《桥梁预应力损失及有效应力计算案例综述》3800字

桥梁预应力损失及有效应力计算案例综述目录TOC\o"1-2"\h\u22800桥梁预应力损失及有效应力计算案例综述 1131721.1预应力损失计算 132051.1预应力钢筋与管道之间摩擦引起的应力损失 191621.2由锚具变形、钢筋回缩和接缝压缩引起的应力损失 294721.3混凝土弹性压缩引起的应力损失 32551.4由钢筋松弛引起的应力损失的终极值 3286901.5由混凝土收缩和徐变引起的预应力损失 3296531.6有效预应力计算 41.1预应力损失计算按《公路钢筋混凝土及预应力混凝土桥涵设计规范》(JTGD62—2012)规定，预应力混凝土构件在正常使用极限状态计算中，应考虑由下列因素引起的预应力损失值：管道摩阻损失锚具变形、钢筋回缩和拼装构件的接缝压缩温差应力损失混凝土的弹性压缩预应力钢筋的应力松弛混凝土的收缩和徐变本次设计采用后张法，因此不计算先张法所独有的温差应力损失。此外，尚应考虑预应力钢筋与锚圈口之间的摩擦、台座的弹性变形等因素引起的其他预应力损失。1.1预应力钢筋与管道之间摩擦引起的应力损失在后张法构件中，张拉时预应力钢筋在预留孔道中发生滑动，因而产生摩阻力。钢筋在远离张拉端处的应力会由于这种摩阻力的存在而小于张拉端处的应力。这种预应力的减小称为管道摩阻损失。由《公路钢筋混凝土及预应力混凝土桥涵设计规范JTGD62-2012》第6.2.2条，后张法构件张拉时，预应力钢筋与管道之间摩擦引起的应力损失可按下式计算： （6-1）式中—张拉钢筋时锚下的控制应力(取)—预应力钢筋与管道壁的摩擦系数—从张拉端至计算界面曲线管道部分切线的夹角之和，以rad计—管道每米局部偏差对摩擦的影响系数—从张拉端至计算截面的管道长度，可近似地取该段管道在构件纵轴上的投影长度(m)表6.1系数K及值管道成型方式k钢绞线、钢丝束精压螺纹钢筋预埋金属波纹管预埋塑料波纹管预埋铁皮管预埋钢管抽心成型0.00150.00150.0030.0010.00150.20～0.250.14～0.170.350.250.550.5—0.4—0.6对于预埋金属波纹管k＝0.0015,对应钢绞线＝0.25,张拉控制应力。1.2由锚具变形、钢筋回缩和接缝压缩引起的应力损失在对钢筋进行锚固时，钢丝会发生回缩，由于受压也会使锚具变形、使垫圈之间和分块拼装的混凝土块件之间的接缝压缩，从而引起的预应力损失。由《公路钢筋混凝土及预应力混凝土桥涵设计规范JTGD62-2004》第6.2.3条，预应力直线钢筋由锚具变形、钢筋回缩和接缝压缩引起的预应力损失可按下式计算： （6-2）式中—锚具变形、钢筋回缩和接缝压缩值，统一取6mml—张拉端至锚固端之间的距离(mm)—预应力钢筋的弹性模量，取1.95×105MPa本设计采用夹片式锚具，无顶压时＝6mm，＝195000MPa。1.3混凝土弹性压缩引起的应力损失后张法分批张拉时，后张拉的预应力使得构件受压而弹性缩短，因此会使前面已经锚固的预应力钢筋变得松弛而造成预应力损失，这部分损失叫做弹性压缩损失。由《公路钢筋混凝土及预应力混凝土桥涵设计规范JTGD62-2004》第6.2.5条，弹性压缩损失可按下式计算： （6-3）式中—在先张拉钢筋重心处，由后张拉各批钢筋而产生的混凝土法向应力—预应力钢筋与混凝土弹性模量比1.4由钢筋松弛引起的应力损失的终极值由预应力钢筋应力松弛产生的预应力损失，由《公路钢筋混凝土及预应力混凝土桥涵设计规范JTGD62-2004》第6.2.6条，可按下式计算： （6-4）式中—张拉系数，一次张拉时，=1，超张拉时，=0.9—钢筋松弛系数，低松弛时=0.3—传力锚固的钢筋应力，对后张法构件1.5由混凝土收缩和徐变引起的预应力损失在本次设计中，由于时间的变化，会引起混凝土的收缩以及构件受到预应力的持续压缩使得混凝土产生徐变变形，从而引起构件缩短并引起预应力的损失。简称为混凝土收缩徐变损失。根据规范，可以用下述公式计算其损失值： （6-5）式中 —钢束弹性模量，取195000MPa —混凝土收缩终极值，根据规范，取 —混凝土徐变终极值，查规范，取=2.881.6有效预应力计算各个阶段有效预应力计算如下所示：1.传力锚固时的有效预应力为：2.使用阶段有效预应力应减掉所有预应力损失，具体如下：根据上述计算公式，就可以各个阶段的预应力损失及其有效预应力值，由于钢束较多，本文中仅仅给出几个典型的钢束预应力损失，如下所示：表6.2迈达斯计算的腹板钢束预应力损失单元位置应力(考虑瞬时损失):A(kN/m^2)弹性变形损失:B(kN/m^2)比值(A+B)/A徐变/收缩损失(kN/m^2)松弛损失(kN/m^2)应力(考虑所有损失)/应力(考虑瞬时损失)端部有效钢束数钢束组[001-F0]的应力损失钢束组001-F0阶段收缩徐变续表单元位置应力(考虑瞬时损失):A(kN/m^2)弹性变形损失:B(kN/m^2)比值(A+B)/A徐变/收缩损失(kN/m^2)松弛损失(kN/m^2)应力(考虑所有损失)/应力(考虑瞬时损失)端部有效钢束数14I910590.9-31604.91.0-49813.90.00.9214J1043120.7-27223.71.0-46684.4-9896.70.9215I1043120.7-27146.91.0-46618.8-9896.70.9215J1061140.7-25470.01.0-44574.4-11671.40.9216I1061140.7-25480.91.0-44576.