40.0m连续箱梁张拉(后张法)应力控制计算

****桥40.0m连续箱梁张拉（后张法）应力控制计算1、基本情况及要求：1.1、40.0m连续箱梁设计砼标号C50，设计要求砼强度应达到设计强度的80%后方可进行钢绞线束张拉；横向预应力钢绞线要求砼强度应达到设计强度的100%后方可进行钢绞线束张拉。1.2、预应力采用江阴ASTMA416-92标准中低松弛270的钢绞线，公称直径Φj15.24mm标准抗拉强度Ryb=1860MPa，Ey=1.95×105MPa，设计张拉控制应力0.75Ryb，见钢绞线试验数据。1.3、锚具采用YM15-16（腹板、底板钢束）、YMH15-7（墩顶箱梁顶板负弯矩钢束）及YMH15-4（横向预应力钢绞线）系列锚下铸件锚座锚具。规范要求钢绞线张拉后尽早进行压浆；压浆应密实，并应符合相关规范关于预应力孔道压浆的技术要求。1.4、应力控制计算中k值和μ值暂按规范k=0.0015，μ=0.25计入，如有k和μ的试验数据，应以试验数据为准。1.5、箱梁采用支架现浇施工，腹板、底板、顶板负弯矩钢束采用一端固定，横向预应力钢束采用单根两端张拉。张拉遵循先上后下，先外后内的原则，采用分批，分阶段对称张拉。1.6、连续箱梁张拉端横断面图：2、设计张拉控制应力及基本数据：2.1δcon=0.75Ryb=0.75×1860=1395MPa（N/mm2）2.2Ey=1.95×105MPa（N/mm2）2.3Ag16=140×16=2240.02.4Ag7=140×7=980.0mm2；Ag1=140×1=140.02.5千斤顶选用YCW400B型（①千斤顶编号20321#相应油压表编号636#，回归方程Y=0.15+0.01238X；②千斤顶编号20322#，相应油压表编号545#，回归方程Y=0.091+0.01245X）。2.6千斤顶选用YCW150B型（①千斤顶编号20500#相应油压表编号1324#，回归方程Y=0.746+0.03351X；②千斤顶编号20499#，相应油压表编号600#，回归方程Y=0.486+0.03369X）。2.7千斤顶选用YCJ26型（①千斤顶编号20553#相应油压表编号586#，回归方程Y=1.46+0.1988X；②千斤顶编号20552#，相应油压表编号613#，回归方程Y=1.58+0.2081X）。3、张拉程序及张拉控制应力达到后的油表读数根据JTJ041-2000《公路桥涵施工技术规范》P134表12.10.3-1规定：钢绞线束使用夹片式等具有自锚性能的锚具：低松弛力筋采用：0初应力〈约15%δcon〉δcon〈持荷2min锚固〉3.1P16=1395×2240=3124800N=3124.8KNP16初=3124800×15%=468720N3.2P7=1395×980=1367100N=1367.0KNP7初=1367100×15%=205065N3.3P1=1395×140=195300N=195.3KNP1初=195300×15%=29295N3.4油表读数：（用YCW400B型张拉16根/束；用YCW150B型张拉7根/束；用YCJ26型张拉4根/束（横向预应力束单根张拉））3.4①千斤顶编号20321#相应油压表编号636#，计算油压表读数：B16初=0.15+0.01238×468720=5.95MPa，划线作标记；B16=0.15+0.01238×3124.8=38.84MPa；②千斤顶编号20322#相应油压表编号545#，计算油压表读数：B16初=0.091+0.01245×468.72=5.93MPa，划线作标记；B16=0.091+0.01245×3124.8=38.99MPa；3.4①千斤顶编号20500#相应油压表编号1324#，计算油压表读数：B7初=0.746+0.03351×205.07=7.62B7=0.746+0.03351×1367.10=46.56②千斤顶编号20499#，相应油压表编号600#，计算油压表读数：B7初=0.486+0.03369×205.07=7.39B7=0.486+0.03369×1367.10=46.543.4①千斤顶编号20553#相应油压表编号586#，计算油压表读数：B4·1初=1.46+0.1988×29.295=7.3MPa，划线作标记；B4·1=1.46+0.1988×195.3=40.3MPa；②千斤顶编号20552#相应油压表编号613#，计算油压表读数：B4·1初=1.58+0.2081×29.295=7.7MPa，划线作标记；B4·1=1.58+0.2081×195.3=42.2MPa；4、计算步骤：4.1、根据规范曲线预应力筋采用分段计算后叠加的方法计算较为精确。4.2、根据图中给出的钢束长度是在标准跨径下的长度，本桥位于圆曲线段内，圆曲线半径R=420.0米。受曲线影响，左、右幅长度不等，施工时要根据各跨的实际长度调整各跨跨中水平段预应力筋〈钢铰线束〉4.3、本计算是依据设计图中给定的钢铰线束坐标进行计算的。4.4、计算了一联的第一跨，中间跨及最末两跨的预应力筋。计算及施工方向一致，均是从大桩号往小桩号进行。５、一联第七跨W1束达到设计初始张拉力及张拉力后钢束伸长值计算：5.1、一联第七跨W1束各段终点应力计算5.1.1、计算简图：5.1.2一联第七跨Ｗ1束各段终点应力计算表：线段LT（m）X（m）θκχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`3.0523.02000.00450.99551131.61`-2`1.5191.5000.07170.01660.98351136.72`-3`1.5191.5000.07170.01660.98351155.83`-3``4.6194.57100.00690.99321175.23``-4`3.9933.9790.14390.03470.96581183.24`-4``5.7195.71900.00860.99151225.1跨中直线段4``-5`3.9953.9850.12190.03040.97011235.65`-5``12.36812.27600.01840.98181273.75``-6`2.9962.9890