《某厂房结构设计中的内力计算案例》5600字【论文】

某厂房结构设计中的内力计算案例1.1恒载作用下内力计算1.1.1弯矩分配系数计算弯矩分配系数计算——对应杆件的相对线刚度——对应杆件的相对线刚度总和表1.1.1分配系数计算表部位相对刚度分配系数左梁上柱下柱右梁左梁上柱下柱右梁5层A柱//11.646//0.3780.622B柱1.646/11.80.37/0.2250.405C柱1.8/11.6460.405/0.2250.37D柱1.646/1/0.622/0.378/4层A柱/111.646/0.2740.2740.451B柱1.646111.80.3020.1840.1840.331C柱1.8111.6460.3310.1840.1840.302D柱1.64611/0.4510.2740.274/3层A柱/111.646/0.2740.2740.451B柱1.646111.80.3020.1840.1840.331C柱1.8111.6460.3310.1840.1840.302D柱1.64611/0.4510.2740.274/2层A柱/111.646/0.2740.2740.451B柱1.646111.80.3020.1840.1840.331C柱1.8111.6460.3310.1840.1840.302D柱1.64611/0.4510.2740.274/1层A柱/11.6231.646/0.2340.380.386B柱1.64611.6231.80.2710.1650.2670.297C柱1.811.6231.6460.2970.1650.2670.271D柱1.64611.623/0.3860.2340.38/1.1.2恒载作用下固端弯矩固端弯矩计算公式q——框架梁上均布荷载l——框架梁计算跨度表1.1.2恒载固端弯矩计算表层次梁跨lqM左M右顶层AB7.226.63-115.04115.04BC2.412.08-5.85.8CD7.226.63-115.04115.04标准层AB7.226.76-115.6115.6BC2.49.9-1.751.75CD7.226.76-115.6115.61.1.3恒载作用下弯矩计算图1.1.1恒载弯矩分配过程图（单位：kN.m）按照内力平衡条件，根据框架梁简支状态下的跨中弯矩以及框架梁两端弯矩计算跨中弯矩，相关计算公式如下：简支状态下框架梁均布荷载：简支状态下框架梁三角形荷载：简支状态下框架梁梯形荷载：M0——框架梁简支状态下的跨中弯矩Mr、Ml——框架梁右、梁左端弯矩q1——均布荷载，见第3章恒载标准值计算q2——三角形或者梯形板的荷载，见第3章恒载标准值计算a——板短边方向长度的1/2表1.1.3恒载简支跨中弯矩计算表层次梁跨板形状laq1q2M01M02M0顶层AB梯形7.22.45.7125.6837141.75178.75BC三角形2.41.21.0512.842.926.169.08CD梯形7.22.45.7125.6837141.75178.75标准层AB梯形7.22.411.5118.7271.58103.33177.91BC三角形2.41.21.059.362.921.497.41CD梯形7.22.411.5118.7271.58103.33177.91表1.1.4恒载作用下跨中弯矩计算表层次梁跨M0M左M右M中5AB178.75-60.9892.75101.89BC9.08-47.2447.24-38.16CD178.75-92.7560.98101.894AB177.91-89.48101.7482.3BC7.41-30.3730.37-22.96CD177.91-101.7489.4882.33AB177.91-86.81101.1183.95BC7.41-31.0631.06-23.65CD177.91-101.1186.8183.952AB177.91-85.76100.8081.63BC7.41-31.4131.41-24CD177.91-100.8085.7681.631AB177.91-86.31100.1381.69BC7.41-29.7029.70-22.29CD177.91-100.1386.3181.69图1.1.2恒载弯矩图（单位：kN.m）1.1.4恒载作用下剪力计算框架梁简支支座剪力计算公式如下：简支状态下框架梁均布荷载：简支状态下框架梁三角形荷载：简支状态下框架梁梯形荷载：q1——均布荷载，见第3章恒载标准值计算q2——三角形或者梯形板的荷载，见第3章恒载标准值计算a——板短边方向长度的1/2梁左端剪力：梁右端剪力：柱剪力：、——框架梁简支状态下左、右端剪力、——框架梁左、右端弯矩、——框架柱上、下端弯矩——框架梁或者框架柱计算长度表1.1.5恒载简支梁端剪力计算表层次梁跨板形状laq1q2R1R2R左R右顶层AB梯形7.22.45.7125.6820.5661.6382.19-82.19BC三角形2.41.21.0512.841.867.712.56-12.56CD梯形7.22.45.7125.6820.5661.6382.19-82.19标准层AB梯形7.22.411.5118.7241.4441.9386.37-86.37BC三角形2.41.21.059.361.865.6210.48-10.48CD梯形