第四章 预应力损失及有效预应力计算

第五章预应力损失及有效预应力计算5．1净截面几何性质计算按第三章布置预应力钢束之后,便可进行净截面及换算截面几何特性计算。其中净截面为扣除预应力孔道的截面，换算截面为孔道压浆后钢束与混凝土梁形成整体后的截面。显然，预加力阶段(即施工阶段)应采用净截面，使用阶段(即运营阶段)应采用换算截面。表5-1截面毛面积惯性矩中性轴到下缘距距离孔洞数净面积A-A6.8642.0210.6942186.7802228L1/85.4451.7340.7105185.3612228L1/45.4451.6330.7395185.36122283L1/85.44661.9930.8236185.3628228L1/25.49991.9240.7901185.41612285L1/85.62242.3850.8624185.53862283L1/46.13913.2010.9535246.02740047L1/86.92834.5671.0566296.7933334B-B7.692413.7581.3028407.506244L/86.27499.1441.3093256.158555L/45.68585.1111.0919185.60202283L/85.50522.7950.9201215.4074666L/25.4451.8930.785295.31003345．2控制应力及有关参数的确定图5-1平曲线影响角计算图式图5-2底板曲线影响角计算图式根据第三章的配筋特点,底板各截面钢束弯曲影响角由三部分组成:第一部分为平曲线(2000m半径)对应的圆心角，如图5-1所示，；第二部分为底板曲线斜率对应的夹角，如图5-2所示，可按下面的方法求得：由梁底曲线方程可得梁底任一截面的斜率==2.973×(34..8-2)进而可得按上式计算的各截面值见表5-1。表5-1各截截面θ2计结果截面L1/43L1/8L1/25L1/83L1/47L1/8L1L/8L/43L/8L/2斜率-0.52×10-22.56×10-24.59×10-26.63×10-28.67×10-210.4×10-28.03×10-25.35×10-22.68×10-20弧度-0.52×10-22.56×10-24.59×10-26.63×10-28.67×10-210.4×10-28.03×10-25.35×10-22.68×10-205．3摩阻损失的计算为了方便计算，根据全桥预应力钢束布置情况，可将.钢束分成六类，即边孔底板正弯矩束(b类)、通束预应力钢筋(A类)、中支点负弯矩顶板束(n类)、中孔正弯矩肋束(Ac类)、中孔正弯矩底板束(a类)和全桥通常束(T类)。摩阻损失计算公式：=式中：——张拉控制应力，=1395Mpa；——摩擦系数，取=0.25；k——局部偏差影响系数，取k=0.0015。5.3.1b类(边孔底板正弯矩束)钢束计算表5-2b类钢束摩阻损失σs1计算项目截面b1b1θ(弧度)边支点处0(θ1)00(θ1)00(θ2)0(θ2)0(θ3)0(θ3)L1/800.174500.1745000.17450.1745L1/400.174500.1745000.17450.17453L1/800.179700.17970.52×100-20.52×100-20.17450.1745L1/200.200100.20012.56×100-22.56×100-20.17450.1745X(m)边支点处0.60.6L1/84.0254.025L1/48.458.453L1/85.0255.025L1/21.61.6σs1(Mpa))边支点处1.25480051.2548005L1/867.58011967.580119L1/476.36088676.3608863L1/871.29133871.291338L1/271.24177571.2417755.3.2a类(中支点负弯矩顶板束)钢束计算表5-3a类钢束摩阻损失σs1计算项目截面A1a2θ(弧度)3L/800.20132.68×100-20.1745L/200.174500.1745000.17450.1745X(m)3L/81.75L/26.252σs1(Mpa))3L/871.936447L/272.00266163.5424445.3.3n类(中孔正弯矩底板束)钢束计算顶板各截面钢束弯曲影响仅由θ1和θ3组成。表5-4n类类钢束σs1计算项目截面n1n2n3n4θ(弧度)θ=θ1+θ35L1/80.17453L1/40.17450.17457L1/80.17450.17450.1745B-B0.17450.17450.17450.1745L/80.17450.1745L/40.1745X(m)5L1/823L1/45.412527L1/88.83755.4252B-B11.146.52.12.1L/86.51252L/42σs1(Mpaa)5L1/863.5424443L1/470.33977363.5424447L1/877.12700170.36455663.542444B-B81.6703372.49855963.74211363.742113L/872.52333963.542444L/463.5424445.3.4T类(两端张拉)钢束计算本桥的为0。表5-5截面Xσs1(Mpaa)A-A0.61.2548005L1/83.4257.1476995L1/46.8514.2587773L1/810.27521.33344L1/213.728.3717795L1/817.12535.3741113L1/420.5542.3405567L1/823.97549.271331B-B27.456.166555L/831.965.172331L/436.474.117553L/840.983.002551L/245.491.8277765.3.5A类钢束计算。