桥梁工程课程设计 预应力混凝土简支小箱梁桥预应力混凝土简支小箱梁桥设计计算书.doc

桥梁工程课程设计预应力混凝土简支小箱梁桥设计计算书姓 名： 学 号： 班 级： 指导教师： 成 绩： 二一二年七月第一章 设计依据1公路钢筋混凝土及预应力混凝土桥涵设计规范（jtg d62-2004）（以下简称公预规）2公路桥涵设计通用规范（jtg d60-2004）（以下简称桥规)3公路工程技术标准（jtg b012003）第二章 设计资料及上部结构主要尺寸2.1 设计资料1. 桥梁跨径及桥宽标准跨径：35 m；主梁全长：34.94 m；计算跨径：34.19 m；桥面宽度：0.5 m （防撞栏杆）+15.9（净行车道宽度）m + 0.5 m（防撞栏杆） = 16.9 m。分幅：单幅行车方向：单向行车2. 设计荷载公路-i级，无人群荷载，单侧防撞护栏重7.8 kn/m。3. 材料及工艺混凝土：小箱梁梁的预制部分及现浇接缝部分均采用c50（容重为26 kn/m3）；铺装层为10cm厚沥青混凝土混凝土（容重为24kn/m3）；沥青铺装层下设置8cm厚的c40防水混凝土调平层（容重为25kn/m3）。预应力钢筋：钢绞线，mpa，单根面积140mm2。普通钢筋：直径12 mm采用hrb335钢筋；直径0.5377 2号梁图2-6按照2车道加载0.67*0.862=0.57750.4744 3号梁按照2车道加载0.67*0.8163=0.54690.3948根据对称性关系3.2.2 支座处用杠杆原理法1号梁图2-72号梁图2-83号梁图2-9根据对称性关系 表3-4 各梁横向分布系数梁号跨中支座10.88591.078920.8621.132330.81631.132340.8621.132350.88591.07893.2.2 活载计算 荷载值 折减系数 0.67 1号梁 弯矩横向分布系数图2-10剪力横向分布系数图2-11支座处 弯矩m=0 剪力图2-12q=1.143*1.0789*300*0.67+1.143*（0.5*（1.0789*1+0.8859*0.8571）*34.19/7+0. 8859*0.5*6*34.19/7）*10.5*0.67=388.35kn1/8跨处 弯矩图2-13 m=1.143*0.8859*3.74*300*0.67+1.143*0.8859*0.5*3.74*34.19*10.5*0.67=1216.64剪力图2-14 q=1.143*0.91*300*0.67+1.143*（0.5*（0.91*0.875+0.8859*0.8571）*0.61+0.8859*0.5*6*34.19/7）*10.5*0.67=317.26kn 1/4跨处弯矩图2-15m=1.143*0.8859*6.41*300*0.67+1.143*0.8859*0.5*6.41*34.19*10.5*0.67=2085.21剪力图2-16q=1.143*0.75*300*0.8859*0.67+1.143*0.8859*0.5*0.75*0.75*34.19*10.5*0.67=221.05kn3/8跨处弯矩图2-17m=1.143*0.8859*8.013*300*0.67+1.143*0.8859*0.5*8.013*34.19*10.5*0.67=2606.67 剪力图2-18q=1.143*0.625*300*0.8859*0.67+1.143*0.8859*0.5*0.625*0.625*34.19*10.5*0.67=174.77kn跨中处弯矩图2-19 m=1.143*300*8.5475*0.8859*0.67+1.143*0.5*34.19*8.5475*10.5*0.8859*0.67=2780.55剪力图2-20q=129.37kn2号梁弯矩横向分布系数图2-21剪力横向分布系数图2-22支座处m=0q=398.45kn1/8跨处m=1183.82q=311.84kn1/4跨处m=2028.96q=215.18kn3/8跨处m=2536.35q=170.06kn 跨中处 m=2705.54 q=128.64kn3号梁弯矩横向分布系数图2-23剪力横向分布系数支座处m=0q=392.29kn1/8跨处m=1121.06q=296.35kn1/4跨处m=1923.91q=203.75kn3/8跨处m=2401.88q=161.04kn 跨中处 m=2561.79 q=121.82kn4,5号梁活载内力分别于2，1号梁相同表3-5 各梁活载内力值 梁号 支座处 1/8跨处 1/4跨处 3/8跨处 跨中处m(kn.m)q(kn)m(kn.m)q(kn)m(kn.m)q(kn)m(kn.m)q(kn)m(kn.m)q(kn)10388.351216.64317.262085.21221.052606.67174.772780.55129.3720398.451183.82311.842028.96215.182536.35170.062705.54128.6430392.291121.06296.351923.91203.752401.88161.042561.79121.8240398.451183.82311.842028.96215.182536.35170.062705.54128.6450388.351216.64317.262885.21221.052606.67174.772780.55129.37 3.3内力组合表3-6 1号梁内力组合 1号梁 序号 荷载类别 支座处 1/8跨处 1/4跨处 3/8跨处 跨中处 q m q m q m q m q kn kn.m kn kn.m kn kn.m kn kn.m kn 1 自重 662.77742479497.084248.38331.3925310.8188.8885665.0502 二期恒载 292.49731094219.371874.9146.252343.7783.36022500.103 恒载 955.27483573716.456123.27477.6427654.57272.2488165.1504 活载 388.351216.64317.262085.21221.052606.67174.772780.55129.375 承载力极限状态组合 1,690.005,990.901,303.9010,267.20882.612,834.80571.413,691.00181.16 正常使用短期组合 