7.22.411.5118.7241.4441.9386.37-86.37表1.1.6恒载框架梁剪力层次梁跨R左R右l(m)MlMrV左V右5AB82.19-82.197.20-60.9892.7577.78-86.6BC12.56-12.562.40-47.2447.2412.56-12.56CD82.19-82.197.20-92.7560.9886.6-77.784AB86.37-86.377.20-89.48101.7481.67-88.07BC10.48-10.482.40-30.3730.3710.48-10.48CD86.37-86.377.20-101.7489.4888.07-81.673AB86.37-86.377.20-86.81101.1181.38-88.36BC10.48-10.482.40-31.0631.0610.48-10.48CD86.37-86.377.20-101.1186.8188.36-81.382AB86.37-86.377.20-85.76100.881.28-88.46BC10.48-10.482.40-31.4131.4110.48-10.48CD86.37-86.377.20-100.885.7688.46-81.281AB86.37-86.377.20-86.31100.1381.45-88.29BC10.48-10.482.40-29.729.710.48-10.48CD86.37-86.377.20-100.1386.3188.29-81.45表1.1.7恒载作用下框架柱剪力柱轴号层次M上M下层高VA560.9847.693.6-30.19441.7943.43.6-23.66343.441.043.6-21.29241.7342.73.6-23.45143.6221.811.6-11.22B5-45.51-36.733.622.844-31.64-35.023.619.353-35.02-35.223.619.512-31.17-33.203.618.711-37.23-18.621.612.14C545.5136.733.6-22.84431.6435.023.6-19.35335.0235.223.6-19.51231.1733.23.6-18.71137.2318.621.6-12.14D5-60.98-47.693.630.194-41.79-43.403.623.663-43.40-41.043.621.292-41.73-42.703.623.451-43.62-21.811.611.22图1.1.3恒载剪力图（单位：kN）1.1.5恒载作用下框架柱轴力计算柱混凝土容重25kN/m3F——对应层的纵向框架梁集中荷载、——柱左端梁、右端梁剪力表1.1.8恒载作用下框架柱轴力柱轴号层次V左V右Nb(m)h(m)l(m)柱重柱顶柱底A5077.7876.560.500.503.6022.5151.3176.84081.6778.090.500.503.6022.5339.6362.13081.3878.090.500.503.6022.5521.6547.12081.2878.090.500.503.6022.5709.57321081.4578.090.600.601.6041.4891.5935.9B5-86.612.5673.390.500.503.6022.5172.6195.14-88.0710.4885.280.500.503.6022.5378.9401.43-88.3610.4885.280.500.503.6022.5585.56082-88.4610.4885.280.500.503.6022.5792.2811.71-88.2910.4885.280.600.601.6041.4998.81040.2C5-12.5686.673.390.500.503.6022.5172.6195.14-10.4888.0785.280.500.503.6022.5378.9401.43-10.4888.3685.280.500.503.6022.5585.56082-10.4888.4685.280.500.503.6022.5792.2811.71-10.4888.2985.280.600.601.6041.4998.81040.2D5-77.78076.560.500.503.6022.5151.3176.84-81.67078.090.500.503.6022.5339.6362.13-81.38078.090.500.503.6022.5521.6547.12-81.28078.090.500.503.6022.5709.57321-81.45078.090.600.601.6041.4891.5935.9图1.1.4恒载轴力图（单位：kN）1.2活载作用下内力计算1.2.1弯矩分配系数计算活载弯矩分配系数和恒载相同，活载作用下固端弯矩计算、梁柱剪力计算方法过程均和恒载相同。