某預(yù)應(yīng)力混凝土T梁橋主梁截面承載力與應(yīng)力驗算計算過程案例目錄TOC\o"1-3"\h\u31666某預(yù)應(yīng)力混凝土T梁橋主梁截面承載力與應(yīng)力驗算計算過程案例 1166841.1.設(shè)計基本資料及構(gòu)造布置 3159851.1.1設(shè)計資料 322931.1.2主要材料 382231.1.3相關(guān)設(shè)計參數(shù) 3321151.1.4結(jié)構(gòu)設(shè)計 4102911.1.5截面幾何特性計算 4241292主梁截面承載力與應(yīng)力驗算 7271162.1持久狀況承載能力極限狀態(tài)承載能力驗算 734362.2持久狀況正常使用極限狀態(tài)抗裂性驗算 1243102.3持久狀況構(gòu)件應(yīng)力計算 20144702.4短暫狀態(tài)構(gòu)件的應(yīng)力驗算 291.1.設(shè)計基本資料及構(gòu)造布置1.1.1設(shè)計資料1.設(shè)計資料標(biāo)準(zhǔn)跨徑：50m(墩中心距)。計算跨徑：49.56m。主梁全長：49.96m。橋面寬度（橋面凈空）：凈-11+2×1(人行道)。2.技術(shù)標(biāo)準(zhǔn)設(shè)計時速：40km/h。環(huán)境標(biāo)準(zhǔn)：I類環(huán)境條件設(shè)計安全等級：二級。1.1.2主要材料1.混凝土主梁采用C50混凝土；鉸縫為C30細(xì)集料混凝土；橋面鋪裝采用瀝青混凝土；欄桿及人行道板為C25混凝土；蓋梁、墩柱用C30混凝土；橋臺基礎(chǔ)用C20混凝土；橋臺臺帽用C25混凝土。2.預(yù)應(yīng)力鋼筋：采用高強度低松馳7絲捻制的預(yù)應(yīng)力鋼絞線，公稱直徑為12.7mm，公稱面積為98.7，標(biāo)準(zhǔn)強度，彈性模型Ep=1.95105MPa1.非預(yù)應(yīng)力鋼筋：采用HPB300；HRB400。4.施工工藝：按后張法施工工藝制作主梁，采用金屬波紋管和夾片錨具，兩端同時張拉。1.1.3相關(guān)設(shè)計參數(shù)相對濕度為：75%。體系整體均勻升溫25℃，均勻降溫23℃。預(yù)應(yīng)力管道采用鋼波紋管成形，管道摩擦系數(shù)μ=0.25。管道偏差系數(shù)。錨具變形和鋼束回縮量為6mm(單端)。預(yù)應(yīng)力混凝土結(jié)構(gòu)重度按計，普通鋼筋混凝土重度按計，瀝青混凝土重度按計。單側(cè)人行道和欄桿線荷載分別為1.6和1.52。1.1.4結(jié)構(gòu)設(shè)計基本要求（1）本設(shè)計圖中，主梁各部分構(gòu)造尺寸所對應(yīng)構(gòu)件溫度為℃。（2）本設(shè)計為預(yù)應(yīng)力簡支T形梁。（3）橋面板橫坡坡度假定為和橋面橫坡度相同，為1.5%。（4）主梁斷面：主梁高度2.5m，粱間距2.6m，其中預(yù)制梁寬度1.6m，翼緣板中間接縫寬度0.4m。主梁跨中肋厚0.20m，馬蹄寬為0.36m，端部腹板厚度加厚到與馬蹄同寬，即：0.36m以滿足端部錨具布置和局部應(yīng)力需要。（5）橫隔梁設(shè)置：橫隔梁共設(shè)置四道，間距9.79m，端橫隔梁寬度0.28m，跨中橫隔梁寬度0.18m。（6）橋面鋪裝：設(shè)計總厚度為17cm，其中水泥混凝土厚度8cm，瀝青混凝土厚度9cm，兩者之間加設(shè)防水層。1.1.5截面幾何特性計算圖3-1橫斷面圖（尺寸單位cm）圖3?2預(yù)應(yīng)力混凝土T形梁結(jié)構(gòu)尺寸圖（尺寸單位cm）內(nèi)梁立面b）外梁立面c）3?3T形梁段截面尺寸圖3?4T形梁中截面尺寸圖表1.1跨中截面幾何特性計算表分塊名稱分塊面積分塊面積至上緣距離分塊面積對上緣靜距分塊面積的自身慣性矩分塊面積對截面形心的慣性矩cm2cmcm3cm4cmcm4cm4大毛截面（含濕接縫）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馬蹄2000225450000416666.76-131.36634514051.913490718.58∑112401052441.367263751.05小毛截面（不含濕接縫）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馬蹄2000225450000416666.67-121.03530275222.4530275345.49∑10840652448.878010698.12大毛截面形心至上翼緣距離91.634小毛截面形心至上翼緣距離101.9652主梁截面承載力與應(yīng)力驗算2.1持久狀況承載能力極限狀態(tài)承載能力驗算1.正截面承載力驗算（1）跨中截面正截面承載力驗算 圖3.18跨中截面承載力計算圖式（單位：cm）本設(shè)計計算如下：故中性軸在腹板內(nèi)。設(shè)中性軸到截面上緣距離為x，則式中：——，對于C50及以下混凝土和鋼絞線取0.4；——梁的有效高度，，。2）驗算正截面承載力正截面承載力計算公式為：式中——1.0；——承載能力極限狀態(tài)的跨中最大彎矩組合設(shè)計值。則上式為：主梁跨中正截面承載力滿足要求。四分點截面正截面承載力驗算：四分點截面承載力計算圖式如圖3.19。圖3.19四分點正截面承載力計算圖式（單位：cm）故中性軸在翼板內(nèi)。