计算书 5 组合
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第五章 内力组合5.1 内力组合形式本设计考虑四种组合形式:(1)由可变荷载效应控制的组合:wk Qk Gk 4.16.04.12.1S S S S ⨯±+= (5-1) Qkwk Gk 4.17.04.12.1S S S S ⨯++= (5-2)(2)由永久荷载效应控制的组合:QkGk 4.17.035.1S S S ⨯+= (5-3)(3)由竖向荷载和地震作用下的组合:EhkQk Gk 3.15.0(2.1S S S S ++=) (5-4)5.2 内力组合计算对梁内力进行组合时,选取AB 梁左端、AB 梁跨中、AB 梁右端、BC 梁左端和BC 梁跨中五个控制截面;对柱内力进行组合时,选取各层A 柱(边柱)、B 柱(中柱)的两个控制截面。
5.2.1 框架梁内力组合与调整框架梁内力组合过程见表5-1。
表中:(1)梁端弯矩均为换算至截面的弯矩。
梁端弯矩以下部受拉为正,上部受拉为负;轴力以受压为正,受拉为负;梁端剪力以向上为正,向下为负;柱子弯矩以左侧受拉为正,右侧受拉为负;剪力以绕柱子顺时针方向为正,逆时针方向为负;(2)进行竖向荷载和地震作用下的组合后,梁端弯矩应按抗震调整系数RE γ进行调整,用于正截面承载力计算,调整系数取0.75;(3)梁端截面组合的剪力设计值应按下式调整:Gb n r b lb V l M M V ++=/)vb (η (5-5)式中,梁端剪力增大系数取 1.1。
剪力增大调整后,梁端剪力应按抗震等级系数RE γ调整,用于斜截面承载力验算,调整系数为0.85。
表中所得结果已根据公式调整。
5.2.2 框架柱内力组合(1)弯矩和轴力组合与调整框架柱弯矩和轴力组合过程见表5-3和表5-4。
表中进行竖向荷载和地震作用下的组合后,柱端弯矩应按抗震调整系数RE γ进行调整。
由于恒荷载作用下轴压比为Af c N=276.46×102/(14.3×450×450)=0.095<0.15 调整系数RE γ取0.75,2~5层轴压比均大于0.15,RE γ取0.80。
组合完成后,对柱端弯矩进行调整,调整过程见表5-5和表5-6。
表中: 1)柱端弯矩组合按公式∑∑=b c c M M η调整,c η取1.1。
上下柱端弯矩按弹性理论分配;2)顶层不调整;3)调整后,底层柱下端截面组合的弯矩设计值,应乘以增大系数1.3。
(2)剪力组合与调整框架柱剪力组合过程见表5-7和表5-8。
剪力设计值应按下式调整n vb /)M (M H V tc b c +=η (5-6)式中,vb η取1.2,H n 为柱净高。
表5-1 框架梁内力组合楼层截面内力S Gk S Qk S wk S Ehk QkGk4.17.035.1SS⨯+wkQkGk4.16.04.12.1SSS⨯±+QkwkGk4.17.04.12.1SSS⨯+±EhkQkGk3.15.0(2.1SSS++)结果左风右风左风右风左震右震5 A支座M(kN·m)-11.93 -3.25 4.21 47.65 -19.29 -15.33 -22.40 -11.61 -23.40 37.51 -57.20 -57.20 V(kN)42.95 15.44 1.16 11.16 73.11 72.18 74.13 65.05 68.30 58.53 57.90 74.13 AB跨中M(kN·m)37.35 13.52 0.69 5.60 63.67 64.33 63.17 59.04 57.10 39.08 28.16 64.33 B支座左M(kN·m)-15.95 -5.07 2.83 36.45 -26.50 -28.62 -23.86 -28.07 -20.15 -49.89 21.18 -49.89 V(kN)-41.42 -14.74 1.16 11.16 -70.36 -71.31 -69.37 -65.77 -62.53 -56.97 -55.45 -71.31 B支座右M(kN·m)-5.53 -2.38 2.90 18.04 -9.80 -7.53 -12.40 -4.91 -13.03 13.44 -22.57 -22.57 V(kN) 2.64 0.00 2.39 16.39 3.56 1.16 5.18 -0.18 6.51 19.96 19.96 19.96 BC跨中M(kN·m)-5.94 -2.38 0.00 0.00 -10.35 -10.46 -10.46 -9.46 -9.46 -5.35 -5.35 -10.464 A支座M(kN·m)-27.65 -5.12 10.93 98.93 -42.35 -31.17 -49.53 -22.90 -53.50 73.80 -123.65 -123.65 V(kN)77.97 15.17 2.62 29.95 120.13 112.60 117.00 104.76 