某6層住宅樓建筑結(jié)構(gòu)的豎向荷載作用下內(nèi)力計(jì)算過程案例目錄TOC\o"1-3"\h\u267961工程概況 157982豎向荷載作用下內(nèi)力計(jì)算 1149552.1一榀框架豎向恒載計(jì)算 1109912.1.1計(jì)算分配系數(shù) 1222992.1.2計(jì)算桿件固端彎矩 3260772.1.3計(jì)算桿端彎矩 567712.1.4恒載作用下梁端剪力的計(jì)算 8189592.1.5恒載作用下柱剪力和軸力的計(jì)算 9172342.2一榀框架豎向活載計(jì)算 13119622.2.1計(jì)算桿件固端彎矩 13226872.2.2計(jì)算桿端彎矩 143882.2.3活載作用下梁端剪力的計(jì)算 1746752.2.4活載作用下柱剪力和軸力的計(jì)算 181工程概況本次設(shè)計(jì)題目為：某住宅樓設(shè)計(jì)，結(jié)構(gòu)類型為框架結(jié)構(gòu)，本工程位于鎮(zhèn)江；根據(jù)查詢抗震設(shè)計(jì)規(guī)范及荷載規(guī)范可知：該地區(qū)抗震設(shè)防烈度為7度，設(shè)計(jì)地震分組為第一組，水平地震影響系數(shù)最大值為0.12，基本風(fēng)壓及雪壓分別為0.4kN/m2、0.35kN/m2。。地面粗糙度類別為B類，場地類別為Ⅱ類。本設(shè)計(jì)建筑物為6層框架結(jié)構(gòu)，建筑平面長為43m，寬為14m，建筑高度為17.55m；對于建筑物底層、標(biāo)準(zhǔn)層以及頂層的高度，根據(jù)任務(wù)書以及相關(guān)規(guī)范的要求，設(shè)計(jì)其高度為2.9m；基于建筑功能以及屋面安全性，本設(shè)計(jì)中屋面采用上人的形式，女兒墻高度為1.2m。2豎向荷載作用下內(nèi)力計(jì)算2.1一榀框架豎向恒載計(jì)算2.1.1計(jì)算分配系數(shù)一榀框架節(jié)點(diǎn)標(biāo)號圖如下：圖6-1框架節(jié)點(diǎn)編號圖根據(jù)一榀框架節(jié)點(diǎn)標(biāo)號進(jìn)行計(jì)算，如下所示：表6-1彎矩分配系數(shù)節(jié)點(diǎn)編號分配系數(shù)計(jì)算1節(jié)點(diǎn)右梁43327/97206=0.446節(jié)點(diǎn)下柱53879/97206=0.5542節(jié)點(diǎn)左梁43327/144264.8=0.3節(jié)點(diǎn)右梁47058.8/144264.8=0.326節(jié)點(diǎn)下柱53879/144264.8=0.3735節(jié)點(diǎn)上柱53879/151085=0.357節(jié)點(diǎn)右梁43327/151085=0.287節(jié)點(diǎn)下柱53879/151085=0.3576節(jié)點(diǎn)上柱53879/198143.8=0.272節(jié)點(diǎn)左梁43327/198143.8=0.219節(jié)點(diǎn)右梁47058.8/198143.8=0.237節(jié)點(diǎn)下柱53879/198143.8=0.2729、13、17節(jié)點(diǎn)上柱53879/151085=0.357節(jié)點(diǎn)右梁43327/151085=0.287節(jié)點(diǎn)下柱53879/151085=0.35710、14、18節(jié)點(diǎn)上柱53879/198143.8=0.272節(jié)點(diǎn)左梁43327/198143.8=0.219節(jié)點(diǎn)右梁47058.8/198143.8=0.237節(jié)點(diǎn)下柱53879/198143.8=0.27221節(jié)點(diǎn)上柱53879/140609=0.383節(jié)點(diǎn)右梁43327/140609=0.308節(jié)點(diǎn)下柱43403/140609=0.30922節(jié)點(diǎn)上柱53879/187667.8=0.287節(jié)點(diǎn)左梁43327/187667.8=0.231節(jié)點(diǎn)右梁47058.8/187667.8=0.251節(jié)點(diǎn)下柱43403/187667.8=0.2312.1.2計(jì)算桿件固端彎矩表6-2常見荷載作用下桿件的固端彎矩荷載形式圖公式集中荷載均布荷載梯形荷載三角形荷載（1）頂層恒載作用下梁固端計(jì)算：頂層邊跨均布恒載：g=12.77kN/m-1/12×12.77×4.82=-32.2kN.m頂層中跨均布恒載：g=7.28kN/m-1/12×7.28×1.72=-1.75kN.m（2）標(biāo)準(zhǔn)層恒載作用下梁固端計(jì)算：標(biāo)準(zhǔn)