1,193.104,318.10910.77,400.306139,251.00379.39,868.0079.27 正常使用长期组合 1,091.203,998.80827.56,853.005558,566.80333.49,138.2045.38 正常使用标准组合 1,343.604,789.601,033.708,208.50698.710,261.2044710,945.70129.4表3-7 2号梁内力组合 2号梁 序号 荷载类别 支座处 1/8跨处 1/4跨处 3/8跨处 跨中处 q m q m q m q m q kn kn.m kn kn.m kn kn.m kn kn.m kn 1 自重 671.662512.02503.7464305.36335.8385382.04191.4185741.0402 二期恒载 292.51093.93219.3711874.9146.2512343.7783.35872500.103 恒载 964.163605.95723.1186180.25482.0897725.81274.7778241.1404 活载 398.451183.82311.842028.96215.182536.35170.062705.54128.645 承载力极限状态组合 1,714.805,984.501,304.3010,256.80879.812,821.90567.813,677.10180.16 正常使用短期组合 1,208.204,330.90914.17,422.80613.99,279.10378.99,898.1078.87 正常使用长期组合 1,103.604,020.20832.26,890.30557.48,613.40334.39,188.00458 正常使用标准组合 1,362.604,789.801,035.008,209.20697.310,262.20444.810,946.70128.6表3-8 3号梁内力组合 3号梁 序号 荷载类别 支座处 1/8跨处 1/4跨处 3/8跨处 跨中处 q m q m q m q m q kn kn.m kn kn.m kn kn.m kn kn.m kn 1 自重 671.662512.02503.7464305.36335.8385382.04191.4185741.0402 二期恒载 292.51093.93219.3711874.9146.2512343.7783.35872500.103 恒载 964.163605.95723.1186180.25482.0897725.81274.7778241.1404 活载 392.291121.06296.351923.91203.752401.88161.042561.79121.825 承载力极限状态组合 1,706.205,896.601,282.6010,109.80863.812,633.60555.213,475.90170.56 正常使用短期组合 1,204.404,292.50904.67,358.50606.99,196.80373.49,810.0074.67 正常使用长期组合 1,101.403,998.30826.86,853.50553.48,566.40331.19,137.7042.68 正常使用标准组合 1,356.504,727.001,019.508,104.20685.810,127.70435.810,802.90121.8第四章 预应力钢筋估束和布置4.1 预应力钢束的估束 由于边梁的内力最大，所以预应力钢筋的布置一边梁为准，其他梁预应力布置与边梁相同。对于预应力钢筋混凝土简支梁桥，控制结构设计的通常是抗裂性验算。因而，可按照抗裂性验算原则完成估束工作。根据公路钢筋混凝土及预应力混凝土桥涵设计规范jtg d62-2004的第6.3.1条(p58)规定：全预应力混凝土构件，在作用(或荷载) 短期效应组合下预制构件： (4-1)式中，为作用(或荷载) 短期效应组合下构件抗裂验算边缘混凝土的拉应力，为扣除全部预应力损失后预加力在构件抗裂验算边缘产生的预压应力。本课程设计，抗裂验算边缘为截面下边缘。根据材料力学知识，作用(或荷载) 短期效应组合下构件抗裂验算边缘混凝土的拉应力按下式求得 (4-2)其中，是弯矩短期效应组合值，是毛截面抗弯惯性矩，是下边缘距截面中性轴的距离。 预加力在构件抗裂验算边缘产生的预压应力的计算按如下方式计算。将预加力等效为作用在截面中性轴位置处的轴力和一外加弯矩，如图4-1所示。图4-1 预加力等效则，预加力在构件抗裂验算边缘产生的预压应按下式计算 (4-3)上式中，是毛截面面积，是预应力钢绞线合力作用点距截面中性轴的距离，和的定义与式(4-2)一致，是预加力，按下式计算 (4-4)其中，和分别为预应力钢束的有效预应力和面积。将式(4-2)(4-4)代入式(4-1)，并将式(4-1)取等号，得到预应力钢束面积估算公式 (4-5)上式中，预应力钢束的有效预应力及预应力钢绞线合力作用点距截面中性轴的距离需要预先假定。一般而言，对于的预应力钢绞线的控制张拉应力取，在估束阶段，根据经验，考虑25%的预应力损失，则有效预应力的估计值为。对于跨中截面，可假设预应力钢绞线合力作用点距截面下边缘18cm进行试算。代入4-5得选配12束5f15.2的钢束实际 图4-1 预应力钢束布置图 表4-1 钢束尺寸钢束号长度（cm）半径（m）弯起角度（） 钢束中心到梁底距离支座处1/8截面处1/4截面处3/8截面处跨中处n11738.043000212.59999n21739.98300075211.02999n31740.34450077429.32202020n41740.69600079649.7231.093131n51741.067500711870.4145.074242n61741.429000714091.6861.725353表4-2 截面特性计算点截面积（）截面重心至底面（mm）wn()梁自重弯矩（kn.m）in（）i（）截面重心至到钢束质心距离（mm）跨中1372504.51418645.71188.61158.84.526*1085665.055.38*10115.76*1011915.6885.81/8跨1372504.51418645.71188.61158.84.526*1085310.85.38*10115.76*1011915.6885.81/4跨1372504.51418645.71188.21159.14.545*1084248.385.40*10115.76*1011895.2866.13/8跨1372504.51418645.71185.31160.84.606*10824795.46*10115.72*1011750725.5支点1599504.51645645.711051097.35.620*10806.21*10116.17*1011284276.34.2 