VA?VB VB?VC VA?VB VB?VC VA 8.44 (4.423) VB 8.36 (3.777) 61.473 (61.531) 61.115 VB?VC N顶 N底 25.16 (12.177) 204.233 (191.308) 382.948 (370.023) 561.621 (548.696) 741.034 (741.034) 5 8.4 (4.2) 8.4 (4.2) 58.8 0.040 (0.423) -2.673 (-2.731) 0 8.4 (4.2) 58.8 12.64 (6.523) 98.167 (91.992) 4 58.8 0 56.127 (56.029) 3 58.8 58.8 -2.315 0 56.485 58.8 184.052 (177.877) 2 58.8 58.8 -2.273 0 56.527 61.073 58.8 269.979 (263.804) 1 58.8 58.8 -3.013 0 55.787 61.813 58.8 355.166 (348.991) 注:括号内为屋面作用雪荷载(0.25kN/㎡)时对应的内力,V向上为正。
4.7.7内力组合
具体过程见内力组合表。
表22(a) 地震组合时A柱的弯矩和轴力,弯矩单位kN.m,轴力力单位kN
层次 柱顶 五 柱底 柱顶 四 柱底 柱顶 三 柱底 柱二 顶 柱M N M N M 0.750 0.750 0.750 0.750 0.750 51.840 480.119 -53.957 630.233 66.055 41.475 177.877 -43.168 263.804 52.846 -50.650 -48.465 62.981 -78.713 -70.171 50.650 48.465 -62.981 78.713 70.171 21.248 619.865 -8.774 812.235 19.751 152.938 745.874 -172.525 1016.889 202.196 M N M N 0.750 0.750 0.750 0.750 52.713 320.033 -52.713 470.096 42.172 91.992 -42.172 177.877 -30.105 -24.474 61.906 -48.465 30.105 24.474 -61.906 48.465 49.422 407.419 -8.081 607.837 127.695 471.051 -169.037 733.846 M N M N 0.750 0.750 0.750 0.750 65.836 159.402 -43.518 310.010 32.161 6.523 -49.186 91.992 -11.581 -7.866 52.715 -24.474 11.581 7.866 -52.715 24.474 83.245 184.970 -13.204 395.391 113.355 205.422 -150.263 459.023 M N 0.750 0.750 -100.329 149.379 -10.506 6.523 32.368 -7.866 -32.368 7.866 -84.620 172.943 -168.777 193.394 截面 内Rre 力 Sgk Sqk雪 Sek左震 Sek右震 雪)+1.3Sek左震 雪)+1.3Sek右震 1.2(Sgk+0.5Sqk1.2(Sgk+0.5Sqk底 柱顶 一 柱底 N M N M N 0.750 0.750 0.750 0.750 0.750 640.256 -33.707 789.447 16.854 801.856 263.804 -26.966 -78.713 41.744 78.713 -41.744 110.314 153.776 110.314 824.263 -2.361 1013.323 -171.594 1028.214 1028.917 -110.895 1300.139 228.223 1315.030 348.991 -110.314 13.483 -153.776 348.991 -110.314 表22(b) 地震组合时B柱的弯矩和轴力,弯矩单位kN.m,轴力力单位kN
层次 截面 柱顶 五 柱底 柱顶 四 柱底 柱顶 三 柱底 柱顶 二 柱底 柱顶 一 柱底 M N 0.750 0.750 -1.853 1161.199 -1.483 728.109 -236.374 4.749 236.374 -4.749 -310.400 1836.478 304.173 1824.131 M N M N 0.750 0.750 0.750 0.750 -4.593 933.291 3.706 1148.790 -3.675 548.696 2.965 728.109 -103.942 5.262 127.278 4.749 103.942 -5.262 -127.278 -4.749 -142.841 1456.007 171.688 1821.587 127.408 1442.326 -159.235 1809.240 M N M N 0.750 0.750 0.750 0.750 -3.912 708.692 3.912 923.268 -3.129 370.023 3.129 548.696 -86.048 3.946 122.265 5.262 86.048 -3.946 -122.265 -5.262 -118.434 1077.574 165.516 1443.980 105.291 1067.314 -152.373 1430.299 M N M N 0.750 0.750 0.750 0.750 -3.912 484.042 3.912 698.669 -3.129 191.308 3.129 370.023 -56.282 2.379 105.170 3.946 56.282 -2.379 -105.170 -3.946 -79.738 698.728 143.293 1065.546 66.595 692.543 -130.149 1055.287 M N M N 0.750 0.750 0.750 0.750 -3.912 259.937 3.912 474.019 -3.129 12.177 3.129 191.308 -26.132 1.126 84.423 2.379 26.132 -1.126 -84.423 -2.379 -40.543 320.694 116.322 686.700 27.400 317.767 -103.178 680.515 内Rre 力 M N 0.750 0.750 12.110 249.914 0.613 12.177 48.531 1.126 -48.531 -1.126 Sgk Sqk雪 Sek左震 Sek右震 雪)+1.3Sek左震 77.990 308.667 雪)+1.3Sek右震 -48.191 305.739 1.2(Sgk+0.5Sqk1.2(Sgk+0.5Sqk表20地震组合时框架梁的弯矩和剪力,弯矩单位kN.m,剪力力单位kN
截层次 面位M A V 五 M B左 V 87.861 3.777 7.866 -7.866 117.925 97.474 -143.816 -7.464 -24.266 24.266 -208.603 -145.512 74.763 4.423 -7.866 7.866 82.144 102.595 -96.664 -10.506 32.368 -32.368 -80.222 -164.379 内力 Sgk Sqk雪 Sek左震 Sek右震 雪)+1.3Sek左震 雪)+1.3Sek右震 1.2(Sgk+0.5Sqk1.2(Sgk+0.5SqkM B右 V 跨间 Mab Mbc M A V M B左 V 四 M B右 V 跨间 Mab Mbc M A V M B左 V 三 M B右 V 跨间 Mab Mbc M A V M B左 V 二 M B右 V 跨间 Mab Mbc M A V 一 M B左 V -131.706 81.312 86.099 74.633 -104.013 68.420 -120.916 73.116 -113.092 70.768 55.915 55.289 -100.085 67.875 -120.916 73.661 -113.092 70.768 57.880 55.289 -100.456 67.926 -120.916 73.610 -113.092 70.768 57.693 55.289 -94.421 67.003 -121.530 74.533 -6.851 4.200 0.377 3.229 -81.347 56.069 24.265 -6.740 4.051 0.000 64.296 -16.608 -24.265 6.740 -4.051 0.000 -64.296 16.608 55.278 -16.608 -55.277 15.355 -4.509 0.000 -92.011 23.991 80.726 -23.991 -80.726 22.424 -5.643 0.000 -113.631 30.248 104.157 -30.248 -104.156 28.932 -4.737 0.000 -111.915 31.601 115.610 -31.601 -130.613 91.332 108.811 91.497 -90.039 94.155 -277.566 146.248 -120.701 100.240 102.924 94.168 -51.094 84.153 -310.648 156.251 -87.617 91.050 105.857 94.168 -23.607 76.105 -341.109 164.298 -57.158 82.590 104.372 94.168 -15.703 72.795 -357.030 167.609 -193.702 108.856 98.279 91.497 -257.209 137.336 -133.843 103.067 -264.421 140.163 91.201 94.168 -290.323 146.529 -100.761 93.874 -297.505 149.353 91.185 94.168 -319.048 154.750 -70.301 85.653 -327.964 157.813 92.055 94.168 -306.682 154.957 -56.444 85.446 -101.009 -55.278 61.531 -94.751 58.800 49.941 46.369 -84.344 56.485 16.608 55.277 -15.355 4.509 0.000 92.011 -23.991 -101.009 -80.726 61.115 -94.751 58.800 48.442 46.369 -84.634 56.527 23.991 80.726 -22.424 5.643 0.000 113.631 -30.248 -101.009 -104.157 61.073 -94.751 58.800 48.303 46.369 -79.812 55.787 30.248 104.156 -28.932 4.737 0.000 111.915 -31.601 -101.502 -115.610 61.813 31.601 M B右 V 跨间 Mab Mbc -113.231 70.768 60.406 55.150 -94.862 58.800 50.461 46.258 115.610 -32.114 -1.848 0.000 -115.610 32.114 1.848 0.000 -42.501 78.453 100.361 93.935 -343.087 161.950 105.166 93.935 4.7.8构件截面验算