層邊跨均布恒載：g=17.66kN/m-1/12×17.66×4.82=-33.91kN.m標(biāo)準(zhǔn)層中跨均布恒載：g=10.32kN/m-1/12×10.32×1.72=-2.49kN.m2.1.3計(jì)算桿端彎矩表6-3恒載下彎矩二次分配表上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱0.5540.4460.3000.3730.3260.3260.3730.3000.4460.5540.000-32.20032.2000.000-1.7501.7500.000-32.20032.2000.00017.84014.360-9.140-11.360-9.9309.93011.3609.140-14.360-17.8402.055-4.5707.180-4.2754.965-4.9654.275-7.1804.570-2.055-0.820-0.660-2.360-2.940-2.5702.5702.9402.3600.6600.82023.08-23.0727.88-18.58-9.299.2918.58-27.8823.07-23.080.3570.3570.2870.2190.2720.2720.2370.2370.2720.2720.2190.2870.3570.3570.000-33.91033.9100.000-2.4902.4900.000-33.91033.9100.00012.11012.1109.730-2.880-8.550-8.550-7.4507.4508.5508.5502.880-9.730-12.110-12.1108.9202.055-3.4404.865-2.680-4.2753.725-3.7252.6804.275-4.8653.440-8.920-2.055-4.118-4.118-3.3110.2990.3710.3710.324-0.324-0.371-0.371-0.2993.3114.1184.11812.9114.05-30.9332.19-13.86-12.45-2.892.8913.8612.45-32.1930.93-12.91-14.050.3570.3570.2870.2190.2720.2720.2370.2370.2720.2720.2190.2870.3570.3570.000-33.91033.9100.000-2.4902.4900.000-33.91033.9100.00012.11012.1109.730-2.880-8.550-8.550-7.4507.4508.5508.5502.880-9.730-12.110-12.1102.0552.055-3.4404.865-4.275-4.2753.725-3.7254.2754.275-4.8653.440-2.055-2.055-3.095-3.095-2.488-0.009-0.011-0.011-0.0090.0090.0110.0110.0092.4883.0953.09512.0712.07-30.1131.89-12.84-12.84-2.222.2212.8412.84-31.8930.11-12.07-12.070.3570.3570.2870.2190.2720.2720.2370.2370.2720.2720.2190.2870.3570.3570.000-33.91033.9100.000-2.4902.4900.000-33.91033.9100.00012.11012.1109.730-2.880-8.550-8.550-7.4507.4508.5508.5502.880-9.730-12.110-12.1102.0552.055-3.4404.865-4.275-4.2753.725-3.7254.2754.275-4.8653.440-2.055-2.055-3.095-3.095-2.488-0.009-0.011-0.011-0.0090.0090.0110.0110.0092.4883.0953.09512.0712.07-30.1131.89-12.84-12.84-2.222.2212.8412.84-31.8930.11-12.07-12.070.3570.3570.2870.2190.2720.2720.2370.2370.2720.2720.2190.2870.3570.3570.000-33.91033.9100.000-2.4902.4900.000-33.91033.9100.00012.11012.1109.730-2.880-8.550-8.550-7.4507.4508.5508.5502.880-9.730-12.110-12.1102.0552.495-3.4404.865-4.275-4.5103.725-3.7254.2754.510-4.8653.440-2.055-2.495-3.252-3.252-2.6150.0430.0530.0530.046-0