Y公司5層宿舍樓的風(fēng)荷載作用下框架計算和豎向荷載作用下內(nèi)力計算案例目錄TOC\o"1-3"\h\u27947Y公司5層宿舍樓的風(fēng)荷載作用下框架計算和豎向荷載作用下內(nèi)力計算案例 1165651風(fēng)荷載作用下框架計算 1238621.1風(fēng)荷載集中力計算 122481.2水平位移在風(fēng)荷載作用下的驗算 2285511.3風(fēng)荷載作用下框架結(jié)構(gòu)內(nèi)力計算 3309351.3.1風(fēng)荷載下框架柱剪力和彎矩計算 3303151.3.2風(fēng)荷載下框架梁端彎矩計算 4313811.3.3風(fēng)荷載下框架梁剪力和柱軸力計算 5233202豎向荷載作用下內(nèi)力計算 719182.1一榀框架豎向恒載計算 765752.1.1計算分配系數(shù) 7228792.1.2計算桿件固端彎矩 8169502.1.3計算桿端彎矩 11122672.1.4恒載作用下梁柱剪力的計算 13200472.1.5恒載作用下柱軸力的計算 15235672.2一榀框架豎向活載計算 17229682.2.1計算桿件固端彎矩 1717752.2.2計算桿端彎矩 17317152.2.3活載作用下梁端剪力的計算 2065702.2.4活載作用下柱剪力和軸力的計算 201風(fēng)荷載作用下框架計算1.1風(fēng)荷載集中力計算根據(jù)《建筑結(jié)構(gòu)荷載規(guī)范》（GB50009-2012）表8.3.1條第30項知，本工程的體型系數(shù)μs=0.8-（-0.5）=1.3?？扇ˇ聑表6.1荷載集中力計算樓層5F18.7510.558.644.754F15.1510.5212.966.743F11.5510.4812.966.222F7.9500.4612.965.961F4.3500.4614.316.58圖8-1荷載受力圖（kN）1.2水平位移在風(fēng)荷載作用下的驗算由抗震結(jié)構(gòu)設(shè)計課本可知：其中：表6.2相對轉(zhuǎn)角驗算表8.3各樓層相對轉(zhuǎn)角驗算層號層高D(N/mm)(u)i(mm)(u)i/hi限值5F3.604.754.75900000.0000521/692301/5504F3.606.7411.49900000.0000751/480003F3.606.2217.71900000.0000691/521732F3.605.9623.67900000.0000661/545451F4.356.5830.52538120.0001231/35655各樓層的層間位移均小于1/550，故各樓層均滿足要求。1.3風(fēng)荷載作用下框架結(jié)構(gòu)內(nèi)力計算1.3.1風(fēng)荷載下框架柱剪力和彎矩計算由于框架的對稱性，計算時只取一榀框架的一半。剪力分配公式如下：表6.4框架柱剪力計算層號Vi(kN)∑DDimDim/∑DVim/kNyh(m)Mc上(kN.m)Mc下(kN.m)5層4.7590000175000.19440.921.082.151.004層11.4990000175000.19442.231.444.823.223層17.7190000175000.19443.441.616.815.542層23.6790000175000.19444.61.828.288.371層30.5253812118220.21976.73.6810.5524.68表6.5框架柱端彎矩計算``Vi(kN)∑DDimDim/∑DVim/kNy(m)Mc上(kN.m)Mc下(kN.m)5層4.7590000275000.350561.661.262.151.554層11.4990000275000.350564.031.574.554.683層17.7190000275000.350564.571.626.797.42層23.6790000275000.350566.211.88.12111層30.5253812150840.28038.562.9912.2520.91.3.2風(fēng)荷載下框架梁端彎矩計算梁左、右彎矩計算公式：梁左彎矩:梁右彎矩:其中：為節(jié)點(diǎn)左右梁線剛度。表6..6梁端彎矩計算層號邊跨軸中跨軸MC上MC下μB1MABMC上MC下μB1μB2MBAMBC5F2.1551.0912.142.141.560.540.461.170.9864F3.993.2215.824.554.680.540.462.462.093F6.815.5419.936.797.40.540.4643.42F8.288.37113.828.12110.540.464.393.741F10.5524.68119.9212.2520.90.540.4611.39.61.3.3風(fēng)荷載下框架梁剪力和柱軸力計算梁的剪力計算公式如：—KL左端彎矩—KL右端彎矩；—KL計算跨度。柱子軸力計算公式如下：—Vz左端剪力—Vz右端梁的剪力。