112.10 118.50 117.16 120.13 AB跨M(kN·m)60.69 9.11 1.63 8.41 90.86 86.95 84.22 84.03 79.48 66.92 50.53 90.86- 44 -中B支座左M(kN·m)-32.23 -5.58 7.68 82.12 -48.98 -52.94 -40.04 -54.90 -33.39 -111.59 53.80 -111.59 V(kN)-76.23 -15.01 2.61 29.95 -117.62-114.68-110.3-109.84-102.53 -116.64 -115.30 -117.62B支座右M(kN·m)-7.75 -1.13 7.79 40.62 -11.57 -4.34 -17.43 0.50 -21.31 33.37 -47.09 -47.09 V(kN) 2.64 0.00 6.32 36.92 3.56 -2.14 8.48 -5.68 12.02 41.27 41.27 41.27BC跨中M(kN·m)-8.71 -1.13 0.00 0.00 -12.87 -12.03 -12.03 -11.56 -11.56 -8.35 -8.35 -12.873 A支座M(kN·m)-13.99 -3.6816.90 132.06-22.49 -7.74 -36.14 3.27 -44.05 116.89 -143.01 -143.01 V(kN)36.61 15.37 3.90 41.48 64.49 62.17 68.73 53.53 64.45 85.60 84.71 85.60 AB跨中M(kN·m)24.72 10.21 1.49 11.72 43.38 45.21 42.71 41.76 37.58 38.27 15.42 45.21 B支座左M(kN·m)-16.26 -5.51 13.92 108.6 -27.35 -38.92 -15.53 -44.40 -5.42 -123.02 91.64 -123.02 V(kN)-35.75 14.81 3.90 41.48 -33.75 -25.44 -18.89 -33.85 -22.93 -69.33 -68.44 -69.33 B支座右M(kN·m)-3.97 -2.42 13.72 53.74 -7.73 3.37 -19.68 12.07 -26.34 48.51 -57.06 -57.06 V(kN) 2.64 0.00 10.27 48.84 3.56 -5.46 11.79 -11.21 17.55 53.31 53.31 53.31- 45 -BC跨中M(kN·m)-3.99 -2.42 0.00 0.00 -7.76 -8.18 -8.18 -7.16 -7.16 -4.68 -4.68 -8.182 A支座M(kN·m)-14.31 -4.8023.22 168.66-24.02 -4.39 -43.40 10.63 -54.38 151.91 -179.48 -179.48 V(kN)36.51 -15.20 5.25 50.00 34.39 18.12 26.94 21.57 36.27 80.50 79.94 80.50 AB跨中M(kN·m)24.67 9.42 2.67 15.58 42.54 45.03 40.55 42.57 35.10 41.63 11.25 45.03B支座左M(kN·m)-16.03 -5.39 17.89 137.5 -26.92 -41.81 -11.75 -49.56 0.53 -150.92 120.02 -150.92 V(kN)-35.85 14.98 5.2550.00-33.72 -26.46 -17.64 -35.69 -20.99 -79.94 -79.38 -79.94 B支座右M(kN·m)-3.05 -1.21 18.06 68.30 -5.30 9.82 -20.52 20.44 -30.13 63.85 -69.88 -69.88 V(kN) 2.64 0.00 15.05 61.83 3.56 -9.47 15.81 -17.90 24.24 66.82 66.82 66.82 BC跨中M(kN·m)-2.83 -1.21 0.00 0.00 -5.01 -5.09 -5.09 -4.58 -4.58 -3.09 -3.09 -5.091 A支座M(kN·m)-11.62 -3.83 40.49 228.13 -19.44 14.71 -53.32 38.99 -74.38 212.28 -234.61 -234.61 V(kN)36.72 -15.28 6.71 65.59 34.60 17.04 28.31 19.70 38.48 96.83 95.92 96.83 AB跨M(kN·m)27.33 10.39 5.41 26.19 47.08 51.89 42.80 50.55 