《豎向荷載作用下框架內(nèi)力分析案例》3900字

II豎向荷載作用下框架內(nèi)力分析案例綜述1.1計(jì)算方法及負(fù)荷轉(zhuǎn)移路徑1.1.1.彎矩二次分配方法一種近似計(jì)算方法，即每個(gè)節(jié)點(diǎn)的不平衡彎矩同時(shí)分布與傳遞，且僅限于兩種分布。 圖6-1負(fù)載轉(zhuǎn)移路徑1.2垂直荷載計(jì)算1.2.1.靜載計(jì)算(1)頂梁在線荷載標(biāo)準(zhǔn)值：ⅰ橫梁重量：側(cè)跨梁：4.225千牛/米中跨梁：2.275kN/mⅱ屋面板荷載：屋面板邊跨為3×7.5m，為雙向板。減少系數(shù)：α=1.5/7.5=0.2(6-1)1-2×α2+α3=0.928中跨為3×9，為單向板∴頂梁上的荷載標(biāo)準(zhǔn)值為：邊跨：g1=5.32×3×0.928+4.225=19.04kN/m中跨：g2=5.32×3+2.275=18.235kN/m(2)樓板梁在線荷載標(biāo)準(zhǔn)值：側(cè)展：g3=3.49×3×0.928+4.225=13.94kN/m中跨：g4=3.49×3+2.275=12.745kN/m1.2.2.活荷載(1)屋頂：邊跨：q1=0.5×7.5×0.928=3.48kN/m中跨：q2=0.5×3=1.5kN/m(2)樓層：邊跨：q3=2.0×3×0.928=11.99kN/m中跨：q4=2.5×3=7.5kN/m1.3梁固定端彎矩：梁端彎矩繞梁端順時(shí)針方向?yàn)檎?，否則為負(fù)(6-2)表6-1豎向荷載下框架梁固定端彎矩加載部分側(cè)跨直流中跨CB跨度均勻載荷固定結(jié)束時(shí)刻跨度均勻載荷固定結(jié)束時(shí)刻剩下對剩下對靜載頂樓7.519.04-89.2589.253.018.235-13.6813.68其他層7.513.94-65.3465.343.012.745-9.569.56活荷載頂樓7.53.48-11.3111.313.01.5-1.1251.125其他層7.55.568-21.121.13.07.5-5.6255.625加載部分邊跨AB跨度均勻載荷固定結(jié)束時(shí)刻剩下對靜載頂樓1.919.04-75.5475.54其他層1.913.94-55.3155.31活荷載頂樓1.93.48-13.8113.81其他層1.95.568-22.0922.091.4內(nèi)力分布系數(shù)的計(jì)算1.4.1.旋轉(zhuǎn)剛度S的計(jì)算：6-2旋轉(zhuǎn)剛度S組件名稱旋轉(zhuǎn)剛度S(KNm)框架梁側(cè)跨直流4Kb=4×48056=192224邊跨AB4Kb=4×52226=208904中跨CB2Kb=2×18753=37506框架柱一樓4Kc=4×49000=196000其他層4Kc=4×58700=2348001.4.2分配系數(shù)計(jì)算：(6-3)各成員的分配系數(shù)如下表所示：表6-3各成員的分配系數(shù)節(jié)點(diǎn)層u左（右）光束u右（左）光束你在柱子上u下欄節(jié)點(diǎn)層u（右）光束u右（左）光束你在柱子上u下欄邊緣節(jié)點(diǎn)D軸50.430.55邊節(jié)點(diǎn)A軸50.470.5340.300.350.3540.310.3450.34530.300.350.3530.310.3450.34520.300.350.3520.310.3450.34510.310.380.3110.330.370.30中間節(jié)點(diǎn)C軸50.410.080.51中間節(jié)點(diǎn)B軸50.080.400.5240.270.050.340.3440.050.290.330.3330.270.050.340.3430.050.290.330.3320.270.050.340.3420.050.290.330.3310.290.060.360.2910.060.310.350.281.5彎矩分布與傳遞方法：先在對應(yīng)的方框中填入各點(diǎn)的分布系數(shù)，在框架梁對應(yīng)位置填入梁的固定端彎矩，然后松弛節(jié)點(diǎn)，分配各節(jié)點(diǎn)的不平衡彎矩同時(shí)。假設(shè)遠(yuǎn)端固定傳遞（不向滑動(dòng)端），右（左）梁將彎矩分配給左（右）梁，上（下）將彎矩分配給下（上）梁)列（傳遞系數(shù)均為0.5）。在傳遞第一次彎矩分布后，進(jìn)行第二次彎矩分布。