1.2.2活载作用下固端弯矩表1.2.1活载固端弯矩计算表层次梁跨lqM左M右顶层AB7.27.82-33.7833.78BC2.43-1.441.44CD7.27.82-33.7833.78标准层AB7.219.56-81.581.5BC2.47.5-3.63.6CD7.219.56-81.581.51.2.3活载作用下弯矩计算图1.2.1活载弯矩分配过程图（单位：kN.m）按照内力平衡条件，根据框架梁简支状态下的跨中弯矩以及框架梁两端弯矩计算跨中弯矩，相关计算公式如下：简支状态下框架梁三角形荷载：简支状态下框架梁梯形荷载：M0——框架梁简支状态下的跨中弯矩Mr、Ml——框架梁右、梁左端弯矩q2——三角形或者梯形板的荷载，见第3章恒载标准值计算a——板短边方向长度的1/2表1.2.2活载简支跨中弯矩计算表层次梁跨板形状laqM0顶层AB梯形7.22.49.652.99BC三角形2.41.21.82.3CD梯形7.22.49.652.99标准层AB梯形7.22.424132.48BC三角形2.41.2125.76CD梯形7.22.424132.48表1.2.3活载作用下跨中弯矩计算表层次梁跨M0M左M右M中5AB52.99-22.2328.7627.5BC2.3-11.8811.88-9.58CD52.99-28.7622.2327.54AB132.48-61.1072.8065.53BC5.76-21.0721.07-18.31CD132.48-72.8061.1065.533AB132.48-63.4473.9563.79BC5.76-22.8122.81-17.05CD132.48-73.9563.4463.792AB132.48-62.6873.7261.28BC5.76-23.0723.07-17.31CD132.48-73.7262.6861.281AB132.48-63.0873.2361.33BC5.76-21.8121.81-16.05CD132.48-73.2363.0861.33图1.2.2活载弯矩图（单位：kN.m）1.2.4活载作用下剪力计算表1.2.4活载简支梁端剪力计算表层次梁跨板形状laqR左R右顶层AB梯形7.22.49.623.04-23.04BC三角形2.41.21.82.88-2.88CD梯形7.22.49.623.04-23.04标准层AB梯形7.22.42457.6-57.6BC三角形2.41.2127.2-7.2CD梯形7.22.42457.6-57.6表1.2.5活载框架梁剪力层次梁跨R左R右l(m)MlMrV左V右5AB23.04-23.047.20-22.2328.7622.13-23.95BC2.88-2.882.40-11.8811.882.88-2.88CD23.04-23.047.20-28.7622.2323.95-22.134AB57.6-57.67.20-61.172.855.98-59.23BC7.2-7.22.40-21.0721.077.2-7.2CD57.6-57.67.20-72.861.159.23-55.983AB57.6-57.67.20-63.4473.9556.14-59.06BC7.2-7.22.40-22.8122.817.2-7.2CD57.6-57.67.20-73.9563.4459.06-56.142AB57.6-57.67.20-62.6873.7256.07-59.13BC7.2-7.22.40-23.0723.077.2-7.2CD57.6-57.67.20-73.7262.6859.13-56.071AB57.6-57.67.20-63.0873.2356.19-59.01BC7.2-7.22.40-21.8121.817.2-7.2CD57.6-57.67.20-73.2363.0859.01-56.19表1.2.6活载作用下框架柱剪力柱轴号层次M上M下层高VA522.2327.953.6-13.94433.1431.723.6-18.02331.7232.183.6-17.75230.4931.213.6-17.14131.8815.941.6-10.4B5-16.88-22.463.610.934-26.27-25.573.611.403-25.57-25.713.611.242-21.94-21.243.613.661-27.18-13.591.68.86C516.8822.463.6-10.93426.2725.573.6-11.4325.5725.713.6-11.24221.9421.243.6-13.66127.1813.591.6-8.86D5-22.23-27.953.613.944-33.14-31.723.618.023-31.72-32.183.617.752-30.49-31.213.617.141-31.88-15.941.610.40图1.2.3活载剪力图（单位：kN）1.2.5活载作用下轴力计算F——对应层的纵向框架梁集中荷载、——柱左端梁、右端梁剪力表1.2.7活载作用下框架柱轴力柱轴号层次NV左V右柱顶柱底A511.520.0022.1333.7033.70428.800.0055.98118.50118.50328.800.0056.14203.40203.40228.800.0056.07288.30288.30128.800.0056.19373.30373.30B520.16-23.952.8847.0047.00450.40-59.237.20163.80163.80350.40-59.067.20280.50280.50250.