组合梁桥课程设计

混凝土龄期表2工况时间单元-1单元-2单元-3单元-4单元-5单元-6单元-7单元-8单元-9单元-10单元-11单元-12单元-13单元-14单元-15平均龄期t0浇筑单元-100.00浇筑单元-2330.19浇筑单元-36630.56浇筑单元-499631.13浇筑单元-512129631.88浇筑单元-61515129632.81浇筑单元-7181815129633.94浇筑单元-821211815129635.25浇筑单元-92424211815129636.75浇筑单元-10272724211815129638.44浇筑单元-11303027242118151296310.31浇筑单元-1233333027242118151296312.38浇筑单元-133636333027242118151296314.63浇筑单元-14393936333027242118151296317.06浇筑单元-1542423936333027242118151296319.69桥面硬化完成4545423936333027242118151296322.50桥面系施工11092898683807774716865625956535066.56当n=n0时截面特性表3（移动荷载与温度荷载）区段翼缘厚度

t（mm）腹板厚度

tw（mm）下翼缘宽度b下（mm）上翼缘宽度b上（mm）腹板高度hw（mm）梁高h（mm）弹模比

n换算后

截面面积A0mm2换算后截面惯

性矩I0（mm4）y0cmmy0smm边跨0-40m401812001000272028005.9712805.974.887E+11676.1262537.87440-45.0m551812001000269028005.9712805.975.9596E+11758.77322455.22745.0-55.5m处802612001000264028005.9712805.977.8914E+11909.39272304.60755.5-67.5m处1202612001000256028005.9712805.971.0117E+121043.4952170.505中跨0-8m1202612001000256028005.9712805.971.0117E+121043.4952170.5058-18m802612001000264028005.9712805.977.8914E+11909.39272304.60718-30m551812001000269028005.9712805.975.9596E+11758.77322455.22730-60m401812001000272028005.9712805.974.887E+11676.1262537.87460-72m551812001000269028005.9712805.975.9596E+11758.77322455.22772-82m802612001000264028005.9712805.977.8914E+11909.39272304.60782-90m1202612001000256028005.9712805.971.0117E+121043.4952170.505边跨0-12m1202612001000256028005.9712805.971.0117E+121043.4952170.50512-22m802612001000264028005.9712805.977.8914E+11909.39272304.60722-27.0m551812001000269028005.9712805.975.9596E+11758.77322455.22727.0-67.5m401812001000272028005.9712805.974.887E+11676.1262537.874当n=n1时截面特性表4（收缩）区段翼缘厚度

t（mm）腹板厚度

tw（mm）下翼缘宽度b下（mm）上翼缘宽度b上（mm）腹板高度hw（mm）梁高h（mm）弹模比

n换算后

截面面积A0mm2换算后截面惯

性矩I0（mm4）y0cmmy0smm边跨0-40m4018120010002720280014.762690743.9933E+111045.4392168.56140-45.0m5518120010002690280014.763015344.8133E+111141.632072.3745.0-55.5m8026120010002640280014.763767546.2392E+111293.5551920.44555.5-67.5m12026120010002560280014.764626747.9667E+111412.6811801.319中跨0-8m12026120010002560280014.764626747.9667E+111412.6811801.3198-18m8026120010002640280014.763767546.2392E+111293.5551920.44518-30m5518120010002690280014.763015344.8133E+111141.632072.3730-60m4018120010002720280014.762690743.9933E+111045.4392168.56160-72m5518120010002690280014.763015344.8133E+111141.632072.3772-82m8026120010002640280014.763767546.2392E+111293.5551920.44582-90m12026120010002560280014.764626747.9667E+111412.6811801.319边跨0-12m12026120010002560280014.764626747.9667E+111412.6811801.31912-22m8026120010002640280014.763767546.2392E+111293.5551920.44522-27.0m5518120010002690280014.763015344.8133E+111141.632072.3727.0-67.5m4018120010002720280014.762690743.9933E+111045.4392168.561当n=n2时截面特性表5（一期恒载）区段翼缘厚度

t（mm）腹板厚度

tw（mm）下翼缘宽度b下（mm）上翼缘宽度b上（mm）腹板高度hw（mm）梁高h（mm）弹模比

n换算后

截面面积A0mm2换算后截面惯

性矩I0（mm4）y0cmmy0smm边跨0-40m4018120010002720280015.292644943.9567E+111060.6812153.31940-45.0m5518120010002690280015.292969544.7685E+111156.692057.3145.0-55.5m8026120010002640280015.293721746.1797E+111307.441906.5655.5-67.5m12026120010002560280015.294580947.8943E+111425.1531788.847中跨0-8m12026120010002560280015.294580947.8943E+111425.1531788.8478-18m8026120010002640280015.293721746.1797E+111307.441906.5618-30m5518120010002690280015.292969544.7685E+111156.692057.3130-60m4018120010002720280015.292644943.9567E+111060.6812153.31960-72m5518120010002690280015.292969544.7685E+111156.692057.3172-82m8026120010002640280015.293721746.1797E+111307.441906.5682-90m12026120010002560280015.294580947.8943E+111425.1531788.847边跨0-12m12026120010002560280015.294580947.8943E+111425.1531788.84712-22m8026120010002640280015.293721746.1797E+111307.441906.5622-27.0m5518120010002690280015.292969544.7685E+111156.692057.3127.0-67.5m4018120010002720280015.292644943.9567E+111060.6812153.319当n=n3时截面特性表6（二期恒载）区段翼缘厚度