D軸C軸上欄下柱右梁左光束上欄下柱右梁0.550.450.410.0000.510.08-89.2589.25-13.6849.0940.16-30.98-38.54-1.0511.44-15.4920.08-9.492.482.231.825.36-1.67-1.0462.76-62.7672.99-54.7-18.290.350.350.30.270.340.340.05-65.3465.34-9.5622.8722.8719.6-15.06-18.97-18.97-2.7824.5511.44-7.539.8-19.27-9.481.15-9.96-9.96-8.544.811.051.050.8937.4624.35-61.8164.89-32.19-22.4-10.30.350.350.30.270.340.340.05-65.3465.34-9.5622.8722.8719.6-15.06-18.97-18.97-2.7811.4411.44-7.539.8-9.48-9.481.15-5.37-5.37-4.612.162.722.720.4128.9428.94-57.8862.24-25.73-25.73-10.780.350.350.30.270.340.340.05-65.3465.34-9.5622.8722.8719.6-15.06-18.97-18.97-2.711.4410.13-7.539.8-9.48-8.091.15-4.91-4.91-4.221.792.252.250.3329.428.09-57.4961.87-21.2-24.81-10.860.380.310.310.290.360.290.06-65.3465.34-9.5624.8220.2620.26-11.18-20.08-11.18-4.1411.44-8.0910.13-9.481.38-1.27-1.04-1.04-0.59-0.73-0.59-0.1234.9919.22-54.2158.7-30.29-11.77-12.449.61-8.39恒載下的彎矩分布A軸B軸下柱上欄左光束左光束上欄下柱右梁0.530.470.080.520.475.5413.68-75.54-40.04-35.54.9532.1724.74-9.5412.37-3.037.55-17.75-1.5-1.331.061.885.29-51.0851.0811.6641.6-63.260.3450.3450.310.050.330.330.2955.319.56-55.31-19.08-19.08-17.152.2915.115.113.26-9.54-9.541.63-1.3911.087.55-8.587.977.977.17-0.68-4.51-4.51-3.96-20.65-20.6551.969.7821.6718.14-54.590.3450.3450.310.050.330.330.2955.319.56-55.31-19.08-19.08-17.152.2915.115.113.26-9.54-9.541.63-1.397.557.55-8.584.34.33.85-0.26-1.69-1.69-1.49-24.32-24.3248.6410.220.9620.96-52.120.3450.3450.310.050.330.330.2955.319.56-55.31-19.08-19.08-17.152.2915.115.113.26-8.3-9.541.63-1.397.551.41-8.583.873.873.47-0.2-1.32-1.32-1.15-23.51-24.7548.2610.2621.3320.19-51.780.30.370.330.060.350.280.3155.319.56-55.31-11.6-20.46-18.252.7511.0112.8114.18-9.547.09-2.077.55-9.310.730.910.810.221.281.021.13-15.87-29.0944.9610.4624.8413.83-49.13-7.941.92恒載下的彎矩分布D軸C軸上欄下柱右梁左光束上欄下柱右梁0.550.450.410.510.08-11.3111.31-1.1258.977.34-1.23-7.74-1.214.57-3.123.67-3.480.51-0.8-0.65-0.29-0.36-0.0612.74-12.7413.46-11.58-1.880.350.350.30.270.340.340.05-21.121.1-5.6259.149.147.83-5.53-1.96-1.96-1.024.494.57-2.773.92-3.87-3.480.41-2.2-2.2-1.930.821.031.