混凝土橋梁結(jié)構(gòu)課程設(shè)計(jì)計(jì)算書

預(yù)應(yīng)力混凝土簡(jiǎn)支T形梁設(shè)計(jì)計(jì)算書一、內(nèi)力計(jì)算結(jié)果（1）恒載內(nèi)力①預(yù)制主梁（包括橫隔梁）的自重g1p=15.3+1.35=16.66kN/m②現(xiàn)澆混凝土板自重g1m=2.25kN/m③二期恒載g2=6.27+0.24=6.51kN/m計(jì)算結(jié)果見下表恒載內(nèi)力計(jì)算結(jié)果截面位置距支點(diǎn)截面的距離x（mm）預(yù)制梁自重現(xiàn)澆段自重二期恒載彎矩剪力彎矩剪力彎矩剪力MG1Pk（kN?m）VG1Pk（kN）MG1mk（kN?m）VG1mk（kN）MG2k（kN?m）VG2k（kN）支點(diǎn)00.00242.90.0032.810.00124.22變截面4600941.09166.26127.1022.46481.2785.03L/472901328.05121.45179.3616.40679.1862.11跨中145801770.760.00239.150.00905.580.00（2）活載內(nèi)力車輛荷載原要求按城-A級(jí)車道荷載計(jì)算，實(shí)際計(jì)算根據(jù)《公路橋涵設(shè)計(jì)通用規(guī)范（JTGD60-2004）》取公路-I級(jí)荷載，其中車道荷載qk=10.5kN/m，插值得Pk=277kN,剪力增長(zhǎng)系數(shù)1.2，沖擊系數(shù)1+μ=1.1188；人群荷載按3.5kN/m計(jì)算，雙車道不折減ζ=1。活載內(nèi)力以1號(hào)邊梁為準(zhǔn)，跨中截面按偏心壓力法計(jì)算橫向分布系數(shù)，支點(diǎn)截面按杠桿法計(jì)算橫向分布系數(shù)。現(xiàn)計(jì)算簡(jiǎn)略過程如下：支座處橫向分布系數(shù)moq=0.41跨中和其他截面的橫向分布系數(shù)mcq=計(jì)算結(jié)果如下表所示?；钶d內(nèi)力計(jì)算結(jié)果截面位置距支點(diǎn)截面的距離x（mm）A級(jí)車道荷載人群荷載最大彎矩最大剪力最大彎矩最大剪力MQ1k（kN?m）對(duì)應(yīng)V（kN）VQ1k（kN）對(duì)應(yīng)M（kN?m）MQ2k（kN?m）VG2k（kN）VQ2k（kN）對(duì)應(yīng)M（kN?m）支點(diǎn)00.00<260.46260.460.000.00<39.3039.300.00變截面46001268.10293.05295.961196.94129.3422.8723.70108.95L/472901791.63248.26255.551632.19182．7516.7118.80137.06跨中145802388.93126.63155.792271.39243.700.008.36121.50（3）內(nèi)力組合截面位置項(xiàng)目基本組合Sd短期組合Ss長(zhǎng)期組合SlMdVdMSVSMlVl(kN?m)(kN)(kN?m)(kN)(kN?m)(kN)支座最大彎矩0.00479.920.00399.98最大剪力0.00888.580.00602.19變截面最大彎矩3779.55764.382472.21479.97最大剪力3657.09769.392407.30482.62L/4最大彎矩5336.87606.233490.31371.99最大剪力5062.48618.783344.86378.65跨中最大彎矩7116.03177.284653.8779.23最大剪力6814.61227.474458.13105.83二、預(yù)應(yīng)力鋼筋及普通鋼筋數(shù)量的確定及布置（1）預(yù)應(yīng)力筋鋼筋數(shù)量的確定及布置為滿足抗裂要求，所需的有效預(yù)加力為NMs為短期效應(yīng)彎矩組合設(shè)計(jì)值，查得Ms=4653.87kN；A、W為估算鋼筋數(shù)量時(shí)近似采用毛截面積幾何性質(zhì)，按給定的截面尺寸計(jì)算：AIep為預(yù)應(yīng)力鋼筋重心至毛截面重心的距離，ep=解得N擬采用?j15.2鋼絞線，單根鋼絞線的公稱截面面積Ap1=139mm2，抗拉強(qiáng)度標(biāo)準(zhǔn)值fpk=1860MPa，張拉控制應(yīng)力σcon=所需預(yù)應(yīng)力鋼絞線的面積為：Ap=4067.52mm2采用3束7?j15.2和1束Ap=3X7X139+8X139=4031mm2采用中橋預(yù)應(yīng)力設(shè)備有限公司YJM15YP-7/8型錨具，?70金屬波紋管成孔，預(yù)留管道直徑為75mm。