35.40 54.80 3.74 54.80- 46 -中B支座左M(kN·m)-14.46 -4.81 29.67 175.7 -24.23 -49.01 0.84 -63.60 19.47 -186.54 158.72 -186.54 V(kN)-35.64 14.90 6.71 65.59 -33.51 -27.54 -16.27 -37.56 -18.77 -95.94 -95.02 -95.94B支座右M(kN·m)-3.96 -1.11 30.42 86.96 -6.43 19.25 -31.86 36.75 -48.43 81.40 -88.85 -88.85 V(kN) 2.64 0.00 19.58 81.10 3.56 -13.28 19.62 -24.24 30.58 84.33 84.33 84.33BC跨中M(kN·m)-3.97 -1.11 0.00 0.00 -6.45 -6.32 -6.32 -5.85 -5.85 -4.07 -4.07 -6.45- 47 -表5-2框架柱控制截面汇总表层次截面恒载作用下内力活载作用下内力风载作用下内力地震作用下内力M N V M N V M N V M N V5 A柱柱顶26.10 276.46 -15.528.08 48.56-4.384.16 1.16 2.00 47.6511.16 ±22.05柱底-29.55 288.46 -5.92 48.56 2.24 30.55B柱柱顶-23.17 275.6317.39-7.18 67.743.905.66 1.23 2.95 54.495.23 32.48柱底26.50 287.63 5.29 67.74 ±3.78 40.804 A柱柱顶25.31 607.00 -11.754.43 90.58-2.738.29 3.77 4.32 68.3841.5 33.98柱底-16.28 619.17 -4.31 90.58 5.53 53.86B柱柱顶-23.30 664.9213.00-4.15 131.202.4510.90 4.94 6.35 81.9312.250.77柱底14.29 676.00 3.68 131.20 9.42 67.033 A柱柱顶10.73 897.48-6.724.31 132.82-2.8310.24 7.67 6.48 78.23 83.03 43.50柱底-12.81 909.48 -4.66 132.82 10.24 78.23B柱柱顶-9.77 1013.77.36-3.68 194.442.4915.2011.3 9.5095.3319.56 64.98柱底11.72 1025.7 4.26 194.44 15.20 95.332 A柱柱顶14.58 1187.3-8.705.30 176.87-3.5213.9212.928.70 90.43133.0350.28柱底-16.37 1199.3 -5.95 176.87 13.92 90.43B柱柱顶-13.24 1362.69.67-4.84 257.873.1820.4621.10 12.79110.231.3975.11柱底14.81 1374.6 5.34 257.87 20.46 110.2- 48 -- 49 -1A 柱 柱顶 7.721477.2-2.262.81 219.00 -0.8917.3519.63 12.05 137.7198.62 54.38柱底 -3.86 1489.20 -1.40 219.00 28.44 167.9 B 柱柱顶 -7.17 1711.34 2.44 -2.62 321.22 0.83 25.9433.97 15.17152.5 46.9081.24柱底3.58 1723.341.31 321.2231.79 186.0表5-3 A 柱弯矩和轴力组合楼层截面内力QkGk 4.17.035.1S S ⨯+wkQkGk 4.16.04.12.1S S S ⨯±+Qkwk Gk 4.17.04.12.1S S S ⨯+± EhkQk Gk 3.15.0(2.1S S S ++)NM m axm axN Mm inN M 左风右风 左风 右风 左震 右震 5柱顶 M 43.15 39.14 46.13 33.41 45.06-26.88 69.95 69.95 43.15 69.95 N 420.81 400.71 398.76 380.96 377.72 259.70 237.93 237.93 420.81 237.93 柱底M -45.69 -41.87 -45.63 -38.13 -44.40 3.19 -56.38 -56.38 -45.69 -56.38 N437.01 415.11 413.16 395.36 392.12 270.50 248.73 248.73 437.01 248.73 4 柱顶M 38.51 29.61 43.54 23.11 46.32 -49.10 97.54 97.54 38.51 97.54 N908.22858.38852.05822.45811.89669.41582.99582.99908.22582.99柱底M -26.20 -20.92 -30.22 -16.02 -31.50 41.27 -73.71 -73.71 -26.20 -73.71 N 924.65 872.98 866.65 837.05 826.49 681.09 594.67 594.67 924.65 594.673 柱顶M 18.71 10.31 27.51 2.76 31.44 -71.05 93.73 93.73 18.71 93.73 N 1341.76 1269.37 1256.48 1217.88 1196.40 1011.69 838.98 838.98 1341.76 838.98 柱底M -21.86 -13.29 -30.50 -5.60 -34.27 69.25 -95.89 -95.89 -21.86 -95.89 N 1357.96 1283.77 1270.88 1232.28 1210.80 1023.21 850.50 850.50 1357.96 850.502 柱顶M 24.88 13.22 36.61 3.20 42.18 -80.26 110.59 110.59 24.88 110.59 N 1776.13 1683.18 1661.48 1616.13 1579.96 1363.02 1086.32 1086.32 1776.13 1086.32 柱底M -27.93 -16.28 -39.67 -5.99 -44.96 78.57 -112.62 -112.62 -27.93 -112.62 N 1792.33 1697.58 1675.88 1630.53 1594.36 1374.54 1097.84 1097.84 1792.33 1097.841 柱顶M 13.18 -1.38 27.77 -12.27 36.31 -135.91 151.97 151.97 13.18 151.97 N 2208.84 2095.73 2062.75 2014.74 1959.78 1729.80 1316.67 1959.78 2208.84 1316.67 柱底M -6.58 17.30 -30.48 33.81 -45.82 171.01 -179.04 -179.04 -6.58 -179.04 N 2225.04 2110.13 2077.15 2029.14 1974.18 1741.32 1328.19 1328.19 2225.04 1328.19- 50 -- 51 -表5-4 B 柱弯矩和轴力组合楼层 截面 内力QkGk 4.17.035.1S S ⨯+wkQkGk 4.16.04.12.1S S S ⨯±+Qkwk Gk 4.17.04.12.1S S S ⨯+± EhkQk Gk 3.15.0(2.1S S S ++)NM m axm axN Mm inN M 左风 右风 左风 右风 左震 右震 5柱顶M -38.32 -42.61 -33.10 -42.76 -26.92 -70.51 32.27 -70.51 -38.32 -70.51 N 438.49 426.63 424.56 398.86 395.42 253.17 242.97 253.17 438.49 242.97 柱底M 40.96 42.38 36.03 42.28 31.69 63.63 -15.93 63.63 40.96 63.63 N454.69 441.03 438.96 413.26 409.82263.97253.77 263.97454.69253.774柱顶M -35.52-42.93-24.61 -47.29 -16.77 -105.51 60.85 -105.51 -35.52 -105.51 N 1026.22 985.73 977.43 933.40 919.56 713.99 688.61 713.99 1026.22 688.61 柱底M 22.9030.2114.39 33.94 7.57 82.62 -54.23 82.6222.9082.62N1041.18 999.03 990.73 946.69 932.86 724.62 699.25 724.62 1041.18 699.25 3柱顶M -16.80-29.64-4.11-36.615.95-108.4388.00-108.43 -16.80 -108.43N 1559.09 1498.19 1479.19 1422.86 1391.19 1086.85 1046.17 1086.85 1559.09 1046.17 柱底M 20.0032.807.2639.52-3.04110.22-85.85110.2220.00110.22N1575.29 