六、竖向荷载作用下框架结构的内力计算
1.框架内力计算
（1）计算单元
取④轴线处框架进行计算，计算单元如图2.6所示。由于房间内布置右次梁，故直接传给该框架的楼面荷载如图中的水平阴影线所示，计算单元范围内的其余楼面荷载则通过次梁和纵向框架以集中力的形式传给横向框架。由于纵梁对柱有偏心，所以在框架节点上还作用有中力矩。
330016503300D39001350135016507200C270039001650B16507200A660034图2.6 横向框架计算单元66005（2）荷载计算
① 恒载计算
在图2.7中，q1，q1’为均布荷载形式的横梁自重。q2 ，q2’为房间和走道板传给梁的梯形荷载和三角形荷载。由图中的几何关系可得顶层
q1=3.544kN/m q1’=2.363kN/m
q2=4.3×3.3=14.19kN/m q2’=4.3×2.7=11.61kN/m
P1 ，P2为由边纵梁，中纵梁直接传给柱的恒载，包括梁自重、楼板重和女儿墙等的重力荷载，计算如下：
P1=[(3.3×1.65×1/2)×2+（3.9+7.2）/2×1.65]×4.3+4.594×6.6+2.297×3.6+6.6×6.6=144.94kN
M1P1P2q1M2P2q2'M2q2M1P1A7200B'q1C7200D2700图2.7 各层梁上作用的恒载P2=（1.65+7.2）×1.65×4.3+（1.95+3.3）/2×1.35×2×4.3+2.297×3.6+4.594×
6.6=131.86kN
集中力矩
M1=P1e1=144.94×（0.6-0.35）/2=18.12kN·m
M2=P2e2=131.86×0.125=16.48kN·m
4～6层，q1包括梁自重和其上横墙自重，为均布荷载。其他荷载计算方法同顶层。 q1=3.544+2.08×3.05=9.89kN/m q1’=2.363kN/m
q2=3.4×3.3=11.22kN/m q2’=3.4×2.7=9.18kN/m
P1=（1.65+7.2）×1.65×3.4+4.594×6.6+2.297×7.2/2+2.09×（3×6-2.4×2.1×2）+0.4×2.4×2.1×2=108.82kN
P2=[1.65+7.2]×1.65+（1.95+3.3）/2×1.35×2]×3.4+4.594×6.6+2.297×7.2/2+2.08×3×（6.6-0.6）=149.78kN
M1=P1e1=108.82×（0.6-0.35）/2=13.62kN·m
M2=P2e2=149.78×0.125=18.72kN·m 1～3层计算结果见2.15。
② 活荷载计算
活荷载作用下各层框架梁上的荷载分布图如图2.8。
P1P2q1M2P2q2''q1M1q2MC72002M1P1A7200BD2700图2.8 各层梁上作的活载
对于顶层，在屋面活荷载作用下
q2=3.3×0.5=1.65kN/m q2’=0.5×2.7=1.35kN/m P1=（1.65+7.2）×1.65×0.5=7.3kN
P2=[1.65+7.2]×1.65+（1.95+3.3）/2×1.35×2]×0.5=10.85kN M1=P1e1=7.3×（0.6-0.35）/2=0.9125kN·m
M2=P2e2=10.85×0.125=1.356kN·m 在屋面雪荷载作用下
q2=3.3×0.2=0.66kN/m q2’=0.2×2.7=0.54kN/m P1=（1.65+7.2）×1.65×0.2=2.92kN
P2=[1.65+7.2]×1.65+（1.95+3.3）/2×1.35×2]×0.2=4.34kN M1=P1e1=2.92×（0.6-0.35）/2=0.365kN·m M2=P2e2=4.34×0.125=0.543kN·m
3～6层
q2=3.3×2=6.6kN/m q2’=2×2.7=5.4kN/m P1=29.2kN P2=43.38kN M1=P1e1=.29.2×（0.6-0.35）/2=3.651kN·m M2=P2e2=43.38×0.125=5.423kN·m 1～2层
q2=3.3×2=6.6kN/m q2’=2×2.7=5.4kN/m P1=29.2kN P2=43.38kN M1=P1e1=.29.2×（0.7-0.35）/2=5.112kN·m M2=P2e2=43.38×0.175=7.592kN·m 将以上计算结果汇总，见表2.16。
表2.15 横向框架恒荷载汇总表
层次 7 6 5 4 3 2 1
q1 q1' q2 q2' P1 P2 M1 M2 /（kN/m） /（kN/m） /（kN/m） /（kN/m） /kN /kN / kN·m / kN·m 3.544 9.89 9.89 9.89 10.83 10.83 10.83 2.363 2.363 2.363 2.363 3.675 3.675 3.675 14.19 11.22 11.22 11.22 11.22 11.22 11.22 11.61 9.18 9.18 9.18 9.18 9.18 9.18