t（mm）腹板厚度

tw（mm）下翼缘宽度b下（mm）上翼缘宽度b上（mm）腹板高度hw（mm）梁高h（mm）弹模比

n换算后

截面面积A0mm2换算后截面惯

性矩I0（mm4）y0cmmy0smm边跨0-40m4018120010002720280013.982764454.0496E+111021.9662192.03440-45.0m5518120010002690280013.983089054.8826E+111118.3292095.67145.0-55.5m8026120010002640280013.983841256.332E+111271.9011942.09955.5-67.5m12026120010002560280013.984700458.0803E+111393.1171820.883中跨0-8m12026120010002560280013.984700458.0803E+111393.1171820.8838-18m8026120010002640280013.983841256.332E+111271.9011942.09918-30m5518120010002690280013.983089054.8826E+111118.3292095.67130-60m4018120010002720280013.982764454.0496E+111021.9662192.03460-72m5518120010002690280013.983089054.8826E+111118.3292095.67172-82m8026120010002640280013.983841256.332E+111271.9011942.09982-90m12026120010002560280013.984700458.0803E+111393.1171820.883边跨0-12m12026120010002560280013.984700458.0803E+111393.1171820.88312-22m8026120010002640280013.983841256.332E+111271.9011942.09922-27.0m5518120010002690280013.983089054.8826E+111118.3292095.67127.0-67.5m4018120010002720280013.982764454.0496E+111021.9662192.0342.4未开裂时恒载内力计算2.4.1一期恒载集度主梁与混凝土板的换算均布荷载:式中q1——一期恒载Ac——混凝土横截面面积As——钢梁横截面面积qc——一混凝土容重qs——一钢梁容重横梁的换算均布荷载：端横梁采用焊接组合工字钢，钢的容重为78.5kN/m3，端横梁长为8m。中间横梁每8m布置一个，共27个，采用63b热轧工字钢，横梁长为7m。63b热轧工字钢质量为131.5kg/m。横梁的换算均布荷载为q=eq\f(2×[300×40×2+(1500-40×2)×30]×78.5×8×10-6+131.5×7×27×10×10-3,225)=1.454kN/m端横梁尺寸见图2-1。端横梁截面尺寸图2-1单位mm带入各截面面积得一期恒载见表1一期恒载表7钢梁面积长度m钢容重钢梁自重kN混凝土容重混凝土面积Ac（mm2）混凝土自重kNAsmm2kN/m3kN/m30-40m处1369604078.5430.052519500001950.0040-45.0m处169420578.566.50251950000243.7545.0-55.5m处24464010.578.5201.64251950000511.8855.5-67.5m处3305601278.5311.39251950000585.000-8m处330560878.5207.59251950000390.008-18m处2446401078.5192.04251950000487.5018-30m处1694201278.5159.59251950000585.0030-60m处1369603078.5322.542519500001462.5060-72m处1694201278.5159.59251950000585.0072-82m处2446401078.5192.04251950000487.5082-90m处330560878.5207.59251950000390.000-12m处3305601278.5311.39251950000585.0012-22m处24464010.578.5201.64251950000511.8822-27.0m处169420578.566.50251950000243.7527.0-67.5m处1369604078.5430.052519500001950.00∑3460.1610968.75换算均布荷载kN/m64.13横梁自重换算均布荷载kN/m1.45一期恒载kN/m65.58一期恒载集度为g1=65.58kN/m2.4.2二期恒载二期恒载集度在15.5~23.8kN/m本设计中二期恒载集度取为:g2=16kN/m2.4.3恒载内力计算①一期恒载内力计算采用Midas软件加载。加载图式如图2-2。用软件计算得内力结果见表8。恒载加载图式图2-2一期恒载内力表8截面位置X（m）剪力Q(MN)弯矩M(MN*m)0-1.510.0015-0.5215.23300.4615.69401.127.80451.451.4055.52.13-17.39602.43-27.6667.5-2.95-47.7275-2.46-27.4375.5-2.43-26.2085.5-1.77-5.2190-1.482.0997.5-0.9811.32105-0.4916.851200.4916.85127.50.9811.321351.482.09139.51.77-5.21149.52.43-26.201502.46-27.43157.5-2.92-47.72165-2.43-27.66169.5-2.13-17.39180-1.451.40185-1.127.80195-0.4615.692100.5215.232251.510.00②二期恒载内力计算二期恒载内力表9截面位置X（m）剪力Q(MN)弯矩M(MN*m)0-0.370.0015-0.133.71300.113.83400.271.90450.350.3455.50.52-4.24600.59-6.7567.5-0.72-11.6475-0.60-6.6975.5-0.59-6.3985.5-0.43-1.2790-0.360.5197.5-0.242.76105-0.124.111200.124.11127.50.242.761350.360.51139.50.43-1.27149.50.59-6.391500.60-6.69157.5-0.71-11.64165-0.59-6.75169.5-0.52-4.24180-0.350.34185-0.271.90195-0.113.832100.133.712250.370.002.5为开裂时车辆活载2.2.1活载等级：公路Ⅰ级荷载。其中qk=10.5kN，本桥全长为225m，Pk=360kN/m。2.5.2车道横向布置1号梁的横向影响线图2-3本设计中横向加载采用车道荷载。本设计中1号梁与2号梁对称，因此可以计算一片主力的力。由图中1号梁的横向影响线可以换算得到Pk与qk。其中共有三个车道，考虑横向折减，折减系数为0.78。Pk=0.78×(eq\f(1.5,7)×360+eq\f(4.5,7)×360+eq\f(7.5,7)×360)=541.54kNqk=0.78×(eq\f(9,7)×9×0.5×eq\f(10.5,3))=15.80kN/m2.5.3移动活载内力采用Midas加载得到内力结果。移动活载内力结果表10截面位置X（m）剪力Qmax(MN)弯矩Mmax(MN*m)剪力Qmin(MN)弯矩Mmin(MN*m)01.450.00-1.450.00150.9614.49-0.96-3.85300.7918.94-0.56-7.69401.0417.00-0.36-10.26451.1714.77-0.28-11.5455.51.4514.63-0.14-14.63601.5717.25-0.09-17.2567.51.8423.72-1.84-23.72751.6515.08-1.65-15.0875.51.6314.68-1.63-14.6885.51.378.95-1.37-8.93901.2611.39-1.26-7.6497.51.0715.66-1.07-6.971050.8818.35-0.88-6.401200.8818.35-0.56-6.40127.51.0715.66-0.43-6.971351.2611.39-0.31-7.64139.51.378.95-0.25-8.93149.51.6314.68-0.19-14.681501.6515.08-0.19-15.08157.51.7723.72-1.77-23.721651.5717.25-1.57-17.25169.51.4514.63-1.45-14.631801.1714.77-1.17-11.541851.0417.00-1.04-10.261950.7918.94-0.79-7.692100.9614.49-0.44-3.852251.450.00-0.280.002.6未开裂时温度2.6.1升温与降温升温与降温时考虑钢与混凝土之间的温差为20°。线膨胀系数为αth=1.0×10-5εth=eq\f(αthΔt,2)=eq\f(1.0×10-5×20,2)=1.0×10-4σ=Eεth=2.06×105×1.0×10-4=20.6MPaNth=A0σMth=Nth·ac各个单元应施加的温度力表11区段acmm换算后

