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*：*：班级：指导教师：成绩：二一二年七月第一章设计依据. z.-第二章设计资料及上部构造主要尺寸2.1 设计资料. z.-1. 桥梁跨径及桥宽标准跨径：35m；主梁全长：34.94m；计算跨径：34.19m；桥面宽度：0.5m防撞栏杆+15.9净行车道宽度m+ 0.5m防撞栏杆=16.9m。分幅：单幅行车方向：单向行车2. 设计荷载33. a材料及工艺混凝土：33小箱梁梁的预制局部及现浇接缝局部均采用C50容重为26kN/m；铺装层为10cm厚沥青混凝土混凝土容重为24kN/m；2沥青铺装层下设置8cm厚的C40防水混凝土调平层容重为25kN/m。. z.-预应力钢筋：s15.2 钢绞线，fpk1860MPa，单根面积14。0mm. z.-普通钢筋：直径12 mm采用HRB33钢5筋；直径0.53772号梁图2-6. z.-mcq 20.5*(0.24380.2410.23690.2270.21680.19980.18760.1711)0.8620. z.-按照2车道加载mcq10.5*(0.24380.2410.23690.227)0.4744. z.-0.67*0.862=0.57750.47443号梁. z.-mcq 30.5*(0.18620.19440.20050.20850.21280.21500.21140.2038)0.8163. z.-按照2车道加载mcq10.5*(0.18620.19440.20050.2085)0.3948. z.-0.67*0.8163=0.54690.3948根据对称性关系. z.-mcq4mcq5mcq2mcq10.86200.8859. z.-3.2.2 支座处用杠杆原理法1号梁图2-7. z.-m0 q12号梁图2-80.5 * (1.20540.66970.2827)1.0789m0 q 23号梁图2-90.5 * (0.08820.617610.47060.0882)1.1323m0 q30.5 * (0.08820.617610.47060.0882)1.1323根据对称性关系表3-4梁号各梁横向分布系数12345跨中支座0.88591.07890.8621.13230.81631.13230.8621.13230.88591.0789m0 q 4m0 q21.1323m0 q5m0 q11.0789. z.-3.2.2活载计算. z.-荷载值qk10.5kN / m. z.-Pk300kN折减系数0.67fEIc22lmc0.1767 ln f3.142 * 34.190.01573.45 * 1010 * 0.54856970.1432.45H Z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2-121号梁Q=1.143*1.0789*300*0.67+1.143*0.5*1.0789*1+0.8859*0.8571*34.19/7+0. z.-8859*0.5*6*34.19/7*10.5*0.67=388.35kN1/8 跨处弯矩图2-13M=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 kN .m剪 力 图2-14Q=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=317.26kN1/4 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2-16. z.-Q=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 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2-19M=1.143*300*8.5475*0.8859*0.67+1.143*0.5*34.19*8.5475*10.5*0.8859*0.67=2780.55kN.m. z.-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=0 Q=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.m. z.-Q=170.06kN跨中处M=2705.54kN.mQ=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=0 Q=392.29kN1/8 跨处M=1121.06kN.mQ=296.35kN1/4 跨处M=1923.91kN.mQ=203.75kN3/8 跨处M=2401.88kN.mQ=161.04kN跨中处M=2561.79kN.mQ=121.82kN. z.-4,5 号梁活载力分别于 2，1号梁一样表3-5各梁活载力值支座处1/8 跨处1/4 跨处3/8跨处10388.351216.64317.262085.21221.052606.67174.77278020398.451183.82311.842028.96215.182536.35170.06270530392.291121.06296.351923.91203.752401.88161.04256140398.451183.82311.842028.96215.182536.35170.06270550388.351216.64317.262885.21221.052606.67174.772780梁号M(kN.m)Q(kN)M(kN.m)Q(kN)M(kN.m)Q(kN)M(kN.m)Q(kN)M(kN.m3.3 力组合表3-61号梁力组合1 号梁支座处1/8 跨处1/4 跨处3/8跨处跨中处序QMQMQMQMQ号荷载类别kNkN.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活载承载力极限状态388.351216.64317.262085.21221.052606.67174.772780.55129.375组合1,690.005,990.901,303.9010,267.20882.612,834.80571.413,691.00181.1正常使用短期组6合1,193.104,318.10910.77,400.306139,251.00379.39,868.0079.2正常使用长期组7合1,091.203,998.80827.56,853.005558,566.80333.49,138.2045.3正常使用标准组8合1,343.604,789.601,033.708,208.50698.710,261.2044710,945.70129.4表3-72号梁力组合2 号梁支座处1/8 跨处1/4 跨处3/8跨处跨中处序QMQMQMQMQ号荷载类别kNkN.