教學(xué)樓結(jié)構(gòu)框架內(nèi)力計算的過程案例綜述目錄TOC\o"1-3"\h\u2576教學(xué)樓結(jié)構(gòu)框架內(nèi)力計算的過程案例綜述 1298061.1恒載下框架內(nèi)力 1264681.1.1彎矩分配系數(shù) 1277801.1.2桿件固端彎矩 498691.1.3節(jié)點不平衡彎矩 6127721.1.4內(nèi)力計算 6252071.2活載作用下的框架內(nèi)力 1272091.2.1梁固端彎矩 128331.2.2最不利情況 13281881.2.3各節(jié)點不平衡彎矩 13304871.2.4內(nèi)力計算： 14168201.3地震作用下橫向框架的內(nèi)力計算 19109101.1.1橫向框架內(nèi)力計算 19269561.1.2地震作用下橫向框架內(nèi)力計算 261.1恒載下框架內(nèi)力1.1.1彎矩分配系數(shù)節(jié)點A1：SA1A0=4iA1A0=4×0.669=2.676SA1B1=4iA1B1=4×1.33=5.32SA1A2=4iA1A2=4×0.995=1.98∑S=4×(0.669+1.33+0.995)=11.976μA1A0=SA1A0/∑S=2.676÷11.976=0.223μA1B1=SA1A0/∑S=5.32÷11.976=0.444μA1A2=SA1A0/∑S=1.98÷11.976=0.332節(jié)點B1：SB1D1=iB1D1=2×1.07=6.14∑S=11.976+6.14=18.116μB1A1=1.33×4÷18.116=0.294μB1B2=0.995×4÷18.116=0.22μB1D1=1.07×4÷18.116=0.678μB1B0=0.669×4÷18.116=0.148節(jié)點A2：μA2A1=μA2A3=0.995×4÷[4×(0.995+1.33+0.995)]=0.3μA2B2=1.33×4÷[4×(0.995+1.33+0.995)]=0.401節(jié)點B2：μB2A2=1.33×4÷[4×(1.33+0.995+0.995)+6.14]=0.274μB2B1=μB2B3=0.995×4÷[4×(1.33+0.995+0.995)+6.14]=0.205μB2D2=1.07×2÷[4×(1.33+0.995+0.995)+6.14]=0.316節(jié)點A5：μA5B5=1.33×4÷[4×(1.33+0.995)]=0.572μA5A4=0.995×4÷[4×(1.33+0.995)]=0.428節(jié)點B5：μB5A5=1.33×4÷[4×(1.33+0.995)+6.14]=0.345μB5B4=0.995×4÷[4×(1.33+0.995)+6.14]=0.258μB5D5=1.07×2÷[4×(1.33+0.995)+6.14]=0.3982~4層A、B節(jié)點的計算結(jié)果相同。圖1.1永久荷載圖1.2節(jié)點不平衡彎矩1.1.2桿件固端彎矩橫梁固端彎矩頂層梁自重：板傳永久荷載：=－1/12×17.96×6.9２×（1－2×1.8２÷6.9２＋1.8３÷6.9３）=-62.82kN·m＝-5/96×14.97×3２＝-7.02kN·m=-1/32×14.97×3２＝-4.21kN·m二至五層梁自重：板傳永久荷載：=-1/12×11.65×6.9２×（1－2×1.8２÷6.9２＋1.8３÷6.9３）=-47.75kN·m=-5/96×11.38×3２=-5.33kN·m=-1/32×11.38×3２=-1.2kN·m1.1.3節(jié)點不平衡彎矩節(jié)點A5的不平衡彎矩：-19.38-62.82=-82.2kN·m節(jié)點B5的不平衡彎矩：19.38-4.82+62.82-7.02=70.36kN·m節(jié)點A4的不平衡彎矩：-19.38-47.75=-67.13kN·m節(jié)點B4的不平衡彎矩：19.38-1.29+47.75-5.33=60.51kN·m不平衡彎矩如上圖1.1和圖1.2。1.1.4內(nèi)力計算計算結(jié)果見圖1.3到圖1.5，見表1.1到表1.4。