030.1511.4311.51-22.9725.31-9.8-9.41-1.10.350.350.30.270.340.340.05-21.121.1-5.6259.149.147.83-5.53-1.96-1.96-1.024.574.57-2.773.92-3.48-3.480.41-2.25-2.25-1.760.710.890.890.1311.4611.46-22.825.2-9.55-9.55-1.110.350.350.30.270.340.340.05-21.121.1-5.6259.149.147.83-5.53-1.96-1.96-1.024.574.05-2.773.92-3.48-2.970.41-2.05-2.05-1.760.570.720.720.1111.6611.14-22.825.06-9.72-9.21-1.130.380.310.310.290.360.290.06-21.121.1-5.6259.928.098.09-5.94-7.37-5.94-1.234.57-2.974.05-3.480.5-0.61-0.5-0.5-0.31-0.39-0.31-0.0613.887.59-21.4823.9-11.24-1.25-1.413.8-3.13活載下的彎矩分布A軸B軸下柱左光束上欄左光束上欄下柱右梁0.530.470.080.520.413.811.125-13.81-7.32-1.491.011.65.07-3.812.54-0.612.72-3.250.670.60.090.590.46-10.4610.461.629.91-11.530.3450.310.3450.050.330.330.2922.095.625-22.09-7.62-1.85-7.620.825.435.434.77-3.812.39-3.66-0.513.32.72-3.431.751.571.75-0.1-0.69-0.69-0.6-9.6819.2-9.535.848.047.46-21.350.3450.310.3450.050.330.330.2922.095.625-22.09-7.62-1.85-7.620.825.435.434.77-3.662.39-3.66-0.512.722.72-3.431.71.531.7-0.08-0.5-0.5-0.44-9.5819.16-9.585.817.657.65-21.190.3450.310.3450.050.330.330.2922.095.625-22.09-7.62-1.85-7.620.825.435.434.77-3.322.39-3.66-0.512.722.31-3.431.581.421.58-0.05-0.36-0.36-0.32-9.3619.05-9.75.897.797.38-21.070.30.330.370.060.350.280.3122.095.625-22.09-1.63-7.29-8.170.995.764.615.12.55-3.66-0.622.72-3.650.330.370.410.090.540.430.48-1.317.72-11.421.099.025.04-20.16-3.152.52活載下的彎矩分布1.5.5靜載彎曲距離表6-4靜載彎曲距離地面直流跨CB十字左端中間右端左端中間右端米米米米米米5-62.766672.99-18.293.0411.664-61.8134.6764.89-10.34.39.783-57.8837.9662.24-10.783.8510.22-57.4938.3461.87-10.863.7810.261-54.2141.5658.7-12.442.8910.46建造層AB交叉左端中間右端米米米5-63.2651.1451.084-54.529.7351.963-52.1232.5848.642-51.7832.9448.261-49.1333.4249.96注：1）M'為調(diào)幅后的彎曲距離。2)彎矩符號(hào)逆時(shí)針為正1.5.6。活載彎曲距離表6-5活載彎曲距離地面直流跨CB十字左端中間右端左端中間右端米米米米米米5-12.7411.3713.46-1.880.781.624-22.915.0525.31-1.12.475.843-22.9715.0725.2-1.112.455.862-22.815.2225.06-1.132.435.891-21.4811.4623.9-1.412.191.09地面AB交叉左端中間右端米米米5-11.539.7210.464-21.3512.8619.23-21.1912.9619.162-21.0713.0819.051-20.1614.217.72注：1）M'為調(diào)幅后的彎曲距離。