预应力混凝土简支小箱梁桥设计

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O二年七月第一章 设计依据第二章 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： 35m；主梁全长：34.94 m；计算跨径：34.19 m；桥面宽度：05m （防撞栏杆）+15.9 （净行车道宽度）m+ 0.5m （防撞栏杆） =16.9 m。分幅：单幅行车方向：单向行车2. 设计荷载3 材料及工a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/m）；沥青铺装层下设置8cm厚的C4（防水混凝土调平层（容重为 25kN/m）。预应力钢筋：si5.2钢绞线，f1860MPa，单根面积140mmpk普通钢筋：直径三12 m采用HRB33钢筋；直径12m采用R235钢筋。工艺：主梁按后张法施工工艺制作，采用内径 55 mr的预埋波纹管 和夹片式锚具。2.1 、基本尺寸图2-1nw平观（中梁）I - r11（中栗）口一时中梁）八判 5!ZJCO,12.5*10CO15門些卜冋允 卜1M/2 囲】叮gJ严艮叫00/2 _1皿/2 胃7平年中梁截面特性：A=1.38 m2；I =0.548 m4 ；xI T 0.849m 4； 中心点到底面的距离 y=1.16m。图2-3边梁截面特性：A=1.401m2 ；I =0.552m 4 ；xI0.899m4 ；T中心点到底面的距离y=1.17m。第三章 内力计算3.1 恒载计算1号梁一期恒载 梁体自重及横隔板：q 26* 1.4011628* 31-401*(17.095 3)13.56* 0.2* 2 *261.64* 0.2* 3 *261217.095347938.77kN / m二期恒载 防撞栏杆：q 7.8* 2 /53.12kN / m2铺装层：q3(15.9* 24* 0.1 25* 0.08 *15.9)13.99kN / mq q 17.11kN / m23总恒载：q q q2 q32号梁防撞栏杆：55.88kN / mq 7.8* 2 /53.12kN / m1铺装层：q2(15.9* 24* 0.125* 0.08*15.9)/513.99kN / mq q1 q217.11kN /m梁体自重及横隔板：q 26* 1.381.628 * 3 1.38* (17.095 3)132-17.0954.99* 0.2 * 2 *262.9* 0.2* 26 * 3341939.29kN / mq q q q 56.4kN /m表3-1 1231号梁恒载表1号梁支座处1/8跨处1/4跨处3/8跨处跨中处QMQMQMQMQ序号荷载类别kNkN.mkNkN.mkNkN.mkNkN.mkN1自重662.77742479497.018424833331.39；25310.3188.8885665.052二期恒载292.49731094219371874)1462j2343.7783.36022500.13恒载955.27483573716456123.27477.64；27654.57272.2488165.15000表3-22号梁恒载表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QMQMQMQMQkNkN.mkNkN.mkNkN.mkNkN.mkN1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964.163605.95723.1186180.25482.0897725.81274.7778241.140表3-33号梁恒载表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QMQMQMQMQkNkN.mkNkN.mkNkN.mkNkN.mkN1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964.163605.95723.1186180.25482.0897725.81274.7778241.1403.2 活载计算3.2.1 横向分布系数计算3.2.1.1 跨中处用刚接板法1号梁活载计算图2-5mcqi 0.5* (0.31020.28040.25780.227 0.20640.1809 0.16430.1448)0.936按照2车道加载 m 0.5* (0.31020.2804 0.2578 0.227)0.5377cq1067*0.936053772号梁图2-6m 0.5* (0.24380.2410.23690.2270.21680.19980.18760.1711)0.8620cq 2按照2车道加载 m 0.5* (0.24380.2410.23690.227)0.4744cq10.67*0.862=0.57750.47443号梁mcq 30.5* (0.18620.19440.20050.2085 0.21280.21500.21140.2038)0.8163按照2车道加载 m 0.5* (0.18620.1944 0.2005 0.2085)0.3948cq10.67*0.8163=0.54690.3948根据对称性关系mm0.8620cq4cq2mm0.8859cq5cq13.2.2 支座处用杠杆原理法1号梁图2-7m0 qi 0.5 *(1.20540.66970.2827)1.07892号梁图2-8m0q 20.5 * (0.08820.6176 10.4706 0.0882)1.13233号梁图2-9m0q30.5*(0.08820.6176 1 0.4706 0.0882)1.1323根据对称性关系叫 q 4 m01-1323m0q5m0q11.0789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 q 10.5kN / m kP 300kN k折减系数 0.671号梁r n El 3.143.45 * 1010*0.548,f 2 c - 2.45HZ2l2 mc 2 * 34.19 丫 56970.1767 In f 0.01570.143弯矩横向分布系数图 2-100.8859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=388.35kN 1/8 跨处弯矩图2-13M=1143*08859*3.74*300*0.67+1.143*0 8859*0 5*3 74*34 19*10 5*067 =1216.64 kN.m剪力图 2-140.125Q=1 143*091*300*0.67+1.143*(0.5* (091*0875+08859*0.8571)*061+08859*0.5*6*34.19/7) *10.5*0.67=31726kN1/4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 kN.m剪力图2-16Q=1.143*0.75*300*0.8859*0 67+1 143*0.8859*05*075*0.75*34.19*10.5 *0.67=221 05Kn3/8跨处弯矩图 2-178-013M=1 