32+48+32箱梁预应力钢束伸长值计算书

1、下曲湾特大桥大桥跨陇海铁路（32+48+32）m连续箱梁预应力钢束伸长值计算书一、 张拉力下曲湾特大桥跨陇海铁路（32+48+32）m连续箱梁纵向预应力钢绞线采用抗拉强度标准值为fpk=1860MPa、弹性模量EP=195GPa, 公称直径j15.20mm，截面面积为140mm2，高强度低松弛钢绞线,其技术标准符合GB5224标准。竖向预应力采用公称直径25mm的PSB830预应力混凝土用螺纹钢筋，其抗拉强度标准值fpk=830MPa、弹性模量EP=200GPa,本梁采用全桥竖向预应力，纵向预应力考虑工作段伸长量及锚圈口预应力损失，张拉控制应力取设计张拉应控制应力值的1.03倍。二、 伸长量计

2、算计算公式：L=PpL/EpAp=pL/Ep其中： p=1-e-(Kx+)/（Kx+）i=(i-1) e-(Kx+)（张拉起点应力与张拉终点应力关系）-预应力钢筋张拉端的张拉应力，MPa;L-预应力钢筋长度，m;-从张拉端到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，取 k=0.0025;-预应力钢筋与孔道壁的摩擦系数，金属波纹管取=0.23，Ep-预应力钢筋弹性模量，钢绞线取Ep=195GPa；p -预应力钢筋的平均张拉应力，取张拉端的拉应力与计算截面处扣除孔道摩阻损失后的拉应力的平均值, MPa；对由多曲线段或直线与曲线段组成的曲线筋张拉伸长量应分段计

3、算，然后叠加，在计算时应将每段两端扣除孔道的摩阻损失后的拉力求出，然后再计算每段的张拉伸长值。三、 伸长量计算表48+80+48梁预应力伸长量计算之考虑工作段长度及应力增大(钢绞线：=0.23，=0.0025，L=6mm；精扎螺纹钢：=0.35，=0.003，L=1mm)钢束编号T1分段编号长度 (m)(弧度)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.4901341.060.3直线AB5.50000.013750.9863440991341.061322.751331.883.8合计11.9808

4、.27.30.9钢束编号T2分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.4901341.060.3直线AB8.50000.021250.978974191341.061312.861326.915.8合计17.98012.2411.241.0钢束编号T3分段编号长度 (m)(弧度)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.4901341.060.3直线AB11.50000.

5、028750.9716593491341.061303.051321.977.8合计23.98016.315.141.1钢束编号T4分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.4901341.060.3直线AB0.31600.000790.9992103121341.061340.001340.530.2曲线BC0.3140.052359880.012828170.987253761340.531323.441331.970.2直线CD13.86100.03465250

6、.9659410221331.971286.601309.169.3合计29.96220.118.781.4钢束编号T5分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.4901341.060.3直线AB0.31600.000790.9992103121341.061340.001340.530.2曲线BC0.3140.052359880.012828170.987253761340.531323.441331.970.2直线CD17.36100.04340250.95752

7、59081331.971275.391303.4811.6合计36.96224.723.221.5钢束编号T6分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.4901341.060.3直线AB0.31600.000790.9992103121341.061340.001340.530.2曲线BC0.3140.052359880.012828170.987253761340.531323.441331.970.2直线CD20.86100.05215250.9491841051

8、331.971264.281297.8313.9合计43.96229.327.621.7钢束编号T7分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.4901341.060.3直线AB0.31600.000790.9992103121341.061340.001340.530.2曲线BC0.3140.052359880.012828170.987253761340.531323.441331.970.2直线CD24.36100.06090250.9409149751331.9

9、71253.271292.2216.1合计50.96233.831.981.8钢束编号T8分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.4901341.060.3直线AB0.31600.000790.9992103121341.061340.001340.530.2曲线BC0.3140.052359880.012828170.987253761340.531323.441331.970.2直线CD27.86100.06965250.9327178831331.971242

10、.351286.6418.4合计57.96238.336.32.0钢束编号T9分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.3直线AB0.31600.000790.9992103121341.061340.001340.530.2曲线BC0.31420.052359880.012828170.987253761340.531323.441331.970.2直线CD31.36100.07840250.9245922031331.971231.53128

11、1.0920.6合计64.9642.740.582.2钢束编号T10分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.3直线AB0.31600.000790.9992103121341.061340.001340.530.2曲线BC0.31420.052359880.012828170.987253761340.531323.441331.970.2直线CD34.86100.08715250.9165373131331.971220.801275.582

12、2.8合计71.9647.144.822.3钢束编号T11分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.3直线AB0.31600.000790.9992103121341.061340.001340.530.2曲线BC0.31420.052359880.012828170.987253761340.531323.441331.970.2直线CD38.36100.09590250.9085525961331.971210.161270.0925.0合计

13、78.9651.549.022.5钢束编号T12单端张拉，两端推导求平均值分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.34直线AB0.36900.00092250.9990779251341.061339.821340.440.25曲线BC0.5240.087266460.021380280.9788466551340.441312.091326.210.36直线CD15.52100.03880250.9619406741326.211275.74