2)彎矩符號(hào)逆時(shí)針為正為減少支座處梁負(fù)配筋過度擁擠，抗震結(jié)構(gòu)中梁端塑性鉸結(jié)構(gòu)設(shè)計(jì)，框架梁允許塑性幅值調(diào)整，支座處彎矩為減小，并相應(yīng)調(diào)整跨中支座的彎曲。彎矩為0.8~0.9中的1.1~1.2，使1/2（左Mb+右Mb）+Mb>M，Mb>M1.6梁端剪力：均布載荷下：(6-4)(6-5)V'=V—q×b/2(6-6)1.1.1恒載下梁端剪力表6-6恒載下梁端剪力直流叉光束結(jié)尾切力量層qkN/mlmqL/2(千牛)(千牛)(千牛)(千牛)(千牛)(千牛)519.047.571.41.3670.0472.7664.867.52413.947.552.280.4151.8752.6948.0448.86313.947.552.280.5851.752.8647.8749.03213.947.552.280.5851.752.8647.8749.03113.947.552.280.651.6852.8847.8549.05CB叉光束末端剪刀力量層qkN/mlmqL/2(千牛)(千牛)(千牛)(千牛)(千牛)(千牛)518.235327.350.5421.8127.8921.822.88412.745319.120.1718.9519.2915.4515.79312.745319.120.1918.9319.3115.4315.81212.745319.120.218.9219.3215.4215.82112.745319.120.6618.4619.7814.9611.28AB叉光束結(jié)尾切力量層qkN/mlmqL/2(千牛)(千牛)(千牛)(千牛)(千牛)(千牛)519.041.965.691.7763.9267.4658.6862.22413.941.948.090.3747.7248.4643.8944.63313.941.948.090.547.5948.5943.7644.76213.941.948.090.5147.5848.643.7544.77113.941.948.090.1247.9748.2144.1444.38注：表中M值在應(yīng)用AM之前。1.1.2活載梁末端剪力表6-7活載梁末端剪力直流叉光束結(jié)尾切力量層qkN/mlmqL/2(千牛)(千牛)(千牛)(千牛)(千牛)(千牛)53.481.913.050.09612.9513.1511.9912.1945.5681.920.880.3220.5621.219.0319.6735.5681.920.880.320.5821.1819.0519.6525.5681.920.880.320.5821.1819.0519.6515.5681.920.880.3220.5621.219.0319.67CB叉光束結(jié)尾切力量層qkN/mlmqL/2(千牛)(千牛)(千牛)(千牛)(千牛)(千牛)51.532.250.092.162.341.751.9347.5311.250.0911.1611.349.19.2837.5311.250.0811.1711.339.119.2727.5311.250.0811.1711.339.119.2717.5311.250.1111.1411.369.089.3AB叉光束結(jié)尾切力量層q千牛/米lmqL/2(千牛)(千牛)(千牛)(千牛)(千牛)(千牛)53.481.912.010.1611.8512.1710.8911.2145.5681.919.210.3118.919.5217.3717.9935.5681.919.210.2918.9219.517.3917.9725.5681.919.210.2918.9219.517.3917.9715.5681.919.210.3518.8619.5617.3318.03注：表中M值在應(yīng)用AM之前。1.7柱軸力與剪力1.7.1.恒載作用下的柱軸向剪力表6-7恒載下邊柱的D軸力與剪力層部分梁剪縱向載荷柱重ΔN(kN)側(cè)柱軸向力側(cè)柱剪(千牛)(千牛)(千牛)(千牛)(千牛)51-170.04245.07.35315.11315.1125.72-2340.46340.4643-351.87244.3725.35291.24631.713.664-4321.59662.0535-551.7231.5425.35283.24945.2914.966-6308.59970.6427-751.7231.5425.35283.241253.8811.178-8308.591279.2319-951.68231.5438.54283.221562.455.8810-10321.761600.99注：①假定外縱墻完全由縱梁承載。