由决定表5-6项目截面A1A2θ(弧度)A-A00L1/80.08720.0872L1/40.08720.08723L1/80.08720.0872L1/20.08720.08725L1/80.08720.08723L1/40.20930.24427L1/80.33140.402B-B0.33140.402L/80.33140.402L/40.33140.55823L/80.74940.7152L/20.74940.7152X(m)A-A0.60.6L1/83.4253.425L1/46.856.853L1/810.27510.275L1/213.713.75L1/817.12517.1253L1/420.5520.557L1/823.97523.975B-B27.427.4L/831.931.9L/436.436.43L/840.940.9L/245.445.4σs1(Mpa))A-A1.25480051.2548005L1/837.07244137.072441L1/444.03011544.0301153L1/850.95222450.952224L1/257.83888757.8388875L1/864.69022164.6902213L1/4111.29117122.442217L1/8156.26006177.93003B-B162.60777184.16663L/8170.89774192.31111L/4179.13115246.146643L/8307.13116297.79114L/2314.44992305.171195.3.6Ab(中支点负弯矩肋束类)钢束计算表5-7项目截面A3A4θ(弧度)7L1/80.2268990.226899B-B0.2268990.226899L/80.2268990.226899X(m)7L1/81.6156B-B5.04062.2165L/81.6156σs1(Mpa))7L1/880.107885B-B86.84500981.292337L/880.1078855.3.7Ac(跨中点正弯矩肋束类)钢束计算表5-8项目截面A5θ(弧度)3L/80L/20.2966X(m)3L/84.5L/20σs1(Mpa))3L/89.3835772L/299.6873345.3.8各截面平均值计算表5-9各截截面摩阻损损失σs1平均值值汇总(单位：Mpa))截面边支点L1/8L1/43L1/8L1/2上缘下缘上缘下缘上缘下缘上缘下缘上缘下缘σs1平0.7173.1377.14749.27514.2556.96221.33359.08728.37163.200截面5L1/83L1/47L1/8B-BL/8上缘下缘上缘下缘上缘下缘上缘下缘上缘下缘σs1平均44.7635564.69022165.643085.558078.016095.8230截面L/43L/8L/2上缘下缘上缘下缘上缘下缘σs1平均92.300246.146660.365213.0691.827128.576655．4锚具变形损失的计算5.4.1计算公式反摩擦影响长度，式中：——张拉端锚下控制张拉应力；——锚具变形值，取=5mm；——扣除沿途管道摩擦损失后锚固端预拉应力；——张拉端到锚固端之间的距离；当时，；离张拉端x处由锚具变形、钢筋回缩和接缝压缩引起的、考虑反摩擦后的预拉力损失为，当时，表示该截面不受反摩擦的影响。当≥，预应力钢筋得全长均处于反摩阻影响长度以内，扣除管道摩阻和钢筋回缩等损失后得预应力线以db线表示，距离张拉端处由锚具变形引起的考虑反摩阻后的预应力损失为：式中：—距张拉端处由锚具变形引起的考虑反摩阻后的预拉力损失；5.4.2计算方法与计算相似，分别按六类钢束计算，最后计算平均值。计算过程中考虑反向摩阻影响。表5-10反反摩擦影响响长度计算算表钢束号σl1(Mpaa)σl=σ0-σl1(Mpa))L(mm)Δσd=(σ00-σl)/L(Mpa/mm)lf(mm)Δσb176.3601318.64484500.009033710253.115185.3099a172.0021322.999862500.0115229080.9113209.23001a263.5421331.455820000.03177715468.2225347.46119n181.6701313.33311012.550.007411611318.11167.87227n272.4981322.500265000.01115549229.0117205.87224n363.7421331.255854250.0117558991.8445211.30226n463.7421331.255821000.03035535594.4666339.62114A1314.441080.566454000.006922611711.772162.23006A2305.17221089.8228454000.006722211888.224159.82119A386.8451308.15556115.60.01420018179.1664232.29776A481.2921313.70082115.60.03842254972.277382.11993A599.6871295.311345000.02215536548.6005290.13881T91.8281303.1772454000.002022321672.11687.6700095.4.3b类钢束计算b1表5-11b类钢束σs2计算A-AL1/8L1/43L1/8L1/2x(mm)604025845050251600Δσd0.00903370.00903370.00903370.00903370