橋梁預應力損失及有效應力計算案例綜述目錄TOC\o"1-2"\h\u22800橋梁預應力損失及有效應力計算案例綜述 1131721.1預應力損失計算 132051.1預應力鋼筋與管道之間摩擦引起的應力損失 191621.2由錨具變形、鋼筋回縮和接縫壓縮引起的應力損失 294721.3混凝土彈性壓縮引起的應力損失 32551.4由鋼筋松弛引起的應力損失的終極值 3286901.5由混凝土收縮和徐變引起的預應力損失 3296531.6有效預應力計算 41.1預應力損失計算按《公路鋼筋混凝土及預應力混凝土橋涵設計規范》(JTGD62—2012)規定，預應力混凝土構件在正常使用極限狀態計算中，應考慮由下列因素引起的預應力損失值：管道摩阻損失錨具變形、鋼筋回縮和拼裝構件的接縫壓縮溫差應力損失混凝土的彈性壓縮預應力鋼筋的應力松弛混凝土的收縮和徐變本次設計采用后張法，因此不計算先張法所獨有的溫差應力損失。此外，尚應考慮預應力鋼筋與錨圈口之間的摩擦、臺座的彈性變形等因素引起的其他預應力損失。1.1預應力鋼筋與管道之間摩擦引起的應力損失在后張法構件中，張拉時預應力鋼筋在預留孔道中發生滑動，因而產生摩阻力。鋼筋在遠離張拉端處的應力會由于這種摩阻力的存在而小于張拉端處的應力。這種預應力的減小稱為管道摩阻損失。由《公路鋼筋混凝土及預應力混凝土橋涵設計規范JTGD62-2012》第6.2.2條，后張法構件張拉時，預應力鋼筋與管道之間摩擦引起的應力損失可按下式計算： （6-1）式中—張拉鋼筋時錨下的控制應力(取)—預應力鋼筋與管道壁的摩擦系數—從張拉端至計算界面曲線管道部分切線的夾角之和，以rad計—管道每米局部偏差對摩擦的影響系數—從張拉端至計算截面的管道長度，可近似地取該段管道在構件縱軸上的投影長度(m)表6.1系數K及值管道成型方式k鋼絞線、鋼絲束精壓螺紋鋼筋預埋金屬波紋管預埋塑料波紋管預埋鐵皮管預埋鋼管抽心成型0.00150.00150.0030.0010.00150.20～0.250.14～0.170.350.250.550.5—0.4—0.6對于預埋金屬波紋管k＝0.0015,對應鋼絞線＝0.25,張拉控制應力。1.2由錨具變形、鋼筋回縮和接縫壓縮引起的應力損失在對鋼筋進行錨固時，鋼絲會發生回縮，由于受壓也會使錨具變形、使墊圈之間和分塊拼裝的混凝土塊件之間的接縫壓縮，從而引起的預應力損失。由《公路鋼筋混凝土及預應力混凝土橋涵設計規范JTGD62-2004》第6.2.3條，預應力直線鋼筋由錨具變形、鋼筋回縮和接縫壓縮引起的預應力損失可按下式計算： （6-2）式中—錨具變形、鋼筋回縮和接縫壓縮值，統一取6mml—張拉端至錨固端之間的距離(mm)—預應力鋼筋的彈性模量，取1.95×105MPa本設計采用夾片式錨具，無頂壓時＝6mm，＝195000MPa。1.3混凝土彈性壓縮引起的應力損失后張法分批張拉時，后張拉的預應力使得構件受壓而彈性縮短，因此會使前面已經錨固的預應力鋼筋變得松弛而造成預應力損失，這部分損失叫做彈性壓縮損失。由《公路鋼筋混凝土及預應力混凝土橋涵設計規范JTGD62-2004》第6.2.5條，彈性壓縮損失可按下式計算： （6-3）式中—在先張拉鋼筋重心處，由后張拉各批鋼筋而產生的混凝土法向應力—預應力鋼筋與混凝土彈性模量比1.4由鋼筋松弛引起的應力損失的終極值由預應力鋼筋應力松弛產生的預應力損失，由《公路鋼筋混凝土及預應力混凝土橋涵設計規范JTGD62-2004》第6.2.6條，可按下式計算： （6-4）式中—張拉系數，一次張拉時，=1，超張拉時，=0.9—鋼筋松弛系數，低松弛時=0.3—傳力錨固的鋼筋應力，對后張法構件1.5由混凝土收縮和徐變引起的預應力損失在本次設計中，由于時間的變化，會引起混凝土的收縮以及構件受到預應力的持續壓縮使得混凝土產生徐變變形，從而引起構件縮短并引起預應力的損失。簡稱為混凝土收縮徐變損失。根據規范，可以用下述公式計算其損失值： （6-5）式中 —鋼束彈性模量，取195000MPa —混凝土收縮終極值，根據規范，取 —混凝土徐變終極值，查規范，取=2.881.6有效預應力計算各個階段有效預應力計算如下所示：1.