预应力混凝土简支小箱梁桥设计_201808211340171.doc

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 ：二一二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： 35 m；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小箱梁梁的预制部分及现浇接缝部分均采用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 ）。预应力钢筋：s15.2 钢绞线，f pk1860 MPa，单根面积14。0mm普通钢筋：直径 12 mm采用HRB33钢5 筋；直径 0.53772号梁图2-6mcq 20.5 *(0.24380.2410.23690.2270.21680.19980.18760.1711)0.8620按照2车道加载mcq10.5 *(0.24380.2410.23690.227)0.47440.67*0.862=0.57750.47443号梁mcq 30.5 *(0.18620.19440.20050.20850.21280.21500.21140.2038)0.8163按照2车道加载mcq10.5 *(0.18620.19440.20050.2085)0.39480.67*0.8163=0.54690.3948根据对称性关系mcq 4mcq 5mcq 2mcq10.86200.88593.2.2 支座处用杠杆原理法1号梁图2-7m0 q 4m0 q21.1323m0 q5m0 q11.07893.2.2活载计算荷载值qk10.5kN / mPk300 kN折减系数0.671号梁Q=1.143*1.0789*300*0.67+1.143* （0.5*（1.0789*1+0.8859*0.8571）*34.19/7+0.8859*0.5*6*34.19/7）*10.5*0.67=388.35kN1/8 跨处弯矩图2-13M=1.143*0.8859*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*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.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=121.82kN4,5 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 内力组合表3-61号梁内力组合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号梁内力组合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JTG D62-2004 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：st0.85pc0(4-1)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 ststybI 0(4-2)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。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NNepcybA0I 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，yb 的定义与式 (4-2)一致， N 是预加力，按下式计算I 0 和Neff Ap(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Ap0.85M stI 0effA0ybeff eyb I 0(4-5)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离e 需要预先假定。一般而言，对于f pk1860MPa 的预应力钢绞线的控制张拉应力取con0.75 f pk0.7518601395MPa ，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eff0.75con0.7513951046MPa 。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18cm 进行试算。M st10459.8kN .m2I 00.552myb1.17me0.99 m代入4-5得 Ap8365mm2选配12束515.2的钢束实际 Ap28400mm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*1011284276.34.2 预应力损失计算4.2.1 磨阻损失(ex)l 1con (1)0.00150.22con1395 MPa表4-3l1 计算表(x)xx1econ (1e (x ) )计算点钢束（） （ rad）mMPaN130.0523617.380.0375890.03689151.46314N270.1221717.380.0529470.0515771.94013N370.1221717.380.0529470.0515771.94013N470.1221717.380.0529470.0515771.94013N570.1221717.380.0529470.0515771.94013N670.1221717.380.0529470.0515771.94013N130.0523613.0050.0310260.0305542.61719N270.1221713.0050.0463850.04532563.229N370.1221713.0050.0463850.04532563.229N470.1221713.0050.0463850.04532563.229N570.1221713.0050.0463850.04532563.229N670.1221713.0050.0463850.04532563.229N130.052368.630.0244640.02416733.71299N270.122178.630.0398220.0390454.46051N370.122178.630.0398220.0390454.46051N46.680.116598.630.0385940.03785852.81241N55.360.093558.630.0335250.0329745.99255N64.480.078198.630.0301460.02969741.42674N130.052364.630.0184640.01829425.52072N24.930.086044.630.0258740.02554235.63166N33.310.057774.630.0196540.01946227.14981N42.590.04524.630.016890.01674823.36313N52.010.035084.630.0146630.01455620.30513N61.670.029154.630.0133570.01326818.50933N1000.120.000180.000180.251077N2000.120.000180.000180.251077N3000.120.000180.000180.251077N4000.120.000180.000180.251077N5000.120.000180.000180.251077N6000.120.000180.000180.251077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l 2按公预规l 2 计算公式如下反向摩擦影响长度：d (l fx) ；N10.00296119877.861738014.79261N20.00413916812.5173800N30.00413916812.5173800N40.00413916812.5173800N50.00413916812.5173800N60.00413916812.5173800N10.00327718895.381300538.6054N20.00486215512.791300524.38526N30.00486215512.791300524.38526N40.00486215512.791300524.38526N50.00486215512.791300524.38526N60.00486215512.791300524.38526N10.00390617306.12863067.78631N20.00631113616.25863062.93248N30.00631113616.25863062.93248N40.0061213827.08863063.60836N50.00532914816.81863065.94368N60.004815611.98863067.03143N1k0.00551214569.244630109.5709N20.00769612330.074630118.5167N30.00586414125.384630111.3597N40.00504615227.134630106.9469N50.00438616333.554630102.6532N60.00399817107.56463099.76298N10.00209223647.212098.45247N20.00209223647.212098.45247N30.00209223647.212098.45247N40.00209223647.212098.45247N50.00209223647.212098.45247N60.00209223647.212098.452473/8 跨支点4.2.3 钢筋松弛引起的预应力损失l 4n p5.4932Ap8400mm表4-5l 4 计算表conl1l 21en1计算点钢束平均AnWn1N1 npNAp ( 1en ) cosAnWpel 4MPacosnMPaMPa/mmN11328.74412.75E-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：l 51.00.3(0.52pef pk0.26)pe钢束pe (MPa )l 5 (N11,255.6834.3N21,250.3033.59N31,250.3033.59N41,250.3033.59表4-6l5 计算表计算点跨中MPa )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：0.9 * E pl 6cs (t ,t0 )Eppc(t,t 0 )2epp1i 2其中115pEp1.95 * 105MPa支座处2A232uEp (t, t0 )(t, t0 )跨中处0.00021361.62762A194uEp (t, t0 )(t, t0 )0.000221.6536Ep5.493Ap0.6%An表4-7l 6 计算表c计算0.9 * Epcs (t ,t0 )Eppcl 6(t ,t 0 )点钢束MPapMPaN127.07259.872.87206.55N226.94258.852.87205.74N326.94258.852.87205.74N426.94258.852.87205.74N526.94258.852.87205.74跨中N626.94258.852.87205.74N126.74257.22.87204.43N226.6256.062.87203.52N326.6256.062.87203.52N426.6256.062.87203.521/8N526.6256.062.87203.52跨N626.6256.062.87203.52N125.82249.722.79199.66N225.48246.932.79197.43N325.48246.932.79197.43N425.5247.12.79197.571/4N525.6247.892.79198.19跨N625.67248.52.79198.68N122.13219.542.26182.4N221.77216.612.26179.97N322.07219.012.26181.97N422.22220.282.26183.01N522.36221.412.26183.95N622.45222.132.26184.55N111.46125.51.2113.29N211.46125.51.2113.99N311.46125.51.2113.99N411.46125.51.2113.29N511.46125.51.2113.29N611.46125.51.2113.293/8跨支点表4-8钢束预应力损失一览表预加应力阶段正常使用阶段计算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点钢束12456N151.4631414.7926173.071,255.6834.3206.551,014.83N271.94013072.761,250.3033.59205.741,010.97N371.94013072.761,250.3033.59205.741,010.97N471.94013072.761,250.3033.59205.741,010.97N571.94013072.761,250.3033.59205.741,010.97N671.94013072.761,250.3033.59205.741,010.97N142.6171938.605472.251,241.5332.44204.431,004.66N263.22924.3852671.891,235.4931.66203.521,000.31N363.22924.3852671.891,235.4931.66203.521,000.31N463.22924.3852671.891,235.4931.66203.521,000.31N563.22924.3852671.891,235.4931.66203.521,000.31N663.