.12190.02890.97151297.36`-6``0.5000.50000.00080.99931335.46``-7`1.7511.750.01760.00610.99391336.37`-8`1.5041.5000.07170.01660.98351344.58`-9`1.5041.5000.07170.01660.98351367.09`-102.4002.40000.00360.99641390.0合计47.43947.1890.6921注：表中LT为预应力筋长度，x为预应力筋水平投影长度5.1.3、根据设计图给定的曲线要素，列表计算Ｗ1后，计算达到设计张拉力后钢束伸长值：（δi1+δi2）Li2Ey119177.42×1.95×105ΔLw1=Σ（δi1+δi2）Li2Ey119177.42×1.95×1055.1.4W11达到设计初始张拉力后的伸长值：306306×4687203124800ΔLW1初=∑=46(mm)（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）5.2、一联第七跨W2束各段终点应力计算5.2.1计算简图：5.2.2一联第七跨W2线段编号LT（m）X（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`3.0443.02000.00450.99551114.11`-2`1.5151.5000.07170.01660.98351119.12`-3`1.5151.5000.07170.01660.98351137.93`-3``3.3423.31600.00500.99501157.03``-4`3.9953.9840.12500.03100.96951162.84`-4``7.4697.46900.01120.98891199.4跨中直线段4``-5`3.9953.9840.12590.03120.96931212.85`-5``11.87211.77800.01770.98251251.25``-6`2.9962.9880.12590.02970.97081273.56`-6``1.3901.39000.00210.99791311.86``-7`2.3152.3100.10630.02470.97561314.67`-8`1.5121.5000.07170.01660.98351347.58`-9`1.5121.5000.07170.01660.98351370.19`-100.9550.95000.00140.99861393.0合计47.42747.1890.7699注：表中LT为预应力筋长度，x为预应力筋水平投影长度5.2.3根据设计图给定的曲线坐标要素，列表计算W2后，计算达到设计（δ（δi1+δi2）LTi2Ey117225.82×1.95×105ΔLw2=∑==0.301(m)=301(mm)5.2.4W16达到初始张拉力后钢束后的伸长值：301301×4687203124800ΔLw2初==45（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）5.3、一联第七跨W3束各段终点应力计算5.3.1计算简图：5.3.2一联第七跨W3束各段终点应力表：线段编号LT（m）X（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`2.0322.02000.00300.99701122.81`-2`1.5121.5000.07170.01660.98351126.22`-3`1.5121.5000.07170.01660.98351145.13`-3``4.0193.99600.00600.99401164.33``-4`3.9963.9890.10700.02740.97301171.44`-4``8.2898.28900.01240.98761203.9跨中直线段4``-5`3.9943.9830.13010.03200.96851219.05`-5``11.37611.28000.01690.98321258.65``-6`2.2492.2370.13010.02940.97111280.16`-7`0.7620.7600.07170.01550.98461318.27`-8`2.9982.9840.09240.02300.97731338.88`-8``0.0040.0040011369.98``-9`2.9992.9950.05570.01560.98451369.99`-101.6551.65200.00250.99751391.5合计47.39447.1890.6587注：表中LT为预应力筋长度，x为预应力筋水平投影长度5.3.3根据设计图给定的曲线坐标要素，列表计算W3后，计算达到设计张拉力后的钢束伸长值：118127.02118127.02×1.95×105（δi1+δi2）LTi2EyΔLw3=∑===0.303(m)=303(mm)5.3.4W3达到初始张拉力后的钢束伸长值：303303×4687203124800ΔLw3初==45（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）5.4、一联第七跨W4束各段终点应力计算5.45.4.2一联第七跨W4束各段线段编号LT（m）X（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`2.5272.52000.00380.99621138.21`-2`1.5081.5000.07170.01660.98351142.52`-3`1.5081.5000.07170.01660.98351161.73`-3``2.7942.78600.00420.99581181.23``-4`3.9983.9940.07580.02120.97911186.24`-4``10.48910.48900.01570.98441211.5跨中直线段4``-5`3.9953.9850.12090.03020.97031230.75`-5``10.34