圖1.3彎矩分配(恒載)圖1.4永久荷載下彎矩圖（kN·m)圖1.5永久荷載下梁剪力、柱軸力（kN）表1.1AB跨梁端剪力（kN）層qga(m)l(m)gl/2u=(l-a)×q/2MAB(kN·m)MBA(kN·m)ΣMik/lVA=gl/+u-ΣMik/lVB=-(gl/2+u+ΣMi/l)517.966.461.86.922.2945.8-44.0377.234.8161.28-72.9411.656.461.86.922.2934.81-51.4362.331.355.8-58.4311.656.461.86.922.2934.81-46.4462.882.3854.72-59.48211.656.461.86.922.2934.81-56.2161.80.8156.29-57.91111.656.461.86.922.2934.81-40.2761.31.0554.05-60.15表1.2BC跨梁端剪力（kN）層q(kN/m)g(kN/m)l(m)gl/2ql/4VB=gl/2+ql/4Vc=-(gl/2+ql/4)514.976.4639.6911.2320.92-20.92411.386.4639.698.5418.23-18.23311.386.4639.698.5418.23-18.23211.386.4639.698.5418.23-18.23111.386.4639.698.5418.23-18.23表1.3AB跨跨中彎矩（kN·m)層q(kN/m)g(kN/m)a(m)l（m)gl/2u=(l-a)×q/2MAB(kN·m)ΣMik/lVA=gl/2+u-ΣMik/lM=gl/2×l/4+u×1.05-MAB-VA×l/2517.966.461.86.922.2945.8-44.034.8161.28-92.76411.656.461.86.922.2934.81-51.451.355.8-69.07311.656.461.86.922.2934.81-46.442.3854.72-72.36211.656.461.86.922.2934.81-56.210.8156.29-68.01111.656.461.86.922.2934.81-40.271.0554.05-76.22表1.4構(gòu)件柱軸力（kN）層A軸、D軸B軸、C軸橫梁壓力縱梁壓力柱構(gòu)件重柱構(gòu)件軸力橫梁壓力縱梁壓力柱構(gòu)件重柱構(gòu)件軸力5柱頂61.2850.3835.1111.6691.8255.1535.1148.97柱底148.76184.074柱頂55.848.2735.1252.8376.6366.2935.1326.99柱底287.93362.093柱頂54.7248.2735.1390.9277.7166.2935.1506.09柱底426.02541.19表1.4(續(xù))2柱頂56.2948.2735.1530.5876.1466.2935.1681.62柱底565.68718.721柱頂54.0548.2737.866878.3866.2937.8861.39柱底705.8901.191.2活載作用下的框架內(nèi)力1.2.1梁固端彎矩頂層=-1/32×2.1×3２=-0.59kN·m二至五層橫梁=-1/32×10.5×3２=-2.95kN·m1.2.2最不利情況活載滿跨布置見圖1.6。1.2.3各節(jié)點不平衡彎矩AB跨、BC跨均布置活載：Ma5=-8.81kN·mMa1=Ma2=Ma3=Ma4=-31.48kN·mMb5=8.81-0.98=7.83kN·mMb1=Mb2=Mb3=Mb4=31.48-4.92=26.56kN·m圖1.6活載滿跨布置1.2.4內(nèi)力計算：計算結(jié)果如圖1.7到圖1.9，見表1.5到表1.8。圖1.7滿跨活載迭代過程圖1.8滿跨活載彎矩（kN·m)圖1.9梁剪力、柱軸力(kN)表1.5AB跨梁端剪力（kN）層q(kN/m)a(m)μ=(l-a)×q/2MAB(kN·m)MBA(kN·m)∑Mik/lV1/A=μ-∑Mik/lVB=-(μ+∑Mik/l)52.521.85.74-6.788.250.215.53-5.95491.822.95-21.3729.261.1521.8-24.1391.822.95-24.2630.870.9621.99-21.91291.822.95-22.6130.191.121.85-24.05191.822.95-22.0429.411.0721.88-24.02表1.6BC跨梁端剪力（kN）層q(kN/m)l(m)ql/4VB=ql/4VB=-ql/452.131.581.58-1.58410.537.887.88-7.88310.537.887.88-7.88210.537.887.88-7.88110.537.887.88-7.88表1.7AB跨跨中彎矩（kN·m）層q(kN/m)a(m)l(m)μ=(l-a)×q/2MAB(kN·m)∑Mik/lV1/A=μ-∑Mik/lM=μ×1.05-MAB-V1/A×l/252.521.86.95.74-6.780.215.53-6.27491.86.922.95-21.371.1521.8-29.74391.86.922.95-24.260.9621.99-27.51291.86.922.95-22.611.121.85-28.68191.86.922.95-22.041.0721.88-29.25表1.8構(gòu)件柱軸力（kN）層A軸B軸橫梁剪力縱梁剪力柱構(gòu)件軸力橫梁剪力縱梁剪力柱構(gòu)件軸力55.532.277.87.534.4812.01421.88.137.731.9819.1361.12321.998