第八章水平地震作用下的內(nèi)力和位移計(jì)算

1、第8章 水平地震作用下的內(nèi)力和位移計(jì)算8.1重力荷載代表值計(jì)算頂層重力荷載代表值包括：屋面恒載：縱、橫梁自重，半層柱自重，女兒墻自重，半層墻體自重。其他層重力荷載代表值包括：樓面恒載，50滋面活荷載，縱、橫梁自重，樓面上、下各半層柱及縱、橫墻體自重。8.1.1第五層重力荷載代表值計(jì)算層高H=3.9m屋面板厚h=120mm8.1.1.1 半層柱自重(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 半層墻自重頂層無(wú)窗墻（190 厚）：14.25 0.19 20 0.02 239 0.66.631.25KN帶窗墻（190厚）：3.914.250.19200.0220.66.621 51 814.250.19200.020.4522墻自重：114.23 KN382.98 KN女兒墻: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 第五層重量48.75+147.16+114.23+37.04+780.78=1

3、127.96 KN8.1.1.6 頂層重力荷載代表值G 5 =1127.96 KN8.1.2第二至四層重力荷載代表值計(jì)算層高H=3.9m,樓面板厚h=100mm8.1.2.1 半層柱自重：同第五層，為 48.75 KN則整層為48.75 X 2=97.5 KN8.1.2.2 樓面梁自重：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 半墻自重：同第五層，為 27.66KN則整層為2X27.66 X 4=221.28 KN8.1.2.4 樓面板自重：4X 6.6

4、 X( 7.6+3+7.6 ) =480.48 KN8.1.2.5 第二至四層各層重量=97.5+154.3+221.28+480.48=953.56 KN8.1.2.6第二至四層各層重力荷載代表值為：G2-4953.5650%2.5 6.6 7.6 2 3.5 6.6 31113.61KN活載:Q2-4=(2.5 6.6 7.6 2 3.5 6.6 3) 50% 160.05KN8.1.3第一層重力荷載代表值計(jì)算層高 H=4.2n,柱高 H2=4.2+0.45+0.55=5.2m，樓面板厚 h=100mm8.1.3.1 半層柱自重：(b X h=500mX 500mm :4 X 25X 0.

5、5 X 0.5 X 5.2/2=65 KN則柱自重：65+48.75=113.75 KN8.1.3.2 樓面梁自重：同第2層，為154.3 KN半層墻自重（190mr）4.214.25 0.19 200.02 220.66.65814.250.19 200.020.4531.14KN二層半墻自重(190mr)： 27.66 KN則墻自重為：(31.14+27.66 ) X 4=235.2 KN8.134樓面板自重：同第2層，為480.48KN第 1 層重量=113.75+154.3+235.2+480.48=983.73KN第1層重力荷載代表值為：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活載：Q=50X( 2.5 X 6.6 X 7.6 X 2+3.5 X 6.6 X 3) =160.05 KN綜上所述，結(jié)構(gòu)等效總重力荷載代表值為：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水平地震作用計(jì)算和位移計(jì)算8.2.1結(jié)構(gòu)基本自振周期的計(jì)算8.2.1.1 框架

7、梁柱的抗側(cè)剛度計(jì)算見(jiàn)表 6-1、表6-2、表6-3.表6-1橫梁、框架柱線剛度計(jì)算桿件截面尺寸混凝土的彈性模量2Ec(kN/m )I(m4)L(m)i=E cl/L(kN.m)i b=2.0I 0(中跨)相對(duì)線剛度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框架柱底層邊柱0.50.53.0 x10 70.00525.243.0x101.0底層中柱0.50.573.0 x100.00525.243.0x101.0其他層邊柱0.50.53.0 x10 70.

8、00523.944.0x101.333其它層中柱0.50.53.0 x10 70.00523.944.0x101.333考慮梁柱線剛度比，用D值法計(jì)算各樓層框架柱的側(cè)向剛度。位置邊柱中柱Kcr柱*產(chǎn) _ u m * aKa.=2+X底層柱477i2kJZI0.5 i Ka =2 + AT表6-2各層柱側(cè)向剛度計(jì)算層次柱別KcDij kN/mDij KN /m屋面層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首層A1.170.53705630354B1.800.618121C1.800.618121D1.170.537056821.2結(jié)構(gòu)在重力荷載代表值作用下的假想頂點(diǎn)位移計(jì)算詳見(jiàn)表6-3.表6-3樓層層咼（mVi kNDy kN /mViDij(m)Ui(m)屋面3.91127.96441800.02550.4381四13.9224