143*0.8859*8.013*300*0.67+1.143*0.8859*0.5*8.013*34.19*10.5*0.67=260 6.67 kN.m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 2-199.5475M=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 kN.m剪力图2-20支座处M=0Q=398.45kN1/8 跨处M=1183.82kN.mQ=311.84kN1/4 跨处M=2028.96kN.mQ=215.18kN3/8 跨处M=2536.35kN.mQ=170.06kN跨中处M=2705.54kN.mQ=128.64kN3号梁弯矩横向分布系数 图2-23支座处M=0Q=392.29kN1/8 跨处M=1121.06kN.m Q=296.35kN1/4 跨处M=1923.91kN.m Q=203.75kN3/8 跨处M=2401.88kN.m Q=161.04kN跨中处M=2561.79kN.mQ=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M(kN.m)Q(kN)M(kN.m)Q(kN)M(kN.m)Q(kN)M(kN.m)Q(kN)M(kN.m10388.351216.64317.262085.21221.052606.67174.77278020398.451183.82311.842028.96215.182536.35170.06270530392.291121.06296.351923.91203.752401.88161.04256140398.451183.82311.842028.96215.182536.35170.06270550388.351216.64317.262885.21221.052606.67174.7727803.3内力组合表3-61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QMQMQMQMQkNkN.mkNkN.mkNkN.mkNkN.mkN1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3-72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QMQMQMQMQkNkN.mkNkN.mkNkN.mkNkN.mkN1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止常使用标准组合1,362.604,789.801,035.008,209.20697.310,262.20444.810,946.70128.6表3-83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QMQMQMQMQkNkN.mkNkN.mkNkN.mkNkN.mkN1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JTGD62-2004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)0.850st pc式中，戏为作用（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戏按下式求得Ms y(4-2)stb其中，M st是弯矩短期效应组合值，1 是毛截面抗弯惯性矩，人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。Ne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pc按下式计算pcN Ne一 一yb pc A I b0 0(4-3)上式中，A0是毛截面面积，e是预应力钢绞线合力作用点距截面中性轴的距离，Io和人的定义与式(4-2)致，N是预加力，按下式计算N Aeff p(4-4)其中，eff和Ap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Mst yI bAopeff0.85eytAb00(4-5)上式中，预应力钢束的有效预应力ef及预应力钢绞线合力作用点距截面中性轴的距离e需要预先假定。一般而言，对于fpk 1860MPa的预应力钢绞线的控制张拉应力取con .75 fpk 0.75 1860 1395MPa，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 eff 0.75 con 0.75 1395 1046MPa 。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 18c m进行试算。M 10459.8kN .m st预应力钢束布置图I0.552m 20yb 1.17me 0.99m代入4-5得 Ap 8365mm2 选配 12束5 15.2的钢束 实际 Ap 8400mm 2 图4-1表4-1钢束尺寸钢 束口号长度(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N11738.043000212.5999.9N21739.98300075211.02999N31740.34450077429.32202020N41740.69600079649.7231.093131N51741.067500711870.4145.074242N61741.429000714091.6861.725353计算占八、截面积（mm2）截面重心至底面（mm）wn（ mm 3）梁自重弯矩（kN.m）In（mm4）I0（mm4）截面重心至到钢束质心距离（mmAnA0yny0ene0跨中1372504.51418645.71188.61158.84.526*10八85665.055.38*10T15.76*10A11915.6885.81/8跨1372504.51418645.71188.61158.84.526*10八85310.85.38*10T15.76*10A11915.6885.81/4跨1372504.51418645.71188.21159.14.545*10八84248.385.40*10A115.76*10A11895.2866.13/8跨1372504.51418645.71185.31160.84.606*10八824795.46*10T15.72*10A11750725.5支点1599504.51645645.711051097.35.620*10八806.21*10A116.17*10A11284276.34.2 预应力损失计算4.2.1磨阻损失(1 e ( x) )l1 con0.00150.221395MPaconl1 计算表表4-3计算点钢束exx1 e ( X)(1e(x)con（）(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N130.052368.630.0244640.02416733.71299N270.122178.630.0398220.0390454.46051N370.122178.630.0398220.0390454.46051N4& 