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益将江大桥第四联方案比选与施工图设计
故: h=
2A=2×6960/691.93=20.51(cm)u
设混凝土收缩和徐变在野外一般条件(相对湿度为75%)下完成,受荷时混凝土加
载龄期为20d。
按照上述条件,查《公预规》表6.2.7得到?(t,t0)=1. 79,?cs(t,to)=0.23×10-3
四分点截面σl6计算表 表19 计算数据 Np0=7147.015kN Mp0=8982.464kN·m Mgl=5688.288kN·m In=52560927cmAn=8011.54cm en=ep=122.33cm Ep=1.95×10MPa aEp=5.65 254 Npo/A(Mpa) 计算σpc ⑴ 8.921 (Mpo-Mgl)×en/In(Mpa) ⑵ 7.667 σpc(Mpa) ⑶=⑴+⑵ 16.588 计算公式:σl6=0.9[Ep?cs(t,t0)?aEp?pc?(t,t0)/1?15??p 计 算 应 力 损 失 ⑹ 0.9[⑷+⑸] 191.349 ⑷ ⑸ 分子式 αEp×σpc×φ(t,to) Epζcs 167.760 44.85 2分母式 i=In/An ρp=1+ep/i ρ=6△Ap/An 1+15ρρp 226560.65 3.281 0.734% 1.361 ?l6?191.349?140.573 1.361注:Np0和Mp0包括N7号预应力筋产生的轴力和弯矩,即近似取N1~N7号钢束徐变情况相同。
5.5.2 计算σl6
混凝土收缩和徐变引起的应力损失列表计算在表19内。
5.6 成桥后张拉N7号钢束混凝土弹性压缩引起的预应力损失
成桥后张拉N7号钢束,此时将引起混凝土弹性压缩,这对已张拉的N1~N6号钢束会引起应力损失,计算结果见表20。但由于张拉N7号束时,N1~N6号钢束已经灌浆,故不能考虑该项损失对混凝土应力的影响。
5.7 预加力计算及钢束预应力损失汇总
施工阶段传力锚固应力σp0及其产生的预加力;
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益将江大桥第四联方案比选与施工图设计
σp0=?con??lI=?con??l1??l2??l4由σp0产生的预加力
纵向力: Npo???po?Apcos?弯矩: Mpo?Npoepi
剪力: Qpo???po?APsin?
式中:α——钢束弯起后与梁轴的夹角,sina与cosa的值可参见表10;
△Ap——单根钢束的截面积;
可用上连同样的方法计算出使用阶段由张控钢束产生的预加力下面将计算结果一并列入表21内。表22示出了各控制截面的钢束预应力损失。
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成桥后四分点σ′14计算表 表20计算数据锚固时预加纵向力Np0=△Apσp0cosɑ (MPa×cm=0.1KN)Np0×epi(N·m)相应钢束到净轴距离ep0(cm)2A0=epi=y0x-ɑi(见表10)(cm)计算应力损失的钢束号预加弯矩Mp0=Np0Np7/A09960.92cm2 △Ap=143.15cm ɑEp=5.65Σ△σpc(MPa)9.8cm2 I0=70764877cm4 y0x=σ′l4=ɑEpΣ△σpc(MPa)Mp7·ep0/I0合计 益将江大桥第四联方案比选与施工图设计 第 34 页 共 88 页
钢锚固时钢束应力束cosɑσ=σ-σ-σ号p0conl1l2σp0×△Ap(见表10) -σl4-σl5-σl6 (Mpa)N7﹡1247.3312223.860.997211N31085.2310635.241.0000N21086.8310650.971.0000N41091.7210698.891.0000N11095.0310731.261.0000N61082.9210612.640.9991N51075.8510543.311.0000N71073.5610520.910.997211Σ﹡12189.7710635.2410650.9710698.8910731.2610602.6310543.3010491.5686543.61106.00126.45134.15126.45134.15122.48134.15106.001292115.391344826.351428827.931352874.541439597.971298610.001414383.241112105.4410683340.86N3N2N4N1N6N5126.45134.15126.45134.15122.48134.151.221.221.221.221.221.222.312.552.552.562.492.463.533.773.783.793.723.6919.9619.9621.3421.4020.9920.82 预加力作用效应计算表 表21预加应力阶段由张拉钢束产生的预加力作用效应使用阶段由张拉钢束产生的预加力作用效应αpo△ApV=σ△ApsinαNpo=σpo△ApcospopoMpoσpo△ApNpo=σpo△Vp=σpo△ApMp(0.1kN)α(kN)(kN·m)(0.1kN)Apcosαsinα(kN)(kN·m)截面钢束号sinαcosα跨中0000007334.62367109358.536111111112796.8411711.6912951.3412352.3011074.1712459.89011377.29四分点1.5050.397147.0163328982.46500000.0013275650.0434176310.07463578511110.9999990.9990570.99721111731.8412295.6312578.9711976.0011293.3311605.34 益将江大桥第四联方案比选与施工图设计 第 35 页 共 88 页