表6.7風(fēng)荷載作用下梁端剪力及柱軸圖6-2彎矩圖圖6-3剪力圖圖6-4軸力圖2豎向荷載作用下內(nèi)力計算2.1一榀框架豎向恒載計算2.1.1計算分配系數(shù)一榀框架節(jié)點(diǎn)標(biāo)號圖如下：圖7-1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)行計算，如下所示：節(jié)點(diǎn)編號分配系數(shù)計算1節(jié)點(diǎn)右梁0.345節(jié)點(diǎn)下柱0.6552節(jié)點(diǎn)左梁0.267節(jié)點(diǎn)右梁0.226節(jié)點(diǎn)下柱0.5075節(jié)點(diǎn)上柱0.396節(jié)點(diǎn)右梁0.208節(jié)點(diǎn)下柱0.3966節(jié)點(diǎn)上柱0.337節(jié)點(diǎn)左梁0.177節(jié)點(diǎn)右梁0.15節(jié)點(diǎn)下柱0.3379、13節(jié)點(diǎn)上柱0.396節(jié)點(diǎn)右梁0.208節(jié)點(diǎn)下柱0.39610、14節(jié)點(diǎn)上柱0.337節(jié)點(diǎn)左梁0.177節(jié)點(diǎn)右梁0.15節(jié)點(diǎn)下柱0.33717節(jié)點(diǎn)上柱0.452節(jié)點(diǎn)右梁0.238節(jié)點(diǎn)下柱0.3118節(jié)點(diǎn)上柱0.377節(jié)點(diǎn)左梁0.198節(jié)點(diǎn)右梁0.167節(jié)點(diǎn)下柱0.258 2.1.2計算桿件固端彎矩表2.1常見荷載作用下桿件的固定彎矩由上表可知：均布荷載下梁端固端彎矩（1）頂層恒載作用下梁固端計算：頂層邊跨：均布恒載：g=23.86kN/m-150.50kN·m頂層中跨：均布恒載：g=5.81kN/m-2.79kN·m（2）標(biāo)準(zhǔn)層恒載作用下梁固端計算：標(biāo)準(zhǔn)層邊跨：均布恒載：g=25.01kN/m-157.75kN·m標(biāo)準(zhǔn)層中跨：均布恒載：g=4.7kN/m-2.26kN·m2.1.3計算桿端彎矩表7-2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0.6490.3510.2670.5070.2260.2260.5070..2670.35450.655偏心矩偏心矩偏心矩偏心矩-150.5150.5-5.335.33-150.5150.50.0098.5853.35-38.760.00-73.60-32.8132.810.0073.6038.76-51.920.00-98.580.007.74-19.3826.680.00-6.4916.40-16.400.0025.48-25.9619.380.00-30.720.007.624.13-9.770.00-18.55-8.273.820.008.564.513.910.007.430.00121.87-121.87133.190.00-107.64-25.5525.550.00107.64-133.19121.870.00-121.870.3960.3960.2080.1770.3370.3370.150.150.3370.3370.1770.2080.3960.396-155.16155.16-3.963.96-155.2155.1661.4461.4432.27-26.76-50.95-50.95-22.6822.6850.9550.9526.76-32.27-61.44-61.4449.2930.72-13.3816.14-36.80-25.4811.34-11.3436.8025.48-16.1413.38-49.29-30.72-26.39-26.39-13.866.1611.7311.735.22-5.22-11.73-11.73-6.1613.8626.3926.3984.3565.78-150.13150.69-76.03-64.70-10.0810.0876.0364.70-150.69150.13-84.35-65.780.3960.3960.2080.1770.3370.3370.150.150.3370.3370.1770.2080.3960.396-155.2155.16-3.963.96-155.2155.1661.4461.4432.27-26.76-50.95-50.95-22.6822.6850.9550.9526.76-32.27-61.44-61.4430.7230.72-13.3816.14-25.48-25.4811.34-11.3425.4825.48-16.1413.38-30.72-30.72-19.03-19.03-10.004.167.917.913.52-3.52-7.91-7.91-4.1610.0019.0319.0373.1373.13-146.26148.69-68.52-68.52-11.7811.7868.5268.52-148.69146.26-73.13-73.130.3960.3960.2080.1770.3370.3370.150.150.3370.3370.1770.2080.3960.396-155.2155.16-3.963.96-155.2155.1661.4461.4432.27-26.76-50.95-50.95-22.6822.6850.9550.9526.76-32.27-61.44-61.4430.7230.72-13.3816.14-25.48-25.4811.34-11.3425.4825.48-16.1413.38-30.72-30.72-19.03-19.03-10.004.167.917.913.52-3.52-7.91-7.91-4.1610.0019.0319.0373.1373.13-146.26148.69-68.52-68.52-11.7811.7868.5268.52-148.69146.26-73.13-73.130.4520.310.2380.1980.3770.2580.1980.1980.3770.2580.1980