风荷载作用下框架内力计算参考资料

1、螆风荷载作用下框架内力计算:蒃框架在风荷载作用下的内力计算采用 D值法。计算时首先将框架各楼层的 层间总剪力Vj，按各柱的侧移刚度值（D值）在该层总侧移刚度所占比例分配到 各柱，即可求得第j层第i柱的层间剪力Vij ;根据求得的各柱层间剪力 Vij和 修正后的反弯点位置丫，即可确定柱端弯矩Me上和Me下；由节点平衡条件，梁 端弯矩之和等于柱端弯矩之和，将节点左右梁端弯矩之和按线刚度比例分配， 可 求出各梁端弯矩；进而由梁的平衡条件求出梁端剪力； 最后，第j层第i柱的轴 力即为其上各层节点左右梁端剪力代数和。肂（1）（2）蕿一榀框架上风荷载的作用计算:蒅前面已经算出风荷载作用下的一榀框架下每层楼

2、的剪力，但是还要计算出一品框架下每根柱子分得的剪力Vij二飞DLvi ,具体的计算结果见下表Z Dij薃F轴1柱蒃层数芁 hi(m)薈Di蚂层刚度和薀层剪力（KN）虿单柱分得 的剪力（KN）螂io肁3.2莁 2.12E+04肆 1.00E+06肆 168.39蒂3.55聿9膆3.6袃 2.12E+04薁 1.00E+06袈 271.54芆 5.72肇8蚇3.6莆 2.12E+04莀 1.00E+06螀368.46莅 7.77螁7膈3.6蒈 2.12E+04薆 1.00E+06膂458.10羀 9.66蚆6薃3.6莈 2.12E+04羆 1.00E+06蚅539.81蚀 11.38螅5螅3.6肁

3、 2.12E+04薈 1.00E+06螈 614.67袅 12.96芀4薇3.8羅 2.32E+04袃 1.03E+06螇686.48莆 15.52芄3葿3.8莈 2.32E+04膅 1.03E+06蒀750.13賺 16.96芅2袁3.8蕿 2.32E+04祎 1.03E+06芅806.61节 18.24蚅i莄6.3蚃 1.14E+05蝿 2.81E+06蚈900.06蒄 36.61螀F轴2柱蒁层数蒇 hi(m)薄Di賺层刚度和罿层剪力(KN)芆单柱分得 的剪力(KN)薂10蚀3.2艿 3.21E+04螄 1.00E+06羂168.39膈5.37袄9莃3.6袀 3.21E+04螆 1.00E

4、+06袄 271.54薀8.67薅8羄3.6羁 3.21E+04羀 1.00E+06薈368.46肃 11.76蒈7莇3.6膃 3.21E+04螃 1.00E+06膀458.10膆 14.62膄6蚈3.6腿 3.21E+04莃 1.00E+06芁539.81荿 17.2353.63.21E+041.00E+06614.6719.6243.83.96E+041.03E+06686.4826.5133.83.96E+041.03E+06750.1328.9723.83.96E+041.03E+06806.6131.1516.31.31E+052.81E+06900.0641.86F轴3柱层数hi(

5、m)Di层刚度和层剪力(KN)单柱分得 的剪力(KN)103.23.21E+041.00E+06168.395.3793.63.21E+041.00E+06271.548.6783.63.21E+041.00E+06368.4611.7673.63.21E+041.00E+06458.1014.6263.63.21E+041.00E+06539.8117.2353.63.21E+041.00E+06614.6719.6243.83.96E+041.03E+06686.4826.5133.83.96E+041.03E+06750.1328.9723.83.96E+041.03E+06806.61

6、31.1516.31.31E+052.81E+06900.0641.86F轴4柱层数hi(m)Di层刚度和层剪力(KN)单柱分得 的剪力(KN)103.22.12E+041.00E+06168.393.5593.62.12E+041.00E+06271.545.7283.62.12E+041.00E+06368.467.7773.62.12E+041.00E+06458.109.6663.62.12E+041.00E+06539.8111.3853.62.12E+041.00E+06614.6712.9643.82.32E+041.03E+06686.4815.5233.82.32E+041.