预应力损失计算4.2.1磨阻损失表4-3 计算表计算点钢束 x （）（rad）mmpa跨中n130.0523617.380.0375890.03689151.46314n270.1221717.380.0529470.0515771.94013n370.1221717.380.0529470.0515771.94013n470.1221717.380.0529470.0515771.94013n570.1221717.380.0529470.0515771.94013n670.1221717.380.0529470.0515771.940131/8跨n130.0523613.0050.0310260.0305542.61719n270.1221713.0050.0463850.04532563.229n370.1221713.0050.0463850.04532563.229n470.1221713.0050.0463850.04532563.229n570.1221713.0050.0463850.04532563.229n670.1221713.0050.0463850.04532563.2291/4跨n130.052368.630.0244640.02416733.71299n270.122178.630.0398220.0390454.46051n370.122178.630.0398220.0390454.46051n46.680.116598.630.0385940.03785852.81241n55.360.093558.630.0335250.0329745.99255n64.480.078198.630.0301460.02969741.426743/8跨n130.052364.630.0184640.01829425.52072n24.930.086044.630.0258740.02554235.63166n33.310.057774.630.0196540.01946227.14981n42.590.04524.630.016890.01674823.36313n52.010.035084.630.0146630.01455620.30513n61.670.029154.630.0133570.01326818.50933支点n1000.120.000180.000180.251077n2000.120.000180.000180.251077n3000.120.000180.000180.251077n4000.120.000180.000180.251077n5000.120.000180.000180.251077n6000.120.000180.000180.2510774.2.2 由锚具变形及钢束回缩引起的预应力损失按公预规计算公式如下反向摩擦影响长度：其中 为预应力钢筋扣除磨阻损失后锚固端应力 l 为张拉端至锚固端的距离 在反影响长度内，距张拉端x处的锚具变形、钢筋回缩损失：；在反影响长度外，锚具变形、钢筋回缩损失：表4-4 计算表计算点钢束影响长度xmpammmmmpa跨中n10.00296119877.861738014.79261n20.00413916812.5173800n30.00413916812.5173800n40.00413916812.5173800n50.00413916812.5173800n60.00413916812.51738001/8跨n10.00327718895.381300538.6054n20.00486215512.791300524.38526n30.00486215512.791300524.38526n40.00486215512.791300524.38526n50.00486215512.791300524.38526n60.00486215512.791300524.385261/4跨n10.00390617306.12863067.78631n20.00631113616.25863062.93248n30.00631113616.25863062.93248n40.0061213827.08863063.60836n50.00532914816.81863065.94368n60.004815611.98863067.031433/8跨n1k0.00551214569.244630109.5709n20.00769612330.074630118.5167n30.00586414125.384630111.3597n40.00504615227.134630106.9469n50.00438616333.554630102.6532n60.00399817107.56463099.76298支点n10.00209223647.212098.45247n20.00209223647.212098.45247n30.00209223647.212098.45247n40.00209223647.212098.45247n50.00209223647.212098.45247n60.00209223647.212098.452474.2.3 钢筋松弛引起的预应力损失 表4-5 