1512.59 1493.59 1437.26 1405.59 1098.37 1057.69 1098.37 1575.29 1057.69第五章 内力组合- 52 -2柱顶M -22.62 -39.85 -5.48 -49.28 8.01 -127.14 99.57 -127.14 -22.62 -127.14N 2092.28 2013.91 1978.46 1917.42 1858.34 1464.56 1399.27 1464.56 2092.28 1399.27 柱底M 25.2342.438.0651.65-5.64128.59-97.83128.5925.23128.59N2108.48 2028.31 1992.86 1931.82 1872.74 1476.08 1410.79 1476.08 2108.48 1410.79 1柱顶M -12.25-34.069.52-47.4925.14-165.40 150.48 -165.409.52-165.40N 2625.10 2531.85 2474.78 2415.96 2320.85 1845.85 1748.30 2415.96 2625.10 1748.30 柱底M 6.1232.83-20.5750.09-38.93196.85 -189.40 196.856.12196.85N2641.30 2546.25 2489.18 2430.36 2335.25 1857.37 1759.82 1857.37 2641.30 1759.82第五章 内力组合- 53 -表5-5 A 柱端弯矩调整楼层 543 21截面位置柱顶 柱底 柱顶 柱底 柱顶 柱底 柱顶 柱底 柱顶 柱底 RE M γ/c93.27 75.18121.9292.14117.16119.87138.24140.77189.96223.79 ∑RE Mγ/c93.27 197.10 209.30 258.10 330.73 223.79 ∑RE M γη/c c99.14 214.32 247.88 311.10 406.65 — 调整后c M74.3561.31106.0687.30111.00115.59133.30138.47186.85232.75表5-6 B 柱端弯矩调整楼层 5432 1截面位置柱顶 柱底 柱顶 柱底 柱顶 柱底 柱顶柱底柱顶 柱底 RE M γ/c94.01 84.84131.88103.27135.54137.78158.92 160.74206.76246.06 ∑RE Mγ/c94.01216.72 238.81 296.70 367.50 246.06 ∑RE M γη/c c 109.78251.25 297.32 372.26 464.44 — 调整后c M82.3473.77122.32102.86135.00138.29159.51162.51209.04255.90第五章 内力组合- 54 -表5-7 A 柱剪力V 组合楼层 QkGk 4.17.035.1S S ⨯+Qk wk Gk 4.17.04.12.1S S S ⨯+±EhkQkGk3.15.0(2.1S S S ++)()n b c t c vc /H M M +η()nb c t c vc /H M M +η 左风 右风 左风 右风 左震 右震 5 -24.47 -26.44 -23.08 -25.72 -20.12 -35.47 7.53 52.51 4 -17.95 -21.55 -14.29 -22.82 -10.73 -46.62 24.06 74.85 3 -11.51 -17.46 -6.58 -19.91 -1.76 -51.69 38.79 87.71 2 -14.76 -22.68 -8.06 -26.07 -1.71 -60.64 43.94 105.20 1-3.81-14.086.16-20.4513.29-58.7254.39108.28表5-8 B 柱剪力V 组合 楼层QkGk 4.17.035.1S S ⨯+Qk wk Gk 4.17.04.12.1S S S ⨯+±EhkQkGk3.15.0(2.1S S S ++)()n b c t c vc /H M M +η()nb c t c vc /H M M +η 左风右风 左风 右风 左震 右震 5 26.43 23.85 28.81 20.56 28.82 -16.02 47.32 60.43 4 19.30 13.70 24.36 9.11 26.89 -40.32 65.28 87.16 3 12.01 4.34 20.30 -2.03 24.57 -60.51 74.64 105.79 2 15.69 5.31 26.80 -3.19 32.63 -68.83 87.40 124.66 13.99-8.6516.83-17.5024.98-82.1586.83119.98第五章内力组合- 55 -。