.046-0.053-0.053-0.0432.6153.2523.25214.9112.35-30.2331.94-12.77-13.01-2.172.1712.7713.01-31.9430.23-14.91-12.350.3830.3090.3080.2310.2870.2310.2510.2510.2870.2310.2310.3080.3830.3090.000-33.91033.9100.000-2.4902.4900.000-33.91033.9100.00012.99010.48010.440-7.260-9.020-7.260-7.8907.8909.0207.2607.260-10.440-12.990-10.4802.0550.000-3.6302.220-4.2750.0003.945-3.9454.2750.000-2.2203.630-2.0550.000-0.929-0.749-0.747-1.130-1.403-1.130-1.2271.2271.4031.1301.1300.7470.9290.74918.129.73-27.8530.74-14.70-8.39-7.667.6614.708.39-30.7427.85-18.12-9.734.87-4.194.19-4.87ABCD框架梁跨中彎矩的計(jì)算公式如下所示：以表格的形式列出框架梁跨中彎矩的計(jì)算結(jié)果。表6-4恒載作用下梁跨中彎矩計(jì)算層號梁跨lMlMrgM中6F邊跨4.80-23.0727.8812.770.125×12.77×4.82-(23.07+27.88)/2=22.82中跨1.70-9.299.297.280.125×7.28×1.72-(9.29+9.29)/2=-2.665F邊跨4.80-30.9332.1917.660.125×17.66×4.82-(30.93+32.19)/2=19.3中跨1.70-2.892.8910.320.125×10.32×1.72-(2.89+2.89)/2=-2.164F邊跨4.80-30.1131.8917.660.125×17.66×4.82-(30.11+31.89)/2=19.86中跨1.70-2.222.2210.320.125×10.32×1.72-(2.22+2.22)/2=-2.493F邊跨4.80-30.1131.8917.660.125×17.66×4.82-(30.11+31.89)/2=19.86中跨1.70-2.222.2210.320.125×10.32×1.72-(2.22+2.22)/2=-2.492F邊跨4.80-30.2331.9417.660.125×17.66×4.82-(30.23+31.94)/2=19.78中跨1.70-2.172.1710.320.125×10.32×1.72-(2.17+2.17)/2=-2.441F邊跨4.80-27.8530.7417.660.125×17.66×4.82-(27.85+30.74)/2=21.57中跨1.70-7.667.6610.320.125×10.32×1.72-(7.66+7.66)/2=-3.932.1.4恒載作用下梁端剪力的計(jì)算恒載作用下梁左右端剪力及柱端剪力計(jì)算公式如下所示：其中Rr，Rl假定框架梁為簡支時梁端的剪力。表6-5恒載作用下梁端剪力層號梁跨lRlRrMlMrVlVr6F邊跨4.8040.25-40.25-23.0727.8839.25-41.25中跨1.702.19-2.19-9.299.292.19-2.195F邊跨4.8042.38-42.38-30.9332.1942.12-42.64中跨1.708.77-8.77-2.892.898.77-8.774F邊跨4.8042.38-42.38-30.1131.8942.01-42.75中跨1.708.77-8.77-2.222.228.77-8.773F邊跨4.8042.38-42.38-30.1131.8942.01-42.75中跨1.708.77-8.77-2.222.228.77-8.772F邊跨4.8042.38-42.38-30.2331.9442.02-42.74中跨1.708.77-8.77-2.172.178.77-8.771F邊跨4.8042.38-42.38-27.8530.7441.78-42.98中跨1.708.77-8.77-7.667.668.77-8.772.1.5恒載作用下柱剪力和軸力的計(jì)算框架柱端剪力計(jì)算公式：框架柱軸力計(jì)算公式：柱頂軸力：Nt=上層柱底軸力+F-V左+V右柱底軸力：Nb=本層柱頂軸力+柱自重表6-6恒載作用下柱端剪力層號層高lMtMbV6F邊柱2.9023.0812.91-13.79中柱2.90-18.58-13.8611.185F邊柱2.9014.0512.07-10.04中柱2.90-12.45-12.848.724F邊柱2.9012.0712.07-10.39中柱2.90-12.84-12.848.853