【《某预应力混凝土T梁桥主梁截面承载力与应力验算计算过程案例》4400字（论文）】

某预应力混凝土T梁桥主梁截面承载力与应力验算计算过程案例目录TOC\o"1-3"\h\u31666某预应力混凝土T梁桥主梁截面承载力与应力验算计算过程案例 1166841.1.设计基本资料及构造布置 3159851.1.1设计资料 322931.1.2主要材料 382231.1.3相关设计参数 3321151.1.4结构设计 4102911.1.5截面几何特性计算 4241292主梁截面承载力与应力验算 7271162.1持久状况承载能力极限状态承载能力验算 734362.2持久状况正常使用极限状态抗裂性验算 1243102.3持久状况构件应力计算 20144702.4短暂状态构件的应力验算 291.1.设计基本资料及构造布置1.1.1设计资料1.设计资料标准跨径：50m(墩中心距)。计算跨径：49.56m。主梁全长：49.96m。桥面宽度（桥面净空）：净-11+2×1(人行道)。2.技术标准设计时速：40km/h。环境标准：I类环境条件设计安全等级：二级。1.1.2主要材料1.混凝土主梁采用C50混凝土；铰缝为C30细集料混凝土；桥面铺装采用沥青混凝土；栏杆及人行道板为C25混凝土；盖梁、墩柱用C30混凝土；桥台基础用C20混凝土；桥台台帽用C25混凝土。2.预应力钢筋：采用高强度低松驰7丝捻制的预应力钢绞线，公称直径为12.7mm，公称面积为98.7，标准强度，弹性模型Ep=1.95105MPa1.非预应力钢筋：采用HPB300；HRB400。4.施工工艺：按后张法施工工艺制作主梁，采用金属波纹管和夹片锚具，两端同时张拉。1.1.3相关设计参数相对湿度为：75%。体系整体均匀升温25℃，均匀降温23℃。预应力管道采用钢波纹管成形，管道摩擦系数μ=0.25。管道偏差系数。锚具变形和钢束回缩量为6mm(单端)。预应力混凝土结构重度按计，普通钢筋混凝土重度按计，沥青混凝土重度按计。单侧人行道和栏杆线荷载分别为1.6和1.52。1.1.4结构设计基本要求（1）本设计图中，主梁各部分构造尺寸所对应构件温度为℃。（2）本设计为预应力简支T形梁。（3）桥面板横坡坡度假定为和桥面横坡度相同，为1.5%。（4）主梁断面：主梁高度2.5m，粱间距2.6m，其中预制梁宽度1.6m，翼缘板中间接缝宽度0.4m。主梁跨中肋厚0.20m，马蹄宽为0.36m，端部腹板厚度加厚到与马蹄同宽，即：0.36m以满足端部锚具布置和局部应力需要。（5）横隔梁设置：横隔梁共设置四道，间距9.79m，端横隔梁宽度0.28m，跨中横隔梁宽度0.18m。（6）桥面铺装：设计总厚度为17cm，其中水泥混凝土厚度8cm，沥青混凝土厚度9cm，两者之间加设防水层。1.1.5截面几何特性计算图3-1横断面图（尺寸单位cm）图3−2预应力混凝土T形梁结构尺寸图（尺寸单位cm）内梁立面b）外梁立面c）3−3T形梁段截面尺寸图3−4T形梁中截面尺寸图表1.1跨中截面几何特性计算表分块名称分块面积分块面积至上缘距离分块面积对上缘静距分块面积的自身惯性矩分块面积对截面形心的惯性矩cm²cmcm³cm4cmcm4cm4大毛截面（含湿接缝）翼板260051300018331.3388.63420425561.4920446396.82三角承托156015.32386815132.4478.3349572496.279587628.71腹板5000110550000142895.83-16.3661339229.781482125.61下三角80194.6715571.3213-101.0364816668.33816881.33马蹄2000225450000416666.76-131.36634514051.913490718.58∑112401052441.367263751.05小毛截面（不含湿接缝）翼板220051100018331.33906.96520684864.720703198.03三角承托156015.32386815132.4486.66511716882.6711732015.11腹板5000110550000142895.83-80.35322806.12514612389.13下三角80197.6715571.3213-92.705687537.362687750.363马蹄2000225450000416666.67-121.03530275222.4530275345.49∑10840652448.878010698.12大毛截面形心至上翼缘距离91.634小毛截面形心至上翼缘距离101.9652主梁截面承载力与应力验算2.1持久状况承载能力极限状态承载能力验算1.正截面承载力验算（1）跨中截面正截面承载力验算 图3.18跨中截面承载力计算图式（单位：cm）本设计计算如下：故中性轴在腹板内。设中性轴到截面上缘距离为x，则式中：——，对于C50及以下混凝土和钢绞线取0.4；——梁的有效高度，，。2）验算正截面承载力正截面承载力计算公式为：式中——1.0；——承载能力极限状态的跨中最大弯矩组合设计值。则上式为：主梁跨中正截面承载力满足要求。四分点截面正截面承载力验算：四分点截面承载力计算图式如图3.19。图3.19四分点正截面承载力计算图式（单位：cm）故中性轴在翼板内。设中性轴到截面上缘距离为x，则式中：——构件的正截面相对界限受压区高度，对于C50及以下混凝土和钢绞线取0.4；——，以四分点为例，=20.15cm。2）验算正截面承载力，正截面承载力计算公式为：则上式为：四分点正截面承载力满足要求。（3）式中；————由此可得最小配筋率满足要求。2.斜截面承载力验算式中：——=1026.69kN（见表3.6）；——；——b=400mm；——取（计算值见表3.9）；则主梁的支点截面尺寸符合要求。（2）截面抗剪承载力验算若满足式则无需进行斜截面抗剪承载力计算。对于距支座中心h/2处截面：b=400mm，，。