第四章 水平地震作用计算及位移内力分析

1、第四章 水平地震作用计算及位移内力分析对于高度不超过40m，以剪切变形为主且质量和刚度沿高度分布比较均匀的结构，以及近似于单质点体系的结构，可以采用底部剪力法的简化方法计算水平地震作用。底部剪力法适用于本工程。此法是将结构简化为作用于各楼层位置的多质点葫芦串，结构底部总剪力与地震影响系数及各质点的重力荷载代表值有关。为计算各质点的重力荷载代表值，先分别计算各楼面层梁板柱的重量，各楼层墙体的重量，然后按以楼层为中心上下各半个楼层的重量集中于该楼层的原则计算各质点的重力荷载代表值。水平地震作用计算还涉及结构的自振周期，本工程采用假想顶点位移法确定。水平作用下内力及位移分析均采用D值法计算。一 重力

2、荷载代表值计算1. 各层梁、板、柱自重标准值见下表：柱重力荷载标准值层数柱编号截面尺寸/mm净高/mgk/(kN/m)数量Gki/kNGki总和kN1KZ14505003.65.625 24486824.26KZ24506003.66.7512291.6GZ2402403.61.44946.662KZ14505003.65.625 24486829.44KZ24506003.66.7512291.6GZ2402403.61.441051.843KZ14505003.65.625 24486829.44KZ24506003.66.7512291.6GZ2402403.61.441051.844K

3、Z14505003.65.625 24486829.44KZ24506003.66.7512291.6GZ2402403.61.441051.845KZ14505003.65.625 24486829.44KZ24506003.66.7512291.6GZ2402403.61.441051.84KZ1为框架柱，GZ为构造柱梁重力荷载代表值层数截面尺寸/mm净跨长/mgk/(kN/m)数量Gki/kNGki总和/kN1300650主梁6.954.125 12344.025996.015.154.125 12254.925450250主梁3.452.187 33249300200次梁3.91 33

4、128.7卫生间41 283.361 13.361#、2#梯41 282均与1层相同996.013均与1层相同996.014均与1层相同996.015均与1层相同996.01楼、屋面重力荷载代表值 层数种类板面积/平方米gk/(kN/m)Gki/kNGki总和kN1露面549.4953.90 2143.0312350.823楼梯44.44.68 207.7922露面549.4953.90 2143.0312350.823楼梯44.44.68 207.7923露面549.4953.90 2143.0312350.823楼梯44.44.68 207.7924露面549.4953.90 2143.0

5、312350.823楼梯44.44.68 207.792屋面593.8954.10 2434.972434.97注：表中楼梯部分板的gk按楼面的1.2倍考虑2.墙自重标准值：一层轴线号净跨高度数量面积门窗数量面积门窗自重重量16.952.95120.50 00077.91 5.152.95115.19 00057.73 36.952.95117.42 1.42.213.11.23267.44 5.152.95115.19 00057.73 45.152.95115.19 00057.73 55.252.95115.49 00058.85 5.152.95115.19 00057.73 75.0

6、52.95114.90 00056.61 5.152.95115.19 00057.73 95.052.95114.90 00056.61 5.152.95115.19 00057.73 106.952.95117.42 1.42.213.11.23267.44 5.152.95115.19 00057.73 126.952.9519.52 6.11.81114.39240.58 5.152.9515.92 5.151.819.33.70826.21 卫生间2.83.618.19 0.92.111.90.75631.88 A3.453.15941.92 3.451.895622.356181.

7、64 3.453.1520.34 1.733.14218.5569.87 B83.3246.64 1.42.226.22.464179.70 C3.453.1517.09 1.23.213.81.51228.44 3.453.15215.58 1.42.226.22.46461.65 3.453.15221.74 00082.59 3.453.1518.89 0.92.2120.79234.56 D3.453.151070.88 2.11.8103815.12284.45 3.453.1516.46 2.12.114.41.76426.30 卫生间3.453.319.50 0.92.111.9

8、0.75636.84 合计1813.69 二层16.952.95118.52 0.92.2120.79271.18 5.152.95115.19 00057.73 A3.453.151151.23 3.451.8116827.324222.01 B83.3246.64 1.42.226.22.464179.70 83.3121.34 2.32.215.12.02483.12 D3.453.151070.88 2.11.8103815.12284.45 3.453.1517.63 1.81.813.21.29630.28 8(增）5.052.95114.90 56.61 增加了8轴将1/A/B/