40-59.137.20397.20397.20150.40-59.017.20513.80513.80C520.16-2.8823.9547.0047.00450.40-7.2059.23163.80163.80350.40-7.2059.06280.50280.50250.40-7.2059.13397.20397.20150.40-7.2059.01513.80513.80D511.52-22.130.0033.7033.70428.80-55.980.00118.50118.50328.80-56.140.00203.40203.40228.80-56.070.00288.30288.30128.80-56.190.00373.30373.30图1.2.4活载轴力图（单位：kN）1.3风荷载作用下内力计算1.3.1风荷载作用下柱剪力分配根据柱的抗侧刚度分配层间剪力，计算公式如下：EQF——为水平风荷载作用下的层间剪力。EQDi——为对应柱的抗侧刚度EQ∑Di——为某层柱抗侧刚度总和5层柱剪力计算如下：A柱：V=19.75×18144/87146=1.11kN；B柱：V=19.75×25429/87146=5.76kNC柱：V=19.75×25429/87146=5.76kN；D柱：V=19.75×18144/87146=1.11kN4层柱剪力计算如下：A柱：V=39.99×18144/87146=8.33kN；B柱：V=39.99×25429/87146=11.67kNC柱：V=39.99×25429/87146=11.67kN；D柱：V=39.99×18144/87146=8.33kN3层柱剪力计算如下：A柱：V=58.55×18144/87146=12.19kN；B柱：V=58.55×25429/87146=17.08kNC柱：V=58.55×25429/87146=17.08kN；D柱：V=58.55×18144/87146=12.19kN2层柱剪力计算如下：B柱：V=58.55×25429/87146=17.08kN；C柱：V=58.55×25429/87146=17.08kND柱：V=58.55×18144/87146=12.19kN；A柱：V=76.52×18144/87146=15.93kN1层柱剪力计算如下：A柱：V=95.61×20068/90962=21.09kN；B柱：V=95.61×25413/90962=26.71kNC柱：V=95.61×25413/90962=26.71kN；D柱：V=95.61×20068/90962=21.09kN1.3.2风荷载作用下柱弯矩计算框架柱弯矩计算采用D值法即修正反弯点法，风荷载作用下应该查询均布水平力反弯点高度比表，计算反弯点高度比y0——为标准反弯点高度i1——为上下层梁刚度比i2——为上层与本层层高比i3——为下层与本层层高比y1——上下层梁刚度变化的修正值y2——上层层高变化的修正值y3——下层层高变化的修正值柱下端弯矩，柱上端弯矩V——框架柱剪力下表中∑M为本层节点上柱和下柱弯矩和，用于计算梁弯矩。A柱反弯点计算5层1.6461010.3820000.3824层1.6461110.4320000.4323层1.6461110.4820000.4822层1.646111.2780.50000.51层1.014200.78300.6490000.649B柱反弯点计算5层3.4461010.450000.454层3.4461110.4720000.4723层3.4461110.50000.52层3.446111.2780.50000.51层2.123200.78300.550000.55C柱反弯点计算5层3.4461010.450000.454层3.4461110.4720000.4723层3.4461110.50000.52层3.446111.2780.50000.51层2.123200.78300.550000.55D柱反弯点计算5层1.6461010.3820000.3824层1.6461110.4320000.4323层1.6461110.4820000.4822层1.646111.2780.50000.51层1.014200.78300.6490000.649表1.3.1风荷载作用下柱端弯矩计算轴号层次h(m)Vy1-yM下M上∑MA53.61.110.3820.618-5.65-9.149.1443.68.330.4320.568-12.95-17.0322.6833.612.190.4820.518-21.15-22.7335.6823.615.930.50.5-28.67-28.6749.8211.621.090.6490.351-62.96-31.0562.72B53.65.760.450.55-9.33-11.411.443.611.670.4720.528-19.83-22.1831.5133.617.080.50.5-30.74-30.7450.5723.622.330.50.5-40.19-40.1970.9311.626.710.550.45-67.58-55.2995.48C53.65.760.450.55-9.33-11.411.443.611.670.4720.528-19.83-22.1831.5133.617