5-11671.40.9216J1043120.7-27169.21.0-46633.1-9896.70.9217I1043120.7-27247.91.0-46700.6-9896.70.9217J910590.9-31532.61.0-49741.60.00.92钢束组[005-F1]的应力损失钢束组005-F1阶段收缩徐变13I952130.1-27484.61.0-45709.4-1767.20.9113J1088697.9-31535.31.0-53421.6-14490.70.9114I1088697.9-31013.41.0-51317.5-14490.70.9114J1104575.1-22756.41.0-43125.7-16172.90.9115I1104575.1-22698.91.0-43069.2-16172.90.9115J1108155.1-21336.91.0-41277.8-16558.10.9116I1108155.4-21347.71.0-41279.9-16558.10.9116J1104575.1-22721.51.0-43083.8-16172.90.9117I1104575.1-22781.01.0-43142.2-16172.90.9117J1088697.9-31071.51.0-51363.4-14490.70.9118I1088697.9-31591.31.0-53467.9-14490.70.9118J952130.1-27277.11.0-45509.9-1767.20.91钢束组[009-F2]的应力损失钢束组009-F2阶段收缩徐变12I988637.4-26604.21.0-45766.6-4862.10.9112J1107291.1-29156.91.0-52127.9-16464.90.9113I1107291.1-28384.51.0-51405.1-16464.90.9113J1136165.4-25961.31.0-50302.2-19645.80.9114I1136165.4-25627.01.0-48545.7-19645.80.9114J1141562.2-18552.31.0-40646.6-20255.80.9115I1141562.2-18507.01.0-40604.8-20255.80.9115J1145121.3-16941.91.0-38399.0-20660.80.9116I1145121.4-16952.81.0-38401.3-20660.80.9116J1141562.2-18536.11.0-40625.5-20255.80.91续表单元位置应力(考虑瞬时损失):A(kN/m^2)弹性变形损失:B(kN/m^2)比值(A+B)/A徐变/收缩损失(kN/m^2)松弛损失(kN/m^2)应力(考虑所有损失)/应力(考虑瞬时损失)端部有效钢束数17I1141562.2-18583.31.0-40669.2-20255.80.9117J1136165.4-25714.21.0-48618.6-19645.80.9118I1136165.4-26046.71.0-50376.3-19645.80.9118J1107291.1-28501.31.0-51513.5-16464.90.9119I1107291.1-29275.71.0-52176.6-16464.90.9119J988637.4-31013.91.0-49587.6-4862.10.91钢束组[013-F3]的应力损失钢束组013-F3阶段收缩徐变11I979739.1-25635.51.0-45121.8-4087.10.9111J1116280.5-27419.71.0-49950.6-17440.20.9112I1116280.5-26664.41.0-49462.8-17440.20.9112J1132159.7-23348.91.0-47480.3-19196.10.9113I1132159.7-22782.21.0-47235.0-19196.10.9113J1137516.3-20646.91.0-45918.3-19798.00.9114I1137516.3-20399.61.0-44531.8-19798.00.9114J1142826.4-14698.31.0-37301.9-20399.40.9115I1142826.4-14656.81.0-37262.5-20399.40.9115J1146350.0-13319.81.0-35234.6-20801.10.9116I1146350.0-13328.61.0-35236.5-20801.10.9116J1142826.4-14684.11.0-37282.9-20399.40.9117I1142826.4-14727.51.0-37324.2-20399.40.9117J1137516.3-20485.31.0-44604.5-19798.00.9118I1137516.3-20730.91.0-45992.1-19798.00.9118J1132159.7-22905.31.0-47350.1-19196.10.9119I1132159.7-23473.71.0-47541.8-19196.10.9119J1116280.5-28109.81.0-50660.5-17440.20.9120I1116280.5-28888.31.0-51212.7-