三跨预应力砼现浇连续箱梁抗震计算书.doc

35+60+35m预应力砼现浇连续箱梁抗震计算书计算 : _校核 : _审核 : _二零一三年 三月一、概述1.1 工程概况本抗震验算桥梁为35+60+35m预应力砼现浇连续箱梁。桥宽8.1m，上部采用现浇箱梁，跨中梁高1.8m，支点处梁高3.2m，采用C50混凝土。主墩柱高6m，墩身采用单柱式矩形桥墩，墩身截面尺寸为顺桥向1.5m，横桥向3m，墩柱及承台均采用C35混凝土。下部基础均采用承台接桩基础的形式，桥墩采用2根桩径为1.8m的桩基，采用C30混凝土。地震动峰值加速度A=0.15g，地震动反应谱特征周期Tg=0.45s，场地类别为II类。1.2 采用的标准、规范及技术规定1、公路桥梁抗震设计细则JTG/T B02-01-20082、公路桥涵设计通用规范JTG D60-20043、公路钢筋混凝土及预应力混凝土桥涵设计规范JTG D62-20044、公路桥涵地基与基础设计规范JTG D63-20075、公路工程技术标准JTG B01-20031.3主要计算参数取值1、水平向设计基本地震动加速度峰值A：0.15g2、特征周期Tg：0.45s3、场地类别：II类4、抗震重要性系数Ci：1.7(E2作用)、0.5(E1作用)5、场地系数Cs：1.06、阻尼调整系数Cd：1.0 根据上述参数及公路桥梁抗震设计细则（JTG/T B02-01-2008）（下文简称抗震细则）5.2.1条，计算E1和E2作用下的水平设计加速度反应谱S（T）如图1.11.2所示。图1.1 E1地震作用反应谱曲线图1.2 E2地震作用反应谱曲线第 20 页 二、计算分析2.1 抗震计算模型本抗震计算分析采用MIDAS/Civil程序进行，建立全桥模型，考虑上部箱梁自重及二期恒载。模型考虑边界条件的影响，如图2.1所示。图2.1 全桥计算模型2.2 动力特性特征值计算结果2.2.1 抗震模态频率计周期表2-1各模态频率及周期模态号频率周期容许误差(rad/sec)(cycle/sec)(sec)15.0961840.8110831.232920.00E+0029.2409941.470750.6799250.00E+00310.3619211.6491510.6063730.00E+00410.8567771.727910.5787340.00E+00521.4223723.4094760.29330.00E+00622.0528063.5098130.2849150.00E+00726.8679634.2761690.2338540.00E+00828.8677774.5944490.2176540.00E+00936.9150075.8752060.1702070.00E+001038.2793396.0923460.164140.00E+001147.5599517.5694010.1321110.00E+001260.688949.6589450.1035310.00E+001361.0043279.709140.1029960.00E+001463.89436710.1691040.0983370.00E+001565.09129910.3596020.0965290.00E+001665.74326510.4633660.0955720.00E+001771.89506811.4424550.0873940.00E+001872.69098111.5691290.0864370.00E+001977.2606212.296410.0813250.00E+002079.3784612.6334740.0791550.00E+002186.83535913.8202770.0723570.00E+002288.04427214.0126810.0713640.00E+002392.16654414.6687610.0681720.00E+0024107.54659417.1165720.0584230.00E+0025121.23597319.2953040.0518260.00E+0026122.93507819.5657250.051110.00E+0027133.18445621.1969650.0471770.00E+0028139.8316622.25490.0449340.00E+0029145.2401523.1156880.0432610.00E+0030146.75250323.3563860.0428150.00E+0031147.23070823.4324950.0426760.00E+0032157.16718725.0139350.0399780.00E+0033159.05062425.3136930.0395040.00E+0034160.63174225.5653360.0391150.00E+0035162.23378825.8203090.0387290.00E+0036164.85379926.2372970.0381140.00E+0037183.02734729.1297070.0343290.00E+0038186.49334829.6813380.0336910.00E+0039198.58769131.6062130.0316390.00E+0040202.10245232.1656040.0310890.00E+0041208.15880933.1295030.0301850.00E+0042225.4931335.8883460.0278640.00E+0043227.50929536.2092290.0276170.00E+0044254.49240140.5037240.0246890.00E+0045272.89295443.4322630.0230240.00E+0046278.40303244.3092190.0225690.00E+0047299.97590347.7426480.0209460.00E+0048303.14074348.2463480.0207270.00E+0049348.90736255.5303310.0180080.00E+0050371.35681959.1032730.016920.00E+0051400.7904763.7877850.0156770.00E+0052458.5593472.9819860.0137020.00E+0053485.69522177.3007950.0129360.00E+0054551.37729187.7544210.0113950.00E+0055556.2490588.5297860.0112960.00E+0056702.134828111.7482290.0089490.00E+0057747.167604118.9154170.0084090.00E+00581000.030642159.159820.0062830.00E+00591215.623595193.4725040.0051690.00E+00601736.296346276.3401460.0036190.00E+002.2.2 