10、1.57441800.05070.4126三層3.93355.18441800.07590.3619二層3.94468.79441800.10110.2860首層5.25612.57303540.18490.1849采用假想頂點(diǎn)位移法近似計(jì)算結(jié)構(gòu)基本自振周期，考慮填充墻對(duì)框架結(jié)構(gòu)的影響， 取周期折減系數(shù)t=0.7，則結(jié)構(gòu)的基本自振周期為：Ti = 1.7 際心=1.7=0.7877s8.3橫向水平地震作用計(jì)算該建筑的質(zhì)量剛度沿高度分布比較均勻，高度不超過(guò)40m并以剪切變形為主（房屋高寬比小于4），故采用底部剪力法計(jì)算橫向水平地震作用。場(chǎng)地影響系數(shù)：本工程所在場(chǎng)地為 7度設(shè)防，設(shè)計(jì)地震分組為第一

11、組，場(chǎng)地土 為U類(lèi)，結(jié)構(gòu)的基本自振周期采用經(jīng)驗(yàn)公式計(jì)算，Ti=0.7877s，根據(jù)建筑抗震設(shè)計(jì)規(guī)范（GB50011-2010 查表 5.141 得 a ma=0.08，查表 5.1.4-2 得，Tg=0.35s。地廉影詭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：括號(hào)中數(shù)值分刷用于設(shè)計(jì)墓本地It加速度為015g和仇初g的地凰表5. L W特征周期值（時(shí)設(shè)計(jì)蝴K場(chǎng)地類(lèi)別qIIKIV第一組仇20:m 25P 0. 35 P 0.45 n0. 65第二須0.250.3040_O.5S0.

12、 75第三組(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根據(jù)表5.2.1可知，Ti=0.7877s1.4Tg=0.49s ,故考慮頂部附加水平地震作用的影響，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計(jì)算各層水平地震作用標(biāo)準(zhǔn)值，進(jìn)而求出各樓層地GjHjj 1震剪力及樓層層間位移，各層水平地震作用標(biāo)準(zhǔn)值、樓層地震剪力及樓層層間位移 計(jì)算，計(jì)算過(guò)

13、程詳見(jiàn)表8.1 o表8.1樓層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樓層最大位移與樓層層高之比故滿(mǎn)足位移要求u0.006111h

14、5.2852 5508.4內(nèi)力計(jì)算橫向框架在水平作用下的內(nèi)力計(jì)算采用D值法8.4.1反彎點(diǎn)高度計(jì)算反彎點(diǎn)高度比的計(jì)算結(jié)果如下表 8.2表8.2樓層A、D軸邊框架柱B、C軸中框架柱K =0.875y0 =0.35K =1.35y =0.371 = 1y1 =01= 1y1=0五層3= 1y3=03= 1y =0y=0.35+0+0=0.35y=0.37+0+0=0.37K =0.875yo =0.40K =1.35yo =0.45四層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 =0三層2= 1y2=02= 1y2=03= 1y3=03= 1紙=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 =0二層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 =0.65一層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彎矩、剪力計(jì)算Vj水平地震作用下的柱端剪力按下式計(jì)算，即:式中Vj-第j層第i柱的層間剪力;Vj -第j層的總剪力標(biāo)準(zhǔn)值；水平地震作用下的柱端彎矩按下式計(jì)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彎矩計(jì)算方法與風(fēng)荷載作用下的柱端 彎矩、柱端剪力計(jì)算方法相同。水平地震作用下柱端彎矩及剪力計(jì)算，具體計(jì)算過(guò) 程如下表8.3 o表8.3柱樓層Vj(KNDj(KN/m)Dj(KN/mDjDjVij(KNyyh(m)Me上(KN m)M c下(KN m)A軸邊柱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軸 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軸 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軸 邊 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、用下的梁端彎矩計(jì)算列于表8.4和表8.5梁端彎矩M AB、M dc計(jì)算：精品表8.4樓層柱端彎 矩柱端彎矩之和MAb (kN.m)柱端彎矩柱端彎矩之和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梁端彎矩MBa=Md

21、 MBc=MCb計(jì)算：表8.5樓層柱端彎 矩柱端彎矩之 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陰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圖8.6 框架在地震作用下的彎矩圖（單位： kN m）