.0090337Δσ(Mpa)185.3099185.3099185.3099185.3099185.3099σl2(Mpa))184.76668148.93551108.94664139.89881170.84998a类钢束计算表5-12aa类钢束σs2计算钢束a1a2截面3L/8L/2L/2x(mm)175062502000Δσd0.011520.011520.031771Δσ(Mpa)209.2301209.2301347.4619σl2(Mpa)189.0701137.2301283.9199n类钢束计算表5-13n1类钢束σs2计算钢束n1截面5L1/83L1/47L1/8B-BL/8L/4x(mm)20005412.58837.511012.556512.52000Δσd0.00741160.00741160.00741160.00741160.00741160.0074116Δσ(Mpa)167.87227167.87227167.87227167.87227167.87227167.87227σl2(Mpa))153.04007127.73336102.3333886.204119.5766153.04007表5-14n2类钢束σs2计算钢束n2截面3L1/47L1/8B-BL/8x(mm)2000542565002000Δσd0.01115540.01115540.01115540.0111554Δσ(Mpa)205.87224205.87224205.87224205.87224σl2(Mpa))183.56444145.3622133.37114183.56444表5-15n3,n4类钢束σs2计算钢束n3n4截面7L1/8B-BB-Bx(mm)200054252100Δσd0.0117550.0117550.0303553Δσ(Mpa)211.30226211.30226339.62114σl2(Mpa))187.80226147.55889275.880015.4.6T类钢束计算L1/2处，x>Lf，σs2==0；表5-16T类钢束σs2计算钢束T截面A-AL1/8L1/43L1/8x(mm)6003425685010275Δσd0.00202230.00202230.00202230.0020223Δσ(Mpa)87.67000987.67000987.67000987.670009σl2(Mpa))83.17866962.03166636.39322410.7548815.4.7A类钢束计算L1/2处，x>Lf，σs2==0；表5-17A1类钢束σs2计算钢束A1截面A-AL1/8L1/43L1/8x(mm)6003425685010275Δσd0.00692260.00692260.00692260.0069226Δσ(Mpa)162.23006162.23006162.23006162.23006σl2(Mpa))153.91994114.7877567.34444919.901443表5-18A2类钢束σs2计算钢束A2截面A-AL1/8L1/43L1/8x(mm)6003425685010275Δσd0.00672220.00672220.00672220.0067222Δσ(Mpa)159.82119159.82119159.82119159.82119σl2(Mpa))151.75557113.7777267.73255721.687991表5-19A3,A4,A5类钢束σs2计算钢束A3A4A5截面7L1/8B-BL/8B-BB-Bx(mm)1615.65040.61615.61615.64500Δσd0.01420010.01420010.01420010.03842250.0221553Δσ(Mpa)232.29776232.29776232.29776382.11993290.13881σl2(Mpa))186.4111389.134448186.41113257.9600490.761115.4.8各截面平均值计算表5-20边边支点截面面下缘σs2平均值值计算钢束号①b1A1A2∑钢束数②43310σis2③184.76668153.91994113.77772②×③739.06772461.75882341.331161542.1557加权平均σs22=(∑②×③)／∑②=154.22157表5-21L1/8截面下缘σs2平均值计算钢束号①b1A1A2∑钢束数②43310σis2③148.93551114.78775113.77772②×③595.74004344.36225341.331161281.4335加权平均σs22=(∑②×③)／∑②=128..14355表5-22LL1/4截面下下缘σs2平均值计计算钢束号①b1A1A2∑钢束数②43310σis2③108.9466467.34444967.732557②×③435.78556202.03335203.19777841.01668加权平均σs22=(∑②×③)／∑②=84.1101688表5-2233L1/8截面下下缘σs2平均值计计算钢束号①b1A1A2∑钢束数②43310σis2③139.8988119.90144321.687991②×③559.5922459.70422965.063773684.36004加权平均σs22=(∑②×③)／∑②=68.4436044表5-23LL1/2截面下下缘σs2平均值计计算钢束号①b1A1A2∑钢束数②43310σis2③170.84998②×③683.39992683.39992加权平均σs22=(∑②×③)／∑②=68.33399225L1/8-LL/4截面面的下缘σs2平均值计计算为0。