.2380.4520.31-155.2155.16-3.963.96-155.2155.1661.4461.4432.27-26.76-50.95-50.95-22.6822.6850.9550.9526.76-32.27-61.44-61.4430.72-13.3816.14-25.4811.34-11.3425.48-16.1413.38-30.72-6.87-6.87-3.61-0.35-0.67-0.67-0.300.300.670.670.353.616.876.8785.3054.58-139.87144.18-72.11-51.63-15.6015.6072.1151.63-144.18139.87-85.30-54.5822.29-25.8125.81-22.29接著我們需要計算梁的跨中彎矩，公式如下所示：框架梁跨中彎矩計算如下表所示：表7-3恒載作用下跨中彎矩計算層號梁跨5F邊跨8.70-121.87133.1923.8698.22中跨2.40-25.5525.5511.1-17.564F邊跨8.70-150.13150.6924.682.06中跨2.40-10.0810.088.24--4.1863F邊跨8.70-146.26148.6924.684.06中跨2.40-11.7811.788.24-5.8762F邊跨8.70-146.26148.6924.684.06中跨2.40-11.7811.788.24-5.8761F邊跨8.70-139.87144.1824.688.57中跨2.40-13.9113.388.24-7.482.1.4恒載作用下梁柱剪力的計算恒載作用下梁左右端剪力按下列公式計算：，—假定框架梁為簡支時的梁端剪力。柱子剪力按下列公式計算：表7-4恒載作用下邊框架梁剪力層號梁跨5F邊跨8.70112.54115.14121.87133.19112.54115.14中跨2.4024.5424.54-25.5525.5524.54-24.544F邊跨8.70119.62-119.76-150.13150.69119.62-119.76中跨2.4020.0220.02-10.0810.0820.0220.023F邊跨8.70119.41-119.97-146.26148.69119.41-119.97中跨2.4020.02-20.02-11.7811.7820.02-20.022F邊跨8.70119.72120.24-146.26148.69119.72120.24中跨2.4020.02-20.02-11.7811.7820.02-20.021F邊跨8.70119.72-119.93-139.87144.18119.72-119.93中跨2.4020.02-20.02-13.9113.3820.02-20.02表7-5恒載作用下的柱子剪力層號柱層高5F邊柱3.60121.8784.35-52.28中柱3.60-107.64-76.03-51.024F邊柱3.6065.7873.1338.59中柱3.60-64.70-68.52-37.013F邊柱3.6073.1371.4140.15中柱3.60-68.52-67.50-37.782F邊柱3.6075.7693.26-46.26中柱3.60-70.52-85.48-43.331F邊柱5.2545.1922.59-12.91中柱5.25-41.06-20.77-7.822.1.5恒載作用下柱軸力的計算框架柱軸力計算公式：柱頂軸力：柱底軸力：表7-6恒載作用下邊柱軸力層號柱5F邊柱73.930.00112.5434.6186.47221.07中柱58.78-115.1424.5434.6198.46233.064F邊柱115.950.00119.6234.6456.64491.24中柱109.00119.7620.0234.6481.84516.443F邊柱115.950.00119.4134.6726.60761.20中柱109.00119.9720.0234.6765.43800.032F邊柱115.950.00119.7234.6996.881031.48中柱109.00120.2020.0234.61049.241083.841F邊柱115.950.00119.1041.801374.051349.0中柱109.00120.2820.0241.801123.51232.5圖7-2恒載作用下彎矩圖圖7-3恒載作用下剪力圖圖7-4恒載作用下軸力圖2.2一榀框架豎向活載計算2.2.1計算桿件固端彎矩（1）頂層活載作用下梁固端計算：頂層邊跨均布活載：=1.66kN/m-10.47kN·m頂層中跨均布活載：=0.75kN/m-0.36kN·m（2）標(biāo)準(zhǔn)層活載作用下梁固端計算：標(biāo)準(zhǔn)層邊跨均布活載：=6.6kN/m-41.63kN·m標(biāo)準(zhǔn)層中跨均布活載：=3kN/m-1.44kN·m2.2.2計算桿端彎矩表7-11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0.6490.3510.2670.5070.2260.2260.5070.2670.35450.655偏心矩偏心矩偏心矩偏心矩0.000－10.4710.4700.000－0.3560.35600.000－10.4710.4700.0006.8603.610-2.700-5.130-2.2802.2805.1302.700-3.610-6.8608.280-1.3501.805-6.8051.140-1.1406.805-1.8051.350-8.280-4.539-2.3911.0311.9570.872-0.872-1.957