14、1300.8110.35曲线DE1.0470.174532930.042760570.9581407731300.811246.361273.390.68直线EF1.74100.00435250.9956569581273.391267.861270.631.13工作段0.4900.0012250.998775751270.631269.071269.850.32小计20.1813.44工作段0.491341.060.34直线AB1.74100.00435250.9956569581341.061335.241338.151.19曲线BC1.0470.174532930.042760570.9

15、581407731338.151282.131309.940.70直线CD15.52100.03880250.9619406741309.941260.081284.8510.23曲线DE0.5240.087266460.021380280.9788466551284.851257.671271.210.34直线EF0.36900.00092250.9990779251271.211270.041270.630.24工作段0.4900.0012250.998775751270.631269.071269.850.32小计20.1813.36靠近梁端8.64远离梁端3.74设计值12.38A1.

16、0213.40钢束编号T13单端张拉，两端推导求平均值分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.34直线AB0.36900.00092250.9990779251341.061339.821340.440.25曲线BC0.5240.087266460.021380280.9788466551340.441312.091326.210.36直线CD12.06100.03015250.9702975521326.211286.821306.428.0

17、8曲线DE1.0470.174532930.042760570.9581407731306.421251.731278.880.69直线EF1.700.004250.9957590181278.881273.461276.171.11工作段0.4900.0012250.998775751276.171274.601275.390.32小计16.6811.15工作段0.491341.060.34直线AB1.700.004250.9957590181341.061335.371338.211.17曲线BC1.0470.174532930.042760570.9581407731338.211282

18、.201310.010.70直线CD12.06100.03015250.9702975521310.011271.101290.457.98曲线DE0.5240.087266460.021380280.9788466551290.451263.161276.760.34直线EF0.36900.00092250.9990779251276.761275.581276.170.24工作段0.4900.0012250.998775751276.171274.601275.390.32小计16.6811.09靠近梁端7.75远离梁端2.41设计值10.16A0.9611.12钢束编号H分段编号长度 (

19、m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.3直线AB1.76800.004419640.9955901081341.061335.151338.101.2曲线BC1.0470.174532930.042760570.9581407731338.101282.091309.900.7直线CD4.41200.011030.9890306071309.901295.531302.702.9合计15.4310.409.281.1钢束编号M1分段编号长度 (m)(rad)

20、kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.3直线AB1.56400.003910.9960976341341.061335.831338.441.1曲线BC4.8870.610865240.152716310.85837321338.441148.881241.253.1直线CD0.14100.00035250.9996475621241.251240.811241.030.1合计14.169.227.521.7钢束编号M2分段编号长度 (m)(rad)kx+e-(kx+)起

21、点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.3直线AB1.39700.003491250.9965148371341.061336.391338.721.0曲线BC4.8870.610865240.152716310.85837321338.721149.121241.513.1直线CD2.70400.006760.9932627971241.511233.151237.321.7合计18.9512.2510.981.3钢束编号M3分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mp

22、a)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.3直线AB1.28300.00320750.9967976391341.061336.771338.910.9曲线BC4.8870.610865240.152716310.85837321338.911149.291241.693.1直线CD5.79700.01449250.9856120111241.691223.821232.733.7合计24.9115.9914.321.7钢束编号M4分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应

23、力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.3直线AB1.08300.00270750.9972961621341.061337.431339.250.7曲线BC4.8870.610865240.152716310.85837321339.251149.571242.003.1直线CD8.96100.02240250.9778465731242.001214.481228.195.6合计30.8419.6717.722.0钢束编号M5分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平

24、均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.3直线AB1.14300.00285750.9971465791341.061337.231339.150.8曲线BC4.8870.610865240.152716310.85837321339.151149.491241.903.1直线CD12.41100.03102750.9694489131241.901203.961222.837.8合计37.8624.0321.522.5钢束编号M6分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(

25、Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.3直线AB1.03000.0025750.9974283121341.061337.611339.330.7曲线BC4.8870.610865240.152716310.85837321339.331149.651242.083.1直线CD16.00400.040010.9607798311242.081193.361217.5610.0合计44.8228.3025.343.0钢束编号M7分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(

26、cm)设计伸长量(cm)量差(cm)工作段0.491341.060.3直线AB1.17900.00294750.997056841341.061337.111339.090.8曲线BC4.8870.610865240.152716310.85837321339.091149.441241.853.1直线CD19.38300.04845750.9526978281241.851183.111212.2412.0合计51.8832.6229.243.4钢束编号M8分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸

27、长量(cm)量差(cm)工作段0.491341.060.3直线AB3.38500.00846250.9915732061341.061329.761335.402.3曲线BC3.4910.436332310.109083080.8966559221335.401197.401265.142.3直线CD22.00400.055010.9464756831265.141197.431230.9813.9合计58.7437.6234.33.3钢束编号SB1单端张拉，两端推导求平均值分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长

28、量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.34直线AB2.36700.00591750.9940999741341.061333.151337.101.62曲线BC1.0470.174532930.042760570.9581407731337.101281.131308.920.70直线CD1.09500.00273750.9972662441308.921305.341307.130.73曲线DE13.50.053407080.046023630.9550193971307.131248.331277.508.84曲线EF1.40.227940.0558454