.080.50.5-30.74-30.7450.5723.622.330.50.5-40.19-40.1970.9311.626.710.550.45-67.58-55.2995.48D53.61.110.3820.618-5.65-9.149.1443.68.330.4320.568-12.95-17.0322.6833.612.190.4820.518-21.15-22.7335.6823.615.930.50.5-28.67-28.6749.8211.621.090.6490.351-62.96-31.0562.721.3.3风荷载作用下梁弯矩计算根据节点内力平衡的原则将上节表格计算的∑M按照梁的相对线刚度大小进行分配，节点左右梁端弯矩公式如下：左端：右端：5层梁端弯矩AB左：1.646/(0+1.646)×9.14=9.14kN.mAB右：1.646/(1.646+1.8)×11.4=5.45kN.mBC左：1.8/(1.646+1.8)×11.4=5.95kN.mBC右：1.8/(1.8+1.646)×11.4=5.95kN.mCD左：1.646/(1.8+1.646)×11.4=5.45kN.mCD右：1.646/(1.646+0)×9.14=9.14kN.m4层梁端弯矩AB左：1.646/(0+1.646)×22.68=22.68kN.mAB右：1.646/(1.646+1.8)×31.51=15.05kN.mBC左：1.8/(1.646+1.8)×31.51=16.46kN.mBC右：1.8/(1.8+1.646)×31.51=16.46kN.mCD左：1.646/(1.8+1.646)×31.51=15.05kN.mCD右：1.646/(1.646+0)×22.68=22.68kN.m3层梁端弯矩AB左：1.646/(0+1.646)×35.68=35.68kN.mAB右：1.646/(1.646+1.8)×50.57=21.16kN.mBC左：1.8/(1.646+1.8)×50.57=26.41kN.mBC右：1.8/(1.8+1.646)×50.57=26.41kN.mCD左：1.646/(1.8+1.646)×50.57=21.16kN.mCD右：1.646/(1.646+0)×35.68=35.68kN.m2层梁端弯矩AB左：1.646/(0+1.646)×49.82=49.82kN.mAB右：1.646/(1.646+1.8)×70.93=33.88kN.mBC左：1.8/(1.646+1.8)×70.93=37.05kN.mBC右：1.8/(1.8+1.646)×70.93=37.05kN.mCD左：1.646/(1.8+1.646)×70.93=33.88kN.mCD右：1.646/(1.646+0)×49.82=49.82kN.m1层梁端弯矩AB左：1.646/(0+1.646)×62.72=62.72kN.mAB右：1.646/(1.646+1.8)×95.48=45.61kN.mBC左：1.8/(1.646+1.8)×95.48=49.87kN.mBC右：1.8/(1.8+1.646)×95.48=49.87kN.mCD左：1.646/(1.8+1.646)×95.48=45.61kN.mCD右：1.646/(1.646+0)×62.72=62.72kN.m图1.3.1风荷载弯矩图（单位：kN.m）1.3.4风荷载作用下梁剪力、柱轴力计算框架梁剪力计算公式：表1.3.2风荷载作用下剪力计算梁跨层次lM左M右VAB梁57.29.145.45-2.0347.222.6815.05-5.2437.235.6821.16-8.3127.249.8233.88-11.6317.262.7245.61-15.05BC梁52.45.955.95-1.9642.416.4616.46-13.7232.426.4126.41-22.0122.437.0537.05-30.8812.449.8749.87-41.56CD梁57.25.459.14-2.0347.215.0522.68-5.2437.221.1635.68-8.3127.233.8849.82-11.6317.245.6162.72-15.05表1.3.3风荷载作用下的轴力计算层次A柱B柱C柱D柱5-2.03-2.932.932.034-7.27-11.4111.417.273-15.58-25.1125.1115.582-27.21-41.3641.3627.211-42.26-70.8770.8742.26图1.3.2风荷载剪力图（单位：kN）图4-3-3风荷载轴力图（单位：kN）1.4地震作用下内力计算1.1.1地震作用下柱剪力分配根据柱的抗侧刚度分配层间剪力，计算公式如下：EQF——为水平风荷载作用下的层间剪力。EQDi——为对应柱的抗侧刚度EQ∑Di——为某层柱抗侧刚度总和EQF——为水平地震作用下的层间剪力。