9、更换2160.86 三五层与二层墙体相同2160.86 女儿墙（43.15+13.5）*2*0.6*3.8258.32 3.各层（各质点）自重标准值计算一层（墙+梁+板+柱）：（1813.69+2160.86）/2+996.01+2350.823+(824.26+829.44)/2=6160.958 kN二层（墙+梁+板+柱）：2160.86+996.01+2350.823+829.44=6337.13kN三层（墙+梁+板+柱）：2160.86+996.01+2350.823+829.44=6337.13kN四层（墙+梁+板+柱）：2160.86+996.01+2350.823+829.44=

10、6337.13kN五层（墙+梁+板+柱）：2160.86/2+258.32+996.01+2434.97+829.44/2=5184.45kN4.重力荷载代表值 重力荷载代表值G取结构和构件自重标准值和可变荷载组合值之和，各可变荷载组合值取为雪荷载：0.5；屋面活载：0.0；按等效均布荷载计算的楼面活载：0.5；即，G=恒载+0.5（楼板面积+楼梯面积）活载标准值。一层：G1=6160.958 +0.5（549.495*2.0+44.4*2.5）=6765.953KN二层：G2=6337.13+0.5（549.495*2.0+44.4*2.5）=6942.125KN三层：G3=6337.13+

11、0.5（549.495*2.0+44.4*2.5）=6942.125KN四层：G4=6337.13+0.5（549.495*2.0+44.4*2.5）=6942.125KN五层：G5=5184.45+0.5593.895*0.2=5303.229KN重力荷载代表值二侧移刚度的计算地震作用是根据各受力构件的抗侧移刚度来分配的，同时，若用顶点位移法求结构的自振周期时也要用到结构的抗侧刚度，为此先计算各楼层柱的侧移刚度。（一） 梁柱线刚度计算梁的线刚度Kb=EcIb/lEc混凝土的弹性模量；l梁的计算跨度；Ib梁的截面惯性矩，对于现浇的楼面，中框架梁Ib=2.0Io,边框架梁Ib=1.5Io；柱的线

12、刚度Kb=EcIb/hEc混凝土的弹性量；h柱的计算跨度；Iz柱的截面惯性矩；中框架梁截面特性计算表层数梁编号截面尺寸mmmm梁跨/mm混凝土弹性模量Ec/pa截面惯性矩Ib/mm4(Ib=2Iz)线刚度i/N*mm(i=EI/l)刚度比15AC跨3006507500300001.37310105.49310100.76CD跨3006505700300001.37310107.22710101边框架梁截面特性计算表层数梁编号截面尺寸mmmm梁跨/mm混凝土弹性模量Ec/pa截面惯性矩Ib/mm4(Ib=1.5Iz)线刚度i/N*mm(i=EI/l)15AC跨3006507500300001.0

13、310104.1210100.57CD跨3006505700300001.0310105.4210100.75柱截面特性计算表层数柱编号截面尺寸mmmm柱高/mm混凝土弹性模量Ec/pa截面惯性矩Ib/mm4(Ib=Iz)线刚度i/N*mm(i=EI/l)15A/D4505003600300000.46910103.90610100.54B4506003600300000.8110106.7510100.93注：混凝土强度C30.梁柱相对线刚度如图所示.梁、柱相对线刚度计算简图如下(CD梁线刚度为1)： (二)柱侧移刚度计算中框架柱侧移刚度层数/轴i1i2i3i4icKcic/(105)Di/

14、(105)根数1/A0.760.541.4074070.5597830.39060.2024547101/C0.7610.931.8924730.6146410.6750.3841506101/D10.541.8518520.6105770.39060.22082531025层/A0.760.760.541.4074070.4130430.39060/C0.7610.7610.931.8924730.4861880.6750.30386741025层/D110.541.8518520.4807690.39060.173878210边框架柱侧移刚度层数/轴i1i2i3i

15、4icKcic/(105)Di/(105)根数1/A0.570.541.0555560.5090910.39060.184121221/C0.570.750.931.4193550.5613210.6750.350825521/D0.750.541.3888890.5573770.39060.2015847225层/A0.570.570.541.0555560.3454550.39060.1249394225层/C0.570.750.570.750.931.4193550.4150940.6750.259434225层/D0.750.750.541.3888890.4098360.39060.

