第八章--水平地震作用下的內(nèi)力和位移計算

1、第8章 水平地震作用下的內(nèi)力和位移計算8.1重力荷載代表值計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%樓面活荷載，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算層高H=3.9m，屋面板厚h=120mm8.1.1.1半層柱自重(b X h=500mm x 500mm) :4X 25X 0.5X 0.5x 3.9/2=48.75KN 柱自重：48.75KN8.1.1.2 屋面梁自重0.3m2 1.495kN/m (3m1.495kN/m (6.6m 0.25m)0.3m)2

2、3.16kN/m 7.6m3.16 6.6 0.5 4147.16kN屋面梁自重：8.1.1.3半層墻自重147.16KN頂層無窗墻（190厚）：14.25 0.19200.02 23 9 0.66.631.25KN26.5kN/m2 6.6m (7.6m 2 3m)780.78kN帶窗墻（190厚）:14.250.19200.0223.920.66.6382.98 KNd c d Q14.25 0.192020.020.45墻自重：114.23 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

3、.16+114.23+37.04+780.78=1127.96 KN8.1.1.6 頂層重力荷載代表值G5 =1127.96 KN8.1.2第二至四層重力荷載代表值計算 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&=97.5 KN8.1.2.2 樓面梁自重：3.3kN/m7.6m 0.3m 2 1.6kN/m (3m 0.3m)3.3 6.6 0.5 4 1.6kN / m (6.6m 0.25m) 2 154.3kN8.1.2.38.1.2.48.1.2.58.1.2.6半墻自重：同第五層，為27.66KN則整

4、層為2X27.664=221.28 KN樓面板自重：40.6X(7.6+3+7.6) =480.48 KN第二至四層各層重量=97.5+154.3+221.28+480.48=953.56 KN第二至四層各層重力荷載代表值為：二層半墻自重(190mm):27.66 KN02.4 953.56 50% 2.5 6.6 7.6 2 3.5 6.6 3 1113.61KN 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算層高 H=4.2m，柱高 H2=4.2+0.45+0.55=5.2m,樓面板厚 h=100mm8.1.3

5、.1 半層柱自重：(b X h=500mmX 500mm) :4X 25 X 0.5X 0.5X 5.2/2=65 KN 則柱自重：65+48.75=113.75 KN為 154.3 KN8.1.3.2 樓面梁自重：同第2層，8.1.3.3 半層墻自重(190mm)：14.25 0.19 20 0.02 24 20.6 6.620.02 0.4531.14KNd C d Q-一14.25 0.19 202則墻自重為：(31.14+27.66)X 4=235.2 KN8.1.3.4 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

6、.73KN第1層重力荷載代表值為：G1=983.73+50%X( 2.5X 6.6X 7.6X 2+3.5X 6.6X 3) = 1143.78 KN 活載：Q=50%X( 2.5X 6.6X 7.6X 2+3.5X 6.6X 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 (G1+G2+G3+G4+G5)=O.85 X (1127.96+1113.61 X3+1143.78)=4770.68KN8.2水平地

7、震作用計算和位移計算821結(jié)構(gòu)基本自振周期的計算8.2.1.1框架梁柱的抗側(cè)剛度計算見表 6-1、表6-2、表6-3.表6-1橫梁、框架柱線剛度計算桿件截面尺寸混凝土的彈性模量2Ec(kN/m )l(m4)L(m)i=E cl/L(kN.m)i b=2.0I o(中跨)相對線剛度b(m)h(m)中框架梁AB CD跨0.250.62. 8x1070.00457.33.5x10 41.167BC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0.50.53.0 x10 70.0052

8、5.243.0x101.0其他層邊柱0.50.53.0 x10 70.00523.944.0x101.333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值法計算各樓層框架柱的側(cè)向剛度。巾柱kGgL鯊a =2+XQ.S + KX 2十盍：表6-2各層柱側(cè)向剛度計算層次柱別KcDj kN/mDjj KN /m屋面層A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.309467四A0.8750.30946744180B1.350.4012623C1.350.4012623D0.87