截面面积A0NNMkN.mm边跨0-40m处511.00463538.4695488924879531.6440-45.0m处593.65495998.46105041516235812.5545.0-55.5m处744.27571218.46120971459003562.8855.5-67.5m处878.37657138.461391674012224105.06中跨0-8m处878.37657138.461391674012224105.068-18m处744.27571218.46120971459003562.8818-30m处593.65495998.46105041516235812.5530-60m处511.00463538.4698167205016393.0360-72m处593.65495998.46105041516235812.5572-82m处744.27571218.46120971459003562.8882-90m处878.37657138.461391674012224105.06边跨0-12m处878.37657138.461391674012224105.0612-22m处744.27571218.46120971459003562.8822-27.0m处593.65495998.46105041516235812.5527.0-67.5m处511.00463538.4698167205016393.032.6.2温度内力的计算采用Midas加载，计算得到梁的内力图温度内力计算结果表12截面位置X（m）剪力Qmax(MN)弯矩Mmax(MN*m)剪力Qmin(MN)弯矩Mmin(MN*m)00.124.88-0.12-4.88150.123.04-0.12-3.04300.121.19-0.12-1.19400.121.15-0.12-1.15450.123.23-0.12-3.2355.50.125.07-0.12-5.07600.124.52-0.12-4.5267.50.003.600.00-3.60750.003.600.00-3.6075.50.000.460.00-0.4685.50.00-2.230.002.23900.00-2.230.002.2397.50.00-3.410.003.411050.00-3.410.003.411200.00-3.410.003.41127.50.00-2.230.002.231350.00-2.230.002.23139.50.000.460.00-0.46149.50.003.600.00-3.601500.003.600.00-3.60157.5-0.123.600.12-3.60165-0.124.520.12-4.52169.5-0.121.940.12-1.94180-0.120.540.12-0.54185-0.12-0.030.120.03195-0.121.190.12-1.19210-0.123.040.12-3.04225-0.124.880.12-4.882.7未开裂时收缩内力计算2.7.1未考虑受拉区混凝土开裂时的收缩内力与弯矩收缩内力Nb=Ecm×εcs×AbMb=Nb×acEcm=eq\f(34500,2.47235)=13954.33MPaεcs=2.4×10-4其中Ab为混凝土板的面积，为1.95m2。其中ac是换算截面形心至混凝土板形心间的距离混凝土未开裂时时，应在各单元施加的力与弯矩表13区段NbkNac（mm）MbkN·m边跨0-40m处6550.63880.31777615766.63640-45.0m处6550.63976.50929866396.75145.0-55.5m处6550.631128.4338337391.95355.5-67.5m处6550.631247.5601948172.305中跨0-8m处6550.631247.5601948172.3058-18m处6550.631128.4338337391.95318-30m处6550.63976.50929866396.75130-60m处6550.63880.31777615766.63660-72m处6550.63976.50929866396.75172-82m处6550.631128.4338337391.95382-90m处6550.631247.5601948172.305边跨0-12m处6550.631247.5601948172.30512-22m处6550.631128.4338337391.95322-27.0m处6550.63976.50929866396.75127.0-67.5m处6550.63880.31777615766.636将这些收缩引起的力施加在各个单元上，采用midas加载。计算得到的那里结果为：未考虑开裂时收缩内力计算结果表14截面位置X（m）剪力Q(MN)弯矩M(MN*m)0-0.12-5.7715-0.12-4.0230-0.12-2.2740-0.12-1.7345-0.12-2.1455.5-0.12-1.7060-0.12-1.1767.50.00-0.30750.00-0.3075.50.000.4885.50.001.48900.001.4897.50.002.111050.002.111200.002.11127.50.001.481350.001.48139.50.000.48149.50.00-0.301500.00-0.30157.50.12-0.301650.12-1.17169.50.12-0.921800.12-1.151850.12-1.101950.12-2.272100.12-4.022250.12-5.772.8正常使用极限状态短期效应组合此时正常使用极限状态各内力组合表15截面位置X（m）QmaxMNMmaxMN*mQminMNMminMN*m0-0.41-0.89-3.57-10.65150.3132.44-1.858.04301.3737.38-0.238.36402.4326.120.79-3.44452.9717.591.28-15.1855.54.11-3.632.28-43.04604.59-13.812.69-57.3567.5-1.83-32.34-5.51-86.9875-1.41-15.74-4.71-53.0975.5-1.39-16.97-4.65-47.2685.5-0.831.71-3.57-11.7190-0.5813.24-3.09-1.3397.5-0.1628.44-2.2912.631050.2738.00-1.5020.091201.5038.000.0520.09127.52.2928.990.8010.811353.0913.241.52-1.33139.53.573.411.95-15.40149.54.65-14.622.83-51.181504.71-15.742.87-53.09157.5-1.87-32.34-5.16-86.98165-1.46-13.81-4.35-57.35169.5-1.21-5.98-3.86-39.13180-0.6415.89-2.73-11.49185-0.3625.57-2.19-1.621950.2137.38-1.128.362101.6032.440.458.042253.32-0.891.84-10.65正常使用极限状态下的内力包络图单位MN·m图中系列2为Mmax，系列1为Mmin。2.9考虑混凝土开裂当混凝土板受拉应力作用时，混凝土拉应力>2fctm时考虑混凝土板开裂。此时应该重新计算各种荷载下的内力，其中开裂区不计收缩产生的内力。查规范可得fctm=2.65MPa，根据混凝土截面的特性，可以换算出开裂时的弯矩值。根据σc=eq\f(M,n0I0)y0c，此时开裂弯矩M=eq\f(n0I0σc,y0c)开裂弯矩表16区段开裂时拉应力σMPa弹模比