16、1482242横向框架层间侧移刚度层次12345Di(105)9.5473685987.3364914647.3364914647.3364914647.33649146同时可以得出：Di 0.7Di+1，说明该结构竖向规则. 三自振周期计算 对于质量和高度分布比较均匀的框架结构，框架剪力墙结构和剪力墙结构，一般多采用顶点位移法计算结构基本周期，公式为：考虑非结构墙体刚度影响的周期折剪系数，当采用实砌填充砖墙时取0.6-0.7，本工程取0.7：假想集中在各楼层面处的重力荷载代表值Gi为水平荷载，按弹性方法所求得的结构顶点假想位移横向框架顶点假想位移（T）计算表 层数Gi/KnVGi/KnDi/

17、(kN/m)u/KnNu/m55303.2295303.229733649.1460.0072290.12014446942.12512245.35733649.1460.0166910.11291636942.12519187.48733649.1460.0261530.09622526942.12526129.6733649.1460.0356160.07007116765.95332895.56954736.85980.0344550.034455 故由上表得，uT=0.120144m；所以T1=1.70.7=0.4125s4 横向地震作用计算1.水平地震作用及楼层地震剪力计算地震作用按

18、GB50011-2001 A. 扬州场地，抗震设防烈度为7度，0.15g，设计地震第一组，则Tg=0.35s,max=0.12，=0.05。由此计算相应的结构基本自振周期的水平地震影响系数为1= ()0.9max=0.1035 结构等效总重力荷载 Geq= 0.85Gi=0.8532895.56=27961.23kN由于T1=0.4125s1.4Tg=0.49 s，故应不考虑顶点附加地震作用，结构底部剪力为：FEK =1Geq= 0.103527961.23=2894kN2.各质点水平地震作用的标准值Fi= FEK= 2894计算结果见下表各质点横向水平地震作用及楼层地震剪力计算表层数Hi/m

19、Gi/KNGiHi/(kN*m)GiHi/GjHjFi/KNVi/KN5185303.22995458.1220.276899801.3444801.3444414.46942.12599966.60.289976839.19191640.536310.86942.12574974.950.217482629.39392269.9327.26942.12549983.30.144988419.59592689.52613.66765.95324357.4310.070654204.4739289432895.557344740.412894 水平地震作用分布 层间剪力分布 五变形验算 水平地震

20、作用下框架结构的层间位移i=Vi/Dij和顶点位移i=i，其计算机构见下表；表中还计算了各层的层间弹性位移角：e=i/hi. 由表得最大层间弹性位移角发生在第二层，其值为1/792e=1/550。满足要求！其中e钢筋混凝土框架弹性位移角限值。横向水平地震作用下的位移验算 层次 VGi/kN Di/(kN/m)ui/muT/mhi/me=i/hi5801.3444401733649.1460.0010922720.0010922723.60.00030340941640.536302733649.1460.0022361320.0033284043.60.00062114832269.93019

21、8733649.1460.0030940270.0064224313.60.00085945222689.526129733649.1460.0036659570.0100883883.60.00101832112894954736.85980.0030312020.0131195893.60.000842ui=Vi/DiuT=ui六、水平地震作用下框架内力计算 对2轴线横向框架内力进行计算。框架在水平节点荷载作用下，采用D值法分析内力。1.计算依据柱端剪力：Vij=下端弯矩：Mb=Vijyh上端弯矩：MU=Vij(1-y)h上式中，y=y0+y1+y2+y3。其中y0查表得，y1由于各层梁线

22、刚度一致，y1=0；y2、y3为层高对y的修正，查表可得。横向水平地震作用下KJ-2轴框架各层柱端弯矩及剪力计算表层次轴号hi/mVGi/kN Di/(kN/m)Di/(kN/m)Vi/kNk-yMb/(kN/m)Mu/(kN/m)5A3.6801.34444733649.14614938.4116.32 1.41 0.3721.73 37.01 C30386.7433.19 1.89 0.39547.20 72.29 D17387.8218.99 1.85 0.39326.87 41.50 4A3.61640.5363733649.14614938.4133.40 1.41 0.4250.5

23、1 69.75 C30386.7467.95 1.89 0.445108.85 135.76 D17387.8238.88 1.85 0.44362.01 77.97 3A3.62269.9302733649.14614938.4146.22 1.41 0.4778.20 88.19 C30386.7494.02 1.89 0.495167.54 170.92 D17387.8253.80 1.85 0.49395.48 98.19 2A3.62689.52613733649.14614938.4154.76 1.41 0.52102.52 94.63 C30386.74111.40 1.89 0.545218.56 182.47 D17387.8263.74 1.85 0.543124.60 104.87 1A3.62894954736.859820245.4761.37 1.41 0.6