阵型参与质量百分比表2-2各振型参与质量百分比模态号TRAN-XTRAN-YTRAN-ZROTN-XROTN-YROTN-Z质量(%)合计(%)质量(%)合计(%)质量(%)合计(%)质量(%)合计(%)质量(%)合计(%)质量(%)合计(%)164.1164.110000003.93.9002064.1120.4720.47008.628.6203.937.9837.9830.0364.14020.475.415.4208.6203.9037.984064.1438.9659.4305.4215.2223.8403.94.4142.3950.0564.19059.4305.42023.8420.224.1042.396064.192.8162.2405.421.1524.98024.120.4862.877064.19062.2436.642.02024.98024.1062.8784.6168.8062.240.0742.09024.980.0324.13062.879068.81062.24042.09024.9828.0352.16062.8710068.813.8166.05042.090.525.48052.162.3765.24114.0472.85066.050.0242.1025.480.0852.24065.2412072.851.6867.73042.12.0427.52052.241.1466.3813072.85067.7317.7859.89027.52052.25066.3814072.85067.73059.89027.52052.250.0366.4115072.850.1967.92059.890.0327.55052.255.5171.9216072.855.3773.29059.890.5928.14052.250.6272.5417072.85073.295.0664.95028.143.3255.57072.5418072.86073.296.9971.93028.142.257.77072.54190.0372.89073.290.1972.13028.14057.77072.54201.9374.82073.290.0372.15028.140.1257.88072.5421074.820.1873.46072.15028.14057.880.1472.6822074.82073.46072.15028.1411.8869.76072.6823074.820.9874.44072.15028.14069.761.5374.2124074.82074.4414.6786.83028.14069.76074.2125074.820.274.65086.830.1528.29069.762.0176.22260.0174.83074.650.0186.84028.297.0776.83076.22273.6578.48074.650.0186.85028.290.3777.19076.22283.7582.23074.65086.85028.290.3677.56076.2229082.234.9279.57086.854.2932.58077.560.0176.23300.0282.25079.570.6387.48032.58077.56076.2331082.250.1279.69087.480.5333.11077.562.2578.4832082.250.0779.75087.480.934.01077.561.4979.9733082.25079.75087.48034.01077.560.038034082.25079.75087.48034.010.177.6608035082.25079.75087.48034.01077.660.0380.0236082.26079.75087.49034.010.2677.93080.0237082.261.9781.73087.490.8834.89077.931.4481.4738082.260.9782.7087.490.5535.44077.930.9682.4339082.26082.7087.490.5435.97077.930.4582.88400.0382.28082.7087.49035.970.7678.69082.88412.4884.76082.7087.49035.970.3779.06082.88420.0984.86082.70.0687.55035.970.1779.23082.8843084.860.0782.77087.550.0936.06079.230.483.2844084.860.8383.6087.551.9838.05079.230.7884.0645084.861.0284.62087.551.7539.79079.230.484.46460.3585.21084.620.0587.6039.790.179.33084.4647085.210.0984.71087.60.0139.8079.330.2984.75480.9486.14084.710.0387.63039.80.2379.56084.7549086.141.1585.86087.631.0940.89079.560.0884.83502.0488.19085.860.0287.64040.890.7680.32084.8351088.192.3988.25087.646.3147.21080.320.1684.99523.3691.55088.250.0387.67047.211.281.52084.9953091.553.5191.76087.679.3656.57081.520.2585.24546.898.35091.760.0187.68056.574.7586.27085.2455098.355.7697.53087.6828.9285.49086.270.1485.3856098.351.2698.78087.684.6490.13086.270.2185.58571.1799.52098.780.0387.72090.130.9487.21085.5858099.520.7499.53087.72393.12087.210.0385.62590.4799.99099.530.0287.74093.120.5187.73085.6260099.990.4799.99087.740.0393.15087.730.9886.62.2.3 