n换算后截面惯

性矩I0（m4）y0cm开裂弯矩MMN·m边跨0-40m处5.35.9710.48870.676122.8740-45.0m处0.59600.758824.8645.0-55.5m处0.78910.909427.4655.5-67.5m处1.01171.043530.68中跨0-8m处1.01171.043530.688-18m处0.78910.909427.4618-30m处0.59600.758824.8630-60m处0.48870.676122.8760-72m处0.59600.758824.8672-82m处0.78910.909427.4682-90m处1.01171.043530.68边跨0-12m处1.01171.043530.6812-22m处0.78910.909427.4622-27.0m处0.59600.758824.8627.0-67.5m处0.48870.676122.87从包络图中可以看出混凝土板的开裂区段，从50.5m-80m区段内的混凝土板开裂，从144m-175m区段内的混凝土板开裂。此时应该重新计算混凝土板由于收缩引起的内力，不计入开裂区段内的混凝土板的收缩产生的内力。混凝土开裂后进行迭代计算，计算发现第二次计算的开裂区与第一次大致一致，故采用第二次计算结果为最后内力计算结果。第三章混凝土板开裂后内力计算3.1开裂后截面特性开裂后截面特性表1区段n0n1n2n3Iomm4Iomm4Iomm4Iomm4边跨0-40m48870342215439932660878339567156251540495856707640-45.0m59595540879948132539384147684650378448825851117545.0-50m78914215117762392128178361797349752663319925009250-55.5m52442104116752442104116752442104116752442104116755.5-67.5m681000490000681000490000681000490000681000490000中跨0-8m6810004900006810004900006810004900006810004900008-12.5m52442104116752442104116752442104116752442104116712.5-18m78914215117762392128178361797349752663319925009218-30m59595540879948132539384147684650378448825851117530-60m48870342215439932660878339567156251540495856707660-72m59595540879948132539384147684650378448825851117572-76.5m78914215117762392128178361797349752663319925009276.5-82m52442104116752442104116752442104116752442104116782-90m681000490000681000490000681000490000681000490000边跨0-12m68100049000068100049000068100049000068100049000012-17.5m52442104116752442104116752442104116752442104116717.5-22m78914215117762392128178361797349752663319925009222-27m59595540879948132539384147684650378448825851117527-67.5m4887034221543993266087833956715625154049585670763.2开裂后恒载计算①一期恒载内力计算采用Midas软件加载。加载图式如图2-2。一期恒载内力表2截面位置X（m）剪力Q(MN)弯矩M(MN*m)0-1.530.0015-0.5415.51300.4416.26401.108.56451.432.25501.75-5.7055.52.11-16.34602.41-26.5267.5-2.95-46.4475-2.46-26.1475.5-2.43-24.9280-2.13-14.6685.5-1.77-3.9290-1.483.3997.5-0.9812.62105-0.4918.161200.4918.16127.50.9812.631351.483.41139.51.77-3.891442.07-12.53149.52.43-24.881502.46-26.10157.5-2.90-46.39165-2.41-26.48169.5-2.11-16.30175-1.75-5.67180-1.432.28185-1.108.59195-0.4416.282100.5415.522251.530.00②二期恒载内力计算一期恒载内力表3截面位置X（m）剪力Q(MN)弯矩M(MN*m)0-0.370.0015-0.133.79300.113.99400.272.12450.350.58500.43-1.3555.50.52-3.94600.59-6.4267.5-0.72-11.2875-0.60-6.3375.5-0.59-6.0380-0.52-3.5285.5-0.43-0.9190-0.360.8897.5-0.243.13105-0.124.481200.124.48127.50.243.131350.360.88139.50.43-0.901440.50-3.00149.50.59-6.021500.60-6.32157.5-0.71-11.27165-0.59-6.41169.5-0.51-3.93175-0.43-1.34180-0.350.59185-0.272.12195-0.113.992100.133.802250.370.003.3开裂后车辆活载内力计算采用与2.5节相同的荷载，采用Midas加载，计算得到全桥的内力。