29、50.945685281277.501208.121242.490.87直线FG1.64100.00410250.9959059041242.491237.401239.941.04工作段0.4900.0012250.998775751239.941238.421239.180.31小计21.9914.46工作段0.491341.060.34直线AB1.64100.00410250.9959059041341.061335.571338.311.13曲线BC1.36770.227940.055845450.945685281338.311265.621301.630.91曲线BC13.4960

30、.174532930.073882570.9287807521301.631208.931254.718.68直线CD1.09500.00273750.9972662441254.711251.281252.990.70曲线BC1.0470.087266460.022688790.9775666681252.991224.881238.880.67直线CD2.36700.00591750.9940999741238.881231.581235.231.50工作段0.4900.0012250.998775751235.231233.711234.470.31小计21.9914.24靠近梁端8.0

31、1远离梁端5.34设计值13.35A1.0014.35钢束编号SB2单端张拉，两端推导求平均值分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.34直线AB0.54000.001350.9986509111341.061339.251340.160.37曲线BC1.0470.174532930.042760570.9581407731340.161284.061311.910.70直线CD7.92600.0198150.9803800271311.911

32、286.171298.995.28曲线DE16.80.066689030.057456730.9441627461298.991226.461262.3810.91曲线EF1.40.241221960.05909930.9426131631262.381189.941225.800.91直线FG1.71700.00429250.99571671225.801220.551223.171.08工作段0.4900.0012250.998775751223.171221.681222.430.31小计30.5019.89工作段0.491341.060.34直线AB1.71700.00429250.9

33、9571671341.061335.321338.191.18曲线BC1.40.241221960.05909930.9426131631338.191261.391299.410.96曲线BC16.80.066689030.057456730.9441627461299.411226.861262.7910.91直线CD7.92600.0198150.9803800271262.791238.011250.365.08曲线BC1.0470.174532930.042760570.9581407731250.361198.021224.000.66直线CD0.54000.001350.9986

34、509111224.001222.351223.170.34工作段0.4900.0012250.998775751223.171221.681222.430.31小计30.5019.78靠近梁端11.11远离梁端7.43设计值18.54A1.2919.83钢束编号SB3单端张拉，两端推导求平均值分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.34直线AB1.85700.00464250.995368261341.061334.851337.951.27

35、曲线BC1.5710.261799390.064140860.9378728821337.951254.831295.951.04直线CD6.15400.0153850.9847327451295.951276.161286.034.06曲线DE20.20.080023350.068941120.9333816361286.031200.351242.7012.88曲线EF1.50.254556270.062366190.9395387721242.701167.561204.740.94直线FG1.78100.00445250.9955573981204.741199.391202.061.

36、10工作段0.4900.0012250.998775751202.061200.591201.330.30小计34.0821.94工作段0.491341.060.34直线AB1.78100.00445250.9955573981341.061335.101338.081.22曲线BC1.50.254556270.062366190.9395387721338.081257.181297.211.02曲线BC20.20.080023350.068941120.9333816361297.211210.791253.5012.99直线CD6.15400.0153850.9847327451253.

37、501234.361243.913.93曲线BC1.5710.261799390.064140860.9378728821243.911166.631204.860.97直线CD1.85700.00464250.995368261204.861199.271202.061.14工作段0.4900.0012250.998775751202.061200.591201.330.30小计34.0821.91靠近梁端10.91远离梁端9.63设计值20.54A1.3921.93钢束编号SB4单端张拉，两端推导求平均值分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(

38、Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.34直线AB1.85700.00464250.995368261341.061334.851337.951.27曲线BC1.5710.261799390.064140860.9378728821337.951254.831295.951.04直线CD6.51400.0162850.9838468841295.951275.011285.454.29曲线DE23.30.092240650.079467350.9236081761285.451187.251235.7014.77曲线EF1.6

39、0.266773580.065359420.9367307211235.701157.521196.180.98直线FG1.83300.00458250.9954279841196.181190.721193.451.12工作段0.4900.0012250.998775751193.451191.991192.720.30小计37.6624.12工作段0.491341.060.34直线AB1.83300.00458250.9954279841341.061334.931337.991.26曲线BC1.60.266773580.065359420.9367307211337.991253.341

40、295.201.06曲线BC23.30.092240650.079467350.9236081761295.201196.261245.0814.88直线CD6.51400.0162850.9838468841245.081224.971234.994.13曲线BC1.5710.261799390.064140860.9378728821234.991158.271196.220.96直线CD1.85700.00464250.995368261196.221190.681193.451.14工作段0.4900.0012250.998775751193.451191.991192.720.30小计37.6624.06靠近梁端11.85远离梁端10.59设计值22.44A1.6524.09钢束编号SB5单端张拉，两端推导求平均值分段编号长度 (m)(rad)kx+e-(kx+)起点张拉应力(Mpa)终点张拉应力(Mpa)平均张拉应力(Mpa)伸长量(cm)设计伸长量(cm)量差(cm)工作段0.491341.060.34直线AB0.54000.0013