預(yù)應(yīng)力筋束的布置如下圖所示預(yù)應(yīng)力筋束的曲線要素和有關(guān)計(jì)算參數(shù)列于下表:預(yù)應(yīng)力筋束曲線要素表鋼束編號(hào)起彎點(diǎn)距跨中（mm）曲線水平長(zhǎng)度（mm）曲線方程1014800y=200+4.428×12200012800y=120+4.943×13、490005800y=120+5.945×1各計(jì)算截面預(yù)應(yīng)力筋束的位置和傾角計(jì)算截面錨固截面支點(diǎn)截面變截面點(diǎn)L/4截面跨中截面截面距離跨中（mm）1480014580998072900鋼束到梁底距離（mm）1號(hào)束11701141.4641.1435.32002號(hào)束930902.4434.8258.41203、4號(hào)束320305．1125.7120120合力點(diǎn)685663.5331.8233.4140鋼束與水平線夾角（°）1號(hào)束7.51047.39885.06453.699402號(hào)束7.52157.12694.52092.996903、4號(hào)束3.95143.80160.667700平均值5.66625.53222.73021.67410累計(jì)角度1號(hào)束00.11162.44593.81107.51042號(hào)束00.12462.73064.25467.25153、4號(hào)束00.14983.28373.95143.9514（2）普通筋鋼筋數(shù)量的確定及布置設(shè)預(yù)應(yīng)力筋和普通鋼筋的合力點(diǎn)到截面底邊的距離為apshhb帶入公式γ0Md≤fcdbf'A取10根直徑為25的HRB400鋼筋，提供截面面積為4908mm2，鋼筋布置如圖所示。梁底布置成一排，鋼筋間距為30mm,鋼筋重心到截面底邊距離45mm。二、截面幾何性質(zhì)計(jì)算階段截面Ay’yepIW(*109mm3)階段1：鋼束灌漿、錨固前支點(diǎn)1.00313576.5723.560.00.167270.290130.231202.78909變截面0.61032541.0759.0427.20.142440.263300.187660.33342L/40.61032538.1761.9528.50.141330.262660.185510.26743跨中0.61032535.4764.6624.60.139700.260920.182710.22366階段2：現(xiàn)澆600mm連階段支點(diǎn)1.03748578.5721.558.00.172050.297400.238462.96698變截面0.64467563.7736.3404.40.150020.266110.203750.37092L/40.64467566.3733.7500.30.150980.266630.205780.30179跨中0.64467568.7731.3591.30.152430.268030.268430.25778階段3：二期荷載、活載支點(diǎn)1.12748538.3761.798.20.193210.893520.253671.96794變截面0.73467503.9796.1464.30.169050.335510.212340.36408L/40.73467506.1793.9560.50.170210.336330.214400.30369跨中0.73467508.2791.8651.80.171840.338130.217030.26365三、承載能力極限狀態(tài)計(jì)算（1）正截面承載力計(jì)算跨中截面尺寸及配筋情況見圖。其中預(yù)應(yīng)力束合力點(diǎn)到截面底邊距離ap=140mm，預(yù)應(yīng)力束和普通鋼筋的合力點(diǎn)到截面底邊距離:ah上翼緣平均厚度有效寬度為:hb因?yàn)閒所以屬于第二類T型截面，現(xiàn)驗(yàn)算截面承載力如下。由X=x=M=8081.92kN計(jì)算結(jié)果表明，跨中截面的抗彎承載力滿足要求。(2)斜截面承載力計(jì)算選距支點(diǎn)h/2和變截面處進(jìn)行斜截面承載力計(jì)算。其中截面尺寸如圖，預(yù)應(yīng)力鋼筋束的位置要素信息如表。箍筋采用HRB335鋼筋，鋼筋直徑8mm，雙肢箍，間距sv=200mm支點(diǎn)1300mm范圍內(nèi)箍筋間距sv=100mm。距支點(diǎn)h/2斜截面抗剪承載力計(jì)算距離支點(diǎn)h/2=650mm處，V取預(yù)應(yīng)力提高系數(shù)a2=1.25,b=599.01mm，縱向鋼筋合力點(diǎn)h0=1160mm將上述數(shù)據(jù)帶入公式，截面抗剪上下限復(fù)核：0.5×1即截面尺寸滿足要求，下面計(jì)算抗剪鋼筋。VVVh/2處截面滿足抗剪承載力要求。B)變截面處斜截面抗剪承載力計(jì)算VVVV綜上，截面抗剪承載力是足夠的。四、預(yù)應(yīng)力損失計(jì)算(1)摩阻損失σσ 計(jì)算結(jié)果如下表所示：摩擦損失計(jì)算表鋼束號(hào)截面1234總計(jì)支點(diǎn)x(m)0.179660.179660.179660.17966?