移动活载内力表3截面位置X（m）剪力Qmax(MN)弯矩Mmax(MN*m)剪力Qmin(MN)弯矩Mmin(MN*m)01.140.00-1.140.00150.7511.39-0.75-2.72300.5915.01-0.44-5.44400.7913.55-0.28-7.26450.8911.79-0.22-8.16500.999.39-0.16-9.0755.51.1110.18-0.10-10.18601.2011.96-0.07-11.9667.51.4316.79-1.43-16.79751.2710.32-1.27-10.3275.51.2610.03-1.26-10.03801.177.84-1.17-7.8485.51.067.58-1.06-6.13900.979.91-0.97-5.5297.50.8213.39-0.82-5.131050.6815.51-0.68-4.741200.6815.51-0.43-4.73127.50.8213.38-0.33-5.111350.979.90-0.24-5.50139.51.067.56-0.19-6.091441.157.41-0.15-7.41149.51.269.99-0.13-9.991501.2710.28-0.13-10.28157.51.3616.76-1.36-16.761651.2011.95-1.20-11.95169.51.1110.18-1.11-10.181750.999.42-0.99-9.071800.8911.82-0.89-8.161850.7913.58-0.79-7.261950.5915.03-0.59-5.442100.7511.39-0.33-2.722251.140.00-0.200.003.4开裂后温度荷载内力计算采用与2.6节相同的荷载，采用Midas加载，计算全桥的内力分布。温度荷载内力表4截面位置X（m）剪力Qmax(MN)弯矩Mmax(MN*m)剪力Qmin(MN)弯矩Mmin(MN*m)00.134.88-0.13-4.88150.132.95-0.13-2.95300.131.02-0.13-1.02400.130.93-0.13-0.93450.132.97-0.13-2.97500.132.33-0.13-2.3355.50.134.76-0.13-4.76600.134.18-0.13-4.1867.50.003.220.00-3.22750.003.220.00-3.2275.50.000.080.00-0.08800.000.080.00-0.0885.50.00-2.610.002.61900.00-2.610.002.6197.50.00-3.800.003.801050.00-3.800.003.801200.00-3.800.003.80127.50.00-2.610.002.611350.00-2.610.002.61139.50.000.080.00-0.081440.000.080.00-0.08149.50.003.220.00-3.221500.003.220.00-3.22157.5-0.133.220.13-3.22165-0.134.180.13-4.18169.5-0.131.620.13-1.62175-0.132.330.13-2.33180-0.130.280.13-0.28185-0.13-0.260.130.26195-0.131.020.13-1.02210-0.132.950.13-2.95225-0.134.880.13-4.883.5开裂后收缩内力的计算开裂后混凝土板收缩产生的力为：开裂时收缩力的计算表5区段NbkNac（mm）MbkN·m边跨0-40m6550.63880.325766.6440-45.0m6550.63976.516396.7545.0-50m6550.631128.437391.9550-67.5m6550.63／／中跨0-8m6550.63／／8-12.5m6550.63／／12.5-18m6550.631128.437391.9518-30m6550.63976.516396.7530-60m6550.63880.325766.6460-72m6550.63976.516396.7572-76.5m6550.631128.437391.9576.5-82m6550.63／／82-90m6550.631247.56／边跨0-12m6550.631247.56／12-17.5m6550.63／／17.5-22m6550.631128.437391.9522-27m6550.63976.516396.7527-67.5m6550.63880.325766.64将这些收缩引起的力施加在各个单元上，采用midas加载。计算得到的那里结果为：开裂后收缩内力计算结果表6截面位置X（m）剪力Q(MN)弯矩M(MN*m)0-0.12-5.7715-0.12-4.0130-0.12-2.2640-0.12-1.7145-0.12-2.1250-0.12-1.5455.5-0.12-1.6860-0.12-1.1567.50.00-0.27750.00-0.2775.50.000.51800.000.5185.50.001.50900.001.5097.50.002.131050.002.131200.002.13127.50.001.501350.001.50139.50.000.511440.000.51149.50.00-0.271500.00-0.27157.50.12-0.271650.12-1.15169.50.12-0.901750.12-1.541800.12-1.131850.12-1.091950.12-2.262100.12-4.012250.12-5.77第四章内力组合4.1承载能力极限状态γ0Sud=γ0(∑γGiSGik+γQ1SQ1k+ΨcγQ2SQ2)其中结构重要性系数γ0=1.2，γGi为永久作用分项系数，恒载与收缩都为1.0。γQ1，γQ2分别为汽车活载与温度活载作用效应的分项系数，取为1.4。Ψc为可变荷载的组合系数，取为1.0。