周期与阵型图图2.2 第一阶振型（顺桥向一致平动）图2.3第二阶振型(竖向一阶对称)图2.4第三阶振型(横桥向一致平动)图2.5第四阶振型(竖向一阶反对称)2.3 E1地震作用下计算结果根据模型计算结果，组合采用抗震规范规定，对恒载和地震力进行系数为1的组合，并且，纵横向不同时组合，计算结果如表2-32-4所示：表2-3 E1作用下1#主墩底内力计算结果 (单位：kN.m)位置荷载轴向(kN)剪力-y(kN)剪力-z(kN)扭矩 (kN.m)弯矩-y (kN.m)弯矩-z (kN.m)墩底恒载+纵向反应谱-8024.28735.17214.4225.441286.515605.33墩底恒载+横向反应谱-7977.180520.3503032.350表2-4 E1作用下2#主墩底内力计算结果 (单位：kN.m)位置荷载轴向(kN)剪力-y(kN)剪力-z(kN)扭矩 (kN.m)弯矩-y (kN.m)弯矩-z (kN.m)墩底恒载+纵向反应谱-8017.45825.41-257.62389.2-1545.726122.19墩底恒载+横向反应谱-7969.50155.110834.30由于1#、2#主墩配筋一致，墩身配筋均为7028 HRB335，故取上表1#、2#中最不利内力值进行强度验算。计算长度L0=1.2L（L为柱高），强度验算结果如2-52-6所示：表2-5 E1地震作用2#主墩纵向强度验算表 (单位：kN.m)偏心受压构件正截面抗压承载力验算Md (kNm)6122Nd (kN)801711.000e0=Md/Nd0.76421.000e=es1.454偏心距增大系数1.000e=es0.074受压区高度 x (m)0.688相对受压区高度=x/h00.478受压区高度x 确定：fcdbx(es-h0+x/2)=sAses-fsdAses （式中 s=fsd） 采用大偏心受压构件计算结果钢筋应力s=fsd (MPa)280x=0.68842a=0.12满足规范5.2.2-4、5要求0Nd8017.0满足规范要求公式5.3.5-15.3.5-1右33247.80Nde11653.7满足规范要求公式5.3.5-25.3.5-2右48330.0表2-6 E1地震作用1#主墩横向强度验算表 (单位：kN.m)偏心受压构件正截面抗压承载力验算Md (kNm)3032Nd (kN)797710.549e0=Md/Nd0.38021.000e=es1.820偏心距增大系数1.000e=es-1.060受压区高度 x (m)2.561相对受压区高度=x/h00.871受压区高度x 确定：fcdbx(es-h0+x/2)=sAses-fsdAses （式中 s=fsd）采用小偏心受压构件验算结果0Nd7977.2满足规范要求公式5.3.5-15.3.5-1右60604.90Nde14519.5满足规范要求公式5.3.5-25.3.5-2右110308.6e1.060满足规范要求公式5.3.5-40Nde8454.85.3.5-4右114258.9由以上计算可知，在E1地震作用下，1#、2#桥墩强度均满足规范要求。2.4 E2地震作用验算结果2.4.1 墩柱有效抗弯刚度计算根据抗震规范6.1.6条：E1地震作用下，常规桥梁的所有构件抗弯刚度均按毛截面计算；E2地震作用下，延性构件的有效截面抗弯刚度应按（6.1.6）计算，但其他构件抗弯刚度仍按毛截面计算。根据B.0.1，对于矩形截面，截面屈服曲率可按下式计算。其中，钢筋屈服时的应变。 顺桥向：，横桥向：，纵向屈服弯矩：截面调整系数：横向屈服弯矩：截面调整系数：2.4.2桥墩内力计算结果表2-7 E2作用下1#主墩底内力计算结果 (单位：kN.m)位置荷载轴向 (kN)剪力-y (kN)剪力-z (kN)扭矩 (kN.m)弯矩-y (kN.m)弯矩-z (kN.m)墩底恒载+纵向反应谱-8223.60764.1804306.120墩底恒载+横向反应谱-8324.371558.65-64.4215.47-386.549840.81表2-8 E2作用下2#主墩底内力计算结果 (单位：kN.m)位置荷载轴向 (kN)剪力-y (kN)剪力-z (kN)扭矩 (kN.m)弯矩-y (kN.m)弯矩-z (kN.m)墩底恒载+纵向反应谱-8236.2601889.22011201.170墩底恒载+横向反应谱-8323.222742.2779.732831.71478.3816052.22.4.3 墩身屈服弯矩计算及是否进入塑性工作的判定屈服弯矩计算采用Midas程序进行计算，1#、2#桥墩墩身配筋均为7028 HRB335，保护层厚度均为6.0cm，箍筋均为12 HRB335，间距为10cm，由上述内力计算表格可知，最不利截面均出现在墩底，墩底屈服弯矩计算结果如下：1、桥墩的纵向M-曲线。图2.6桥墩纵向M-曲线2、桥墩横向M-曲线图2.7桥墩横向M-曲线表2-9 墩身屈服判断表类别桥墩纵向桥墩横向E2作用下墩身最大弯矩(kN*m)11201.1716052.2初始屈服弯矩(kN*m)12502.7023915.3由上表可知在E2地震作用下各墩墩底铰区均未进入塑性工作范围。2.4.4 墩身能力保护构件计算抗震细则规范6.2.1条，钢筋混凝土墩柱梁桥在抗震设计时，墩柱宜作为延性构件设计。桥梁基础、盖梁、梁体和节点宜作为能力保护构件设计。墩柱的抗剪强度宜按能力保护原则设计。根据抗震细则规范6.8条，公式（6.8.2-1）有：顺桥向： 其中：；，代入上式可得。 公式（6.8.2-3）有：横桥向： 其中：；，代入上式可得。根据抗震细则7.3.4条规定，墩柱塑性铰区域顺桥向和横桥向的斜截面抗剪强