F邊柱2.9012.0714.91-10.34中柱2.90-12.84-12.778.832F邊柱2.9012.3518.12-11.54中柱2.90-13.01-14.709.551F邊柱3.609.734.87-4.05中柱3.60-8.39-4.193.5表6-7恒載作用下柱軸力層號柱FVlVrG柱NtNb6F邊柱29.460.0039.2519.5268.7188.23中柱33.58-41.252.1919.5281.02100.545F邊柱33.880.0042.1219.52164.23183.75中柱42.40-42.648.7719.52194.35213.874F邊柱33.880.0042.0119.52259.64279.16中柱42.40-42.758.7719.52307.79327.313F邊柱33.880.0042.0119.52352.05374.57中柱42.40-42.758.7719.52421.23440.752F邊柱33.880.0042.0319.52450.48470.00中柱42.40-42.738.7719.52534.65554.171F邊柱33.880.0041.7824.23542.66569.89中柱42.40-42.988.7724.23648.32672.55圖6-2恒載作用下彎矩圖圖6-3恒載作用下剪力圖圖6-4恒載作用下軸力圖2.2一榀框架豎向活載計(jì)算2.2.1計(jì)算桿件固端彎矩（1）頂層活載作用下梁固端計(jì)算：頂層邊跨均布活載：q=2.46kN/m-1/12×2.46×4.82=-10.48kN.m頂層中跨均布活載：q=2.13kN/m-1/12×2.13×1.72=-0.51kN.m（2）標(biāo)準(zhǔn)層活載作用下梁固端計(jì)算：標(biāo)準(zhǔn)層邊跨均布活載：q=2.46kN/m-1/12×2.46×4.82=-10.48kN.m標(biāo)準(zhǔn)層中跨均布活載：q=2.13kN/m-1/12×2.13×1.72=-0.51kN.m2.2.2計(jì)算桿端彎矩表6-8活載下框架彎矩二次分配表上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱0.5540.4460.3000.3730.3260.3260.3730.3000.4460.5540.000-10.48010.4800.000-0.5100.5100.000-10.48010.4800.0002.8104.670-2.990-3.720-3.2503.2503.7202.990-4.670-2.8101.870-1.4952.340-1.3551.625-1.6251.355-2.3351.495-1.870-0.210-0.170-0.780-0.970-0.8500.8500.9700.7800.1700.2107.48-7.489.05-2.05-2.992.992.05-9.057.48-7.480.3570.3570.2870.2190.2720.2720.2370.2370.2720.2720.2190.2870.3570.3570.000-10.48010.4800.000-0.5100.5100.000-10.48010.4800.0003.7403.7403.010-2.180-2.710-2.710-2.3602.3602.7102.7102.180-3.010-3.740-3.7402.9051.870-1.0901.505-1.860-1.3551.180-1.1801.8601.355-1.5051.090-2.905-1.870-1.316-1.316-1.0580.1160.1440.1440.126-0.126-0.144-0.144-0.1161.0581.3161.3162.334.29-9.629.92-4.43-3.92-1.561.564.433.92-9.929.62-2.33-4.290.3570.3570.2870.2190.2720.2720.2370.2370.2720.2720.2190.2870.3570.3570.000-10.48010.4800.000-0.5100.5100.000-10.48010.4800.0003.7403.7403.010-2.180-2.710-2.710-2.3602.3602.7102.7102.180-3.010-3.740-3.7401.8701.870-1.0901.505-1.355-1.3551.180-1.1801.3551.355-1.5051.090-1.870-1.870-0.946-0.946-0.7610.0050.0070.0070.006-0.006-0.007-0.007-0.0050.7610.9460.9464.664.66-9.329.81-4.06-4.06-1.681.684.064.06-9.819.32-4.66-4.660.3570.3570.2870