第八章水平地震作用下的內(nèi)力和位移計(jì)算

1、精品文檔第 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%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。第五層重力荷載代表值計(jì)算層高 H=3.9m，屋面板厚 h=120mm半層柱自重（b×h=500mm×500mm）:4× 25×0.5×0.5×3.9/2=48.75KN柱自重： 48.75KN屋面梁自重3.16kN / m7.6m0.3m 21.495kN / m(3m0.3

2、m)3.16 6.60.541.495kN / m(6.6m0.25m)2147.16kN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 0.19200.02 23.96.6 31 .25KN0.62帶窗墻（ 190 厚）：14.250.19200.0223.96.620.6382 .98 KN1.51.80.19200.020.45214 .25墻自重： 114.23 KN女兒墻： 14.250.19200.0221.66.637.04KN屋面板自重6.5kN / m26.6m(7.6m23m)780.78kN.精品文檔第五層重量48.75+14

3、7.16+114.23+37.04+780.78=1127.96 KN頂層重力荷載代表值G5 =1127.96 KN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 48.75×2=97.5 KN8.1.2.2樓面梁自重：3.3kN / m 7.6m0.3m 21.6kN / m (3m0.3m)3.3 6.6 0.5 41.6kN / m(6.6m 0.25m)2154.3kN半墻自重 ：同第五層，為27.66KN 則整層為 2×27.66×4=221.28 KN樓面板自

4、重 ： 4×6.6×（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：G2-4953.5650%2.56.67.623.56.631113.61KN活載 :Q2-4=（2.56.67.623.56.63） 50%160.05KN第一層重力荷載代表值計(jì)算層高 H=4.2m，柱高 H2=4.2+0.45+0.55=5.2m，樓面板厚半層柱自重：（b×h=500mm× 500mm）:4×25×0.5× 0.5

5、5; 5.2/2=65 KN 則柱自重： 65+48.75=113.75 KN樓面梁自重： 同第 2 層，為 154.3 KN半層墻自重 （ 190mm）：14.250.19200.0224.20.66.621.51.814.250.19200.020.4531.14KN2二層半墻自重（ 190mm）：27.66 KN則墻自重為：（31.14+27.66）× 4=235.2 KN.精品文檔樓面板自重： 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：G1=983.73+50%×

6、;（ 2.5×6.6×7.6×2+3.5× 6.6× 3）= 1143.78 KN 活載： Q=50%×（ 2.5×6.6×7.6×2+3.5× 6.6× 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 0.85G1G2G3 G4G50.851013.46917.3731106.654141.39 KNGeq=0.85GE=0.85×(G1+G2+G3+G4+G5)=0.85 × (1127.96+1113.61 ×3

7、+1143.78)=4770.68KN8.2水平地震作用計(jì)算和位移計(jì)算結(jié)構(gòu)基本自振周期的計(jì)算框架梁柱的抗側(cè)剛度計(jì)算見表6-1 、表 6-2 、表 6-3.表 6-1橫梁、框架柱線剛度計(jì)算截面尺寸混凝土的彈i=E CI/L(kN.m)桿件b(m)h(m)性模量I(m 4)L(m)i b=2.0I 0( 中跨 )相對(duì)線剛度Ec(kN/m 2 )中 框AB、 CD跨0.250.62 8x1070.00457.33.5x10架梁BC跨0.200.42 8x1070.00113.31.9x10底層邊柱0.50.53.0 x1070.00525.23.0x10底層中柱0.50.53.0 x1070.005

8、25.23.0x10框 架其他層邊柱0.50.53.0 x1070.00523.94.0x10柱其它層中柱0.50.53.0 x1070.00523.94.0x104444441.1670.6331.01.01.3331.333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。.精品文檔表 6-2各層柱側(cè)向剛度計(jì)算層次柱別KcDij kN/mDij KN / mA0.8750.309467屋面層B1.350.401262344180C1.350.4012623D0.8750.309467A0.8750.309467四B1.350.401262344180C1.350.4012623D0.

9、8750.309467A0.8750.309467三B1.350.401262344180C1.350.4012623D0.8750.309467A0.8750.309467二B1.350.401262344180C1.350.4012623D0.8750.309467A1.170.537056首層B1.800.61812130354C1.800.618121D1.170.537056.精品文檔結(jié)構(gòu)在重力荷載代表值作用下的假想頂點(diǎn)位移計(jì)算詳見表6-3.表 6-3層高Viui樓層Vi kNDij kN / mui（m）Dij(m)(m)屋面3.91127.96441800.02550.4381層

10、3.92241.57441800.05070.4126四層三層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：T1=1.7= 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

11、震分組為第一組，場(chǎng)地土為類，結(jié)構(gòu)的基本自振周期采用經(jīng)驗(yàn)公式計(jì)算，T1=0.7877s ，根據(jù)建筑抗震設(shè)計(jì)規(guī)范（ GB50011-2010）查表 得 max =0.08，查表 得， Tg=0.35s。.精品文檔因 Tg=0.35s <T1=0.7877s <5Tg=1.75s，查圖，則地震影響系數(shù)為：Tg0. 90.35（其中0.9 , 2 =1.0）12 max1.0 0.08 0.0386T0.7877各個(gè)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)算對(duì)于多質(zhì)點(diǎn)體系，根據(jù)式FEKGeq 1FEK - 結(jié)構(gòu)總水平地震作用標(biāo)準(zhǔn)值；Geq -結(jié)構(gòu)等效總重力荷載；nGeq = GE