（弧度）0.001950.002170.002610.002611.141.221.371.375.10變截面x(m)4.824.824.824.82?（弧度）0.042690.047660.057310.0573124.7526.4529.7529.75110.71L/4截面x(m)7.517.517.517.51?（弧度）0.066510.074260.068960.0689638.3741.0039.2039.20157.78跨中x(m)14.8014.8014.8014.80?（弧度）0.131080.126560.068960.0689674.6173.1253.9553.95255.63（2）錨具變形損失σ相應(yīng)計(jì)算結(jié)果如下表所示：反摩擦影響長(zhǎng)度計(jì)算表鋼束號(hào)1234σcon（MPa1395139513951395σpe,11320.391321.881341.051341.05?σd0.0050410.0049410.0036450.003645lf12438.512564.814628.014628.0錨具變形損失計(jì)算表鋼束號(hào)截面1234總計(jì)支點(diǎn)x(mm)220220220220?σ(MPa)125.42124.16106.65106.65σl2123.20121.98105.04105.04455.26變截面x(mm)4820482048204820?σ(MPa)125.42124.16106.65106.65σl276.8276.5371.5171.51296.35L/4截面x(mm)7150715071507150?σ(MPa)125.42124.16106.65106.65σl245.6949.9551.8951.89203.43跨中x(mm)14800148001480014800?σ(MPa)125.42124.16106.65106.65σl20.000.000.000.000.00(3)分批張拉損失σσ 其中αEp分批張拉損失計(jì)算表截面張拉束號(hào)有效張拉力鋼束偏心距（mm）計(jì)算偏心距（mm）各鋼束預(yù)應(yīng)力損失234234234支點(diǎn)31253.7418.4418.415.3721414.3-178.9-178.9418.4418.44.664.6611236.4-417.9-417.9-417.9-178.9418.4418.410.71-0.36-0.36總計(jì)（MPa）10.714.3019.67變截面31258.8633.3633.333.6421436.7503.5503.5633.3633.333.4233.4211258.5117.9117.9117.9324.2633.3633.314.4016.3316.33總計(jì)（MPa）14.4049.7583.39L/431268.8641.9641.934.6721450.1503.5503.5641.9641.934.1534.1511271.7326.6326.6326.6503.5641.9641.921.3823.8223.82總計(jì)（MPa）21.3857.9792.64跨中31304.8644.6644.636.1121469.9644.6644.6644.6644.640.6840.6811284.7564.6564.6564.6644.6644.6644.632.7132.7132.71總計(jì)（MPa）32.7173.39109.5(4)鋼筋應(yīng)力松弛損失σσ計(jì)算結(jié)果如下表所示：鋼筋松弛損失計(jì)算表鋼束截面σσ12341234支點(diǎn)1270.71261.091284.291268.9236.3035.0638.1636.07變截面1293.41277.621243.991210.3539.4337.2532.7638.46L/41306.91282.671245.941211.2741.3237.9433.0238.57跨中1320.41289.17`1267.661231.5543.2338.8335.9031.15(5)混凝土收縮、徐變損失σσ分別計(jì)算各個(gè)截面處對(duì)應(yīng)的參數(shù)，結(jié)果匯總?cè)缦卤硭荆夯炷潦湛s徐變損失計(jì)算表截面epsρρNpeM自重σ預(yù)σ自重σσ支點(diǎn)438.80.007932.1245123.00.005.120.005.1266.17變截面621.80.012222.6805067.31549.4614.16-5.708.4675.33L/4663.90.012222.9025088.82186.5918.05-8.539.5279.43跨中704.00.012223.1195150.02915.4920.76-11.948.8273.49(6)預(yù)應(yīng)力組合損失 上述各項(xiàng)損失組合情況見下表：預(yù)應(yīng)力損失組合截面σσ1234平均1234平均支點(diǎn)124.34133.91110.71126.08123.76102.47101.23104.33102.24102.47變截面101.57117.38151.01184.65138.65114.76112.58108.09113.79114.76L/488.07112.33149.15183.73133.32120.75117.37112.45118.00120.75跨中74.61105.83127.34163.45117.81116.72112.32109.39104.64116.72五、正常使用極限狀態(tài)計(jì)算 1、抗裂性驗(yàn)算 （1）正截面抗裂驗(yàn)算 ①荷載短期效應(yīng)組合作用下的抗裂性截面抗裂性驗(yàn)算以跨中截面受拉邊緣正應(yīng)力控制。