因此需进行斜截面抗剪承载力计算；斜截面的水平投影此时，其距支座距离为：；箍筋计算预应力混凝土T梁腹板内箍筋直径应不小于10mm，且采用带肋钢筋，间距不应大于250mm，在本设计中选用的双肢箍筋，则箍筋的总面积为；箍筋间距为200，箍筋为HRB335钢筋，其抗拉设计强度为，则箍筋的配筋率为：式中：抗剪承载力计算主梁斜截面抗剪承载力应满足下式的要求；式中：——885.456kN；————=1.0；——=1.25；——=1.1；——此处为379.3mm；——此处为1232.1mm；，当，取；表3.26斜截面受压端正截面处的钢束位置及钢束群重心位置计算表截面钢束号x4R/cm距支座h/2处斜截面顶端N4未弯起1361.164201.00001010.0023.9874N3172.641303.04040.1324900.9911841024.27N2、272.361618.71260.16826570.9857432447.078324.62324.621832.8120.17711580.9841903866.976则上述计算说明主梁距支点h/2处的斜截面抗剪承载力满足要求。（3）斜截面抗弯承载力验算在该设计中由于钢束都在梁端锚固，钢束根数沿梁跨没有变化，配筋率也满足要求，可不必进行该项承载力验算。2.2持久状况正常使用极限状态抗裂性验算正截面抗裂性验算正截面抗裂性验算的计算过程和结果见表3.27。表3.27正截面抗裂性验算计算表应力部位跨中下缘四分点下缘支点下缘1124807.0903110023.55125129.67721034431.4917994.61035880.3310653.73510653.73512112.3354767049.786767357.923929193.4085436501.998435079.041386882.2196245902.00122328073445845253012908=1/311.714510.32710.3319=2/41.34861.196311.1148210=8+913.063411.523611.445611=6/40.320581.60203012=(7-6)/58.45766.09649013=11+128.77827.6985014=13-0.85×10-2.3257-2.09656-9.7288由以上计算可见，各截面的正截面抗裂性均符合的要求斜截面抗裂性验算表3.28（a）跨中截面计算表截面应力部位a-ao-on-nb-b跨中截面1124807.0903124807.0903124807.0903124807.090321034431.41034431.41034431.41034431.4310653.73510653.73510653.73510653.735477554869.7477554869.7477554869.7477554869.74584.74310.61420-37.256667854672.0767854672.0767854672.0767854672.07782.20320-4.3214-32.23682459022459022459022459029344584534458453445845344584510=1/311.714811.714811.714811.714811=2×5/41.30310.141570-24.655312=10-1110.588111.573211.714816.370113=8×5/40.268690.0336500.2766614=(9-8)×7/63.87660-2.04721-15.271615=13+144.145290.03365-2.04721-14.99516=12+1514.733411.60699.66761.3752表3.28（b）四分点截面计算表截面应力部位a-ao-on-nb-b四分点截面1110023.55110023.55110023.55110023.552917994.6917994.6917994.6917994.6310653.73510653.73510653.73510653.735477699593.8377699593.8377699593.8377699593.83584.732110.92550-87.0543667692207.6567692207.6567692207.6567692207.65782.20220-10.9255-82.94381223281223281223281223289253012925301292530129253012910=1/310.32710.32710.32710.32711=2×5/41.00108130.1290801.0285212=10-119.328210.197910.3279.298513=8×5/40.133400.0172010-0.13705614=(9-8)×7/62.923950-0.38862-1.171815=13+143.057350.017201-0.38862-1.034716=12+1512.3832710.21519.93848.2638表3.28（c）支点截面计算表截面应力部位a-ao-on-n1125129.677125129.677125129.67721035880.31035880.31035880.3312112.33512112.33512112.335478091272.3578091272.3578091272.35支点截面575.01728.95840667281216.4867281216.4867281216.48770.05870-8.95848000900010=1/310.3307610.3307610.3307611=2×5/40.99510.1183012=10-119.335710.212510.3307613=8×5/400014=(9-8)×7/600015=13+1400016=12+159.335710.212510.33076表3.29（a）跨中计算表跨中一期恒载短期组合预加力短期组合剪应力0114.80407755869.7467854672.0725上梗肋276192.65—276192.65——341623.74——00.987200.9872净轴297432.74—297432.74——35742.643——00.