表5-233L/8截面下缘σs2平均值计算钢束号①a1A1A2∑钢束数②43310σis2③189.0701②×③756.2804756.2804加权平均σs2=(∑②×③)／∑②=75.62804表5-24L/2截面下缘σs2平均值计计算钢束号①a1A1A2a2A5∑钢束数②4338321σis2③137.23001283.9199990.76111②×③548.92004002271.3559272.283333092.5663加权平均σs22=(∑②×③)／∑②=147..26499表5-25A--A截面上上缘σs2平均值计计算钢束号①T∑钢束数②88σis2③83.178669②×③665.429952665.429952加权平均σs22=(∑②×③)／∑②=83.1178699表5-26LL1/8截面上上缘σs2平均值计计算钢束号①T∑钢束数②88σis2③83.178669②×③665.429952665.429952加权平均σs22=(∑②×③)／∑②=83.1178699L1/4截面：加权平均σs2236.33932443L1/8截面：加权平均σs2210.7754811表5-2655L1/8截面上上缘σs2平均值计计算钢束号①n1T∑钢束数②4812σis2③153.04007②×③153.04007612.16228加权平均σs22=(∑②×③)／∑②=51.00135表5-273L1/4截面上缘σs2平均值计算钢束号①n1n2A1T∑钢束数②443819σis2③127.73336183.56444②×③510.93444734.257761245.1992加权平均σs22=(∑②×③)／∑②=65.5536422表5-287L1/8截面上缘σs2平均值计算钢束号①n1n2n3A3∑钢束数②444329σis2③102.33338145.3622187.8022186.41113②×③409.33552581.4488751.2088559.233392301.2225加权平均σs22=(∑②×③)／∑②=79.3352599表5-29B-B截面上缘σs2平均值计算钢束号①n1n2n3n4A3A4∑钢束数②44483340σis2③86.204133.3711147.5588275.880089.13444257.9600②×③344.8166533.4844590.23222207.044267.40332773.884716.8555加权平均σs22=(∑②×③)／∑②=117..921表5-30L/8截面上缘σs2平均值计算钢束号①n1n2A3∑钢束数②44325σis2③119.5766183.56444186.41113②×③478.3044734.25776559.233391771.7996加权平均σs22=(∑②×③)／∑②=70.88718表5-31L/4截面上缘σs2平均值计算钢束号①n1∑钢束数②415σis2③153.04007②×③612.16228612.16228加权平均σs22=(∑②×③)／∑②=153..04077表5-32各各截面锚具具变形损失失σs2平均值值汇总(单位：Mpa))截面边支点L1/8L1/43L1/8L1/2上缘下缘上缘下缘上缘下缘上缘下缘上缘下缘σs2平83.178154.215583.178128.143336.39384.10110.75468.43668.339截面5L1/83L1/47L1/8B-BL/8上缘下缘上缘下缘上缘下缘上缘下缘上缘下缘σs2均51.014065.536079.3520117.9211070.8710截面L/43L/8L/2上缘下缘上缘下缘上缘下缘σs2平153.04000075.628147.26445.5预应力筋分批张拉损失的计算5.5.1计算公式式中：m——钢束张拉批数；——=；——钢束形心处由该预加力产生的混凝土的正应力，如计入一期恒载影响则可按下式计算式中：——扣除后的有效预加力，，应计弯起角度影响；——混凝土净净面积；——钢束重心心至混凝土土净截面形形心之距离离；——混凝土净净截面惯矩矩；———一期恒载载产生的弯弯矩。5.5.2计算结结果表表5-333分批张拉拉损失σs4计算项目截面边支点L1/8L1/4上缘下缘上缘下缘上缘下缘σs1(Mpa))0.71703313.13701137.147699549.275552214.25877756.9624434σs2(Mpa))83.178154.215583.178128.143336.39384.101Ay(m2)0.01167760.00333360.00667720.0083440.00667720.008344Aj(m2)6.78022285.36122285.36122285.36282285.41612285.5386228Ij(m4)1.95834491.95834491.68024461.68024461.58237771.5823777eyj(m)0.40580.59420.38950.61050.36050.6395Mg1(kN·mm)003592.5779-3592.55795433.9118-5433.9918m(批数)424444Ny(kN)15308.4464128.79948704.788710154.6638969.499110457.8831σs4(Mpa))7.32100072.08509986.69599935.866366617.49784454.94576642项目截面3L1/8L1/25L1/8上缘下缘上缘下缘上缘下缘σs1(Mpa))21.3334459.0879928.37177963.200002244.7635550σs2(Mpa))10.75468.436068.33951.0140Ay(m2)0.00667720.0083440.00667720.0083