.167.7931.7919.13114.04221.858.197.9431.9319.13165.1121.888.1127.7231.919.13216.131.3地震作用下橫向框架的內(nèi)力計算1.1.1橫向框架內(nèi)力計算頂層橫梁：雪載邊跨0.4×1.6×0.5=0.72kN/m中間跨0.4×3×0.5＝0.6kN/m其余層橫梁：活載邊跨9×0.5＝4.5kN/m中間跨10.5×0.5＝5.25kN/m固端彎矩圖1.10圖1.10固端彎矩頂層橫梁二到五層橫梁不平衡彎矩MA5=-2.52kN·mMA1=MA2=MA3=MA4=-15.74kN·mMB5=2.52-0.28=2.24kN·mMB1=MB2=MB3=MB4=15.74-2.46=11.28kN·m彎矩分配計算計算結(jié)果如圖1.11到圖1.13，表1.9到表1.12。圖1.110.5(雪+活)下迭代計算圖1.120.5(雪+活)下桿端彎矩(kN·m)圖1.130.5(雪+活)下框架軸力、剪力(kN)表1.90.5（雪＋活）下AB跨梁端剪力標(biāo)準(zhǔn)值層q(kN/m)a(m)l(m)μ=(l-a)×q/2（kN）MAB(kN·m)MBA(kN·m)Mik/l（kN）V1/A=μ-∑Mik/l（kN）VB=-(μ+∑Mik/l)（kN）50.721.86.91.84-2.462.28-0.031.87-1.8744.51.86.911.48-11.2815.40.610.88-12.0834.51.86.911.48-12.214.760.3711.11-11.8524.51.86.911.48-12.3712.780.0611.42-11.5414.51.86.911.48-10.8814.760.5610.92-12.04表1.100.5（雪＋活）下BC跨梁端剪力標(biāo)準(zhǔn)值層q(kN/m)l(m)ql/4(kN)VB=ql/4(kN)VC=－ql/4(kN)50.630.450.45-0.4545.2531.941.94-1.9435.2531.941.94-1.9425.2531.941.94-1.9415.2531.941.94-1.94表1.110.5（雪+活）下AB跨跨中彎矩（kN·m)層q(kN/m)a(m)l(m)μ=(l-a)×q/2MAB(kN·m)Mik/lV1/A=μ-∑Mik/lM=μ×1.05-MAB-V1/A×l/250.721.86.91.84-2.46-0.031.87-2.0644.51.86.911.48-11.280.610.88-14.234.51.86.911.48-12.20.3711.11-14.0824.51.86.911.48-12.370.0611.42-14.9814.51.86.911.48-10.880.5610.92-14.74表1.120.5（雪＋活）下構(gòu)件柱軸力標(biāo)準(zhǔn)值（kN）層A軸B軸橫梁剪力縱梁剪力柱構(gòu)件軸力橫梁剪力縱梁剪力柱構(gòu)件軸力５1.870.652.522.261.281.54４10.884.0517.4516.029.5729.13３11.114.0532.6115.799.5754.49２11.424.0548.0815.489.5779.54１10.924.0561.0515.989.57105.091.1.2地震作用下橫向框架內(nèi)力計算計算結(jié)果如表1.13到表1.14，圖1.14到圖1.15。表1.13地震下構(gòu)件柱剪力（kN）及彎矩（kN·m）層次層間剪力總剪力柱別Di(kN/mm)∑D(kN/mm)Vi（kN）yh(m)M下M上5436.43436.43邊柱941.5736776.6811.170.351.9-15.25-28.32中柱1495.4417.750.4-27.69-41.544411.98850.41邊柱941.5736776.6821.770.41.9-31.96-50.94中柱1495.4434.580.45-60.69-74.173321.721172.13邊柱941.5736776.68300.451.9-52.65-64.35中柱1495.4447.660.5-92.94-92.942229.461401.59邊柱941.5736776.6835.880.51.9-69.97-69.97中柱1495.4456.990.5-111.13-111.131165.971567.56邊柱1061.3437314.4844.590.65.8-155.17-101.45中柱1340.6456.320.55-179.66-147表1.14地震下梁端彎矩（kN·m)層次柱別M下M上節(jié)點左右梁線剛度比M邊M中地震下梁端剪力邊跨梁跨中彎矩M左M右VAVB左VB右5邊柱-15.25-28.32028.32-5.91-7.93中柱-27.69-41.540.4312.4929.05-5.91-