开裂后承载能力极限状态全桥内力表1截面位置X（m）QmaxMNMmaxMN*mQminMNMminMN*m04.541.280.29-15.12152.4342.44-0.538.82300.4448.54-1.7310.7340-0.8135.08-3.04-2.9945-1.4125.66-3.70-17.8650-1.999.39-4.36-29.4655.5-2.62-1.25-5.09-51.4560-3.13-13.79-5.69-68.0267.56.80-35.982.01-103.19755.81-16.541.53-62.0275.55.75-19.531.50-53.51805.15-7.901.22-34.5185.54.424.370.87-9.89903.8319.190.582.0397.52.8537.570.0919.211051.8849.40-0.4128.13120-0.0149.41-1.8828.17127.5-0.9238.82-2.8516.51135-1.8019.21-3.832.10139.5-2.327.70-4.42-15.51144-2.83-5.45-5.02-30.61149.5-3.40-15.22-5.74-59.59150-3.45-16.56-5.81-61.90157.56.26-35.952.12-103.081655.26-13.761.65-67.94169.54.66-5.531.37-45.191753.939.481.02-29.421803.2622.420.71-12.101852.6033.920.39-0.201951.2948.59-0.2610.76210-0.6242.47-2.008.84225-2.311.28-4.11-15.12承载能力极限状态弯矩包络图M单位MN·m系列1为Mmax，系列2为Mmin。承载能力极限状态剪力包络图Q单位MN系列1为Qmax，系列2为Qmin。4.2正常使用极限状态4.2.1短期组合Ssd=∑SGik+∑Ψ1jSQjkSGik，SQjk为永久作用与活载作用的标准值。Ψ1j为第j个可变作用效应的频遇值系数，汽车活载Ψ1j=0.7，温度梯度作用为0.8。开裂后短期效应组合下全桥内力表2截面位置X（m）QmaxMNMmaxMN*mQminMNMminMN*m02.91-1.861.12-9.67151.4225.630.1611.0330-0.0229.32-0.9513.3740-0.9519.19-1.903.1545-1.4011.35-2.38-7.3850-1.85-0.15-2.86-16.8055.5-2.34-11.02-3.39-32.8960-2.73-22.37-3.83-45.8067.54.67-43.662.67-72.31753.95-22.942.17-42.5375.53.90-23.342.14-37.52803.47-12.121.83-23.2285.52.94-0.101.46-5.52902.5110.621.163.9997.51.8024.210.6517.321051.0932.590.1424.49120-0.3132.60-1.0924.50127.5-0.9924.55-1.8015.78135-1.6710.64-2.514.04139.5-2.071.07-2.94-8.61144-2.46-9.77-3.38-20.27149.5-2.93-21.61-3.90-40.74150-2.97-22.92-3.95-42.46157.54.34-43.632.64-72.241653.62-22.342.14-45.75169.53.19-12.711.84-29.561752.66-0.091.47-16.771802.1710.241.14-4.201851.6918.920.804.761950.7429.360.1213.39210-0.6725.64-1.2211.04225-1.98-1.86-2.71-9.67正常使用极限状态下短期效应组合弯矩包络图M单位MN·m正常使用极限状态下短期效应组合剪力包络图Q单位MN4.2.1长期组合Sld=∑SGik+∑Ψ2jSQjkSGik，SQjk为永久作用与活载作用的标准值。Ψ2j为第j个可变作用效应的准永久值系数，汽车活载Ψ1j=0.4，温度梯度作用为0.8。开裂后长期效应组合下全桥内力表3截面位置X（m）QmaxMNMmaxMN*mQminMNMminMN*m02.57-1.861.46-9.67151.2022.210.3911.8430-0.1524.82-0.7715.0040-1.0315.13-1.675.3245-1.477.81-2.11-4.9350-1.90-2.97-2.56-14.0855.5-2.37-14.08-3.06-29.8460-2.75-25.96-3.46-42.2267.54.24-48.703.10-67.27753.57-26.032.55-39.4375.53.53-26.352.51-34.51803.12-14.472.18-20.8785.52.63-2.381.78-3.68902.227.651.455.6597.51.5520.200.9018.861050.8927.940.3425.91120-0.4427.94-0.8825.92127.5-1.0920.53-1.5517.31135-1.747.67-2.225.68139.5-2.13-1.20-2.63-6.79144-2.51-11.99-3.03-18.05149.5-2.97-24.60-3.52-37.74150-3.01-26.01-3.57-39.37157.53.93-48.653.05-67.211653.26-25.922.50-42.16169.52.85-15.762.17-26.501752.36-2.921.77-14.041801.916.691.40-1.751851.4614.851.046.931950.5624.850.3015.02210-0.7722.22-0.9911.86225-2.04-1.86-2.37-9.67正常使用极限状态下长期效应组合弯矩包络图M单位MN·m正常使用极限状态下短期效应组合剪力包络图Q单位MN第五章ULS验算5.1跨中截面验算5.1.1弯矩验算由承载能力包络图可以跨中截面Max=50MN·m跨中采用的工字钢翼缘厚为40mm，腹板厚度为18mm。工字梁高2800mm。根据钢-混凝土组合桥梁设计规范中5.2.1条可知:当Acfcd+Arfsd≥Asfd+σpu,dAP时，为Ⅰ类截面。