-1.0312.3914.53910.60-10.6010.61-9.98-0.630.639.98-10.6110.60-10.600.35960.35960.2080.1770.35370.35370.1500.1500.35370.35370.1770.2080.35960.35960.000－41.8241.8200.000－1.441.4400.000－41.8241.8200.00016.56016.5608.700-2.150-13.610-13.610-6.0606.06013.61013.6102.150-8.700-16.560-16.5603.4308.280-3.5754.350-2.565-6.8053.030-3.0302.5656.805-4.3503.575-3.430-8.280-3.221-3.221-1.6920.35520.6710.6710.299-0.299-0.671-0.671-0.35521.6923.2213.22116.7721.62-38.3939.37-15.50-19.74-4.174.1715.5019.74-39.3738.39-16.77-21.620.35960.35960.2080.1770.35370.35370.1500.1500.35370.35370.1770.2080.35960.35960.000－41.8241.8200.000－1.441.4400.000－41.8241.8200.00016.56016.5608.700-2.150-13.610-13.610-6.0606.06013.61013.6102.150-8.700-16.560-16.5608.2808.280-3.5754.350-6.805-6.8053.030-3.0306.8056.805-4.3503.575-8.280-8.280-5.142-5.142-2.7011.1032.1002.1000.935-0.935-2.100-2.100-1.1032.7015.1425.14219.7019.70-39.4040.12-18.32-18.32-3.543.5418.3218.32-40.1239.40-19.70-19.700.35960.35960.2080.1770.35370.35370.1500.1500.35370.35370.1770.2080.35960.35960.000－41.8241.8200.000－1.441.4400.000－41.8241.8200.00016.56016.5608.700-2.150-13.610-13.610-6.0606.06013.61013.6102.150-8.700-16.560-16.5608.2809.055-3.5754.350-6.805-2.3303.030-3.0306.8052.330-4.3503.575-8.280-9.055-5.449-5.449-2.8621.1962.2762.2761.013-1.013-2.276-2.276-1.1962.8625.4495.44919.3920.17-39.5640.22-18.14-18.66-3.463.4618.1418.66-40.2239.56-19.39-20.170.45200.31000.23800.19800.37700.25800.19800.19800.37700.25800.19800.23800.27600.1940-41.6341.63-1.44-1.44-41.4741.4718.8212.919.91-7.96-15.15-10.37-7.968.5016.1811.078.50-9.87-18.74-12.868.240.00-3.984.95-6.770.004.25-3.982.230.00-4.934.25-8.210.00-1.93-1.32-1.01-0.48-0.92-0.63-0.480.330.630.430.330.941.791.2325.1311.58-36.7238.15-22.84-11.00-5.633.4124.0411.51-37.5836.79-25.16-11.636.34-5.915.91-6.34活載作用下頂層邊跨跨中彎矩的計算：框架梁跨中彎矩計算如下表所示：表7-12活載作用下跨中彎矩計算層號梁跨5F邊跨8.70-9.859.951.550.125×1.55×8.72-(9.85+9.95)/2=14.49中跨2.40-0.310.310.30.125×0.3×2.42-2=-0.0164F邊跨8.70-34.3434.346.20.125×6.2×8.72-6.56=32.55中跨2.40-2.872.871.20.125×0.3×2.42-2.87=-2.7263F邊跨8.70-36.7837.566.20.125×6.2×8.72-5.46=33.65中跨2.40-2.272.271.20.125×0.3×2.42-2=-2.132F邊跨8.70-36.9737.976.20.125×6.2×8.72-(36.97+37.97)/2=35.74中跨2.40-1.151.151.20.125×0.3×2.42-1.15=--1.011F邊跨8.70-33.8335.896.20.125×6.2×8.72-(33.83+35.89)/2=34.32中跨2.40-3.453.451.20.125×0.3×2.42-2=-3.312.2.3活載作用下梁端剪力的計算恒載作用下梁的左、右兩端剪力計算公式如下計算：，—假定框架梁為簡支時的梁端剪力。表7-13活載作用下梁端剪力計算層號梁跨5F邊跨8.708.64-8.64-10