《恒荷载作用下的内力计算过程案例1400字》

PAGE3恒荷载作用下的内力计算过程案例综述1.1弯矩分配系数计算1．确定各杆件在该节点的转动刚度2．计算弯矩分配系数A5节点弯矩分配系数下柱EQ\f(4×43403,4×(43403+40909))=0.515右梁EQ\f(4×40909,4×(43403+40909))=0.485B5节点弯矩分配系数左梁EQ\f(4×40909,4×(40909+43403+28571))=0.362下柱EQ\f(4×43403,4×(40909+43403+28571))=0.384右梁EQ\f(4×28571,4×(40909+43403+28571))=0.253C5节点弯矩分配系数左梁EQ\f(4×28571,4×(28571+43403+40909))=0.253下柱EQ\f(4×43403,4×(28571+43403+40909))=0.384右梁EQ\f(4×40909,4×(28571+43403+40909))=0.362D5节点弯矩分配系数左梁EQ\f(4×40909,4×(40909+43403))=0.485下柱EQ\f(4×43403,4×(40909+43403))=0.515A4、A3、A2节点弯矩分配系数上柱EQ\f(4×43403,4×(43403+43403+40909))=0.34下柱EQ\f(4×43403,4×(43403+43403+40909))=0.34右梁EQ\f(4×40909,4×(43403+43403+40909))=0.32B4、B3、B2节点弯矩分配系数左梁EQ\f(4×40909,4×(40909+43403+43403+28571))=0.262上柱EQ\f(4×43403,4×(40909+43403+43403+28571))=0.278下柱EQ\f(4×43403,4×(40909+43403+43403+28571))=0.278右梁EQ\f(4×28571,4×(40909+43403+43403+28571))=0.183C4、C3、C2节点弯矩分配系数左梁EQ\f(4×28571,4×(28571+43403+43403+40909))=0.183上柱EQ\f(4×43403,4×(28571+43403+43403+40909))=0.278下柱EQ\f(4×43403,4×(28571+43403+43403+40909))=0.278右梁EQ\f(4×40909,4×(28571+43403+43403+40909))=0.262D4、D3、D2节点弯矩分配系数左梁EQ\f(4×40909,4×(40909+43403+43403))=0.32上柱EQ\f(4×43403,4×(40909+43403+43403))=0.34下柱EQ\f(4×43403,4×(40909+43403+43403))=0.34A1节点弯矩分配系数上柱EQ\f(4×43403,4×(43403+30048+40909))=0.38下柱EQ\f(4×30048,4×(43403+30048+40909))=0.263右梁EQ\f(4×40909,4×(43403+30048+40909))=0.358B1节点弯矩分配系数左梁EQ\f(4×40909,4×(40909+43403+30048+28571))=0.286上柱EQ\f(4×43403,4×(40909+43403+30048+28571))=0.304下柱EQ\f(4×30048,4×(40909+43403+30048+28571))=0.21右梁EQ\f(4×28571,4×(40909+43403+30048+28571))=0.2C1节点弯矩分配系数左梁EQ\f(4×28571,4×(28571+43403+30048+40909))=0.2上柱EQ\f(4×43403,4×(28571+43403+30048+40909))=0.304下柱EQ\f(4×30048,4×(28571+43403+30048+40909))=0.21右梁EQ\f(4×40909,4×(28571+43403+30048+40909))=0.286D1节点弯矩分配系数左梁EQ\f(4×40909,4×(40909+43403+30048))=0.358上柱EQ\f(4×43403,4×(40909+43403+30048))=0.38下柱EQ\f(4×30048,4×(40909+43403+30048))=0.2631.2恒载作用下固端弯矩计算恒载作用下梁固端计算：顶层AB跨均布荷载：=-1/12×4.142×6.6²=-15.035kN.m梯形荷载：=-1/12×17.99×6.6²×(1-2×1.65²/6.6²+1.65³/6.6³)=-58.161kN.m合计：-73.2kN.m顶层BC跨均布荷载：=-1/12×2.832×2.8²=-1.85kN.m三角形荷载：=-5/96×15.26×2.8²=-6.231kN.m合计：-8.08kN.m顶层CD跨均布荷载：=-1/12×4.142×6.6²=-15.035kN.m梯形荷载：=-1/12×17.99×6.6²×(1-2×1.65²/6.6²+1.65³/6.6³)=-58.161kN.m合计：-73.2kN.m标准层AB跨均布荷载：=-1/12×11.042×6.6²=-40.082kN.m梯形荷载：=-1/12×15.81×6.6²×(1-2×1.65²/6.6²+1.65³/6.6³)=-51.113kN.m合计：-91.2kN.m标准层BC跨均布荷载：=-1/12×2.832×2.8²=-1.85kN.m三角形荷载：=-5/96×13.41×2.8²=-5.476kN.m合计：-7.33kN.m标准层CD跨均布荷载：=-1/12×11.042×6.6²=-40.082kN.m梯形荷载：=-1/12×15.81×6.6²×(1-2×1.65²/6.6²+1.65³/6.6³)=-51.113kN.m合计：-91.2kN.m1.3恒载作用下弯矩二次分配过程弯矩二次分配过程如下：图4-1恒载作用下的弯矩图(kN.m)1.4恒载作用下梁柱剪力的计算恒载作用下梁简支状态下的支座反力计算：顶层AB跨均布荷载：=1/2×4.142×6.6=13.669kN梯形荷载：=17.99/2×(6.6-1.65)=44