②地板荷載產(chǎn)生的軸向力。③立柱重量：一樓：7.865×4.9=38.54kN其他層數(shù)：1.500×3.9=25.35Kn縱向載荷：F5=7.28×9+3.25×1.0+5.32×9.0×7.5/2=245.07kNF4=3.74×[(3.9-0.8)×9-2.4×3×1.8]+0.4×2.4×1.8×3+7.28×9+3.49×9×7.5/2=244.37kNF1=3.74×(3.1×9-4×2.1×2)+0.4×4×2.1×2+3.49×9×7.5/2+7.28×9=231.54kN C-恒載下中心柱的軸向力與剪力層部分梁剪力B左梁剪力B右縱向載荷柱重ΔN(kN)中柱軸向力中心柱剪力(千牛)(千牛)(千牛)(千牛)(千牛)(千牛)51-172.7621.81311.8925.35411.46411.4622.282-2441.81441.8143-352.6918.95287.2725.35358.91800.7212.344-4384.26821.0735-552.8618.93278.1625.35349.951171.0213.326-6375.31201.3727-752.8619.32278.1625.35350.341551.7114.138-8375.691577.0619-952.8819.78278.1638.54350.821927.885.1310-10389.361961.42說明：縱向載荷：F5=7.28×9+3.25×1.0+5.32×9.0×(7.5/2+1.5)=311.89kNF4=2.28×[(3.9-0.8)×9-1.5×1.2×2]+7.28×9+3.49×9×(7.5/2+1.5)+0.4×1.5×1.2×2=287.27kNF3=3.49×(3.1×9-1.5×2-1.2×2.7×2)+0.4×1.2×1.5×2+3.49×9×(7.5/2+1.5)+7.28×9+7.28×9+1.2×2.7×2×0.2=278.16kN表6-8恒 載下中柱B的軸向力與剪力層部分梁剪力B左梁剪力B右縱向載荷柱重ΔN(kN)中柱軸向力中心柱剪力(千牛)(千牛)(千牛)(千牛)(千牛)(千牛)51-127.8963.92302.5325.35394.34394.3418.792-2419.69419.6943-319.2947.72277.8425.35404.85824.5410.034-4430.2849.8935-519.3147.59267.7525.35334.651184.5410.846-63601209.8927-719.3247.58267.7525.35334.651544.5411.558-83601569.8919-919.7847.97267.7538.54335.51905.394.2310-10374.041943.93說明：縱向載荷：F5=7.28×9+3.25×1.0+5.32×9.0×4.95=302.53kNF4=2.28×[(3.9-0.8)×9-1.5×1.2×2]+7.28×9+3.49×9×(1.9/2+1.5)=277.84kNF3=2.28×(3.1×9-1.5×2-1.2×2.7×2)+0.4×1.2×1.5+3.49×9×(1.9/2+1.5)+7.28×9+7.28×9+1.2×2.7×2×0.2=267.75kN載下A側(cè)柱的軸向力與剪力層部分梁剪縱向載荷柱重ΔN(kN)側(cè)柱軸向力側(cè)柱剪(千牛)(千牛)(千牛)(千牛)(千牛)51-167.46230.7125.35298.17298.1721.132-2323.52323.5243-348.46234.9425.35283.4601.9211.534-4308.75632.2735-548.59222.1225.35270.71902.9812.586-6291.06928.3327-748.6222.1225.35270.721199.0513.498-8291.071224.419-948.21222.1238.54270.331494.734.8610-10308.871533.27縱向載荷：F5=7.28×9+3.25×1.0+5.32×9.0×1.9/2=245.07kNF4=3.74×[(3.9-0.8)×9-2.4×3×1.8]+0.4×2.4×1.8×3+7.28×9+3.49×9×1.9/2=234.94kNF1=3.74×(3.1×9-4×2.1×2)+0.4×4×2.1×2+3.49×9×1.9/2+7.28×9=222.12k