976200.9762换轴28634.24—28634.24——35142.672——00.974300.9743下梗肋267326.453—26732.453——273243.64——00.372100.3721表3.29（b）四分点计算表四分点一期恒载短期组合预加力短期组合剪应力486.196290.5042776.700277699593.8367692207.6525上梗肋287326.63—287326.63——340314.54——0.65721.73420.87421.2371净轴147069.8322—147069.8322——355742.32——0.69431.74530.94731.2274换轴290438.07—290438.07——350543.27——0.68431.73420.93641.7342下梗肋270342.3—270342.3——262743.62——0.94320.73210.71030.9432表3.29（c）支点计算表支点一期恒载短期组合预加力短期组合剪应力492.429830.2531322.68278091272.3567281216.4840上梗肋292035.98—292035.98——364321.95——0.56780.87320.88640.9378净轴328642.53—328642.53——467823.72——0.65781.78321.07320.9428换轴317423.60—317423.60——367542.67——0.684320.97420.98350.7324下梗肋————————————表3.30计算表截面主应力部位跨中a-a14.73340.9872-0.06585o-o11.60690.9762-0.081365n-n9.66760.9743-0.09328b-b10.28300.3721-0.09423四分点a-a12.383271.2371-0.12238o-o10.21511.2274-0.14541n-n9.93841.2234-0.14838b-b8.26380.9432-0.106286支点a-a9.33570.9378-0.09327o-o10.21250.9428-0.086308n-n10.330760.7324-0.051665由上述计算，最大主拉应力为0.14838，其结果符合的要求。2.3持久状况构件应力计算1.正截面混凝土压应力验算表3.31正截面混凝土法向压应力计算表应力部位跨中上缘跨中下缘四分点上缘四分点下缘支点上缘支点下缘1124807.0903124807.0903110023.55110023.55125129.677125129.67721034431.41034431.48917994.6917994.6125129.677125129.67731653.7351653.7351653.7351653.73512112.33512112.3354767049.7858520880.0321767357.9228522265.9459929193.4075470548.45915717666.7344436501.9979716972.1403435079.0409884187.8902386882.4866245902245902122328122328007146030.19616759616758=1/311.7148711.7148710.327210.327210.330760.33076-1.348581.9858-1.19631.75771-1.114822.2014310=8+910.366313.70469.131912.0849-9.21598.129330.32058-0.472090.15942-0.23423006.8413-0.107915.16104-2.79610013=11+127.1618-0.58005.32046-2.79610014=10+1315.2075813.124614.45269.28889.21598.12933由上表的计算过程和计算结果可以看出，最大压力在跨中截面上缘处，其值为15.20758pMPa，小于16.2MPa，符合要求。2.预应力筋拉应力验算使用阶段预应力筋拉应力应满足式中：表3.322号预应力筋拉应力验算表应力部位跨中四分点支点177699593.8377699593.8378091272.35267854672.0767692207.6567692207.653117.2143107.692704118.327109.30732.41865245902122328065155662382265207=5×3/10.3709570.16954808=(6-5)×4/28.561785.4663909=7+88.932745.63594010=5.65×950.4699631.843101113.704612.08499.215912=10+1160.836340.9759.2159根据上表可知，2号预应力筋的最大拉应力发生在跨中，值为60.8363MPa，符合的要求。斜截面混凝土主压应力验算斜截面混凝土的主压应力，应符合下式要求表3.33为的计算过程及结果，表3.34为的计算过程及结果，混凝土主压应力计算结果见表3.35；表3.33（a）跨中截面计算表截面应力部位a-ao-on-nb-b跨中1124807.903124807.903124807.903124807.90321034431.41034431.41034431.41034431.4310653.73510653.73510653.73510653.735477554869.7477554869.7477554869.7477554869.74584.974210.93550-87.324667854672.0767854672.0767854672.0767854672.07782.20230-10.9355-32.6438245902245902245902245902截面824590224590224590224590295155662515566251556625155662