810.27200.01540.98471268.45``-6`1.9981.9930.12090.02720.97321288.16`-7`1.0511.0500.07170.01590.98421323.57`-8`2.2502.2480.12970.02930.97111344.88`-94.8934.85200.00730.99271384.8合计47.35947.1890.6624注：表中LT为预应力筋长度，x为预应力筋水平投影长度5.4.3根据设计图给定的曲线坐标要素，列表计算W4后，计算达到设计118792.02×1.95×105（δi1+δi2）LTi2E118792.02×1.95×105（δi1+δi2）LTi2Ey5.3.4W4达到初始张拉力后的钢束伸长值：305305×4687203124800ΔLw4初==46（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）5.5、一联第七跨W5束各段终点应力计算5.55.5.2一联第七跨W5束各段线段编号LT（m）X（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`2.0232.02000.00300.99701162.71`-2`1.5051.5000.07170.01660.98351166.22`-3`1.5051.5000.07170.01660.98351185.83`-3``2.7872.78300.00420.99581205.73``-4`3.9993.9970.05530.01710.98311210.74`-4``10.48910.48900.01570.98441231.6跨中直线段4``-5`3.9973.9920.08920.02380.97651251.15`-5``1030510.26400.01540.98471281.25``-6`2.2512.2440.08920.02120.97901301.16`-7`0.7520.7500.07170.01550.98471329.07`-8`2.5972.5920.10790.02550.97491349.68`-95.0885.05800.00760.99241384.4合计47.29847.1890.5567注：表中LT为预应力筋长度，x为预应力筋水平投影长度5.5.3根据设计图给定的曲线坐标要素，列表计算W5后，计算达到设计120300.32×1.95×105（δi1+δi2）LTi2E120300.32×1.95×105（δi1+δi2）LTi2Ey5.5.4W5达到初始张拉力后的308308×4687203124800ΔLw5初==46（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）5.6、一联第七跨W6束各段终点应力计算5.65.6.2一联第七跨W6束各段线段编号LT（m）X（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`3.4723.47100.00520.99481197.61`-2`4.0003.9990.02600.01120.98891203.92`-2``1.0511.05100.00160.99841217.42``-3`1.5041.5000.07170.01660.98351219.33`-4`1.5041.5000.07170.01660.98351239.84`-4``23.76923.76900.03570.96501260.6跨中直线段4``-5`1.5041.5000.07170.01660.98351306.35`-6`1.5041.5000.07170.01660.98351328.26`-6``1.2501.25000.00190.99811350.56``-7`2.9992.9980.04730.01400.98611353.17`-7``0.0030.0030011327.27``-8`2.9992.9980.04730.01400.98611327.28`-91.6501.65000.00250.99751391.5合计47.20947.1890.4074注：表中LT为预应力筋长度，x为预应力筋水平投影长度5.6.3根据设计图给定的曲线坐标要素，列表计算W6后，计算达到设计121493.92×1.95×105（δi1+δi2）LTi2E121493.92×1.95×105（δi1+δi2）LTi2Ey5.6.4W6达到初始张拉力后的钢束312312×4687203124800ΔLw6初==47（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）5.7、一联第七跨W20束各段终点应力计算5.7.1计算简图：5.7.2一联第七跨W20束各段终点应力表：线段编号LT（m）X（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`1.2611.25400.00190.99811240.01`-2`1.4991.4960.10460.02320.97711242.42`-2``35.06935.06900.05260.94881271.5跨中直线段2``-3`1.9951.9840.17810.03860.96211340.13`-41.0321.01600.00150.99851392.9合计40.85640.8190.2827注：表中LT为预应力筋长度，x为预应力筋水平投影长度5.7.3根据设计图给定的曲线坐标要素，列表计算W20后，计算达到设计张拉力后的钢束伸长值：106814.32×1.95×105（δi1+δi2）LTi2Ey106814.32×1.95×105（δi1+δi2）LTi2Ey5.7.4W20达到初始张拉力后的274274×2050501367000ΔLw20初==41（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）6、第六跨—第三跨，各束达到设计初始张拉力及张拉力后各钢束伸长值计算：6.1第六跨—第三跨W7束各段终点应力计算：6.1.1计算简图： 