17440.20.9120J979739.1-30305.81.0-49247.7-4087.10.91钢束组[017-F4]的应力损失钢束组017-F4阶段收缩徐变10I985866.1-26434.51.0-46810.3-4619.30.9110J1117829.9-25601.61.0-49541.9-17609.70.9111I1117829.9-24873.91.0-48779.9-17609.70.9111J1138032.1-21535.81.0-46781.5-19856.20.91续表单元位置应力(考虑瞬时损失):A(kN/m^2)弹性变形损失:B(kN/m^2)比值(A+B)/A徐变/收缩损失(kN/m^2)松弛损失(kN/m^2)应力(考虑所有损失)/应力(考虑瞬时损失)端部有效钢束数12I1138032.1-20991.21.0-46699.8-19856.20.9112J1143393.0-18092.41.0-44753.2-20463.80.9113I1143393.0-17638.81.0-44702.7-20463.80.9113J1148704.5-15484.91.0-43040.6-21070.60.9114I1148704.5-15325.01.0-41665.2-21070.60.9114J1153986.9-10768.21.0-34891.8-21678.80.9115I1153986.9-10733.41.0-34863.5-21678.80.9115J1157495.0-9319.01.0-32525.9-22085.30.9116I1157495.0-9324.91.0-32526.8-22085.30.9116J1153986.9-10764.51.0-34888.9-21678.80.9117I1153986.9-10801.31.0-34919.1-21678.80.9117J1148704.6-15436.21.0-41763.0-21070.60.9118I1148704.6-15594.51.0-43140.4-21070.60.9118J1143393.0-17821.91.0-44876.6-20463.80.9119I1143393.0-18277.71.0-44879.2-20463.80.9119J1138032.1-21829.31.0-47362.0-19856.20.9120I1138032.1-22390.11.0-47486.8-19856.20.9120J1117829.9-26097.31.0-49826.0-17609.70.9121I1117829.9-26850.61.0-50659.3-17609.70.9121J985866.1-31296.81.0-51190.1-4619.30.91钢束组[021-F5]的应力损失钢束组021-F5阶段收缩徐变9I1013035.1-26419.81.0-47336.8-7055.00.919J1139392.8-23895.31.0-47913.0-20010.00.9110I1139392.8-23143.21.0-47320.4-20010.00.9110J1149681.1-19186.91.0-44478.9-21182.70.9111I1149681.1-18676.21.0-44202.1-21182.70.9111J1155106.2-15790.41.0-42164.5-21808.30.9112I1155106.2-15377.91.0-42285.2-21808.30.9112J1160486.8-12928.81.0-40453.8-22433.50.9113I1160486.8-12579.91.0-40513.2-22433.50.9113J1165838.2-10775.41.0-38970.8-23060.20.9114I1165838.2-10664.61.0-37805.5-23060.20.9114J1171165.1-7266.31.0-31721.8-23688.90.9115I1171165.1-7231.91.0-31694.1-23688.90.9115J1174703.1-6062.81.0-29555.0-24109.00.91续表单元位置应力(考虑瞬时损失):A(kN/m^2)弹性变形损失:B(kN/m^2)比值(A+B)/A徐变/收缩损失(kN/m^2)松弛损失(kN/m^2)应力(考虑所有损失)/应力(考虑瞬时损失)端部有效钢束数16I1174703.1-6067.41.0-29554.4-24109.00.9116J1171165.1-7261.81.0-31718.2-23688.90.9117I1171165.1-7298.21.0-31747.8-23688.90.9117J1165838.2-10774.51.0-37902.1-23060.20.9118I1165838.2-10883.81.0-39069.3-23060.20.9118J1160486.8-12762.01.0-40686.1-22433.50.9119I1160486.8-13112.81.0-40584.0-22433.50.9119J1155106.3-16213.21.0-42945.8-21808.30.9120I1155106.3-16642.01.0-42868.3-21808.30.9120