.525kN合计：=58.19kN顶层BC跨均布荷载：=1/2×2.832×2.8=3.965kN三角形荷载：=15.26×2.8/4=10.682kN合计：=14.65kN顶层CD跨均布荷载：=1/2×4.142×6.6=13.669kN梯形荷载：=17.99/2×(6.6-1.65)=44.525kN合计：=58.19kN标准层AB跨均布荷载：=1/2×11.042×6.6=36.439kN梯形荷载：=15.81/2×(6.6-1.65)=39.13kN合计：=75.57kN标准层BC跨均布荷载：=1/2×2.832×2.8=3.965kN三角形荷载：=13.41×2.8/4=9.387kN合计：=13.35kN标准层CD跨均布荷载：=1/2×11.042×6.6=36.439kN梯形荷载：=15.81/2×(6.6-1.65)=39.13kN合计：=75.57kN表4-1恒载作用下AB框架梁剪力(kN)层次5=58.19-(-51.29+62.19)/6.6=56.54=-58.19-(-51.29+62.19)/6.6=-59.844=75.57-(-80.48+84.31)/6.6=74.99=-75.57-(-80.48+84.31)/6.6=-76.153=75.57-(-79.41+84.09)/6.6=74.86=-75.57-(-79.41+84.09)/6.6=-76.282=75.57-(-79.99+84.38)/6.6=74.9=-75.57-(-79.99+84.38)/6.6=-76.241=75.57-(-71.8+79.8)/6.6=74.36=-75.57-(-71.8+79.8)/6.6=-76.78表4-2恒载作用下BC框架梁剪力(kN)层次5=14.65-(-19.94+19.94)/2.8=14.65=-14.65-(-19.94+19.94)/2.8=-14.654=13.35-(-14.66+14.66)/2.8=13.35=-13.35-(-14.66+14.66)/2.8=-13.353=13.35-(-14.81+14.81)/2.8=13.35=-13.35-(-14.81+14.81)/2.8=-13.352=13.35-(-14.61+14.61)/2.8=13.35=-13.35-(-14.61+14.61)/2.8=-13.351=13.35-(-18.33+18.33)/2.8=13.35=-13.35-(-18.33+18.33)/2.8=-13.35表4-3恒载作用下CD框架梁剪力(kN)层次5=58.19-(-62.19+51.29)/6.6=59.84=-58.19-(-62.19+51.29)/6.6=-56.544=75.57-(-84.31+80.48)/6.6=76.15=-75.57-(-84.31+80.48)/6.6=-74.993=75.57-(-84.09+79.41)/6.6=76.28=-75.57-(-84.09+79.41)/6.6=-74.862=75.57-(-84.38+79.99)/6.6=76.24=-75.57-(-84.38+79.99)/6.6=-74.91=75.57-(-79.8+71.8)/6.6=76.78=-75.57-(-79.8+71.8)/6.6=-74.36表4-4恒载作用下A、B轴柱剪力(kN)层次AB5=-(51.29+41.91)/3.6=-25.89=-(-42.17-35.29)/3.6=21.524=-(38.57+39.7)/3.6=-21.74=-(-34.45-34.68)/3.6=19.23=-(39.7+39.08)/3.6=-21.88=-(-34.68-34.38)/3.6=19.182=-(40.91+48.83)/3.6=-24.93=-(-35.47-41.12)/3.6=21.281=-(23.06+11.53)/5.2=-6.65=-(-20.35-10.18)/5.2=5.87表4-5恒载作用下C、D轴柱剪力(kN)层次CD5=-(42.17+35.29)/3.6=-21.52=-(-51.29-41.91)/3.6=25.894=-(34.45+34.68)/3.6=-19.2=-(-38.57-39.7)/3.6=21.743=-(34.68+34.38)/3.6=-19.18=-(-39.7-39.08)/3.6=21.882=-(35.47+41.12)/3.6=-21.28=-(-40.91-48.83)/3.6=24.93续表4-5层次CD1=-(20.35+10.18)/5.2=-5.87=-(-23.06-11.53)/5.2=6.65图4-2恒载作用下的剪力图(kN)1.5恒载作用下柱子轴力计算恒载作用下的柱轴力按下列公式：；，其中F为前面计算的框架柱节点荷载；为柱子右端梁剪力；为柱子左端梁剪力。表4-6恒载作用下A轴柱轴力(kN)层次5=136.631-0+56.54=193.2=193.2+0.5×0.5×3.6×25=215.74=215.7+156.245-0+74.99=446.9=446.9+0.5×0.5×3.6×25=469.43=469.4+156.245-0+74.86=700.5=700.5+0.5×0.5×3.6×25=7232=723+156.245-0+74.9=954.1=954.1+0.5×0.5×3.6×25=976.61=976.6+156.245-0+74.36=1207.2=1207.2+0.5×0.5×5.2×25=1239.7表4-7恒载作用下B轴柱轴力(kN)层次5=152.551--59.84+14.65=227=227+0.5×0.5×3.6×25=249.54=249.5+176.523--76.15+13.35=515.5=515.5+0.5×0.5×3.6×25=5383=538+176.523--76.28+13.35=804.2=804.2+0.5×0.5×3.6×25=826.72=826.7+176.523--76.24+13.35=1092.8=1092.8+0.5×0.5×3.6×25=1115.31=1115.3+176.523--76.78+13.35=1382=1382+0.5×0.5×5.2×25=1414.5表4-8恒载作用下C轴柱轴力(kN