6.1.2第二跨W7束终点应力表：线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`1.5001.50000.00230.99781056.51`-2`2.9902.9460.26920.05830.94341058.92`-3`0.8380.8040.07170.01550.98461122.43`-3``1.9101.83200.00270.99731140.03``-4`3.9723.9180.28680.06320.93871143.04`-4``6.0796.07900.00910.99091217.7跨中直线段4``-5`3.9933.9780.14740.03540.96521228.95`-5``9.6439.53800.01430.98581273.25``-6`2.9952.9840.14740.03400.96661291.56`-6``1.4401.44000.00220.99781336.16``-7`1.7521.7500.02370.00740.99271337.97`-8`1.5041.5000.07170.01660.98351347.78`-9`1.5041.5000.07170.01660.98351370.39`-100.8100.81000.00120.99881393.3合计40.93040.5791.0896注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。6.1.3根据设计图给定的曲线坐标要素，列表计算W7后，计算达到设计张拉力后的钢束伸长值：（δ（δi1+δi2）LTi2Ey101851.72×1.95×105ΔLw7=∑==0.261(m)=261(mm)261×46872031248006.1.4W24达到设计初始张拉力后261×4687203124800ΔLw7初==39（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）6.2第六跨—第三跨W8束各段终点应力计算：6.2 6.2.2第二跨W8束线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`1.5161.50800.00230.99771084.41`-2`3.0052.9560.11060.02660.97381086.92`-3`0.8030.7850.07170.01550.98461116.23`-3``0.8160.79700.00120.99881133.73``-4`3.9843.9530.21690.04930.95191135.04`-4``8.0798.07900.01210.98801192.4跨中直线段4``-5`3.9913.9750.15950.03790.96281206.85`-5``8.6548.54400.01280.98721253.55``-6`2.9942.9810.15950.03640.96431269.76``-7`2.9982.9940.09210.02290.97731316.77`-7``0.1970.19600.00030.99971347.37``-8`1.5041.5000.07170.01660.98351347.78`-9`1.5041.5000.07170.01660.98351370.39`-100.8130.81000.00120.99881393.3合计40.85840.5780.9537注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。6.2.3根据设计图给定的曲线坐标要素，列表计算W8后，计算达到设计（δ（δi1+δi2）LTi2Ey100652.72×1.95×105ΔLw8=∑==0.258(m)=258(mm)258×46872031248006.2.4W24达到设计258×4687203124800ΔLw8初==39（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）6.3第六跨—第三跨W9束各段终点应力计算：6.3 6.3.2第二跨W9束线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`2.7802.75000.00410.99591108.31`-2`1.5211.5000.07170.01660.98351112.92`-3`1.5211.5000.07170.01660.98351131.53`-3``0.1960.19400.00030.99971150.53``-4`3.9933.9780.14810.03560.96501150.94`-4``9.1579.15700.01370.98641192.6跨中直线段4``-5`3.9903.9700.17370.04070.96011209.15`-5``6.8846.78000.01020.98991259.35``-6`0.7900.7730.07170.01550.98461272.26`-7`3.0002.9770.17370.03920.96161292.07`-8`2.9952.9860.13520.03150.96901343.68`-94.0514.01400.00600.99401386.6合计40.87840.5790.8458注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。