J1149681.1-19864.21.0-45218.1-21182.70.9121I1149681.1-20399.81.0-45564.6-21182.70.9121J1139392.8-24763.71.0-48783.2-20010.00.9122I1139392.8-25551.61.0-49577.7-20010.00.9122J1013035.1-29690.11.0-50429.3-7055.00.91钢束组[025-F6]的应力损失钢束组025-F6阶段收缩徐变8I1037048.6-29665.41.0-51145.5-9310.90.918J1147717.1-24897.21.0-51282.8-20957.50.919I1147717.1-24065.31.0-50501.3-20957.50.919J1162352.4-16566.71.0-43999.6-22651.50.9110I1162352.4-16066.01.0-43749.7-22651.50.9110J1167830.6-13069.21.0-41391.7-23294.80.9111I1167830.6-12700.11.0-41227.0-23294.80.9111J1173262.0-10466.71.0-39342.2-23937.60.9112I1173262.0-10155.81.0-39527.3-23937.60.9112J1178663.9-8257.01.0-37899.7-24581.80.9113I1178663.9-7989.81.0-38030.2-24581.80.9113J1184041.1-6134.41.0-36186.0-25228.00.9114I1184041.1-6080.51.0-35011.7-25228.00.9114J1186854.5-3638.31.0-29355.8-25568.01.0115I1186854.5-3605.11.0-29335.6-25568.01.0115J1183299.3-2516.81.0-26990.5-25138.61.0116I1183299.3-2525.71.0-26988.4-25138.61.0116J1186854.6-3645.21.0-29364.3-25568.01.0117I1186854.6-3680.41.0-29386.4-25568.01.0117J1184041.1-6222.91.0-35132.8-25228.00.91续表单元位置应力(考虑瞬时损失):A(kN/m^2)弹性变形损失:B(kN/m^2)比值(A+B)/A徐变/收缩损失(kN/m^2)松弛损失(kN/m^2)应力(考虑所有损失)/应力(考虑瞬时损失)端部有效钢束数18I1184041.1-6275.41.0-36309.8-25228.00.9118J1178663.9-8237.71.0-38261.1-24581.80.9119I1178663.9-8507.31.0-38093.5-24581.80.9119J1173262.1-10410.51.0-39670.0-23937.60.9120I1173262.1-10731.01.0-39507.7-23937.60.9120J1167830.7-13240.11.0-41661.4-23294.80.9121I1167830.7-13625.31.0-41869.3-23294.80.9121J1162352.4-16977.11.0-44573.4-22651.50.9122I1162352.4-17503.11.0-44981.6-22651.50.9122J1147717.1-20374.01.0-47038.8-20957.50.9123I1147717.1-21144.51.0-47716.1-20957.50.9123J1037048.6-28866.11.0-50397.4-9310.90.91钢束组[029-F7]的应力损失钢束组029-F7阶段收缩徐变7I1025209.4-25542.41.0-47217.8-8186.60.917J1150661.0-24048.81.0-56352.5-21295.30.918I1150661.0-19780.71.0-51161.3-21295.30.918J1156466.0-13394.31.0-45944.8-21965.80.919I1156466.0-12913.61.0-45569.4-21965.80.919J1161907.1-6449.71.0-39335.4-22599.40.9110I1161907.1-6157.91.0-39313.2-22599.40.9110J1167308.0-4320.01.0-37283.4-23233.20.9111I1167308.0-4097.21.0-37238.4-23233.20.9111J1172683.2-2560.31.0-35583.8-23868.90.9112I1172683.2-2367.91.0-35819.7-23868.90.9112J1178034.1-987.71.0-34366.0-24506.50.9113I1178034.1-824.31.0-34541.7-24506.50.9113J1181048.6629.71.0-32823.9-24867.81.0114I1181048.66