1792.49支点0.1218690.1218690.2588190.2588190.2588190.2588190.3090176916.26379511756.2112029.5412103.9511894.2911249.2511382.466950.8975830.9925460.9925460.9659260.9659260.9659260.9659260.95105711761.0711974.9012062.4711900.6111231.3411357.490143.331145.937312.200308.011290.688293.9542681.2671792.49N7锚固点1234567∑1234567∑1234567∑1234567∑1494.121107.764110.269134.922132.585266.529269.6851021.7541904.0310.0916650.0916650.1114690.1114690.2369310.2369310.0000000.9957900.9957900.9937680.9937680.9715270.9704171.00000011098.72311170.46111117.41311037.29010610.20510591.0909246.95674872.13810731.25610650.97210635.24210698.88910543.30610612.63710520.90574393.20710837.43710891.54010877.04110815.36410219.73310238.56810855.40274735.08511756.21312029.53512103.95311894.29411249.25111382.46310966.91181382.6211109.8721117.0461111.7411103.7291061.0211059.1099246.95615809.4741073.1261065.0971063.5241069.8891054.3301060.26310491.56116877.7891075.6661081.0361050.6411044.684987.150988.9701032.4107260.5571170.6721197.8891202.8521182.0171092.8951104.5741096.6918047.5891.39969261346.07755351785.2360099832.713132.075132.734281.519279.922264.506264.994335.4501691.201107.764110.269134.922132.585266.529269.6850.0001021.7541904.03 益将江大桥第四联方案比选与施工图设计
预加应力阶段 钢束预应力损失一览表 表22
正常使用阶段 锚固时钢束应力 锚固后预应力损失 截 面 钢 束 号 锚固前预应力损失 钢束有效应力 σlⅠ=σl1+σl2+σl4 σl1(Mpa) σl2(Mpa) σl4(Mpa) σpo=σcon-σlⅠ Mpa 1305.80 1315.90 1321.57 1310.75 1257.66 1263.41 1275.04 1197.13 1254.75 1246.92 1185.40 1127.78 1144.96 1247.33 1200.11 1221.93 1230.86 1214.35 1146.05 1158.93 1232.47 1237.40 1235.10 1231.31 1172.50 1174.01 σlⅡ=σl5+σl6+σl4′ σl5(Mpa) σl6(Mpa) σl4′ 39.68 49.34 54.98 34.93 18.96 22.58 36.90 26.82 36.46 38.06 29.93 17.47 20.64 33.20 39.68 49.34 54.98 34.93 18.96 22.58 27.13 30.63 31.60 28.88 20.98 22.55 70.09 90.09 140.573 118.245 σpe=σpo-σlⅡ (Mpa) 1 2 3 跨 中 4 5 6 7 1 2 四 3 分 4 点 5 6 7 1 2 支 3 点 4 5 6 1 2 3 n7 4 5 6 73.53 73.53 73.43 73.43 109.89 109.73 119.96 54.06 53.96 90.61 90.61 79.38 79.38 81.70 34.31 34.31 34.21 34.21 71.74 71.58 23.82 23.82 28.21 28.21 56.57 57.45 0.00 0.00 0.00 0.00 0 0 57.11 57.11 57.47 57.47 49.68 50.49 65.97 129.49 129.49 129.93 129.93 157.94 159.04 131.64 131.64 131.69 131.69 160.63 160.84 15.67 5.56 0.00 10.82 27.45 21.86 86.70 29.17 0.00 61.53 138.17 120.17 31.09 9.27 0.00 16.52 19.26 5.45 7.07 2.13 0.00 3.79 5.29 2.70 20.421 1127.45 21.162 1127.16 21.162 1127.18 21.127 1136.44 21.013 1099.45 20.370 1102.21 21.405 1008.33 19.959 1057.76 19.959 1048.33 21.340 993.55 20.823 948.91 20.992 962.75 1070.34 1082.50 1085.80 1089.33 1037.01 1046.26 1135.25 1136.69 1133.40 1132.34 1081.44 1081.37 第 36 页 共 88 页