7、03E+06750.1316.9623.82.32E+041.03E+06806.6118.2416.31.14E+052.81E+06900.0636.61(3)风荷载作用下反弯点高度的计算：反弯点高度比即：V=V0+V1+V2+V3式中:V0 标准层反弯点高度比；注：本框架风荷载采用分段式均布荷载, 故可查高层建筑结构设计表 5.8a。V1 因上、下层梁刚度比变化的修正值，查高层建筑结构设计表5.9 ；V2 因上层层高变化的修正值，查高层建筑结构设计表5.10 ；V3 因下层层高变化的修正值，查高层建筑结构设计表5.10。具体计算结果见下表：F轴横向框架柱在风荷载作用下的反弯点高度修正层数

8、纵向轴标梁柱线刚度比V0V1V2V3V110.169646570.8750.000-0.0150.0000.86r 20.3179442180.8410.000-0.050:0.0000.7930.3179442180.8410.000-0.0500.0000.7940.169646570.8750.000-0.0150.0000.86210.2498210790.6000.0000.000:-0.1070.4920.4682037950.5500.0000.000P -0.0640.4930.4682037950.5500.0000.000-0.0640.4940.2498210790.60

9、00.0000.000-0.1070.49310.2498210790.4750.0000.000r 0.0000.4820.4682037950.4500.0000.0000.0000.4530.4682037950.4500.0000.0000.0000.4540.2498210790.4750.0000.000r 0.0000.48410.2498210790.4250.000-0.0130.0000.4120.4682037950.4500.0000.0000.0000.45:30.4682037950.4500.0000.000:0.0000.4540.2498210790.4250

10、.000-0.0130.0000.41510.7480.4500.0000.0000.0000.4521.4018690480.5000.0000.0000.0000.5031.4018690480.5000.0000.0000.0000.5040.7480.4500.0000.0000.0000.45610.7480.4500.0000.0000.0000.45P 21.4018690480.5000.0000.000:0.0000.5031.4018690480.5000.0000.0000.0000.5040.7480.4500.0000.0000.0000.45710.7480.450

11、0.0000.0000.0000.4521.4018690480.5000.0000.0000.0000.5031.4018690480.5000.0000.0000.0000.5040.7480.4500.0000.0000.0000.45810.7480.4240.0000.000r 0.0000.4221.4018690480.4500.0000.0000.0000.4531.4018690480.4500.0000.0000.0000.4540.7480.4240.0000.000r 0.0000.42910.7480.4000.0000.0000.0000.4021.40186904

12、80.4500.0000.0000.0000.45r 31.4018690480.4500.0000.000:0.0000.4540.7480.4000.0000.000P 0.0000.401010.7480.3000.0000.0000.0000.30:21.4018690480.4000.0000.000:0.0000.4031.4018690480.4000.0000.000P 0.0000.4040.7480.3000.0000.0000.0000.30(4)计算各柱端、梁端弯矩： 柱端弯矩计算：柱上下端弯矩按式：Mu二V (1 - y)h , M d= Vyh 计算; 梁端弯矩计算

13、：梁端弯矩按式 M二ib /ib (M u M d )具体结果如下：F轴1柱层数hi(m)单柱分得 的剪力(KN)柱反弯 点高度柱上端弯矩(KN.m柱下端弯矩(KN.m103.23.550.307.953.41r 93.65.720.4012.368.2483.67.770.4216.1111.8673.69.660.4519.1215.64:63.6:11.380.45P22.5318.4353.612.960.4525.6520.9943.815.520.4134.6924.2933.816.960.4833.8330.6123.818.240.4935.1534.1516.336.610

14、.8831.45202.97F轴2柱层数hi(m)单柱分得 的剪力(KN)柱反弯 点高度柱上端弯矩(KN.m柱下端弯矩(KN.m103.25.370.4010.326.8893.6 :8.670.4517.1614.0483.611.760.4523.2819.0573.614.620.5026.3126.3163.617.230.50:31.0131.01:53.619.620.5035.3135.3143.826.510.4555.4145.3433.828.970.4560.5549.5423.831.150.4960.9057.4816.341.860.7955.11208.58F轴3

15、柱层数hi(m)单柱分得 的剪力(KN)柱反弯 点高度柱上端弯矩(KN.m柱下端弯矩(KN.m103.25.370.4010.326.8893.68.670.4517.1614.0483.611.760.4523.2819.0573.614.620.5026.3126.3163.6:17.230.50P31.0131.0153.619.620.5035.3135.3143.826.510.4555.4145.3433.828.970.4560.5549.5423.8 :31.150.4960.9057.4816.341.860.7955.11208.58F轴4柱层数hi(m)单柱分得 的剪力(

16、KN)柱反弯 点高度柱上端弯矩(KN.m柱下端弯矩(KN.m103.23.550.307.953.4193.65.720.4012.368.2483.67.770.4216.1111.8673.69.660.4519.1215.6463.611.380.4522.5318.4353.612.960.4525.6520.9943.815.520.4134.6924.2933.816.960.4833.8330.6123.818.240.4935.1534.1516.336.610.8827.68202.97风荷载作用下的梁端弯矩层数hi1轴右端弯矩2轴左端弯2轴右3轴左3轴右端弯矩4轴左端弯矩风

