第八章水平地震作用下的内力和位移计算

1、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滋面活荷载，纵、横梁自重，楼面上、下各半层柱及纵、横墙体自重。8.1.1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(bx h=500mrK 500mm ：4 X 25X 0.5 X 0.5 X 3.9/2=48.75KN 柱自重：48.75KN8.1.1.2 屋面梁自重3.16kN/m 7.6m 0.3m2 1.495kN /m (3m 0.3m)3.16 6.6

2、 0.5 4 1.495kN/m (6.6m 0.25m) 2 147.16kN屋面梁自重：147.16KN8.1.1.3 半层墙自重顶层无窗墙（190 厚）：14.25 0.19 20 0.02 239 0.66.631.25KN带窗墙（190厚）：3.914.250.19200.0220.66.621 51 814.250.19200.020.4522墙自重：114.23 KN382.98 KN女儿墙:14.25 0.19 20 0.02 21.6 6.6 37.04KN8.1.1.4 屋面板自重8.1.1.5 第五层重量48.75+147.16+114.23+37.04+780.78=1

3、127.96 KN8.1.1.6 顶层重力荷载代表值G 5 =1127.96 KN8.1.2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 48.75 KN则整层为48.75 X 2=97.5 KN8.1.2.2 楼面梁自重：3.3kN /m 7.6m 0.3m 2 1.6kN /m (3m 0.3m)3.3 6.6 0.5 4 1.6kN / m (6.6m 0.25m) 2154.3kN8.1.2.3 半墙自重：同第五层，为 27.66KN则整层为2X27.66 X 4=221.28 KN8.1.2.4 楼面板自重：4X 6.6

4、 X( 7.6+3+7.6 ) =480.48 KN8.1.2.5 第二至四层各层重量=97.5+154.3+221.28+480.48=953.56 KN8.1.2.6第二至四层各层重力荷载代表值为：G2-4953.5650%2.5 6.6 7.6 2 3.5 6.6 31113.61KN活载:Q2-4=(2.5 6.6 7.6 2 3.5 6.6 3) 50% 160.05KN8.1.3第一层重力荷载代表值计算层高 H=4.2n,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 X h=500mX 500mm :4 X 25X 0.

5、5 X 0.5 X 5.2/2=65 KN则柱自重：65+48.75=113.75 KN8.1.3.2 楼面梁自重：同第2层，为154.3 KN半层墙自重（190mr）4.214.25 0.19 200.02 220.66.65814.250.19 200.020.4531.14KN二层半墙自重(190mr)： 27.66 KN则墙自重为：(31.14+27.66 ) X 4=235.2 KN8.134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：Gi=983.73+50%X( 2.5 X 6

6、.6 X 7.6 X 2+3.5 X 6.6 X 3) = 1143.78 KN活载：Q=50X( 2.5 X 6.6 X 7.6 X 2+3.5 X 6.6 X 3) =160.05 KN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 G50.851013.46 917.37 3 1106.654141.39 KNGeq=0.85GE=0.85 X (G+G+G+G+G)=0.85 X (1127.96+1113.61 X 3+1143.78)=4770.68KN8.2水平地震作用计算和位移计算8.2.1结构基本自振周期的计算8.2.1.1 框架

7、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2Ec(kN/m )I(m4)L(m)i=E cl/L(kN.m)i b=2.0I 0(中跨)相对线刚度b(m)h(m)中框架梁AB CD跨0.250.62. 8x1070.00457.343.5x101.167BC跨0.200.42. 8x1070.00113.341.9x100.633框架柱底层边柱0.50.53.0 x10 70.00525.243.0x101.0底层中柱0.50.573.0 x100.00525.243.0x101.0其他层边柱0.50.53.0 x10 70.

8、00523.944.0x101.333其它层中柱0.50.53.0 x10 70.00523.944.0x101.333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。位置边柱中柱Kcr柱*产 _ u m * aKa.=2+X底层柱477i2kJZI0.5 i Ka =2 + AT表6-2各层柱侧向刚度计算层次柱别KcDij kN/mDij KN /m屋面层A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.309467四A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.

9、309467三三三A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.309467二二二A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.309467首层A1.170.53705630354B1.800.618121C1.800.618121D1.170.537056821.2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楼层层咼（mVi kNDy kN /mViDij(m)Ui(m)屋面3.91127.96441800.02550.4381四13.9224

10、1.57441800.05070.4126三层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：Ti = 1.7 际心=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

11、组，场地土 为U类，结构的基本自振周期采用经验公式计算，Ti=0.7877s，根据建筑抗震设计规范（GB50011-2010 查表 5.141 得 a ma=0.08，查表 5.1.4-2 得，Tg=0.35s。地廉影诡6度:7 A1，度|參遇地廉Q. 04o.os(a 120.16(L 24)i0.32罕遇地鳶0.2 0.50(0.72)0.90( J. 20)1.40注：括号中數值分刷用于设计墓本地It加速度为015g和仇初g的地凰表5. L W特征周期值（时设计蝴K场地类别qIIKIV第一组仇20:m 25P 0. 35 P 0.45 n0. 65第二須0.250.3040_O.5S0.