计算表计算点钢束平均cosmpampampa/mm跨中n11328.74412.75e-061.061,255.6873.07n21323.0612.75e-061.061,250.3072.76n31323.0612.75e-061.061,250.3072.76n41323.0612.75e-061.061,250.3072.76n51323.0612.75e-061.061,250.3072.76n61323.0612.75e-061.061,250.3072.761/8跨n11313.77712.75e-061.061,241.5372.25n21307.38612.75e-061.061,235.4971.89n31307.38612.75e-061.061,235.4971.89n41307.38612.75e-061.061,235.4971.89n51307.38612.75e-061.061,235.4971.89n61307.38612.75e-061.061,235.4971.891/4跨n11293.5010.99982.70e-061.061,223.6969.81n21277.6070.99982.70e-061.061,208.6568.95n31277.6070.99982.70e-061.061,208.6568.95n41278.5790.99982.70e-061.061,209.5769.01n51283.0640.99982.70e-061.061,213.8169.25n61286.5420.99982.70e-061.061,217.1069.443/8跨n11259.9080.99772.36e-061.051,200.2259.69n21240.8520.99772.36e-061.051,182.0758.78n31256.4910.99772.36e-061.051,196.9759.52n41264.690.99772.36e-061.051,204.7859.91n51272.0420.99772.36e-061.051,211.7860.26n61276.7280.99772.36e-061.051,216.2460.48支点n11296.2960.99361.13e-061.021,266.2230.08n21296.2960.99361.13e-061.021,266.2230.08n31296.2960.99361.13e-061.021,266.2230.08n41296.2960.99361.13e-061.021,266.2230.08n51296.2960.99361.13e-061.021,266.2230.08n61296.2960.99361.13e-061.021,266.2230.084.2.4 由钢筋应力松弛引起的预应力损失公预规规定，钢绞线由松弛引起的预应力损失的终极值，按下式计算：表4-6 计算表计算点钢束跨中n11,255.6834.3n21,250.3033.59n31,250.3033.59n41,250.3033.59n51,250.3033.59n61,250.3033.591/8跨n11,241.5332.44n21,235.4931.66n31,235.4931.66n41,235.4931.66n51,235.4931.66n61,235.4931.661/4跨n11,223.6930.14n21,208.6528.25n31,208.6528.25n41,209.5728.36n51,213.8128.89n61,217.1029.313/8跨n11,200.2227.2n21,182.0724.99n31,196.9726.8n41,204.7827.77n51,211.7828.64n61,216.2429.2支点n11,266.2235.71n21,266.2235.71n31,266.2235.71n41,266.2235.71n51,266.2235.71n61,266.2235.714.2.5 混凝土收缩徐变引起的预应力损失 根据公预规规定，由混凝土收缩徐变引起的预应力损失可按下式计算：其中支座处跨中处 表4-7 计算表计算点钢束mpampa跨中n127.07259.872.87206.55n226.94258.852.87205.74n326.94258.852.87205.74n426.94258.852.87205.74n526.94258.852.87205.74n626.94258.852.87205.741/8跨n126.74257.22.87204.43n226.6256.062.87203.52n326.6256.062.87203.52n426.6256.062.87203.52n526.6256.062.87203.52n626.6256.062.87203.521/4跨n125.82249.722.79199.66n225.48246.932.79197.43n325.48246.932.79197.43n425.5247.12.79197.57n525.6247.892.79198.19n625.67248.52.79198.683/8跨n122.13219.542.26182.4n221.77216.612.26179.97n322.07219.012.26181.97n422.22220.282.26183.01n522.36221.412.26183.95n622.45222.132.26184.55支点n111.46125.51.2113.29n211.46125.51.2113.99n311.46125.51.2113.99n411.46125.51.2113.29n511.46125.51.2113.29n611.46125.51.2113.29 表4-8 钢束预应力损失一览表 计算点钢束 预加应力阶段 正常使用阶段锚固前的预应力损失锚固时的预应力损失锚固后的预应力损失钢束有效应力12456跨中n151.4631414.7926173.071,255.6834.3206.551,014.83n271.94013072.761,250.3033.59205.741,010.97n371.94013072.761,250.3033.59205.741,010.97n471.94013072.761,250.3033.59205.741,010.97n571.94013072.761,250.3033.59205.741,010.97n671.94013072.761,250.3033.59205.741,010.971/8跨n142.6171938.605472.251,241.5332.44204.431,004.66n263.22924.3852671.891,235.4931.66203.521,000.31n363.22924.3852671.891,235.4931.66203.521,000.31n463.22924.3852671.891,235.4931.66203.521,000.31n563.22924.3852671.891,235.4931.66203.521,000.31n663.22924.3852671.891,235.4931.66203.521,000.311/4跨n133.7129967.78631