設(shè)中性軸到截面上緣距離為x，則式中：——構(gòu)件的正截面相對界限受壓區(qū)高度，對于C50及以下混凝土和鋼絞線取0.4；——，以四分點為例，=20.15cm。2）驗算正截面承載力，正截面承載力計算公式為：則上式為：四分點正截面承載力滿足要求。（3）式中；————由此可得最小配筋率滿足要求。2.斜截面承載力驗算式中：——=1026.69kN（見表3.6）；——；——b=400mm；——?。ㄓ嬎阒狄姳?.9）；則主梁的支點截面尺寸符合要求。（2）截面抗剪承載力驗算若滿足式則無需進(jìn)行斜截面抗剪承載力計算。對于距支座中心h/2處截面：b=400mm，，。因此需進(jìn)行斜截面抗剪承載力計算；斜截面的水平投影此時，其距支座距離為：；箍筋計算預(yù)應(yīng)力混凝土T梁腹板內(nèi)箍筋直徑應(yīng)不小于10mm，且采用帶肋鋼筋，間距不應(yīng)大于250mm，在本設(shè)計中選用的雙肢箍筋，則箍筋的總面積為；箍筋間距為200，箍筋為HRB335鋼筋，其抗拉設(shè)計強度為，則箍筋的配筋率為：式中：抗剪承載力計算主梁斜截面抗剪承載力應(yīng)滿足下式的要求；式中：——885.456kN；————=1.0；——=1.25；——=1.1；——此處為379.3mm；——此處為1232.1mm；，當(dāng)，??；表3.26斜截面受壓端正截面處的鋼束位置及鋼束群重心位置計算表截面鋼束號x4R/cm距支座h/2處斜截面頂端N4未彎起1361.164201.00001010.0023.9874N3172.641303.04040.1324900.9911841024.27N2、272.361618.71260.16826570.9857432447.078324.62324.621832.8120.17711580.9841903866.976則上述計算說明主梁距支點h/2處的斜截面抗剪承載力滿足要求。（3）斜截面抗彎承載力驗算在該設(shè)計中由于鋼束都在梁端錨固，鋼束根數(shù)沿梁跨沒有變化，配筋率也滿足要求，可不必進(jìn)行該項承載力驗算。2.2持久狀況正常使用極限狀態(tài)抗裂性驗算正截面抗裂性驗算正截面抗裂性驗算的計算過程和結(jié)果見表3.27。表3.27正截面抗裂性驗算計算表應(yīng)力部位跨中下緣四分點下緣支點下緣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由以上計算可見，各截面的正截面抗裂性均符合的要求斜截面抗裂性驗算表3.28（a）跨中截面計算表截面應(yīng)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）四分點截面計算表截面應(yīng)力部位a-ao-on-nb-b四分點截面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）支點截面計算表截面應(yīng)力部位a-ao-on-n1125129.677125129.677125129.67721035880.31035880.31035880.3312112.33512112.33512112.335478091272.3578091272.3578091272.35支點截面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）跨中計算表跨中一期恒載短期組合預(yù)加力短期組合剪應(yīng)力0114.80407755869.7467854672.0725上梗肋276192.65—276192.65——341623.74——00.987200.9872凈軸297432.74—297432.74——35742.643——00.976200.9762換軸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）四分點計算表四分點一期恒載短期組合預(yù)加力短期組合剪應(yīng)力486.196290.5042776.700277699593.8367692207.6525上梗肋287326.63—287326.63——340314.54——0.65721.73420.87421.2371凈軸147069.8322—147069.8322——355742.32——0.69431.74530.94731.2274換軸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）支點計算表支點一期恒載短期組合預(yù)加力短期組合剪應(yīng)力492.429830.2531322.68278091272.3567281216.4840上梗肋292035.98—292035.98——364321.95——0.56780.87320.88640.9378凈軸328642.53—328642.53——467823.72——0.65781.78321.07320.9428換軸317423.60—317423.60——367542.67——0.684320.97420.98350.7324下梗肋————————————表3.30計算表截面主應(yīng)力部位跨中a-a14.73340.9872-0.06585o-o11.60690.9762-0.081365n-n9.66760.9743-0.09328b-b10.28300.3721-0.09423四分點a-a12.383271.2371-0.12238o-o10.21511.2274-0.14541n-n9.93841.2234-0.14838b-b8.26380.9432-0.106286支點a-a9.33570.9378-0.09327o-o10.21250.9428-0.086308n-n10.330760.7324-0.051665由上述計算，最大主拉應(yīng)力為0.14838，其結(jié)果符合的要求。