17、荷载作用下的梁端弯矩层数 | hi1轴右端弯矩| 2轴左端弯| 2轴右| 3轴左3轴右端弯矩4轴左端弯矩(KN.M矩(KN.M)端弯矩(KN.M)端弯矩(KN.M)(KN.M)(KN.M)103.27.955.225.105.105.227.9593.615.7712.1611.8711.8712.1615.7783.624.3518.8818.4418.4418.8824.3573.630.9722.9522.4122.4122.9530.9763.638.1729.0028.3228.3229.0038.1753.644.0933.5532.7632.7633.5544.0943.855.

18、6845.9044.8244.8245.9055.6833.858.1253.5852.3152.3153.5858.1223.865.7655.8854.5654.5655.8865.7616.366.4456.9755.6255.6256.9766.44(5)计算各梁端剪力：计算方法：以梁为隔离体根据力矩平衡可得到梁端剪力 具体计算结果如下表：风荷载作用下的梁端剪力层数1轴右端剪力2轴左端剪力2轴右端剪力3轴左端剪力3轴右端剪力4轴左端剪力101.361.361.591.591.361.3692.882.883.713.712.882.8884.464.465.765.764.464.46

19、75.565.567.007.005.565.5666.936.938.858.856.936.9358.008.0010.2410.248.008.00410.4710.4714.0114.0110.4710.47311.5211.5216.3516.3511.5211.52212.5412.5417.0517.0512.5412.54112.7212.7217.3817.3812.7212.72注：单位为KN(6)计算各柱轴力：计算方法：已知梁的剪力，由上到下利用节点的竖向力平衡条件，即可得到 柱的轴力，计算方法同恒。具体计算结果如下:风荷载作用下各柱的轴力(KN截面位置1柱轴力2柱轴力3

20、柱轴力4柱轴力10层柱顶-1.36-0.240.241.369层柱顶-4.24-1.071.074.248层柱顶-8.69-2.37:2.378.697层柱顶-14.25-3.823.8214.256层柱顶-21.18-5.745.7421.185层柱顶-29.18-7.97:7.9729.184层柱顶-39.66-11.5111.5139.663层柱顶-51.17-16.3416.3451.172层柱顶-63.71-20.8520.8563.711层柱顶-76.43-25.5125.5176.431?.：(7)风荷载作用下的内力图绘制风载作用下的梁端、柱端弯矩，梁端柱端剪力，柱的轴力计算完毕

21、，恒载作 用下的标准值如下几图所示：7 95HlrtT327hftflimr1b BB -呼17.161TZ3ff|心4l+.0414.04j2：寸金HLB 111liaa19 051905J26. 19 12 i虑AlL3LQ1 :払叫3T5Iilr anHi nin mt35 3i36迤26 63i?n oa1“JI出55,+1叫34 69.IS. 34 了:诃00.3GJ加33 83V3O.61(U5449 5460,935. iq 鼬5、4BJULZ48qp tfl.-5Mi.LSlhfl.96A2M.50X3 4116.11 f19.1?；22 5125时34 6fI33. ai35

22、.132単5.2?：】u7.951iai611.f=15.778、紺邈却 也电算风荷载作用下两端弯矩图误差分析:风荷载作用下梁柱剪力图的绘制与误差分析:手算风荷载作用下的梁柱剪力图电算风荷载作用下的梁柱剪力图误差分析:风荷载作用下柱轴力图的绘制与误差分析:-1.3i i1 L7f?-O.!037-11LB745- M973933.561 51LI51-5117Hi. 345L.-76 1321858525.616L6371-21-触rz22-2.J-CMfl. 412T-M-LI1.56.：.-W.1:11.1-M-3：St11.1-1771-73-17：4i178-21-7-2 .2-761

23、 i-1&i-?.s-1D.1扣1M.S-ns-15 )12 J15.7-15 C) 12.15.7-55 ；IE. 750-a.:!16 750-3.fs務7U-eac-21.6) 21,2花&-ai.a-IL1r3 09?0-41.3-III66手算风荷载作用下的柱轴力图电算风荷载作用下的柱轴力图误差分析:水平地震作用下框架内力计算：框架在水平地震荷载作用下的内力计算采用D值法。计算时首先将框架各楼层的层间总剪力Vj，按各柱的侧移刚度值(D值)在该层总侧移刚度所占比例分 配到各柱，即可求得第j层第i柱的层间剪力Vij ;根据求得的各柱层间剪力 Vij 和修正后的反弯点位置丫，即可确定柱端弯

