樓宇結構設計中水平地震作用下內力計算案例綜述目錄TOC\o"1-2"\h\u11089樓宇結構設計中水平地震作用下內力計算案例綜述 1123741.1重力荷載代表值計算 1272323．梁荷載計算 1159755．門、窗荷載計算 2254856．墻體荷載計算 2228677．重力荷載代表值計算 2116591.2自振周期計算 383751.3水平地震作用下剪力計算 316411.4地震作用下變形驗算 4111741.5地震作用下剪重比驗算 5156521.6地震作用下柱剪力計算 5144551.7地震作用下柱彎矩計算 6237501.8地震作用下梁端彎矩計算 7317311.9地震作用下梁剪力及柱軸力計算 81.1重力荷載代表值計算1．板恒載計算4層：51×18×5.3=4865.40kN2~3層：(51×18-7.2×7.2)×3.95+7.2×7.2×3.95=3626.10kN1層：(51×18-7.2×7.2)×3.95+7.2×7.2×3.95=3626.10kN2．板活載計算4層：51×18×2=1836kN2~3層：(51×18-7.2×7.2)×2.0+51×3.00×2.5+7.2×7.2×3.5=1990.26kN1層：(51×18-7.2×7.2)×2.0+51×3.00×2.5+7.2×7.2×3.5=1990.26kN3．梁荷載計算4層：0.30×0.65×51×4×25×1.05+0.30×0.65×7.2×18×25×1.05+0.30×0.45×3.00×9×25×1.05+0.25×0.50×7.2×12×25×1.05=2086.80kN2~3層：0.30×0.65×51×4×25×1.05+0.30×0.65×7.2×18×25×1.05+0.30×0.45×3.00×9×25×1.05+0.25×0.50×7.2×12×25×1.05=2086.80kN1層：0.30×0.65×51×4×25×1.05+0.30×0.65×7.2×18×25×1.05+0.30×0.45×3.00×9×25×1.05+0.25×0.50×7.2×12×25×1.05=2086.80kN5．門、窗荷載計算4層：1.8×2.1×28×0.40+1×2.1×26×0.40=64.18kN2~3層：1.8×2.1×28×0.40+1×2.1×26×0.40=64.18kN1層：1.8×2.1×28×0.40+1×2.1×26×0.40=64.18kN6．墻體荷載計算屋面層女兒墻：(1.5×51×2+1.5×18×2)×2.800=579.60kN4層外墻：(3.25×51×2+3.25×7.2×4+3.45×3.00×2-1.8×2.1×28)×2.800=951.89kN2~3層外墻：(3.25×51×2+3.25×7.2×4+3.45×3.00×2-1.8×2.1×28)×2.800=951.89kN1層外墻：(3.25×51×2+3.25×7.2×4+3.45×3.00×2-1.8×2.1×28)×2.800=951.89kN4層內墻：(3.25×51×2+3.25×7.2×24-1×2.1×26)×2.400=2124.72kN2~3層內墻：(3.25×51×2+3.25×7.2×24-1×2.1×26)×2.400=2124.72kN1層內墻：(3.25×51×2+3.25×7.2×24-1×2.1×26)×2.400=2124.72kN7．重力荷載代表值計算重力荷載代表值取結構和構配件自重標準值與可變荷載的組合值之和，集中在各樓層標高處。重力荷載代表值為各層樓面上的重力荷載代表值及上下各半層的門、窗、墻、柱等重量(其中女兒墻荷載全部計入頂層重力荷載)。4865.40+1836/2+2086.80+997.92/2+64.18/2+579.60+951.89/2+2124.72/2=10683.58kN3626.10+1990.26/2+2086.80+997.92/2+997.92/2+64.18/2+64.18/2+951.89/2+951.89/2+2124.72/2+2124.72/2=11175.59kN3626.10+1990.26/2+2086.80+997.92/2+1360.8/2+64.18/2+64.18/2+951.89/2+951.89/2+2124.72/2+2124.72/2=11337.19kN圖4-11重力荷載代表值1.2自振周期計算；；框架結構的自振周期采用頂點位移法計算，計算過程用表格的形式列出。表4-23結構頂點位移計算層號410683.5810683.587226160.0147850.1610311175.5921859.177226160.0302500.1462211175.5933034.767226160.0457160.1159111337.1944371.946318540.0702250.0702由計算基本周期取，由表可知0.1610m，所以=0.477s1.3水平地震作用下剪力計算各樓層剛度分布較均勻，沒有剛度突變，宜采用底部剪力法對其進行地震力計算，通過對建筑物工程地點查詢《EQ建筑抗震設計規(guī)范》可知，該地區(qū)抗震設防烈度為7度(0.10g)，場地類別為Ⅱ類，設計地震分組為第二組，特征周期0.40s。對于地震影響系數(shù);當0.1<＜時，；當<＜時，=0.0682用底部剪力法計算水平地震作用，即結構等效總重力荷載：0.85×44371.97=37716.15kN由于＜1.4×0.40=0.56s因此頂部附加地震作用系數(shù)=0470956.20kN·m0×2572.99=0kNEQ框架橫向水平地震作用標準值計算公式如下結構底部：結構最頂層：其他層：表4-24水平地震剪力計算層號416.610683.58176813.22965.99965.99312.6511175.59141371.22772.361738.3528.7511175.5997786.41534.242272.5814.8511337.1954985.35300.402572.991.4地震作用下變形驗算EQ水平地震作用下框架結構的層間位移按下式計算各樓層的層間位移均小于1/550，故各樓層均滿足要求。