根据内力组合结果,选取结构最不利内力组合进行截面验算 1.框架柱
框架柱的截面验算包括强度、刚度、整体稳定验算和局部稳定验算。框架柱承载力主要有轴力控制,中柱轴力、弯矩均大于A柱轴力,故只需验算中柱B即可。
选取Nmax和Mmax时两组最不利内力,考虑承载力抗震调整系数,Re?0.75。 (一) M??50.774kN.m N=2431.593kN V=?16.230kN (二) M??310.400kN.m N=1836.478kN V=?92.709kN 调整后 M??322.8kN.m N=1377.359kN V=?69.532kN
例表19 基本组合时框架梁的弯矩和剪力,弯矩单位为kN.m,剪力单位为kN
截1.2Sgk+1.4Swk层面内Sgk 次 位置 M A V B左 五 B右 跨M V Mab -131.706 81.312 86.099 74.633 -104.013 68.420 -13.701 8.400 5.088 6.459 -81.726 56.127 3.644 -1.012 0.609 0.000 11.242 -2.896 -9.611 2.896 9.610 -2.669 0.812 0.000 18.065 -4.705 -3.644 1.012 -0.609 0.000 -11.242 2.896 9.611 -2.896 -9.610 2.669 -0.812 0.000 -18.065 4.705 15.811 -166.373 104.390 109.158 95.889 -189.168 133.054 -257.543 152.037 -215.112 138.809 117.010 111.788 -177.468 130.218 -266.223 -174.168 108.484 110.954 98.602 -229.789 158.249 -294.585 176.234 -260.289 165.000 137.459 131.263 -223.009 156.577 -299.793 -176.576 107.223 107.452 95.889 -220.646 141.163 -230.633 143.928 -242.020 146.282 114.737 111.788 -228.050 143.392 -221.953 -180.290 110.184 109.930 98.602 -248.675 163.114 -278.439 171.369 -276.434 169.484 136.095 131.263 -253.358 164.481 -273.231 -174.742 108.921 116.745 100.755 -130.974 89.934 -171.310 101.139 -144.602 93.295 76.167 74.640 -119.940 87.679 -176.518 M V 74.763 -143.816 87.861 8.440 -14.927 8.360 -1.182 -3.645 1.182 1.182 3.645 -1.182 96.332 -192.311 115.281 100.539 -196.539 118.130 99.642 -182.105 111.971 102.524 -190.415 116.144 99.937 -197.213 119.605 -96.664 -15.216 4.863 -4.863 -124.100 力 Sqk活 风 风 0.7Sqk活 +1.4Sqk活 -133.214 右风 -137.717 +1.4Sqk活 -141.384 -126.411 Swk左Swk右左风+1.4×左风活+1.4Swk右风风 风 ×0.6Swk×0.7Sqk×0.6Swk×0.6Swk左1.2Sgk+1.41.2Sgk+1.41.2Sgk+1.41.35Sgk+1.41.35Sgk+×0.6Swk-134.58101.92-191.09117.61-180.86110.62115.72间 Mbc M A V B左 四 B右 跨M V Mab M V 100.75-149.8694.800-120.916 -101.009 73.116 -113.092 70.768 55.915 55.289 -100.085 67.875 61.473 -94.751 58.800 49.771 46.369 -84.344 56.485 -155.1696.274-160.7497.77974.803间 Mbc M A 三 BV M 74.640-150.2895.583-120.916 -101.009 -15.811 -149.95左 B右 跨V M V Mab 73.661 -113.092 70.768 57.880 55.289 -100.456 67.926 61.115 -94.751 58.800 48.442 46.369 -84.634 56.527 4.705 15.810 -4.392 1.127 0.000 24.910 -6.644 -4.705 -15.810 4.392 -1.127 0.000 -24.910 6.644 22.929 -6.644 -22.928 6.369 -0.991 0.000 -26.029 7.357 26.938 -7.357 -26.937 7.483 0.455 0.000 154.873 -206.432 136.397 118.507 111.788 -168.615 127.606 -276.189 157.485 -196.467 133.629 117.956 111.788 -155.080 124.775 -283.021 160.316 -191.130 132.069 121.302 111.513 177.906 -255.081 163.552 138.221 131.263 -218.110 