第八章-水平地震作用下的内力和位移计算

第8章水平地震作用下的内力和位移计算8.1重力荷载代表值计算顶层重力荷载代表值包括：屋面恒载：纵、横梁自重，半层柱自重，女儿墙自重，半层墙体自重。其他层重力荷载代表值包括：楼面恒载，50%楼面活荷载，纵、横梁自重，楼面上、下各半层柱及纵、横墙体自重。第五层重力荷载代表值计算层高H=3.9m，屋面板厚h=120mm8.1.1.1半层柱自重（b×h=500mm×500mm）:4×25×0.5×0.5×3.9/2=48.75KN柱自重：48.75KN8.1.1.2屋面梁自重屋面梁自重：147.16KN8.1.1.3半层墙自重顶层无窗墙（190厚）：带窗墙（190厚）：墙自重：114.23KN女儿墙：8.1.1.4屋面板自重8.1.1.5第五层重量48.75+147.16+114.23+37.04+780.78=1127.96KN8.1.1.6顶层重力荷载代表值G5=1127.96KN8.1.2第二至四层重力荷载代表值计算层高H=3.9m，楼面板厚h=100mm8.1.2.1半层柱自重：同第五层，为48.75KN则整层为48.75×2=97.5KN8.1.2.2楼面梁自重：8.1.2.3半墙自重：同第五层，为27.66KN则整层为2×27.66×4=221.28KN8.1.2.4楼面板自重：4×6.6×（7.6+3+7.6）=480.48KN8.1.2.5第二至四层各层重量=97.5+154.3+221.28+480.48=953.56KN8.1.2.6第二至四层各层重力荷载代表值为：活载:Q2-4=8.1.3第一层重力荷载代表值计算层高H=4.2m，柱高H2=4.2+0.45+0.55=5.2m，楼面板厚h=100mm8.1.3.1半层柱自重：（b×h=500mm×500mm）:4×25×0.5×0.5×5.2/2=65KN则柱自重：65+48.75=113.75KN8.1.3.2楼面梁自重：同第2层，为154.3KN8.1.3.3半层墙自重（190mm）：二层半墙自重（190mm）：27.66KN则墙自重为：（31.14+27.66）×4=235.2KN8.1.3.4楼面板自重：同第2层，为480.48KN第1层重量=113.75+154.3+235.2+480.48=983.73KN第1层重力荷载代表值为：G1=983.73+50%×（2.5×6.6×7.6×2+3.5×6.6×3）=1143.78KN活载：Q=50%×（2.5×6.6×7.6×2+3.5×6.6×3）=160.05KN综上所述，结构等效总重力荷载代表值为：Geq=0.85GE=0.85×(G1+G2+G3+G4+G5)=0.85×(1127.96+1113.61×3+1143.78)=4770.68KN8.2水平地震作用计算和位移计算结构基本自振周期的计算8.2.1.1框架梁柱的抗侧刚度计算见表6-1、表6-2、表6-3.表6-1横梁、框架柱线刚度计算杆件截面尺寸混凝土的弹性模量Ec(kN/m2)I(m4)L(m)i=ECI/L(kN.m)ib=2.0I0(中跨)相对线刚度b(m)h(m)中框架梁AB、CD跨0.250.62．8x1070.00457.33.5x1041.167BC跨0.200.42．8x1070.00113.31.9x1040.633框架柱底层边柱0.50.53.0x1070.00525.23.0x1041.0底层中柱0.50.53.0x1070.00525.23.0x1041.0其他层边柱0.50.53.0x1070.00523.94.0x1041.333其它层中柱0.50.53.0x1070.00523.94.0x1041.333考虑梁柱线刚度比，用D值法计算各楼层框架柱的侧向刚度。表6-2各层柱侧向刚度计算层次柱别屋面层A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.309467四A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.309467三A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.309467二A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.309467首层A1.170.53705630354B1.800.618121C1.800.618121D1.170.5370568.2.1.2结构在重力荷载代表值作用下的假想顶点位移计算详见表6-3.表6-3楼层层高（m）(m)屋面层3.91127.96441800.02550.4381四层3.92241.57441800.05070.4126三层3.93355.18441800.07590.3619二层3.94468.79441800.10110.2860首层5.25612.57303540.18490.1849采用假想顶点位移法近似计算结构基本自振周期，考虑填充墙对框架结构的影响，取周期折减系数T=0.7，则结构的基本自振周期为：T1=1.7=1.7=0.7877s8.3横向水平地震作用计算该建筑的质量刚度沿高度分布比较均匀，高度不超过40m，并以剪切变形为主（房屋高宽比小于4），故采用底部剪力法计算横向水平地震作用。场地影响系数：本工程所在场地为7度设防，设计地震分组为第一组，场地土为Ⅱ类，结构的基本自振周期采用经验公式计算，T1=0.7877s，根据《建筑抗震设计规范》（GB50011-2023）查表得αmax=0.08，查表得，Tg=0.35s。因Tg=0.35s<T1=0.7877s<5Tg=1.75s，查图，则地震影响系数为：（其中,=1.0）各个层水平地震作用标准值、楼层地震剪力及楼层层间位移计算对于多质点体系，根据式----结构总水平地震作用标准值；----结构等效总重力荷载；==----等效重力荷载系数，《建筑抗震设计规范》规定=0.85；----集中于质点j的重力荷载代表值；=4770.68×0.0386=184.15KN根据表可知，T1=0.7877s>1.4Tg=0.49s，故考虑顶部附加水平地震作用的影响，即=0.08×0.7877+0.07=0.13由式由式计算各层水平地震作用标准值，进而求出各楼层地震剪力及楼层层间位移，各层水平地震作用标准值、楼层地震剪力及楼层层间位移计算，计算过程详见表8.1。