表4-25位移驗算層號4965.997226161.3373.91/291731738.357226162.4063.91/162122272.587226163.1453.91/124012572.996318544.0724.851/11911.5地震作用下剪重比驗算根據(jù)規(guī)范可知，任一樓層的地震剪力與樓層的比例（剪重比）要滿足一定的限值，公式如下所示：——第i層水平地震剪力標準值；——為剪力系數(shù)；——第j層的重力荷載代表值；表4-26剪重比驗算層號剪重比剪重比限值4965.9910683.580.0900.01631738.3521859.170.08022272.5833034.760.06912572.9944371.940.058各樓層剪重比均滿足要求。1.6地震作用下柱剪力計算EQ水平荷載內力計算采用D值法，將對應層的層間剪力根據(jù)抗側剛度分配每根柱子，剪力分配公式，EQVi為柱子的剪力EQDi為對應柱子的抗側剛度EQ∑Di為某層柱子抗側剛度總和EQF為水平荷載作用下的層間剪力。表4-27水平地震作用下柱剪力層號柱軸號4A16788722616.01965.9922.44B25049722616.01965.9933.48C25049722616.01965.9933.48D16788722616.01965.9922.443A16788722616.011738.3540.39B25049722616.011738.3560.26C25049722616.011738.3560.26D16788722616.011738.3540.392A16788722616.012272.5852.80B25049722616.012272.5878.78C25049722616.012272.5878.78D16788722616.012272.5852.801A16184631853.932572.9965.90B19633631853.932572.9979.95C19633631853.932572.9979.95D16184631853.932572.9965.901.7地震作用下柱彎矩計算反彎點即為彎矩為零的點，反彎點的位置主要由梁柱線剛度、上下層的層高、以及上下層梁線剛度等因素決定。各層柱反彎點，通過查表計算，如下所示：表4-28反彎點高度比y計算結果層號A軸線邊柱B軸線中柱C軸線中柱D軸線邊柱40.3000.3880.3880.30030.4000.4500.4500.40020.5000.4880.4880.50010.6500.5770.5770.650柱端彎矩計算公式：；、EQ分別為柱下、上端彎矩；為柱子剪力；為柱反彎點高度比以1層A柱為例，進行詳細的過程演算，其余如下表格形式列出。-4.85×0.65×65.9=-207.76kN.m-4.85×0.35×65.9=-111.87kN.m表4-29柱下端彎矩計算層號柱號(m)(kN)(kN.m)4A3.90.30022.44-26.26B3.90.38833.48-50.69C3.90.38833.48-50.69D3.90.30022.44-26.263A3.90.40040.39-63.00B3.90.45060.26-105.75C3.90.45060.26-105.75D3.90.40040.39-63.002A3.90.50052.80-102.96B3.90.48878.78-149.97C3.90.48878.78-149.97D3.90.50052.80-102.961A4.850.65065.90-207.76B4.850.57779.95-223.70C4.850.57779.95-223.70D4.850.65065.90-207.76表4-30柱上端彎矩計算層號柱號(m)(kN)(kN.m)4A3.90.70022.44-61.27B3.90.61233.48-79.90C3.90.61233.48-79.90D3.90.70022.44-61.273A3.90.60040.39-94.51B3.90.55060.26-129.25C3.90.55060.26-129.25D3.90.60040.39-94.512A3.90.50052.80-102.96B3.90.51278.78-157.26C3.90.51278.78-157.26D3.90.50052.80-102.961A4.850.35065.90-111.87B4.850.42379.95-164.05C4.850.42379.95-164.05D4.850.35065.90-111.871.8地震作用下梁端彎矩計算節(jié)點梁端彎矩計算公式：梁左彎矩:梁右彎矩:、EQ為節(jié)點左、右梁端彎矩EQ分別為節(jié)點上、下端柱彎矩EQ為節(jié)點左右梁線剛度表4-31梁端彎矩計算(kN·m)層號AB梁左AB梁右BC梁左BC梁右CD梁左CD梁右461.2744.4835.4235.4244.4861.273120.76100.1779.7779.77100.17120.762165.96146.41116.60116.60146.41165.961214.83174.81139.21139.21174.81214.83圖4-12地震作用下彎矩圖(kN.m)1.9地震作用下梁剪力及柱軸力計算水平荷載梁剪力、EQ分別為梁左、右端彎矩，l為梁計算跨度以1層AB跨梁為例，進行詳細的過程演算，其余如下表格形式列出。-(214.83+174.81)/7.2=-54.12kN表4-32梁剪力計算(kN)層號梁跨l(m)M左(kN.m)M右(kN.m)(kN)4AB7.261.2744.48-14.69BC335.4235.42-23.61CD7.261.2744.48-14.693AB7.2120.76100.17-30.69BC379.7779.77-53.18CD7.2120.76100.17-30.692AB7.2165.9648.00-29.72BC3116.60116.60-77.73CD7.2165.9648.00-29.721AB7.2214.83174.81-54.12BC3139.21139.21-92.81CD7.2