515566210=1/311.714811.714811.714811.714811=2×5/41.132121.45580-1.164712=10-1110.582710.25911.714810.549313=8×5/40.269420.034670-0.27687614=(9-8)×7/61.884600.0830860.12972615=13+142.153990.034670.083068-0.147150116=12+1512.736910.293711.798810.40215表3.33（b）四分点截面计算表截面应力部位a-ao-on-nb-b四分点截面1110023.55110023.55110023.55110023.552917994.6917994.6917994.6917994.6310653.73510653.73510653.73510653.735477699593.8377699593.8377699593.8377699593.83584.972110.93550-37.0279667692207.6567692207.6567692207.6567692207.65782.20230-10.9355-32.983481223281223281223281223289253012925301292530129253012910=1/310.32710.32710.32710.32711=2×5/40.10038640.12919901.0282112=10-1110.427410.456210.32711.355213=8×5/40.1337780.01721700.13701414=(9-8)×7/62.9239230-0.38897-1.1732115=13+143.0577010.017217-0.38897-0.13701416=12+1513.485110.47349.9380311.2182表3.33（c）支点截面计算表截面应力部位a-ao-on-n支点截面1125129.677125129.677125129.67721035880.31035880.31035880.3312112.33512112.33512112.335478091272.3578091272.3578091272.35575.01728.9584066781216.486781216.486781216.48770.05870-8.95848000900010=1/310.3307610.3307610.3307611=2×5/40.995110.2125012=10-119.335710.212510.3307613=8×5/400014=(9-8)×7/600015=13+1400016=12+159.335710.212510.33076表3.34（a）跨中计算表跨中一期恒载标准组合预加力短期组合剪应力01770.44407755869.7467854672.0725上梗肋2671923.657—2671923.657——341623.74——00.372100.3721净轴2974326.745—2974326.745——357426.643——00.370300.3703换轴286342.214—286342.214——351424.672——00.365400.3654下梗肋267326.453—267326.453——273243.64——00.364200.3642表3.34（b）四分点计算表四分点一期恒载标准组合预加力短期组合剪应力486.196290.5042776.700277699593.8367692207.6525上梗肋287326.63—287326.63——340314.54——0.65721.73420.087421.5742净轴296432.74—296432.74——355742.32——0.70041.61880.86821.5832换轴290438.07—290438.07——350543.25——0.68811.59660.85301.5934下梗肋270342.34—270342.34——262743.62——0.51341.65770.63640.9596表3.34（c）支点计算表支点一期恒载标准组合预加力短期组合剪应力492.429830.2531322.68278091272.3567281216.4840上梗肋292035.98—292035.98——364291.95——0.56780.87320.88640.8590净轴328642.53—328642.53——467823.72——0.64941.65861.25220.9324换轴317423.65—317423.65——367542.67——0.59421.27071.16321.3427下梗肋————————————表3.35计算表截面主应力部位跨中a-a12.73690.37216.78447o-o10.29370.370311.05741n-n11.79790.365411.70223b-b10.40220.36545.6093四分点a-a13.48511.57428.5026o-o10.47341.583210.7075n-n9.93801.59346.7505b-b11.21820.95966.6820支点a-a9.33570.85905.5282o-o10.21250.932410.2969n-n10.33081.342710.5024由上述计算可知，混凝土最大主压应力为111.70223MPa，符合的要求。2.4短暂状态构件的应力验算1.预加应力阶段的应力验算表3.36为预加应力阶段混凝土法向应力的计算过程及结果。表3.36预加应力阶段法向应力计算表应力部位跨中上缘跨中下缘四分点上缘四分点下缘支点上缘支点下缘112480.709012480.709011002.35511002.35512512.96812512.96821034.43141034.4314917.9946917.99461035.8801035.880310653.73510653.73510653.7351065