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1,714.805,984.501,304.3010,256.80879.812,821.90567.813,677.10180.1正常使用短期组6合1,208.204,330.90914.17,422.80613.99,279.10378.99,898.1078.8. z.-7正常使用长期组合正常使用标准组合1,103.604,020.20832.26,890.30557.48,613.40334.39,188.004581,362.604,789.801,035.008,209.20697.310,262.20444.810,946.70128.6表3-8支座处1/8 跨处3号梁内力组合3 号梁1/4 跨处3/8 跨处跨中处序QMQMQMQMQ67正常使用短期组合正常使用长期组合正常使用标准组合1,204.404,292.50904.67,358.50606.99,196.80373.49,810.0074.61,101.403,998.30826.86,853.50553.48,566.40331.19,137.7042.681,356.504,727.001,019.508,104.20685.810,127.70435.810,802.90121.8号荷载类别kNkN.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1,706.205,896.601,282.6010,109.80863.812,633.60555.213,475.90170.5. z.-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一样。对于预应力钢筋混凝土简支梁桥，控制构造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JTGD62-2004的第条(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：. z.-st0.85pc0(4-1). z.-式中，st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，pc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st按下式求得M ststybI0(4-2). z.-其中，M st 是弯矩短期效应组合值，轴的距离。I 0 是毛截面抗弯惯性矩，yb 是下边缘距截面中性. z.-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。. z.-NNeeN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NNepcyb. z.-A0I0(4-3). z.-. z.-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，yb 的定义与式 (4-2)一致，N 是预加力，按下式计算I 0 和. z.-. z.-Neff Ap(4-4). z.-. z.-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)，. z.-并将式 (4-1)取等号，得到预应力钢束面积估算公式. z.-Ap0.85M stI 0effA0ybeff eybI 0(4-5). z.-上式中，预应力钢束的有效预应力eff及预应力钢绞线合力作用点距截面中性轴的距. z.-离e需要预先假定。一般而言，对于fpk1860MPa的预应力钢绞线的控制拉应力取. z.-. z.-con0.75 fpk0.7518601395MPa，在估束阶段，根据经历，考虑25%的预应力损失，. z.-. z.-则有效预应力的估计值为eff0.75con0.7513951046MPa 。对于跨中截面，可假设. z.-预应力钢绞线合力作用点距截面下边缘18cm进展试算。. z.-M st10459.8kN .m. z.-2I00.552myb1.17me0.99m. z.-代入4-5得Ap8365mm2. z.-选配12束515.2的钢束. z.-实际Ap28400mm. z.-图4-1预应力钢束布置图钢束号表4-1长度cm半径m钢束尺寸弯起角支座度处1/8处钢束中心到梁底距离截面1/4截面3/8截面处处跨中处N11738.043000212.59999N21739.98300075211.02999N31740.34450077429.32202020N41740.69600079649.7231.093131N51741.067500711870.4145.074242N61741.429000714091.6861.725353. z.-计算点截面积 mm2截面重心至底面mm截面重心至到钢束质心距离AnA0yny0Wn( mm 3 )梁自重弯矩kN.mIn mm4 I0 mm4 mmene0表4-2截面特性跨中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*1011284276.3. z.-4.2 预应力损失计算4.2.1 磨阻损失(e*)l1con(1)0.00150.22con1395MPa表4-3l1计算表. z.-. z.-(*)*1econ (1e(* ). z.-计算点钢束radmMPaN130.0523617.380.0375890.03689151.46314N270.1221717.380.0529470.0515771.94013N370.1221717.380.0529470.0515771.94013N470.1221717.380.0529470.0515771.94013N570.1221717.380.0529470.0515771.94013N670.1221717.380.0529470.0515771.94013N130.0523613.0050.0310260.0305542.61719N270.1221713.0050.0463850.04532563.229N370.1221713.0050.0463850.04532563.229N470.1221713.0050.0463850.04532563.229N570.1221713.0050.0463850.04532563.229N670.1221713.0050.0463850.04532563.229N130.052368.630.0244640.02416733.71299N270.122178.630.0398220.0390454.46051N370.122178.630.0398220.0390454.46051N46.680.116598.630.0385940.03785852.81241N55.360.093558.630.0335250.0329745.99255N64.480.078198.630.0301460.02969741.42674N130.052364.630.0184640.01829425.52072N24.930.086044.630.0258740.02554235.63166N33.310.057774.630.0196540.01946227.14981N42.590.04524.630.016890.01674823.36313N52.010.035084.630.0146630.01455620.30513N61.670.029154.630.0133570.01326818.50933N1000.120.000180.000180.251077N2000.120.000180.000180.251077N3000.120.000180.000180.251077N4000.120.000180.000180.251077N5000.120.000180.000180.251077N6000.120.000180.000180.251077跨中1/8跨1/4跨3/8跨支点4.2.2 