在荷載短期效應(yīng)組合作用下，應(yīng)滿足：σ其中σst=In1/yn1IMG1Pk=1770.76kN?m;MG1mkMQ1k=2388.93kN?m;M帶入公式可得：σ而σpcNPe∴σσst-σpc=0.73Mpa<0.7ftk=0.7x2.4=1.68Mpa計(jì)算結(jié)果表明，在短期效應(yīng)組作用下，正截面抗裂性滿足要求。荷載長(zhǎng)期效應(yīng)組合作用下的抗裂性在長(zhǎng)期效應(yīng)組合作用下，應(yīng)滿足：σlt-σpc≤0σlt=M=1770.76=19.4Mpaσlt-σpc=19.4-22.28<0計(jì)算結(jié)果表明，在長(zhǎng)期效應(yīng)組合作用下，正截面抗裂性滿足要求。（2）斜截面抗裂性驗(yàn)算部分預(yù)應(yīng)力混凝土A類構(gòu)件的斜截面抗裂性驗(yàn)算，以主拉應(yīng)力控制，一般取變截面點(diǎn)分別計(jì)算截面上梗肋、形心軸和下梗肋處在短期效應(yīng)組合作用下的主拉應(yīng)力，應(yīng)滿足σtp≤0.7ftkσtp=στ短期效應(yīng)組合作用的主拉應(yīng)力計(jì)算方法與方案一相同，在計(jì)算預(yù)加力時(shí)，應(yīng)考慮非預(yù)應(yīng)力鋼筋對(duì)混凝土收縮、徐變損失的影響，取NP下表為各計(jì)算點(diǎn)的積和性質(zhì)。主拉應(yīng)力計(jì)算過程從略，計(jì)算結(jié)果匯總于表。計(jì)算結(jié)果表明，下梗肋處的主拉應(yīng)力最大，其數(shù)值為σtp,max=-0.31，小于規(guī)范規(guī)定的限制值1.68Mpa計(jì)算點(diǎn)幾何性質(zhì)計(jì)算點(diǎn)受力階段A1(×106mmyx1(mm)d(mm)S1×上梗肋處階段10.287200448.6311.00.12883階段20.287200471.4333.70.13537階段30.377200415.6273.90.15677形心位置階段10.336502408.437.10.13743階段20.336502431.259.90.14509階段30.426502383.40.00.16354下梗肋處階段10.193520615.7409.00.11915階段20.227872593.2386.30.13517階段30.227872653.0446.10.14881變截面處不同計(jì)算點(diǎn)主應(yīng)力匯總表計(jì)算點(diǎn)位置正應(yīng)力σ剪應(yīng)力τ主拉應(yīng)力σtp(Mpa)上梗肋7.551.43-0.26形心軸7.251.52-0.29下梗肋5.801.38-0.312.變形計(jì)算（1）使用階段的撓度計(jì)算部分預(yù)應(yīng)力混凝土A類構(gòu)件使用階段的撓度計(jì)算方法與方案一相同，取剛度B0=0.95ECI0=0.95X3,25X104X0.17184X1012=0.5306X1016Nmm2荷載短期效應(yīng)組合作用下的撓度fs=5自重產(chǎn)生的撓度fG=548扣除自重影響后的長(zhǎng)期撓度為fL=ηθ（2）由預(yù)加力產(chǎn)生的反拱度及預(yù)拱度的設(shè)置部分預(yù)加力混凝土A類構(gòu)件預(yù)加力階段的撓度計(jì)算方法與方案一相同，取剛度B0=0.95ECI0=0.95X3,25X104X0.139697X1012=0.4313X1016Nmm2fp=-η式中，2ωm,l2=L216MP=NPepσl,Ⅰ、σl,Ⅱ、σl6近似取L/4截面的損失值。NP=1395-133.32-120.75×4031-79.43×4908epn=σypn1為距支點(diǎn)L/3ypn1=ep0=590.9mmysn1為距支點(diǎn)L/3ysn1=753.2epn=575.87mm由此得MP=NPep=2423.9KN?m取ηfp=-ηθ2ωm,l2預(yù)加力產(chǎn)生的長(zhǎng)期反拱值小于按荷載短期效應(yīng)組合計(jì)算的長(zhǎng)期撓度。（六）持久狀況的應(yīng)力驗(yàn)算部分預(yù)應(yīng)力混凝土A類構(gòu)件在使用荷載作用荷載作用階段的正截面法