其中Ac--为混凝土板面积，Ac=1.95m2fcd--为混凝土的抗压强度设计值，C50混凝土fcd=22.4MpaAr--为塑性中和轴上侧混凝土桥面板内纵向钢筋的截面面积。As--为钢梁的截面面积，As=136960mm2fsd--混凝土桥面板内纵向钢筋的抗拉强度设计值，HRB400的fsd=330Mpa。fd--钢材的抗拉强度设计值，当t=40mm时Q420钢fd=305Mpa。当t=18mm时，Q420钢fd=320Mpa。σpu,d--为体外预应力筋的设计值，本设计中无体外预应力筋。假设为Ⅰ类截面，且混凝土的纵向钢筋都在塑性中和轴的上方。半截面中混凝土板上下配筋各80根Φ25mmHRB400。此时Ar=80×2×eq\f(π,4)×252=78539.82mm2此时塑性中和轴上侧混凝土桥面板受压区高度为为xc=eq\f(Asfd-Arfsd,bcfcd)其中bc为有效宽度，bc=w+w1其中根据《钢-混凝土组合桥梁设计规范》（征求意见稿）4.1条，w=eq\f(b,2)+c+6hc1=500+0+6×307=2342mmw1=w=eq\f(b,2)+c+6hc1=500+0+6×307=2342mmbc=w+w1=4684mmxc=eq\f(Asfd-Arfsd,bcfcd)=eq\f(88000×305+48960×320-78539.82×330,4684×22.4)=158mm>eq\f(307,2)=153.5mm此时混凝土板下部的纵向钢筋位于塑性中和轴下方，此时塑性中和轴上侧混凝土桥面板的受压区高度xc=eq\f(Asfd-Arfsd,bcfcd)=eq\f(88000×305+48960×320-0.5×78539.82×330,4684×22.4)=281mm表明此时塑性中和轴在混凝土板中，此时跨中的确为Ⅰ类截面。对塑性中和轴取矩得：Mu=281×4684×22.4×140+40×1000×305×(20+109+26)+2720×18×320×(0.5×2720﹢40﹢109﹢26)+40×1200×305×(20+2720+40+109+27)=7.275×1010N·mm=72.7MN·mMu大于跨中截面Max=50MN·m，跨中截面弯矩的验算满足要求。5.1.2剪力Q验算规范中规定剪力都有钢梁的腹板承担。根据《钢-混凝土组合桥梁设计规范》（征求意见稿）5.3.1条规定Vu=hwtwfvd=2720×18×185=9057600N=9.0MN。根据承载能力极限状态下的剪力包络图，跨中剪力为0MN，偏离跨中，剪力为2.8MN，小于9.0MN。跨中的剪力满足要求。5.2支座处验算5.2.1弯矩验算支座处为负弯矩，弯矩值为116.51MN·m，此时截面为Ⅲ类截面，截面受力为弹性状态。此时混凝土板已经开裂。截面惯性矩取为钢梁的惯性矩，考虑混凝土板中的钢筋的贡献，此时I=6.44×1011mm4，惯性矩到上翼缘的距离为1180mm，到下翼缘的距离为1620mm。σ上=eq\f(M,I)y上=eq\f(103.19×109,6.44×1011)×1180=189.1MPa<305Mpaσ下=eq\f(M,I)y下=eq\f(103.19×109,6.44×1011)×1620=259.6MPa<305Mpa验算通过，满足要求。5.2.2剪力验算规范中规定剪力都有钢梁的腹板承担。根据《钢-混凝土组合桥梁设计规范》（征求意见稿）5.3.1条规定Vu=hwtwfvd=2560×26×185=12313600N=12.31.0MN。根据承载能力极限状态下的剪力包络图，支座剪力为6.80MN<12.31MN。验算通过，满足要求。第六章疲劳验算6.1内力计算加载模型为：疲劳荷载模型Ⅰ为等效的车道荷载。集中荷载为0.7Pk，均布荷载为0.3qk。Pk与qk为上部分计算的等效荷载。采用midas加载只考虑疲劳荷载引起的内力。疲劳荷载加载时钢梁下翼缘应力表1截面位置X（m）σFmaxMPaσFminMPa|σFmax-σFmin|MPa00.000.000.001537.82-9.5447.363048.47-19.0967.554043.17-25.4568.624529.87-22.7152.5855.520.36-20.3640.736017.15-17.1534.2967.522.08-22.0844.157514.45-14.4528.9175.514.16-14.1628.3285.513.68-12.9626.649023.74-15.8039.5497.531.17-13.6944.8510545.41-15.0060.4112045.41-15.0060.41127.539.29-17.2556.5413523.74-15.8039.54139.519.31-18.2837.58149.519.27-19.2738.5515014.45-14.4528.91157.522.08-22.0844.1516517.15-17.1534.29169.514.96-14.9629.9218029.87-22.7152.5818543.17-25.4568.6219548.47-19.0967.5521037.82-9.5447.362250.000.000.00疲劳荷载作用下应力包络图图5.1-16.2疲劳验算参考《公路钢桥设计规范》，最大应力与最小应力之差的绝对值小于限制。即|σFmax-σFmin|≤ΔσD由规范可知ΔσD=80MPa由上图可知|σFmax-σFmin|=69MPa≤ΔσD=80MPa验算通过，符合要求。第七章剪力钉的计算7.1剪力钉的尺寸及抗剪能力栓钉静力抗剪强度(Pu)(kN)栓钉混凝土强度等级/MPa直径d/mm高度h/mm20304050251001391541681832210011212613915319100901001091191975788796105167566748290136542475257取直径25mm，高度100mm剪力钉，抗剪强度为183kN承载能力极限状计算时取0.8Pu=146.4kN正常使用极限状态时取0.6Pu=109.8kN7.2水平剪力的计算及剪力钉个数VL=eq\f(μcVEd,I)其中uc——混凝土板对结合梁结合面的面积矩。VEd——为竖向剪力。I——未开裂区取换算后截面惯性矩I0，开裂区取钢梁惯性矩Is承载能力极限状态效应组合表1截面位置X（m）vEd