6.3.3根据设计图给定的曲线坐标要素，列表计算W9后，计算达到设计（δ（δi1+δi2）LTi2Ey101514.12×1.95×105ΔLw9=∑==0.260(m)=260(mm)260×46872031248006.3.4W9达到设计260×4687203124800ΔLw9初==39（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）6.4第六跨—第三跨W10束各段终点应力计算：6.4 6.4.2第二跨W10束线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`5.0475.00500.00750.99251153.01`-2`1.9971.9920.12970.02890.97151161.72`-3`1.2531.2500.07170.01620.98391195.83`-3``11.83211.83200.01770.98241215.3跨中直线段3``-4`3.9943.9820.13520.03300.96751237.14`-4``5.8215.76800.00870.99141278.74``-5`0.7650.7640.07170.01550.98461289.75`-6`2.9952.9860.13520.03150.96901309.96`-7`2.9972.9920.10470.02540.97491351.87`-84.0304.00800.00600.99401386.6合计40.73140.5790.6482注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。6.4.3根据设计图给定的曲线坐标要素，列表计算W10后，计算达到设计（δ（δi1+δi2）LTi2Ey102804.22×1.95×105ΔLw10=∑==0.264(m)=264(mm)264×46872031248006.4.4W10达到设计264×4687203124800ΔLw10初==40（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）6.5第六跨—第三跨W11束各段终点应力计算：6.5 6.5.2第二跨W11束线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`4.0314.00800.00600.99401180.21`-2`1.7551.7440.10790.02420.97611187.42`-3`1.5041.5000.07170.01660.98351216.43`-3``13.82713.82700.02070.97951236.9跨中直线段3``-4`3.9963.9890.10400.02680.97361262.74`-4``4.7914.76500.00710.99291297.04``-5`0.7540.7540.07170.01550.98461306.35`-6`3.0052.9920.10400.02530.97501326.76`-7`2.9992.9960.07210.01890.98131360.77`-84.0144.00400.00600.99401386.6合计40.67640.5790.5314注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。6.5.3根据设计图给定的曲线坐标要素，列表计算W11后，计算达到设计（δ（δi1+δi2）LTi2Ey104180.62×1.95×105ΔLw11=∑==0.267(m)=267(mm)267×46872031248006.5.4W11达到设计267×4687203124800ΔLw11初==40（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）6.6第六跨—第三跨W12束各段终点应力计算：6.6 6.6.2第二跨W12束线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`2.2502.25000.00340.99661217.21`-2`1.5101.5000.09440.02110.97911221.32`-3`1.5101.5000.09440.02110.97911247.43`-3``27.57927.57900.04140.95951274.0跨中直线段3``-4`1.5101.5000.09440.02110.97911327.84`-5`1.5101.5000.09440.02110.97911356.15`-64.7504.75000.00710.99291385.1合计40.61940.5790.3776注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。6.6.3根据设计图给定的曲线坐标要素，列表计算W12后，计算达到设计（δ（δi1+δi2）LTi2Ey106174.12×1.95×105ΔLw12=∑==0.272(m)=272(mm)272×46872031248006.6.4W12达到设计272×4687203124800ΔLw12初==41（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）6.7第六跨—第三跨W21束各段终点应力计算：6.7 6.7.2第二跨W21束线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-1`1.5591.55300.00230.99771240.71`-2`1.4991.4970.09110.02050.97971243.62`-2``36.12936.12900.05420.94721269.4跨中直线段2``-3`1.9951.9840.17810.03860.96211340.13`-41.0321.01600.00150.99851392.9合计42.21442.1790.2692注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。