9、50.309467三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位移計算詳見表6-3.表6-3樓層層高（mVi kNDij kN /mViUiIDij(m)Ui(m)屋面3.91127.96441800.02550.4381四層3

10、.92241.57441800.05070.4126三層3.93355.18441800.07590.3619二層3.94468.79441800.10110.2860首層5.25612.57303540.18490.1849采用假想頂點位移法近似計算結(jié)構(gòu)基本自振周期，考慮填充墻對框架結(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：1 = 1.7 卩衛(wèi)二 1.7=0.7877s8.3橫向水平地震作用計算該建筑的質(zhì)量剛度沿高度分布比較均勻，高度不超過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算橫向水平地震作用。場地影響系數(shù)：本工程所在場地為 7度設(shè)防，設(shè)計地

11、震分組為第一組，場地土 為n類，結(jié)構(gòu)的基本自振周期采用經(jīng)驗公式計算，Ti=0.7877s，根據(jù)建筑抗震設(shè)計規(guī)范（GB50011-2010）查表 5.141 得 amax=0.08,查表 5.142 得，Tg=0.35s。表5.1.41水平地）影響系大值地»響1:6度7度8度，度£遇地*10.040, «(). 240.32罕遇地X0.對0,50(0.72)1 0. 90(1.30)1.4«注：S號中（S值井別用于設(shè)計*地加a度為0. isg和0Mg的地區(qū)4« 5. L «特征周期值佃）設(shè)計地A煬地類別【0I.BI第土組0.205 25

12、0.3510- 45t0. 65第二縮0.250.34)0. 400. 55也7S第三坦0.3010.35仇 451(K 65因 Tg=0.35s vTi=0.7877s v5Tg=1.75s,查圖 5.1.5，則地震影響系數(shù)為:0.350.7877Tg10.92 max1.0 0.08 0.0386 (其中0.9, 2=1.0)圖5- L5 地震影響系數(shù)曲線L地®影響系數(shù)J吟X地震彫響系數(shù)最大值,衍一言線下降段的卜'降斜率調(diào)整系數(shù)工減指數(shù)=:G特征周期：盹一阻尼凋整系數(shù)t T 結(jié)構(gòu)振周期各個層水平地震作用標準值、樓層地震剪力及樓層層間位移計算對于多質(zhì)點體系，根據(jù)式Fek G

13、eq 1Fek -結(jié)構(gòu)總水平地震作用標準值;Geq -結(jié)構(gòu)等效總重力荷載;nGeq=Ge= Gjj 1-等效重力荷載系數(shù)，建筑抗震設(shè)計規(guī)范規(guī)定=0.85;Gj -集中于質(zhì)點j的重力荷載代表值;Fek =477O.68X O.O386=184.15KN0. o衰乩盒1頂部附加地W作舄系效Ti>1.4T,6 OSTi-hO.O70.0. osTi +a(n0.0B70,02r>0* 55根據(jù)表521可知，Ti=0.7877s>1.4Tg=0.49s,故考慮頂部附加水平地震作用的影響，即 n=0.08x 0.7877+0.07=0.13由式 FnnFEK0.13 184.15 23

14、.94KN由式FnGiHi (1n)FEK計算各層水平地震作用標準值，進而求出各樓層地GjHjj 1表8.1震剪力及樓層層間位移，各層水平地震作用標準值、樓層地震剪力及樓層層間位移 計算，計算過程詳見表8.1。樓層Gi (KN)Hi(m)GiHiGiHiFi (KN)Vi (KN)D(KN/m )Ve(m)51127.9620.823461.5772839.0251.6075.54441800.001741113.6116.918820.0141.39116.93441800.002631113.611314476.9331.84148.77441800.003421113.619.11013