24、矩 Me上和Me下；由节点平衡条件， 梁端弯矩之和等于柱端弯矩之和，将节点左右梁端弯矩之和按线刚度比例分配， 可求出各梁端弯矩；进而由梁的平衡条件求出梁端剪力； 最后，第j层第i柱的 轴力即为其上各层节点左右梁端剪力代数和。(1) 一榀框架上的地震作用:一品框架下每根柱子分得的剪力Vij,具体的计算结果见下表送Dijj丄F轴1柱层数hi ( mDi层刚度和层剪力(KN单柱分得的剪力(KN103.22.12E+041.00E+061073.6321.5093.62.12E+041.00E+061418.2528.4083.62.12E+041.00E+061728.1234.6173.62.12

25、E+041.00E+062003.2440.1263.62.12E+041.00E+062243.6144.9353.62.12E+041.00E+062449.2249.0543.82.32E+041.03E+062629.3056.4733.82.32E+041.03E+062776.2559.6323.82.32E+041.03E+062883.0261.9216.31.14E+052.81E+062958.80114.33F轴2柱层数hi ( mDi层刚度和层剪力(KN单柱分得的剪力(KN103.23.21E+041.00E+061073.6334.2693.63.21E+041.00

26、E+061418.2545.2683.63.21E+041.00E+061728.1255.1573.63.21E+041.00E+062003.2463.9363.63.21E+041.00E+062243.6171.6053.63.21E+041.00E+062449.2278.1643.83.96E+041.03E+062629.30101.5533.83.96E+041.03E+062776.25107.2223.83.96E+041.03E+062883.02111.3516.31.31E+052.81E+062958.80130.72F轴3柱层数hi ( mDi层刚度和层剪力(KN

27、单柱分得的剪力(KN103.23.21E+041.00E+061073.6334.2693.63.21E+041.00E+061418.2545.2683.63.21E+041.00E+061728.1255.1573.63.21E+041.00E+062003.2463.9363.63.21E+041.00E+062243.6171.6053.63.21E+041.00E+062449.2278.1643.83.96E+041.03E+062629.30101.5533.83.96E+041.03E+062776.25107.2223.83.96E+041.03E+062883.02111.

28、3516.31.31E+052.81E+062958.80130.72F轴4柱层数hi ( mDi层刚度和层剪力(KN单柱分得的剪力(KN103.22.12E+041.00E+061073.6321.5093.62.12E+041.00E+061418.2528.4083.62.12E+041.00E+061728.1234.6173.62.12E+041.00E+062003.2440.1263.62.12E+041.00E+062243.6144.9353.62.12E+041.00E+062449.2249.0543.82.32E+041.03E+062629.3056.4733.82.

29、32E+041.03E+062776.2559.6323.82.32E+041.03E+062883.0261.9216.31.14E+052.81E+062958.80114.33(2)地震作用下反弯点高度的计算：反弯点高度比即：V=V0+V1+V2+V3式中:V0 标准层反弯点高度比；注：本框架地震荷载采用分段式倒三角 形荷载，故可查高层建筑结构设计表 5.8b。V1 因上、下层梁刚度比变化的修正值，查高层建筑结构设计表 5.9 ； V2 因上层层高变化的修正值，查高层建筑结构设计表5.10 ；V3 因下层层高变化的修正值，查高层建筑结构设计表5.10。具体计算结果见下表：层数纵向轴标梁柱

30、线刚度比V0V1V2V3V110.169646570.7950.000-0.0150.0000.7820.3179442180.8820.000-0.0500.000r 0.8330.3179442180.8820.000-0.0500.0000.8340.169646570.7950.000-0.0150.0000.78210.2498210790.6250.0000.000-0.107P 0.5220.4682037950.5500.0000.000-0.0640.4930.4682037950.5500.0000.000-0.0640.4940.2498210790.6250.0000.