2.3持久狀況構(gòu)件應(yīng)力計算1.正截面混凝土壓應(yīng)力驗算表3.31正截面混凝土法向壓應(yīng)力計算表應(yīng)力部位跨中上緣跨中下緣四分點上緣四分點下緣支點上緣支點下緣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由上表的計算過程和計算結(jié)果可以看出，最大壓力在跨中截面上緣處，其值為15.20758pMPa，小于16.2MPa，符合要求。2.預(yù)應(yīng)力筋拉應(yīng)力驗算使用階段預(yù)應(yīng)力筋拉應(yīng)力應(yīng)滿足式中：表3.322號預(yù)應(yīng)力筋拉應(yīng)力驗算表應(yīng)力部位跨中四分點支點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根據(jù)上表可知，2號預(yù)應(yīng)力筋的最大拉應(yīng)力發(fā)生在跨中，值為60.8363MPa，符合的要求。斜截面混凝土主壓應(yīng)力驗算斜截面混凝土的主壓應(yīng)力，應(yīng)符合下式要求表3.33為的計算過程及結(jié)果，表3.34為的計算過程及結(jié)果，混凝土主壓應(yīng)力計算結(jié)果見表3.35；表3.33（a）跨中截面計算表截面應(yīng)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）四分點截面計算表截面應(yīng)力部位a-ao-on-nb-b四分點截面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）支點截面計算表截面應(yīng)力部位a-ao-on-n支點截面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）跨中計算表跨中一期恒載標(biāo)準(zhǔn)組合預(yù)加力短期組合剪應(yīng)力01770.44407755869.7467854672.0725上梗肋2671923.657—2671923.657——341623.74——00.372100.3721凈軸2974326.745—2974326.745——357426.643——00.370300.3703換軸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）四分點計算表四分點一期恒載標(biāo)準(zhǔn)組合預(yù)加力短期組合剪應(yīng)力486.196290.5042776.700277699593.8367692207.6525上梗肋287326.63—287326.63——340314.54——0.65721.73420.087421.5742凈軸296432.74—296432.74——355742.32——0.70041.61880.86821.5832換軸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）支點計算表支點一期恒載標(biāo)準(zhǔn)組合預(yù)加力短期組合剪應(yīng)力492.429830.2531322.68278091272.3567281216.4840上梗肋292035.98—292035.98——364291.95——0.56780.87320.88640.8590凈軸328642.53—328642.53——467823.72——0.64941.65861.25220.9324換軸317423.65—317423.65——367542.67——0.59421.27071.16321.3427下梗肋————————————表3.35計算表截面主應(yīng)力部位跨中a-a12.73690.37216.78447o-o10.29370.370311.05741n-n11.79790.365411.70223b-b10.40220.36545.6093四分點a-a13.48511.57428.5026o-o10.47341.583210.7075n-n9.93801.59346.7505b-b11.21820.95966.6820支點a-a9.33570.85905.5282o-o10.21250.932410.2969n-n10.33081.342710.5024由上述計算可知，混凝土最大主壓應(yīng)力為111.70223MPa，符合的要求。2.4短暫狀態(tài)構(gòu)件的應(yīng)力驗算1.預(yù)加應(yīng)力階段的應(yīng)力驗算表3.36為預(yù)加應(yīng)力階段混凝土法向應(yīng)力的計算過程及結(jié)果。表3.36預(yù)加應(yīng)力階段法向應(yīng)力計算表應(yīng)力部位跨中上緣跨中下緣四分點上緣四分點下緣支點上緣支點下緣112480.709012480.709011002.35511002.35512512.96812512.96821034.43141034.4314917.9946917.99461035.8801035.880310653.73510653.73510653.7351065