12、 =G jj1-等效重力荷載系數(shù)，建筑抗震設(shè)計(jì)規(guī)范規(guī)定=0.85；G j -集中于質(zhì)點(diǎn) j 的重力荷載代表值；FEK =4770.68×0.0386=184.15KN.精品文檔根據(jù)表可知， T1=0.7877s>1.4Tg=0.49s，故考慮頂部附加水平地震作用的影響，即 n =0.08×0.7877+0.07=0.13由式 Fnn FEK 0.13184.15 23.94 KN由式 FinGi H i(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G j H jj1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、程詳見表 8.1。表 8.1樓G(KN)H iGi H iG HFi(KN)V(KN)DVe(m)iii層(m)i（KN/m ）51127.9620.823461.5751.6075.54441800.001741113.6116.918820.0141.39116.93441800.002631113.611314476.9372839.0231.84148.77441800.003421113.619.110133.8522.29171.06441800.003911143.785.25946.6613.08184.14303540.0061樓層最大位移與樓層層高之比:u0.006111故

14、滿足位移要求。h5.28525508.4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。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.精品文檔樓層五層四層三層二層表 8.2A 、D 軸邊框架柱B、C 軸中框架柱K =0.875y0 =0.35K =1.35y0 =0.371= 1y1 =01 = 1y 1 =03= 1y 3 =03 = 1y 3 =0y=0.35+0+0=0.35y=0.37+0+0=0.37K =0.875y0 =0.40K =1.35y0 =0.451= 1y1 =01 = 1y 1 =02 = 1y 2 =02 = 1y 2 =03= 1y 3 =03 = 1y

15、 3 =0y=0.40+0+0+0=0.40y=0.45+0+0+0=0.45K =0.875y0 =0.45K =1.35y0 =0.471= 1y1 =01 = 1y 1 =02 = 1y 2 =02 = 1y 2 =03= 1y 3 =03 = 1y 3 =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 1 =02 = 1y 2 =02 = 1y 2 =03= 1.33y 3 =03 = 1.33y3 =0y=0.50+0+0+0=0.50y=0.50+0+0+0=0.50

16、.精品文檔K =1.17y0 =0.65K =1.80y0 =0.65一層1 = 1y1 =01 = 1y 1 =02 = 0.75y2 =02 = 0.75y 2 =0y=0.65+0+0=0.65y=0.65+0+0=0.65彎矩、剪力計(jì)算VijD ijV jD ij水平地震作用下的柱端剪力按下式計(jì)算，即：式中 Vij - 第 j 層第 i 柱的層間剪力；V j - 第 j 層的總剪力標(biāo)準(zhǔn)值；Dij - 第 j 層所有柱的抗側(cè)剛度之和；D ij - 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(jì)算，即M c上Vij (1y)hM c下Vijyh框架在水平地震作用下的柱端剪

17、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。.精品文檔表 8.3樓VjDijDijDijVijyhM c上M c下y柱Dij層（KN ） (KN/m)（ KN/m ）（KN ）(m)(KN m)(KN m)575.549467441800.21416.170.351.3740.9922.15A116.939467441800.21425.020.401.5658.5539.034軸148.779467441800.21431.840.451.7668.3056.043邊柱 2171.069467441800.

18、21436.610.501.9571.3971.391184.147056303540.23242.720.653.3877.75144.39575.5412623441800.28621.600.371.4453.0731.10B116.9312623441800.28633.440.451.7671.7358.854軸148.7712623441800.28642.550.471.8387.9577.873中171.0612623441800.28648.920.501.9595.3995.392柱184.148121303540.26849.350.653.3889.82166.8015

19、75.5412623441800.28621.600.371.4453.0731.10C116.9312623441800.28633.440.451.7671.7358.854軸148.7712623441800.28642.550.471.8387.9577.873中柱 2171.0612623441800.28648.920.501.9595.3995.391184.148121303540.26849.350.653.3889.82166.80575.549467441800.21416.170.351.3740.9922.15D116.939467441800.21425.020.4

20、01.5658.5539.034軸148.779467441800.21431.840.451.7668.3056.043邊171.069467441800.21436.610.501.9571.3971.392柱1184.147056303540.23242.720.653.3877.75144.39水平地震作用下的梁端彎矩計(jì)算列于表8.4 和表 8.5。梁端彎矩 M AB 、 M DC 計(jì)算：.精品文檔表 8.4樓柱端彎柱端彎矩之M AB（kN.m ）柱端彎矩之M DC層矩和柱端彎矩（kN.m）和5/40.9940.99/40.9940.9940.9940.99422.1580.780.7

21、22.1580.758.5580.758.55339.03107.33107.3339.03107.3368.30107.3368.30256.04127.43127.4356.04127.4371.39127.4371.39171.39149.14149.1471.39149.1477.75149.1477.75梁端彎矩 M BA =M CD、 M BC=M CB 計(jì)算：表 8.5樓柱端彎柱端彎矩之左右（ kN/m ） M BA（ kN.m ）M BC層矩和K B （kN.m ） K B（kN.m）553.073.5x1041.9x10434.4018.6753.07431.10102.833.5x1041.9x10466.6536.1871.73358.85146.803.5x1041.9x10495.1551.6587.95277.87173.263.5x1041.9x104112.3060.9695.39195.39185.213.5x1041.9x104120.0465.1789.82依據(jù)表 8.4表 8.5，畫