15、3.8522.29171.06441800.003911143.785.25946.6613.08184.143O3540.0061樓層最大位移與樓層層高之比：u 0.0061115.2852 550故滿足位移要求。8.4內(nèi)力計算橫向框架在水平作用下的內(nèi)力計算采用 D值法。8.4.1反彎點高度計算反彎點高度比的計算結(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 =0.875y。=0.35K =1.35y =0.37五層1 = 1y1 =01= 1y1=03= 1y3 =03= 1y3 =0y=0.35+0+0=0.35y=0.37+0+0=0.37K=0.875y。=0.40K

16、 =1.35yo =0.45四層1 = 1y1 =01= 1y1=02= 1y2=02= 1y2 =03= 1y =03= 1y =0y=0.40+0+0+0=0.40y=0.45+0+0+0=0.45K=0.875yo =0.45K =1.35y =0.47三層1 = 1y1 =01= 1y1=02= 1y2=02= 1y2 =03= 1y =03= 1y =0y=0.45+0+0+0=0.45y=0.47+0+0+0=0.47K =0.8751 = 1y =0.50屮=0K =1.351= 1y =0.50y1=0二層2= 1y2=02= 1y2 =03= 1.333y =03= 1.33

17、3y =0y=0.50+0+0+0=0.50y=0.50+0+0+0=0.50K=1.17y。=0.65K =1.80y。=0.65一層1 = 1屮=01= 1y1=02= 0.75y2 =02= 0.75y2 =0y=0.65+0+0=0.65y=0.65+0+0=0.658.4.2彎矩、剪力計算Vij 水平地震作用下的柱端剪力按下式計算，即：jVjDij j式中Vij -第j層第i柱的層間剪力;Vj -第j層的總剪力標準值;Dij -第j層所有柱的抗側(cè)剛度之和;Dij -第j層第i柱的抗側(cè)剛度。 水平地震作用下的柱端彎矩按下式計算，即Mc上Vij(1 y)hMe下Vij yh框架在水平地震

18、作用下的柱端剪力和柱端彎矩計算方法與風(fēng)荷載作用下的柱端 彎矩、柱端剪力計算方法相同。水平地震作用下柱端彎矩及剪力計算，具體計算過 程如下表8.3。表8.3柱樓層Vj(KN)Dij(KN/m)Dij(KN/m)DijDijVij(KN)yyh(m)Mc上(KN m)Mc下(KN m)A軸 邊 柱575.549467441800.21416.170.351.3740.9922.154116.939467441800.21425.020.401.5658.5539.033148.779467441800.21431.840.451.7668.3056.042171.069467441800.2143

19、6.610.501.9571.3971.391184.147056303540.23242.720.653.3877.75144.39B軸 中 柱575.5412623441800.28621.600.371.4453.0731.104116.9312623441800.28633.440.451.7671.7358.853148.7712623441800.28642.550.471.8387.9577.872171.0612623441800.28648.920.501.9595.3995.391184.148121303540.26849.350.653.3889.82166.80C軸

20、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軸 邊575.549467441800.21416.170.351.3740.9922.154116.939467441800.21425.02

21、0.401.5658.5539.033148.779467441800.21431.840.451.7668.3056.042171.069467441800.21436.610.501.9571.3971.391184.147056303540.23242.720.653.3877.75144.39水平地震作用下的梁端彎矩計算列于表8.4和表8.5。柱梁端彎矩M AB、Mdc計算: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M DC（kN.m）5/40.9940.99/40.9940.9940.9940.99422.1580.780.722.1580.780

22、.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表8.5梁端彎矩Mba=Mcd、Mbc=Mcb計算:87.95277.87173.263.5X1041.9X104112.3060.9695.39195.39185.213.5X1041.9X104120.0465.1789.82依據(jù)表8.4表8.5,畫出框架在地震作用下的彎矩圖，如圖8.6所示。kN m)圖8.6框架在地震作用下的彎矩圖（單位:地震作用下的梁端剪力計算見詳表8.7：