12、 75第三组(1.300.35a 45EL砧0,90因 Tg=0.35s T i=0.7877sl. 4T*350+6 070. 0a550” OBTi 十 0” 01Ta0. 550. OSTt 0, 02根据表5.2.1可知，Ti=0.7877s1.4Tg=0.49s ,故考虑顶部附加水平地震作用的影响，即 n =0.08 X 0.7877+0.07=0.13由式 FnnFEK 0.13 184.15 23.94KN由式FnGiHi (1n)FEK计算各层水平地震作用标准值，进而求出各楼层地GjHjj 1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

13、程详见表8.1 o表8.1楼层Gi (KN)Hi(m)GHiGHFFi (KN)V (KN)D(KN/mVe(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u0.006111h

14、5.2852 5508.4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K =0.875y0 =0.35K =1.35y =0.371 = 1y1 =01= 1y1=0五层3= 1y3=03= 1y =0y=0.35+0+0=0.35y=0.37+0+0=0.37K =0.875yo =0.40K =1.35yo =0.45四层1 = 1y =01= 1y =0=12y2=0=12y =03= 1y3=03= 1y =0y=0.40+0+0+0=0.40y=0.45+0+0+0=0.45K

15、 =0.8751 = 1yo =0.45y1 =0K =1.351= 1y。=0.47y =0三层2= 1y2=02= 1y2=03= 1y3=03= 1纸=0y=0.45+0+0+0=0.45y=0.47+0+0+0=0.47K =0.875y0 =0.50K =1.35y0 =0.501 = 1y1 =01= 1y =0二层2= 1y2 =02= 1y2 =03= 1.33y3=03= 1.33y =0y=0.50+0+0+0=0.50y=0.50+0+0+0=0.50K=1.17y0 =0.65K =1.80y0 =0.65一层1 = 1y1 =01= 1y1=02= 0.75牡=02=

16、 0.75y2=0y=0.65+0+0=0.65y=0.65+0+0=0.65842弯矩、剪力计算Vj水平地震作用下的柱端剪力按下式计算，即:式中Vj-第j层第i柱的层间剪力;Vj -第j层的总剪力标准值；水平地震作用下的柱端弯矩按下式计算，即Mc上Vj(1 y)hMe下 Vj yh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 o表8.3柱楼层Vj(KNDj(KN/m)Dj(KN/mDjDjVij(KNyyh(m)Me上(KN m)M c下(KN m)A轴边柱575.5494674

17、41800.21416.170.351.3740.9922.154116.939467441800.21425.020.401.5658.5539.033148.779467441800.21431.840.451.7668.3056.042171.069467441800.21436.610.501.9571.3971.391184.147056303540.23242.720.653.3877.75144.39B575.5412623441800.28621.600.371.4453.0731.10轴 中 柱4116.9312623441800.28633.440.451.7671.735

18、8.853148.7712623441800.28642.550.471.8387.9577.872171.0612623441800.28648.920.501.9595.3995.391184.148121303540.26849.350.653.3889.82166.80C轴 中 柱575.5412623441800.28621.600.371.4453.0731.104116.9312623441800.28633.440.451.7671.7358.853148.7712623441800.28642.550.471.8387.9577.872171.0612623441800.28

19、648.920.501.9595.3995.391184.148121303540.26849.350.653.3889.82166.80D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

20、用下的梁端弯矩计算列于表8.4和表8.5梁端弯矩M AB、M dc计算：精品表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=Md

21、 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)Me (kN.m)553.073.5x10441.9x1034.4018.6753.07431.10102.833.5x10441.9x1066.6536.1871.73358.85146.803.5x10441.9x1095.1551.6587.95277.87173.263.5x10441.9x10112.3060.9695.39195.39185.213.5x10441.9x10120.0465.1789.821B672.9953.071H.67：731；022.380.736.1995.15107 3351.656F6658 0539 0J51.6107.330阴BC 9656.0460U91412 L31?0 M77.7539.871.39%9.卩1制144 39W7740男713977.759539112.3/）5.3X/ /巧初 7 112.380 7 595573L.I-510图8.6 框架在地震作用下的弯矩图（单位： kN m）