440.01000080.0050004Aj(m2)6.02740046.79333347.5062446.1585557.3077.307Ij(m4)1.93121171.93121171.86435561.86435562.31106652.3110665eyj(m)0.27840.72360.36490.69015.19470.7624Mg1(kN·mm)5676.8888-5676.8894135.9225-4135.99251335.5996-1335.5596m(批数)444460Ny(kN)9093.355310570.7759118.144310537.226513002.6626980.588σs4(Mpa))5.55928844.73939975.52515595.93050099359.343380项目截面3L1/47L1/8B-B上缘下缘上缘下缘上缘下缘σs1(Mpa))65.643994085.558772078.0169980σs2(Mpa))65.536079.3520117.92110Ay(m2)0.020011600.024188600.0333660Aj(m2)7.9627.9628.7528.75224.87324.87Ij(m4)3.10176693.10176694.42542234.425422313.3315513.3315502eyj(m)5.29560.52540.5472Mg1(kN·mm)-3322.4433322.4229-9800.8839800.8226-18366..418366.4424m(批数)80130170Ny(kN)25296.662029750.994040000.7710σs4(Mpa))545.02001010.39933904.54232270项目截面L/8L/43L/8上缘下缘上缘下缘上缘下缘σs1(Mpa))95.823663092.300228246.1466460.365446213.066656σs2(Mpa))70.8710153.040075.628Ay(m2)0.02085500.0125110.00250020.00917740.008344Aj(m2)8.2028.2027.077.076.836.83Ij(m4)8.86053368.86053364.95255594.95255592.70835552.7083555eyj(m)0.18270.24910.58990.8201Mg1(kN·mm)-7848.0077848.0772-669.8998669.89883578.1441-3578.1141m(批数)1107144Ny(kN)25610.117014382.2242874.4331712243.9949226.58874σs4(Mpa))7.652433805.146911708.56030025.28393304项目截面L/2上缘下缘σs1(Mpa))91.827776128.57665σs2(Mpa))147.2644Ay(m2)0.00667720.0175114Aj(m2)6.726.72Ij(m4)1.83431171.8343117eyj(m)0.3150.685Mg1(kN·mm)5023.5009-5023.551m(批数)46Ny(kN)8694.766519600.996σs4(Mpa))5.424800113.8933355.6钢筋应力松松弛损失的的计算式中：———超张拉系系数，；——钢筋松弛弛系数，==1.0；；———传力锚固固时的钢筋筋应力，表5-34钢钢筋应力松松弛损失项目截面边支点L1/8L1/4上缘下缘上缘下缘上缘下缘σs1(Mpa))0.71703313.1370117.147749.2755514.25877756.962443σs2(Mpa))83.178154.215583.178128.143336.39384.101σs4(Mpa))7.32100072.08516.6959995.8663777.49784454.9457664σpe(MPa))1303.78841235.5661297.9881211.7221336.8551248.9991σpe(MPa))122.6199494.99455120.177785.89022136.85118100.24668项目截面3L1/8L1/25L1/8上缘下缘上缘下缘上缘下缘σs1(Mpa))21.3334459.0879928.3718863.244.763555σs2(Mpa))10.75468.436068.33951.014σs4(Mpa))5.55928844.73945.5251665.930511359.34338σpe(MPa))1357.35531262.7441361.11257.533939.87886σpe(MPa))145.9533105.7177147.64103.63442.3361447项目截面3L1/47L1/8B-B上缘下缘上缘下缘上缘下缘σs1(Mpa))65.64399485.5587778.016998σs2(Mpa))65.53679.352117.9211σs4(Mpa))545.0200110.399444.5423227σpe(MPa))718.81219.6991194.522σpe(MPa))-38.1977588.9028879.503113项目截面L/8L/43L/8上缘下缘上缘下缘上缘下缘σs1(Mpa))95.82366392.30033246.146660.365446213.06666σs2(Mpa))70.871153.040075.628σs4(Mpa))7.65243385.14692208.56030025.283933σpe(MPa))1220.65531144.5111148.8551326.07741101.0222σpe(MPa))89.26888261.7741163.26322132.1533147.37833项目截面L/2上缘下缘σs1(Mpa))91.827776128.5766σs2(Mpa))147.2644σs4(Mpa))5.424800113.89344σpe(MPa))1297.74471105.277σpe(MPa))120.0800648.741445.7混凝土徐变变收缩损失失的计算5.7.1计算算公式在不变的应力长长期持续作作用下，混混凝土的变变形会随着着时间而不不断增长，这这就是混凝凝土的徐变变。