(MN/m)钢梁惯性矩Is（mm4）换算后截面惯

性矩I0（mm4）μc（mm3）水平剪力

vL(kN)剪力kN剪力钉抗

剪强度kN剪力

钉数排数剪力钉形心距mm0--450-40m处5.0196894498791.28488703422153.62384227190.53.96158400146.41082412540-45.0m处255817290495.53595955408798.69384227190.53.2516250146.4111415045--85.545.0-55.5m处7.0363554091420.10789142151176.94384227190.57.9383265146.456947055.5-67.5m处507577006012.261011666180523.39384227190.55.6868160146.446641000-8m处507577006012.261011666180523.39384227190.55.6845440146.431041008-18m处363554091420.10789142151176.94384227190.57.9379300146.454247085.5--139.518-30m处5.0255817290495.53595955408798.69384227190.53.1938280146.4261418030-60m处196894498791.28488703422153.62384227190.53.89116700146.4797415060-72m处255817290495.53595955408798.69384227190.53.1925520146.41744250139.5--17572-82m处7.0363554091420.10789142151176.94384227190.57.4174100146.450647082-90m处507577006012.261011666180523.39384227190.55.3142480146.429041000-12m处507577006012.261011666180523.39384227190.55.3163720146.4435410012-17.5m处363554091420.10789142151176.94384227190.57.4140755146.4278470175--22517.5-22m处4.5363554091420.10789142151176.94384227190.52.2410080146.469425022-27.0m处255817290495.53595955408798.69384227190.52.9714850146.4101418027.0-67.5m处196894498791.28488703422153.62384227190.53.62144800146.49894150剪力钉总数6982正常使用极限状态短期效应组合表2截面位置X（m）vEd

(kN)钢梁惯性矩Is（mm4）换算后截面惯

性矩I0（mm4）μc（mm3）水平剪力

vL(kN)剪力kN剪力钉抗

剪强度kN剪力钉数排数剪力钉形心距mm0--450-40m处3.0196894498791488703422154384227190.502.4497600109.8889417040-45.0m处255817290496595955408799384227190.502.0010000109.891420045--85.5

45.0-55.5m处4.7363554091420789142151177384227190.505.2455020109.850148055.5-67.5m处5075770060121011666180523384227190.503.7545000109.841041100-8m处5075770060121011666180523384227190.503.7530000109.827341108-18m处363554091420789142151177384227190.505.2452400109.847748085.5--

139.518-30m处3.0255817290496595955408799384227190.502.0424480109.8223421030-60m处196894498791488703422154384227190.502.4974700109.8680417060-72m处255817290496595955408799384227190.502.0416320109.81494310139.5--175

72-82m处4.6363554091420789142151177384227190.504.9549500109.845148082-90m处5075770060121011666180523384227190.503.5428320109.825841200-12m处5075770060121011666180523384227190.503.5442480109.8387412012-17.5m处363554091420789142151177384227190.504.9527225109.8248480175--22517.5-22m处2.8363554091420789142151177384227190.501.416345109.858430022-27.0m处255817290496595955408799384227190.501.869300109.885422027.0-67.5m处196894498791488703422154384227190.502.2790800109.88274190剪力钉总数6006正常使用极限状态长期效应组合表3截面位置X（m）vEd(kN)钢梁惯性矩Is（mm4）换算后截面惯

性矩I0（mm4）μc（mm3）水平剪力

vL(kN)剪力kN剪力钉抗

剪强度kN剪力

钉数排数剪力钉形心距mm0--450-40m处2.5196894498791.28488703422153.62384227190.502.1084000109.8765420040-45.0m处255817290495.53595955408798.69384227190.501.728600109.878425045--85.5

45.0-55.5m处4.4363554091420.10789142151176.94384227190.504.6648930109.844649055.5-67.5m处507577006012.261011666180523.39384227190.503.3440080109.836541250-8m处507577006012.261011666180523.39384227190.503.3426720109.824341258-18m处363554091420.10789142151176.94384227190.504.6646600109.842449085.5--

139.518-30m处2.6255817290495.53595955408798.69384227190.501.7721240109.8193424030-60m处196894498791.28488703422153.62384227190.502.1664800109.8590420060-72m处255817290495.53595955408798.69384227190.501.7721240109.81934240139.5--175

72-82m处4.0363554091420.10789142151176.94384227190.504.3943900109.8400410082-90m处507577006012.261011666180523.39384227190.503.1425120109.822941300-12m处507577006012.261011666180523.39384227190.503.1437680109.8343413012-17.5m处363554091420.10789142151176.94384227190.504.3924145109.82204100175--22517.5-22m处2.4363554091420.10789142151176.94384227190.501.195355109.849434022-27.0m处255817290495.53595955408798.69384227190.501.587900109.872427027.0-67.5m处196894498791.28488703422153.62384227190.501.9378165109.87124220剪力钉总数53237.3剪力钉个数的选取通过比较上述三种组合的剪力钉数目,选取承载能力极限状态效应组合下的剪力钉数,全桥剪力钉总数为6982,排布如表中所示.截面位置X（m）剪力

钉数排数剪力钉形心距mm0--450