表8.1楼层(KN)(m)(KN)(KN)（KN/m）(m)51127.9620.823461.5772839.0251.6075.54441800.001741113.6116.918820.0141.39116.93441800.002631113.611314476.9331.84148.77441800.003421113.619.110133.8522.29171.06441800.003911143.785.25946.6613.08184.14303540.0061楼层最大位移与楼层层高之比:故满足位移要求。8.4内力计算横向框架在水平作用下的内力计算采用D值法。8.4.1反弯点高度计算反弯点高度比的计算结果如下表8.2表8.2楼层A、D轴边框架柱B、C轴中框架柱五层=0.875=0.35=1=0=1=0y=0.35+0+0=0.35=1.35=0.37=1=0=1=0y=0.37+0+0=0.37四层=0.875=0.40=1=0=1=0=1=0y=0.40+0+0+0=0.40=1.35=0.45=1=0=1=0=1=0y=0.45+0+0+0=0.45三层=0.875=0.45=1=0=1=0=1=0y=0.45+0+0+0=0.45=1.35=0.47=1=0=1=0=1=0y=0.47+0+0+0=0.47二层=0.875=0.50=1=0=1=0=1.33=0y=0.50+0+0+0=0.50=1.35=0.50=1=0=1=0=1.33=0y=0.50+0+0+0=0.50一层=1.17=0.65=1=0=0.75=0y=0.65+0+0=0.65=1.80=0.65=1=0=0.75=0y=0.65+0+0=0.658.4.2弯矩、剪力计算水平地震作用下的柱端剪力按下式计算，即：式中----第j层第i柱的层间剪力；----第j层的总剪力标准值；-----第j层所有柱的抗侧刚度之和；----第j层第i柱的抗侧刚度。水平地震作用下的柱端弯矩按下式计算，即框架在水平地震作用下的柱端剪力和柱端弯矩计算方法与风荷载作用下的柱端弯矩、柱端剪力计算方法相同。水平地震作用下柱端弯矩及剪力计算，具体计算过程如下表8.3。表8.3柱楼层（KN）(KN/m)（KN/m）（KN）y(m)A轴边柱575.549467441800.21416.170.351.3740.9922.154116.939467441800.21425.020.401.5658.5539.033148.779467441800.21431.840.451.7668.3056.042171.069467441800.21436.610.501.9571.3971.391184.147056303540.23242.720.653.3877.75144.39B轴中柱575.5412623441800.28621.600.371.4453.0731.104116.9312623441800.28633.440.451.7671.7358.853148.7712623441800.28642.550.471.8387.9577.872171.0612623441800.28648.920.501.9595.3995.391184.148121303540.26849.350.653.3889.82166.80C轴中柱575.5412623441800.28621.600.371.4453.0731.104116.9312623441800.28633.440.451.7671.7358.853148.7712623441800.28642.550.471.8387.9577.872171.0612623441800.28648.920.501.9595.3995.391184.148121303540.26849.350.653.3889.82166.80D轴边柱575.549467441800.21416.170.351.3740.9922.154116.939467441800.21425.020.401.5658.5539.033148.779467441800.21431.840.451.7668.3056.042171.069467441800.21436.610.501.9571.3971.391184.147056303540.23242.720.653.3877.75144.39水平地震作用下的梁端弯矩计算列于表8.4和表8.5。梁端弯矩、计算：表8.4楼层柱端弯矩柱端弯矩之和MAB（kN.m）柱端弯矩柱端弯矩之和MDC（kN.m）5/40.9940.99/40.9940.9940.9940.99422.1580.780.722.1580.780.758.5558.55339.03107.33107.3339.03107.33107.3368.3068.30256.04127.43127.4356.04127.43127.4371.3971.39171.39149.14149.1471.39149.14149.1477.7577.75梁端弯矩MBA=MCD、MBC=MCB计算：表8.5楼层柱端弯矩柱端弯矩之和KB左（kN.m）KB右（kN/m）MBA（kN.m）MBC（kN.m）5——53.073.5x1041.9x10434.4018.6753.07431.10102.833.5x1041.9x10466.6536.1871.73358.85146.803.5x1041.9x10495.1551.6587.95277.87173.263.5x1041.9x104112.3060.9695.39195.39185.213.5x1041.9x104120.0465.1789.82依据表8.4—表8.5，画出框架在地震作用下的弯矩图，如图8.6所示。图8.6框架在地震作用下的弯矩图（单位：）地震