6.7.3根据设计图给定的曲线坐标要素，列表计算W21后，计算达到设计110248.12×1.95×105（δi1+δi2）LTi2Ey110248.12×1.95×105（δi1+δi2）LTi2Ey283×20505013670006.7.4W21达到设计283×2050501367000ΔLw21初==42（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）7、第二跨各束达到设计初始张拉力及张拉力后各钢束伸长值计算：7.1第二跨W13束各段终点应力计算：7.1.1计算简图：7.1.2W13束各段终点应力表：线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-22.2352.21700.00330.99671103.12-31.5171.5460.15170.03270.96791106.83-42.6012.52400.00380.99621143.54-52.4392.4660.24390.05250.94891147.85-63.1223.12200.00470.99531209.6跨中直线段6-72.1122.0970.21120.04540.95561215.47-87.0846.92700.01040.98971271.88-92.1122.0970.21120.04540.95561285.19-101.2181.21800.00180.99821344.810-111.4261.4360.14260.03070.96981347.211-122.8152.78600.00420.99581389.1合计28.68128.4360.9606注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。7.1.3根据设计图给定的曲线坐标要素，列表计算W13后，计算达到设计张拉力后的钢束伸长值：（（δi1+δi2）LTi2Ey71571.52×1.95×105ΔLw13=∑==0.18471571.52×1.95×1057.1.4W13达到设计初始张拉力后的伸长值计算：184184×468723124800ΔLw13初==28（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）7.2第二跨W14束各段终点应力计算：7.2.1计算简图：7.2.2W14各段终点应力表：线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-22.8522.82600.00420.99581106.92-30.3520.3480.03520.00760.99251111.63-43.5363.48500.00520.99481120.04-51.7021.6950.17020.03660.96411125.85-64.3914.39100.00660.99341167.8跨中直线段6-72.3672.3450.23670.05090.95041175.57-85.8515.68800.00850.99151236.98-92.3672.3450.23670.05090.95041247.59-100.4800.48000.00070.99931312.610-112.6482.6140.26480.05690.94471313.511-122.2962.21600.00330.99671390.4合计28.81528.4330.9436注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。7.2.3根据设计图给定的曲线坐标要素，列表计算W14后，计算达到设计张力后的钢束伸长值：（δ（δi1+δi2）LTi2Ey70368.82×1.95×105ΔLw14=∑==0.180（m）=180(mm)7.2.4W14达到设计初始张拉力后的伸长值计算：180×4687203124800ΔLw14初==180×4687203124800（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）7.3、第二跨W15束各段终点应力计算：7.3.1计算简图：7.3.2W15束各段终点应力表：线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-22.6172.60300.00390.99611130.52-30.8000.7900.05160.01150.98861135.03-41.2131.19800.00180.99821148.14-51.5651.8350.15650.03410.96651150.15-67.5467.54600.01130.98871190.0跨中直线段6-71.9211.9070.19210.04130.95961203.67-85.2065.11000.00770.99241254.38-91.9211.9070.19210.04130.95961263.99-100.8020.80200.00120.99881317.110-112.462.4330.24600.05280.94851318.711-122.3732.30200.00350.99661390.3合计28.42428.4330.8383注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。70444.42×1.95×105（δi1+δi270444.42×1.95×105（δi1+δi2）LTi2EyΔLw15=∑==0.181(m)=181(mm)7.3.4达到初应力时的伸长值计算：181181×4687203124800ΔLw15初==27（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）7.4、第二跨W16束各段终点应力计算：7.4.1计算简图：7.4.2W16束各段终点应力表：线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-22.5282.52800.00380.99621238.02-30.9610.9420.09610.02060.97961242.83-40.5630.56000.00080.99921268.64-50.9610.9420.09610.02060.97961269.75-615.98915.98900.02400.97631296.1跨中直线段6-70.9610.9420.09610.02060.97961327.67-80.5630.56000.00080.99921355.28-90.9610.9420.09610.02060.97961356.39-105.0285.02800.00750.99251384.5合计28.51528.4870.3844注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。