155.068 -305.772 179.415 -249.102 161.892 137.688 131.263 -203.178 152.326 -310.567 182.158 -246.057 160.956 142.750 130.941 141.699 -250.700 148.694 115.351 111.788 -238.363 146.209 -211.987 138.882 -260.666 151.462 115.181 111.788 -227.962 145.375 -207.595 139.717 -266.554 153.022 122.576 111.513 170.002 -281.642 170.931 136.328 131.263 -259.959 166.230 -267.251 168.253 -287.621 172.592 136.023 131.263 -246.906 164.685 -265.311 169.798 -291.311 173.527 143.515 130.941 103.395 -139.394 91.848 79.085 74.640 -114.691 86.119 -182.497 104.954 -133.415 90.187 78.718 74.640 -105.604 84.274 -186.693 106.799 -130.235 89.251 81.166 74.453 95.490-165.9599.22677.191间 Mbc M A V B左 二 B右 跨M V Mab M V 74.640-156.5497.281-120.916 -101.009 -22.929 73.610 -113.092 70.768 57.693 55.289 -94.421 67.003 61.073 -94.751 58.800 48.303 46.369 -79.812 55.787 6.644 22.928 -6.369 0.991 0.000 26.029 -7.357 -143.9793.793-171.93100.8877.053间 Mbc M A V B左 一 B右 跨M V Mab M V 74.640-149.3396.634-121.530 -101.502 -26.938 74.533 -113.231 70.768 60.406 55.150 61.813 -94.862 58.800 50.461 46.258 7.357 26.937 -7.483 -0.455 0.000 -141.4394.440-175.48101.8281.930间 Mbc 74.453梁的剪力向上为正,对柱子弯矩右边受拉为正,梁下边受拉为正,轴力压为正,拉为负 例表21(a) 基本组合时A柱的弯矩和轴力,弯矩单位为kN.m,轴力单位为kN
1.2Sgk+1.41.2Sgk+1.4Swk层截内Sgk 次 面 力 Sqk活 风 风 0.7Sqk活 +1.4Sqk活 柱顶 五 柱底 柱顶 四 柱底 柱顶 三 柱底 柱二 顶 N 630.233 269.979 -15.427 15.427 999.261 1121.292 1042.457 1147.209 1115.394 837.856 M N M 51.840 480.119 -53.957 41.475 184.052 -43.168 -10.318 -8.783 14.592 10.318 8.783 -14.592 88.408 744.218 -86.624 111.606 826.438 -112.926 117.299 768.810 -127.482 128.940 841.193 -137.441 110.630 828.532 -115.147 61.317 640.783 -60.585 M N M N 52.713 320.033 -52.713 470.096 42.172 98.167 -42.172 184.052 -5.455 -4.078 12.610 -8.783 5.455 4.078 -12.610 8.783 96.947 474.534 -86.930 732.190 117.714 518.048 -111.704 814.410 112.221 485.952 -122.238 756.782 126.879 524.899 -132.889 829.166 112.491 528.248 -112.491 815.001 66.580 428.619 -60.570 627.252 M N M N 65.836 159.402 -43.518 310.010 33.546 12.640 -48.216 98.167 -1.690 -1.182 9.552 -4.078 1.690 1.182 -9.552 4.078 109.512 202.015 -86.100 462.506 124.548 207.986 -111.700 506.020 114.244 205.324 -112.846 473.925 127.387 209.971 -127.748 512.871 121.754 227.580 -106.001 514.717 87.459 214.200 -50.726 415.088 M N -100.329 -15.216 149.379 12.640 4.863 -1.182 -4.863 1.182 -128.498 189.987 -137.612 195.958 右风 -142.115 193.297 +1.4Sqk活 -145.782 197.944 -150.356 214.049 -131.359 200.669 Swk左Swk右左风+1.4×左风活+1.4Sqk右风×0.7Sqk活 风 ×0.6Swk×0.7Sqk×0.6Sqk1.35Sgk+1.4×0.6Swk左1.2Sgk+1.41.2Sgk+1.41.35Sgk+1.4