由锚具变形及钢束回缩引起的预应力损失l2按公预规l2计算公式如下反向摩擦影响长度：. z.-. z.-d (l f*) ；. z.-l fl * E pdl6mm0ldlEp1.95 * 10MPa5其中01395MPal 为预应力钢筋扣除磨阻损失后锚固端应力l 为*拉端至锚固端的距离l 22d l f在反影响长度内， 距*拉端 *处的锚具变形、 钢筋回缩损失：l 22在反影响长度外，锚具变形、钢筋回缩损失：l 20表4-4l 2 计算表钢束l 2d计算点MPa影响长度mm*mmMPa跨中1/8 跨1/4 跨N10.00296119877.861738014.79261N20.00413916812.5173800N30.00413916812.5173800N40.00413916812.5173800N50.00413916812.5173800N60.00413916812.5173800N10.00327718895.381300538.6054N20.00486215512.791300524.38526N30.00486215512.791300524.38526N40.00486215512.791300524.38526N50.00486215512.791300524.38526N60.00486215512.791300524.38526N10.00390617306.12863067.78631N20.00631113616.25863062.93248N30.00631113616.25863062.93248N40.0061213827.08863063.60836N50.00532914816.81863065.94368. z.-N60.004815611.98863067.03143N1k0.00551214569.244630109.5709N20.00769612330.074630118.5167N30.00586414125.384630111.3597N40.00504615227.134630106.9469N50.00438616333.554630102.6532N60.00399817107.56463099.76298N10.00209223647.212098.45247N20.00209223647.212098.45247N30.00209223647.212098.45247N40.00209223647.212098.45247N50.00209223647.212098.45247N60.00209223647.212098.452473/8 跨支点4.2.3 钢筋松弛引起的预应力损失l4np5.4932Ap8400mm表4-5l4计算表. z.-conl1l 21en1. z.-计算点钢束平均AnWn1N1npNAp ( 1en ) cosAnWpel4. z.-MPacosnMPaMPa/mm. z.-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-061.061,250.3072.76N11313.77712.75E-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-061.061,235.4971.89跨中1/8 跨. z.-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-061.061,217.1069.44N11259.9080.99772.36E-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-061.051,216.2460.48N11296.2960.99361.13E-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-061.021,266.2230.081/4跨3/8跨支点4.2.4 由钢筋应力松弛引起的预应力损失l5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：. z.-l 51.00.3(0.52pefpk0.26)pe. z.-钢束pe (MPa )l 5 (N11,255.6834.3N21,250.3033.59N31,250.3033.59N41,250.3033.59表4-6l5计算表. z.-计算点跨中MPa ). z.-N51,250.3033.59N61,250.3033.59N11,241.5332.44N21,235.4931.66N31,235.4931.66N41,235.4931.66N51,235.4931.661/8 跨N61,235.4931.66N11,223.6930.14N21,208.6528.25N31,208.6528.25N41,209.5728.36N51,213.8128.891/4 跨N61,217.1029.31N11,200.2227.2N21,182.0724.99N31,196.9726.8N41,204.7827.77N51,211.7828.643/8 跨N61,216.2429.2N11,266.2235.71N21,266.2235.71N31,266.2235.71N41,266.2235.71N51,266.2235.71支点N61,266.2235.714.2.5 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：. z.-0.9* E pl 6cs (t,t0 )Eppc(t,t0 ). z.-2epp1i2其中115p. z.-Ep1.95*105MPa支座处. z.-2A232u. z.-Ep (t,t0 )(t,t0 )跨中处0.00021361.6276. z.-2A194u. z.-Ep (t,t0 )(t,t0 )0.000221.6536. z.-Ep5.493Ap0.6%An表4-7l6计算表. z.-c计算0.9*Epcs(t,t0)Eppcl