75244.02×1.95×105（δi1+δi2）L75244.02×1.95×105（δi1+δi2）LTi2EyΔLw16=∑==0.193(m)=193(mm)7.4193193×4687203124800ΔLw16初==29（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）8、第一跨各束达到设计初始张拉力及张拉力后各钢束伸长值计算：8.1第一跨W17束各段终点应力计算：8.8.1.2W线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-22.4252.34100.00350.99651225.32-32.6452.6140.26450.05680.94481229.63-42.2562.25600.00340.99661301.5跨中直线段4-52.7162.6820.27160.05830.94331305.95-65.2785.08400.00760.99241384.4合计15.32014.9770.5361注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。40506.72×1.95×105（δi1+δi2）LTi240506.72×1.95×105（δi1+δi2）LTi2EyΔLw17=∑==0.104(m)=104(mm)8.104104×4687203124800ΔLw17初==16（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）8.2第一跨W18束各段终点应力计算：8.28.2.2W18线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-20.7450.72300.00110.99891250.72-32.4532.4330.24530.05270.94871252.03-45.7275.72700.00890.99141319.7跨中直线段4-51.8841.8730.18840.04050.96031331.25-64.2984.22200.00630.99371386.2合计15.10714.9780.4227注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。8.2.3根据设计图纸给定的曲线坐标要素，列表计算W18后，计算达到设计40402.72×1.95×105（δi1+δi2）LTi2Ey40402.72×1.95×105（δi1+δi2）LTi2Ey8.2104104×4687203124800ΔLw18初==16（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）8.3第一跨W19束各段终点应力计算：8.38.3.2W19线段编号LT（m）χ（m）θ(rgd)κχ+μθe-（κχ+μθ）终点应力（MPa）备注1-20.5280.52800.00080.99921283.22-30.9610.9420.09610.02060.97961284.33-40.5630.56000.00080.99921311.04-50.9610.9420.09610.02060.97961312.15-68.4388.43800.01270.98741339.4跨中直线段6-71.1371.1330.11370.02440.97591356.57-82.4512.43500.00370.99641390.0合计15.03914.9780.3059注：表中LT为预应力筋长度，χ为预应力筋水平投影长度。8.3.3根据设计图纸给定的曲线坐标要素，列表计算W19后，计算达到设计40571.42×1.95×105（δi1+δi2）LTi2E40571.42×1.95×105（δi1+δi2）LTi2Ey8.3104104×4687203124800ΔLw19初==16（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）9、顶板负弯矩钢束伸长值计算：9.1顶板负弯矩W22束按平均张拉力计算：Ρ22=0.75Ryb×A=1860×0.75×140×7=1367100N=1367.1KN9.1.1顶板负弯矩W22束（L=14.0米1367100×1367100×140001.95×105×140×7PLEyAΔLw22====0.100（m）=100（mm）100×20506513671009.1.2顶板负弯矩W22束（L=100×2050651367100ΔLw22初==15（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）9.2顶板负弯矩W23束按平均张拉力计算：Ρ23=0.75Ryb×A=1860×0.75×140×7=1367100N=1367.1KN9.2.1顶板负弯矩W23束（L=11367100×1367100×100001.95×105×140×7PLEyAΔL23====0.072（m）=72（mm）72×20506513671009.2.2顶板负弯矩W22束（L=72×2050651367100ΔLw23初==11（mm）（或采用实际张拉过程中相邻级的伸长值，作为初应力伸长值，即应力增加15%的伸长值）10、桥面横向钢束伸长值计算：10.1桥面横向钢束WH束