.972601717583.3 591.4 397629.78 DE4.02400.0060360.99398218579.8 581.5 402429.63 L伸长量（mm）95.20 L3=2*L=2*95.2190mmN4分段Xm(rad)Kx+Qe-( Kx+Q)终点力Ps( kN)平均力Pp (kN)钢绞线长度(mm)伸长量L( mm)AB0.5000603.5 603.5 5003.82 BC0.000100.000000150.99999985603.5 603.5 0.10.00 CD1.7970.024434610 0.0088041520.991234491598.2 600.8 179713.67 DE10.24800.0153720.984745546589.1 593.6 1024877.04 L伸长量（mm）94.54 L4=2*L=2*94.54189mm四、千斤顶张拉应力与油泵压力值换算根据浙江省计量科学研究院/浙江省方正校准有限公司所出具的检准证书JX-2011121216号、JX-2011121214号、JX-2011121437号、JX-2011121220号检定, 液压千斤顶YCW250B-200 11112409#,压力表:10.06.15.2759#；液压千斤顶YCW250B-200 11112410#,压力表:10.03.25.0712#；液压千斤顶100T 1#,压力表:10020334#；液压千斤顶100T 2#,压力表:10015063#；检定结论为：合格 所需负荷值通过内插法求得，结果如下表：10孔锚张拉：名称千斤顶11112409#油表量10.06.15.2759#张拉力（KN）油表读数（Mpa）10%195.34.320%390.68.650%976.521.4103%2011.644.4名称千斤顶11112410#油表量10.03.25.0712#张拉力（KN）油表读数（Mpa）10%195.33.820%390.68.150%976.521.2103%2011.643.29孔锚张拉：名称千斤顶11112409#油表量10.06.15.2759#张拉力（KN）油表读数（Mpa）10%175.83.920%351.57.750%878.919.3103%1810.439.9名称千斤顶11112410#油表量10.03.25.0712#张拉力（KN）油表读数（Mpa）10%175.83.420%351.57.250%878.919.0103%1810.439.08孔锚张拉：名称千斤顶11112409#油表量10.06.15.2759#张拉力（KN）油表读数（Mpa）10%156.23.420%312.56.950%781.217.1103%1609.335.5名称千斤顶11112410#油表量10.03.25.0712#张拉力（KN）油表读数（Mpa）10%156.23.020%312.56.350%781.216.9103%1609.334.77孔锚张拉：名称千斤顶11112409#油表量10.06.15.2759#张拉力（KN）油表读数（Mpa）10%136.73.020%273.46.050%683.615.0103%1408.130.9名称千斤顶11112410#油表量10.03.25.0712#张拉力（KN）油表读数（Mpa）10%136.72.720%273.45.450%683.614.7103%1408.130.44孔锚张拉：名称千斤顶1#表号10020334#张拉力（KN）油表读数（Mpa）10%78.13.920%156.27.950%390.619.9103%804.641.0名称千斤顶2#表号10015063#张拉力（KN）油表读数（Mpa）10%78.14.120%156.28.250%390.620.4103%804.641.83孔锚张拉：名称千斤顶1#表号10020334#张拉力（KN）油表读数（Mpa）10%58.62.920%117.25.950%293.014.9103%603.530.9名称千斤顶2#表号10015063#张拉力（KN）油表读数（Mpa）10%58.63.020%117.26.150%293.015.4103%603.531.414