傳力錨固時的有效預應力為：2.使用階段有效預應力應減掉所有預應力損失，具體如下：根據上述計算公式，就可以各個階段的預應力損失及其有效預應力值，由于鋼束較多，本文中僅僅給出幾個典型的鋼束預應力損失，如下所示：表6.2邁達斯計算的腹板鋼束預應力損失單元位置應力(考慮瞬時損失):A(kN/m^2)彈性變形損失:B(kN/m^2)比值(A+B)/A徐變/收縮損失(kN/m^2)松弛損失(kN/m^2)應力(考慮所有損失)/應力(考慮瞬時損失)端部有效鋼束數鋼束組[001-F0]的應力損失鋼束組001-F0階段收縮徐變續表單元位置應力(考慮瞬時損失):A(kN/m^2)彈性變形損失:B(kN/m^2)比值(A+B)/A徐變/收縮損失(kN/m^2)松弛損失(kN/m^2)應力(考慮所有損失)/應力(考慮瞬時損失)端部有效鋼束數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鋼束組[005-F1]的應力損失鋼束組005-F1階段收縮徐變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鋼束組[009-F2]的應力損失鋼束組009-F2階段收縮徐變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續表單元位置應力(考慮瞬時損失):A(kN/m^2)彈性變形損失:B(kN/m^2)比值(A+B)/A徐變/收縮損失(kN/m^2)松弛損失(kN/m^2)應力(考慮所有損失)/應力(考慮瞬時損失)端部有效鋼束數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鋼束組[013-F3]的應力損失鋼束組013-F3階段收縮徐變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鋼束組[017-F4]的應力損失鋼束組017-F4階段收縮徐變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續表單元位置應力(考慮瞬時損失):A(kN/m^2)彈性變形損失:B(kN/m^2)比值(A+B)/A徐變/收縮損失(kN/m^2)松弛損失(kN/m^2)應力(考慮所有損失)/應力(考慮瞬時損失)端部有效鋼束數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鋼束組[021-F5]的應力損失鋼束組021-F5階段收縮徐變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續表單元位置應力(考慮瞬時損失):A(kN/m^2)彈性變形損失:B(kN/m^2)比值(A+B)/A徐變/收縮損失(kN/m^2)松弛損失(kN/m^2)應力(考慮所有損失)/應力(考慮瞬時損失)端部有效鋼束數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鋼束組[025-F6]的應力損失鋼束組025-F6階段收縮徐變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續表單元位置應力(考慮瞬時損失):A(kN/m^2)彈性變形損失:B(kN/m^2)比值(A+B)/A徐變/收縮損失(kN/m^2)松弛損失(kN/m^2)應力(考慮所有損失)/應力(考慮瞬時損失)端部有效鋼束數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鋼束組[029-F7]的應力損失鋼束組029-F7階段收縮徐變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