680.116598.630.0385940.03785852.81241N55360.093558.630.0335250.0329745.99255N64.480.078198.630.0301460.02969741.426743/8跨N130.052364.630.0184640.01829425.52072N24.930.086044.630.0258740.02554235.63166N33310.057774.630.0196540.01946227.14981N42.590.04524.630.016890.01674823.36313N52.010.035084.630.0146630.01455620.30513N61.670.029154.630.0133570.01326818.50933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 l2按公预规12计算公式如下反向摩擦影响长度：1I * EIpfdl 6mm0 IlE 1.95*10 5MPa p其中 01395MPaI为预应力钢筋扣除磨阻损失后锚固端应力I为张拉端至锚固端的距离2 II 2d f在反影响长度内，距张拉端X处的锚具变形、钢筋回缩损失:I 20I2 2d(l f x)在反影响长度外，锚具变形、钢筋回缩损失:计算占八、钢束d影响长度XI 2MPaMPammmm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 93248N40.0061213827.08863063.60836N50.00532914816.81863065.94368表4-4I 2计算表N60.004815611.98863067.031433/8跨N1k0.00551214569.244630109.5709N20.00769612330.074630118.5167N30.00586414125.384630111.3597N40.00504615227.134630106.9469N50.00438616333.554630102.6532N60.00399817107.56463099.76298支点N10.00209223647.212098.45247N20.00209223647.212098.45247N30.00209223647.212098.45247N40.00209223647.212098.45247N50.00209223647.212098.45247N60.00209223647.212098.45247423钢筋松弛引起的预应力损失14n 5.493pA 8400mm2p表牛5|4计算表计算钢束con111 :MPa平均cos1enAn Wn1 JVn A (- cosP P Ann1peMPal4MPa/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-061.021,266.2230.08424由钢筋应力松弛引起的预应力损失15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:1 51.0(0.52-fpePk0.26)pe0.3表牛615计算表计算点钢束MPa )1 5(MPa)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N11,266.2235.71N21,266.2235.71N31,266.2235.71N41,266.2235.71N51,266.2235.71N61,266.2235.71425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:l 60.9* E(t,t )(t,t )p cs 0Ep pc 01 15pep21ppi2其中Ep p1.95*10八5MPa支座处2A232(t,t ) 0.0002136Ep 0(t,t0 ) 1.6276 跨中处2A194u(t,t )0.00022Ep 0 1(t,t0)1.65365.493EpA丄 0.6%An表牛716计算表计算占八、钢束c.9*Epcs(t，t。)Ep pc (g)】p1 6MPaMPa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表牛8钢束预应力损失一览表计算占八、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N151.4631414.7926173.071,255.6834.3206.551,014.83N271.94013072.761,250.3033.59205.741,010.97N371.94013072.761,250.3033.59205.741,010.97N471.94013072.761,250.3033.59205.741,010.97N571.94013072.761,250.3033.59205.741,010.9733.591,010.97N671.94013072.761,250.30205.741/8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N133.7129967.7863169.811,223.6930.14199.66993.89N254.4605162.9324868.951,208.6528.25197.43982.97N354.4605162.9324868.951.208.6528.25197.43982.97N452.8124163.6083669.011,209.5728.36197.57983.641. = = =N545.9925565.9436869.251,213.8128.89198.19986.73N641.4267467.0314369.441,217.1029.31198.68989.113/8跨N125.52072109.570959.691,200.2227.2182.4990.62N235.63166118.516758.781,182.0724.99179.97977.11N327.14981111.359759.521,196.9726.8181.97988.2N423.36313106.946959.911,204.7827.77183.01994N520.30513102.653260.261,211.7828.64183.95999.19N618.5093399.7629860.481,216.2429.2184.551,002.49支点N10.25107798.4524730.081,266.2235.71113.291,117.22N20.25107798.4524730.081,266.2235.71113.291,117.22N30.25107798.4524730.081,266.2235.71113.291,117.22N40.25107798.4524730.081,266.2235.71113.291,117.22N50.2