5层柱剪力计算A柱：V=129.77×18144/87146=27.02kN；B柱：V=129.77×25429/87146=37.87kNC柱：V=129.77×25429/87146=37.87kN；D柱：V=129.77×18144/87146=27.02kN4层柱剪力计算A柱：V=259.13×18144/87146=53.95kN；B柱：V=259.13×25429/87146=75.61kNC柱：V=259.13×25429/87146=75.61kN；D柱：V=259.13×18144/87146=53.95kN3层柱剪力计算A柱：V=358.25×18144/87146=71.59kN；B柱：V=358.25×25429/87146=101.54kNC柱：V=358.25×25429/87146=101.54kN；D柱：V=358.25×18144/87146=71.59kN2层柱剪力计算B柱：V=358.25×25429/87146=101.54kN；C柱：V=358.25×25429/87146=101.54kND柱：V=358.25×18144/87146=71.59kN；A柱：V=427.13×18144/87146=88.93kN1层柱剪力计算A柱：V=467.32×20068/90962=103.1kN；B柱：V=467.32×25413/90962=130.56kNC柱：V=467.32×25413/90962=130.56kN；D柱：V=467.32×20068/90962=103.1kN1.1.2地震作用下柱弯矩计算框架柱弯矩计算采用D值法即修正反弯点法，地震荷载作用下应该查询倒三角形水平力反弯点高度比表，计算反弯点高度比y0——为标准反弯点高度i1——为上下层梁刚度比i2——为上层与本层层高比i3——为下层与本层层高比y1——上下层梁刚度变化的修正值y2——上层层高变化的修正值y3——下层层高变化的修正值柱下端弯矩，柱上端弯矩V——框架柱剪力下表中∑M为本层节点上柱和下柱弯矩和，用于计算梁弯矩。A柱反弯点计算5层1.6461010.3820000.3824层1.6461110.450000.453层1.6461110.4820000.4822层1.646111.2780.50000.51层1.014200.78300.650000.65B柱反弯点计算5层3.4461010.450000.454层3.4461110.50000.53层3.4461110.50000.52层3.446111.2780.50000.51层2.123200.78300.6380000.638C柱反弯点计算5层3.4461010.450000.454层3.4461110.50000.53层3.4461110.50000.52层3.446111.2780.50000.51层2.123200.78300.6380000.638D柱反弯点计算5层1.6461010.3820000.3824层1.6461110.450000.453层1.6461110.4820000.4822层1.646111.2780.50000.51层1.014200.78300.650000.65表1.1.1地震作用下柱端弯矩计算轴号层次h(m)Vy1-yM下M上∑MA53.627.020.3820.618-37.16-60.1160.1143.653.950.450.55-87.4-106.82143.9833.671.590.4820.518-129.43-139.1226.523.688.930.50.5-160.07-160.07289.511.6103.10.650.35-308.27-165.99326.06B53.637.870.450.55-61.35-71.9871.9843.675.610.50.5-136.1-136.1197.4533.6101.540.50.5-188.17-188.17321.2723.6121.640.50.5-221.35-221.35412.5211.6130.560.6380.362-383.17-217.41441.76C53.637.870.450.55-61.35-71.9871.9843.675.610.50.5-136.1-136.1197.4533.6101.540.50.5-188.17-188.17321.2723.6121.640.50.5-221.35-221.35412.5211.6130.560.6380.362-383.17-217.41441.76D53.627.020.3820.618-37.16-60.1160.1143.653.950.450.55-87.4-106.82143.9833.671.590.4820.518-129.43-139.1226.523.688.930.50.5-160.07-160.07289.511.6103.10.650.35-308.27-165.99326.061.1.3地震作用下梁弯矩计算根据节点内力平衡的原则将上节表格计算的∑M按照梁的相对线刚度大小进行分配，节点左右梁端弯矩公式如下：左端：右端：5层梁端弯矩AB梁左：1.646/(0+1.646)×60.11=60.11kN.mAB梁右：1.646/(1.646+1.8)×71.98=35.81kN.mBC梁左：1.8/(1.646+1.8)×71.98=39.17kN.mBC梁右：1.8/(1.8+1.646)×71.98=39.17kN.mCD梁左：1.646/(1.8+1.646)×71.98=35.81kN.mCD梁右：1.646/(1.646+0)×60.11=60.11kN.