由于混混凝土收缩缩和徐变的的影响，会会使预应力力混凝土构构件产生变变形，因而而引起预应应力钢筋的的应力损失失。《桥规规》（JTGD62）规定，由由混凝土收收缩、徐变变引起的构构件受拉区区预应力钢钢筋的应力力损失，可可按下式计计算：式中：——由混混凝土收缩缩、徐变引引起的构件件受拉区预预应力钢筋筋的应力损损失；———构件受拉拉区全部钢钢筋重心处处，由预加加力（扣除除相应阶段段的预应力力损失）和和结构自重重产生的混混凝土法向向应力；———预应力钢钢筋弹性模模量；———预应力钢钢筋弹性模模量和混凝凝土的弹性性模量的比比值；———构件受拉拉区全部纵纵向钢筋配配筋率；———计算参数数；———截面回转转半径，,,A、J为构件截截面面积和和惯性矩，《桥桥规》（JTGD62）规定，对对先张法取取换算截面面；对后张张法取净截截面；——构件截面受拉区区全部纵向向钢筋截面面重心至构构件截面重重心的距离离；——预应力钢筋传力力锚固龄期期为t0，计算考考虑的龄期期为t时的混凝凝土收缩应应变，其终终值可按《桥桥规》（JTGD62）中相关关表格取用用；——加载龄期为t00，计算考考虑的龄期期为t时的徐变变系数，其其终值可按按《桥规》（JTGD62）中相关关表格取用用；5.7.2计算结结果按照以上的计算算思路和方方法，很容容易求出混混凝土收缩缩和徐变损损失，查规范得数值表5-35混凝凝土收缩和和徐变引起起的预应力力损失值项目边支点L1/8L1/4上缘下缘上缘下缘上缘下缘σ11+σl2++σl491.216004159.4377197.021669183.2844958.149662146.00992Aj(m2)6.78022285.36122285.36122285.36282285.36122285.3612228Ij(m4)1.30121.30121.30121.30121.12581.1258eps(m)0.44730.55270.38440.61560.38440.6156Ay(m2)0.01167760.00333360.00667720.0083440.00667720.008344ρ0.00272220.00162220.00224440.00255550.00224440.0025556i20.19191110.24270060.20998890.20992270.21105520.2344443Npe15222.9984121.83388660.111110105.778919.466610416.558ρps2.04255532.25863331.70367712.80521191.70012262.6164444σpe1303.78841235.56631297.97781211.71151336.8551248.9991σpc(MPa))4.58594441.7364992.59875584.82759982.83439955.4493446σpc4.58594441.7364992.59875584.82759982.83439955.4493446εcs(t,288)0.0001330.0001330.0001330.0001330.0001330.000133Ф(t,28)1.441.441.441.441.441.44σl6（Mpa）52.58911133.54288339.6453353.09700941.3384457.726557项目3L1/8L1/25L1/8上缘下缘上缘下缘上缘下缘σ11+σl2++σl437.646668132.2633333.896995137.46995455.121140Aj(m2)5.36122285.36122285.41612285.41612285.53862285.5386228Ij(m4)1.13151.13151.25691.25691.57781.5778eps(m)0.38490.61710.40620.64880.45480.7222Ay(m2)0.00667720.0083440.00667720.0083440.01000080.0050004ρ0.00224440.00255560.00223320.0025440.00280070.0019003i20.29429980.42676680.65690080.95717780.93600080.9360008Npe9056.266110531.2229081.28810487.889406.30056980.588ρps1.50339941.89231171.25117741.43977731.22098841.5572331σpe1357.35531262.73371361.10031257.533939.878861395σpc(MPa))2.87495565.50867712.86884485.44881152.93143373.5679113σpc2.87495565.50867712.86884485.44881152.93143373.5679113εcs(t,288)0.0001330.0001330