31、000-0.107P 0.52310.2498210790.5250.0000.0000.0000.5320.4682037950.5000.0000.0000.0000.5030.4682037950.5000.0000.0000.0000.5040.2498210790.5250.0000.0000.000r 0.53410.2498210790.4500.000-0.0130.0000.4420.4682037950.4840.0000.0000.000P 0.4830.4682037950.4840.0000.0000.0000.4840.2498210790.4500.000-0.0

32、130.0000.44510.7480.4740.0000.0000.0000.4721.4018690480.5000.0000.0000.0000.5031.4018690480.5000.0000.0000.0000.5040.7480.4740.0000.0000.0000.47610.7480.4500.0000.0000.0000.4521.4018690480.5000.0000.0000.0000.5031.4018690480.5000.0000.0000.0000.5040.7480.4500.0000.0000.000:0.45710.7480.4500.0000.000

33、0.0000.4521.4018690480.5000.0000.0000.0000.5031.4018690480.5000.0000.0000.000:0.5040.7480.4500.0000.0000.0000.45810.7480.4500.0000.0000.0000.4521.4018690480.4700.0000.0000.000:0.4731.4018690480.4700.0000.0000.0000.4740.7480.4500.0000.0000.0000.45910.7480.4000.0000.0000.000r 0.4021.4018690480.4500.00

34、00.0000.0000.4531.4018690480.4500.0000.0000.0000.4540.7480.4000.0000.0000.000r 0.401010.7480.3240.0000.0000.0000.3221.4018690480.4200.0000.0000.0000.4231.4018690480.4200.0000.0000.0000.4240.7480.3240.0000.0000.0000.32(3)计算各柱端、梁端弯矩： 柱端弯矩计算：柱上下端弯矩按式：Mu二V (1 - y)h , M d = Vyh 计算; 梁端弯矩计算：梁端弯矩按式 M二ib / 二

35、(M u M d )具体结果如下：F轴1柱层数hi ( m单柱分得 的剪力(KN柱反弯 点高度柱上端弯矩(KN.M)柱下端弯矩(KN.M):103.221.500.3246.5122.2993.628.400.4061.3540.9083.634.610.4568.5256.0673.640.120.4579.4364.9963.644.930.4588.9672.7853.649.050.4792.8783.69P 43.856.470.44 :120.8593.7433.859.630.53107.63118.9623.861.920.52113.47121.8316.3114.330.8

36、6 1100.84619.45F轴2柱层数hi ( m单柱分得 的剪力(KN柱反弯 点高度柱上端弯矩(KN.M)柱下端弯矩(KN.M)103.234.260.4263.5946.0593.645.260.4589.6173.32P 83.655.150.47:105.2293.3173.663.930.501115.07115.0763.671.600.50128.88128.88:53.678.160.50140.69:140.6943.8101.550.48199.12186.7733.8107.220.50203.73203.7323.8111.350.49217.69205.4416.

37、3130.720.78181.17 642.34F轴3柱层数hi ( m单柱分得 的剪力(KN柱反弯 点高度柱上端弯矩(KN.M)柱下端弯矩(KN.M)103.234.260.4263.5946.0593.645.260.4589.6173.3283.655.150.47105.2293.3173.663.930.50115.07115.0763.671.600.50128.88128.8853.678.160.50140.69140.6943.8101.550.48199.12186.7733.8107.220.50203.73203.73r 23.8111.350.491217.69205

38、.4416.3130.720.78181.17642.34F轴4柱层数hi( m单柱分得 的剪力(KN柱反弯 点高度柱上端弯矩(KN.M)柱下端弯矩(KN.M)103.221.500.3246.5122.29r 93.628.400.40 :61.3540.9083.634.610.4568.5256.0673.640.120.4579.4364.99:63.644.930.4588.96:72.7853.649.050.4792.8783.6943.856.470.44120.8593.7433.859.630.53107.63118.9623.861.920.52113.47121.831

39、6.3114.330.86100.84619.45水平地震荷载作用下梁端弯矩(KN.m层数hi1轴右端弯 矩2轴左端弯 矩2轴右端弯 矩3轴左端弯 矩3轴右端弯 矩4轴左端弯 矩103.2046.5132.1731.4231.4232.1746.519r 3.6083.6468.6467.0267.0268.6483.6483.60109.4290.3488.2188.2190.34109.4273.60135.49105.43102.95102.95105.43135.496r 3.60153.94123.43120.52120.52123.43153.945r 3.60165.66136.

40、39133.18133.18136.39165.6643.80204.54171.93167.88167.88171.93204.5433.80201.37197.58192.92192.92197.58201.372r 3.80232.43213.22208.20208.20213.22232.4316.30222.67195.61191.00191.00195.61222.67(4)计算各梁端剪力：计算方法：以梁为隔离体根据力矩平衡可得到梁端剪力 具体计算结果如下表：水平地震荷载作用下梁端剪力(KN层数1轴右端剪力2轴左端剪 力2轴右端剪 力3轴左端剪 力3轴右端剪 力4轴左端剪 力108.118.119.