.2190.2720.2720.2370.2370.2720.2720.2190.2870.3570.3570.000-10.48010.4800.000-0.5100.5100.000-10.48010.4800.0003.7403.7403.010-2.180-2.710-2.710-2.3602.3602.7102.7102.180-3.010-3.740-3.7401.8701.870-1.0901.505-1.355-1.3551.180-1.1801.3551.355-1.5051.090-1.870-1.870-0.946-0.946-0.7610.0050.0070.0070.006-0.006-0.007-0.007-0.0050.7610.9460.9464.664.66-9.329.81-4.06-4.06-1.681.684.064.06-9.819.32-4.66-4.660.3570.3570.2870.2190.2720.2720.2370.2370.2720.2720.2190.2870.3570.3570.000-10.48010.4800.000-0.5100.5100.000-10.48010.4800.0003.7403.7403.010-2.180-2.710-2.710-2.3602.3602.7102.7102.180-3.010-3.740-3.7401.8702.005-1.0901.505-1.355-1.4301.180-1.1801.3551.430-1.5051.090-1.870-2.005-0.994-0.994-0.7990.0220.0270.0270.024-0.024-0.027-0.027-0.0220.7990.9940.9944.624.75-9.369.83-4.04-4.11-1.671.674.044.11-9.839.36-4.62-4.750.3830.3090.3080.2310.2870.2310.2510.2510.2870.2310.2310.3080.3830.3090.000-10.48010.4800.000-0.5100.5100.000-10.48010.4800.0004.0103.2403.230-2.300-2.860-2.300-2.5002.5002.8602.3002.300-3.230-4.010-3.2401.8700.000-1.1501.615-1.3550.0001.250-1.2501.3550.000-1.6151.150-1.8700.000-0.276-0.222-0.222-0.349-0.433-0.349-0.3790.3790.4330.3490.3490.2220.2760.2222.603.02-8.629.45-4.65-2.65-2.142.144.652.65-9.458.62-2.60-3.021.51-1.321.32-1.51ABCD框架梁跨中彎矩的計(jì)算公式如下所示：以表格的形式列出框架梁跨中彎矩的計(jì)算結(jié)果。表6-9活載作用下梁跨中彎矩計(jì)算層號梁跨lMlMrqM中6F邊跨4.80-7.489.052.460.125×2.46×4.82-(7.48+9.05)/2=7.46中跨1.70-2.992.992.130.125×2.13×1.72-(2.99+2.99)/2=-2.225F邊跨4.80-9.629.922.460.125×2.46×4.82-(9.62+9.92)/2=2.95中跨1.70-1.561.562.130.125×2.13×1.72-(1.56+1.56)/2=-0.794F邊跨4.80-9.329.812.460.125×2.46×4.82-(9.32+9.81)/2=2.16中跨1.70-1.681.682.130.125×2.13×1.72-(1.68+1.68)/2=-0.913F邊跨4.80-9.329.812.460.125×2.46×4.82-(9.32+9.81)/2=2.16中跨1.70-1.681.682.130.125×2.13×1.72-(1.68+1.68)/2=-0.912F邊跨4.80-9.369.832.460.125×2.46×4.82-(9.36+9.83)/2=2.13中跨1.70-1.671.672.130.125×2.13×1.72-(1.67+1.67)/2=-0.91F邊跨4.80-8.629.452.460.125×2.46×4.82-(8.62+9.45)/2=2.69中跨1.70-2.142.142.130.125×2.13×1.72-(2.14+2.14)/2=-1.372.2.3活載作用下梁端剪力的計(jì)算恒載作用下梁左右端剪力及柱端剪力計(jì)算公式如下所示：其中Rr，Rl假定框架梁為簡支時梁端的剪力。表6-10活載作用下梁端剪力層號梁跨lRlRrMlMrVlVr6F邊跨4.8013.10-13.10-7.489.0512.77-13.43中跨1.701.8