.0001330.0001330.0001330.000133Ф(t,28)1.441.441.441.441.441.44σl6（Mpa）41.89155159.63966942.19800360.20988642.26699147.164993项目3L1/47L1/8B-B上缘下缘上缘下缘上缘下缘σ11+σl2++σl4676.20175.310010200.480030Aj(m2)6.02740046.02740046.79333346.79333347.5062447.506244Ij(m4)2.2882.2883.55793.55795.18425.1842eps(m)0.56040.7160.8711Ay(m2)0.020011600.024188600.0333660ρ0.00432210.0010.0045660.0010.00544440.001i20.47313390.29196660.18691190.16572210.69065520.6906552Npe14387.55029499.442039849.1180ρps1.663755513.742677112.09869941σpe718.813951219.69913951194.5221395σpc(MPa))4.361822608.5929663011.1415560σpc4.361822608.5929663011.1415560εcs(t,288)0.0001330.0001330.0001330.0001330.0001330.000133Ф(t,28)1.441.441.441.441.441.44σl6（Mpa）49.89655621.90144869.53266121.90144891.03988721.901448项目L/8L/43L/8上缘下缘上缘下缘上缘下缘σ11+σl2++σl4174.347710250.48772246.1466468.925776293.97885Aj(m2)6.1585556.1585555.60202285.60202285.40746665.4074666Ij(m4)2.85182.85181.75981.75981.26981.2698eps(m)0.61710.4810.760.75810.6519Ay(m2)0.02085500.0125110.00250020.00917740.008344ρ0.00438860.0010.00323330.00144470.00269970.0025442i20.46306640.46306640.31413360.31413360.23482230.2348223Npe25450.661014317.8862874.433212165.4419182.5119ρps1.822377611.73649992.83869933.44743372.8097558σpe1220.655313951144.51131148.85541326.07741101.0222σpc(MPa))7.531088904.43820031.45654497.75584444.7713002σpc7.531088904.43820031.45654497.75584444.7713002εcs(t,288)0.0001330.0001330.0001330.0001330.0001330.000133Ф(t,28)1.441.441.441.441.441.44σl6（Mpa）70.80099421.90144851.51711831.33522471.07999452.729445项目L/2上缘下缘σ11+σl2++σl497.252556289.73338Aj(m2)5.31003345.3100334Ij(m4)1.12581.1258eps(m)0.38440.6156Ay(m2)0.00667720.0175114ρ0.00225560.0042998i20.21201140.2120114Npe8658.577119357.663ρps1.69695522.7874447σpe1297.74471105.2666σpc(MPa))2.767055910.161559σpc2.767055910.161559εcs(t,288)0.0001330.000133Ф(t,28)1.441.44σl6（Mpa）40.84811884.1034475.8预应力损失失组合项目截面面边支点L1/8L1/4上缘下缘上缘下缘上缘下缘σs10.71703313.1370117.147749.2755514.2588856.96244σs283.178154.215583.178128.143336.39384.101σs47.32100072.08516.6959995.8663777.4978554.945766σsI91.216004159.437797.02177183.285558.14966146.0099σs5122.6199494.99455120.177785.89022136.8522100.2477σs645.99044732.1468844.4798840.2251147.3464436.86822σsⅡ168.60999127.1411164.6577126.1155184.1988137.1155σyI=σk-σsI1303.78841235.5661297.9881211.7221336.8551248.999σyⅡ=σk-σsI-σsⅡ1135.17741108.4221133.3221085.61152.6551111.888σsⅡ加权平均159.39446143.2455158.0411钢束数144810810σyI加权平均1288.622