144.94 108.82 108.82 108.82 108.82 108.20 108.20 131.86 149.78 149.78 149.78 149.78 149.15 149.15 18.12 13.60 13.60 13.60 13.60 18.94 18.94 16.48 18.72 18.72 18.72 18.72 26.10 26.10
表2.16 横向框架活荷载汇总表
层次 7 6 5 4 3 2 1 q2 q2' P1 P2 M1 M2 /（kN/m） /（kN/m） /kN /kN / kN·m / kN·m 1.65 1.35 7.3 10.85 0.9125 1.356 （0.66） （0.54） （2.92） （4.34） （0.365） （0.543） 6.6 6.6 6.6 6.6 6.6 6.6 5.4 5.4 5.4 5.4 5.4 5.4 29.21 29.21 29.21 29.21 29.21 29.21 43.38 43.38 43.38 43.38 43.38 43.38 3.651 3.651 3.651 3.651 5.112 5.112 5.432 5.432 5.432 5.432 7.592 7.592 注：表中括号内数值对应屋面雪荷载作用情况。
（3）内力计算
梁端和柱端弯矩采用弯矩二次分配法计算。先确定梁的固端弯矩以及节点各杆的弯矩分配系数。在竖向荷载作用下，结构为奇数跨对称结构，故可取如图2.9所示的半框架进行计算，计算过程及结果见图2.9，所得弯矩图见图2.10。梁端弯矩求出以后，从框架中截取隔离体，应用平衡条件，梁端剪力可根据梁上竖向荷载引起的剪力与梁端弯矩引起的剪力相叠加而得，柱端剪力可由柱端弯矩确定。柱轴力为柱所在层以上所有与该柱相连的梁端剪力和节点集中力之和，计算恒载作用时的柱轴力要考虑柱的自重。计算结果列于表2.17，2.18，2.19。
上柱下柱0.72218.1238.1115.31-7.2746.16右梁0.278-70.9114.68-5.25-2.80-64.28左梁0.21670.91-10.507.340.8768.62上柱16.48下柱0.562右梁上柱下柱0.7220.91254.014.65-3.005.66右梁0.278-6.471.54-0.50-1.16-6.58左梁0.2166.47-0.990.770.556.80上柱1.356下柱0.562-2.59-3.311.42-4.47右梁0.222-0.51-1.020.56-0.970.222-5.84-27.31-10.79-11.352.250.89-36.40-15.740.41930.6219.06-12.5837.100.4190.16213.6-86.6930.6211.8415.31-4.35-12.58-4.8633.36-84.060.13886.69-8.705.922.6386.540.36018.72-22.70-13.656.87-29.480.360-22.70-11.352.716.87-27.18-11.160.142-4.92-8.950.4199.312.01-2.269.050.4193.6519.314.65-2.2611.700.162-25.863.60-1.27-0.87-24.400.13825.86-2.541.800.3925.510.365.432-6.62-1.291.01-6.900.36-6.62-3.311.01-8.920.142-2.05-2.610.40-4.260.41930.6215.31-11.0134.930.41913.630.6215.31-11.0134.930.162-86.6911.84-4.35-4.26-83.460.13886.69-8.705.922.3286.220.3600.3600.1420.4199.314.65-3.3710.590.4193.6519.314.65-3.3710.590.162-25.863.60-1.27-1.30-24.830.13825.86-2.541.800.6625.790.365.432-6.62-3.311.73-8.190.36-6.62-3.311.73-8.190.142-2.05-2.610.68-3.98-4.9218.72-22.70-22.70-8.95-11.35-11.356.042.386.04-28.01-28.01-11.490.41930.6215.31-10.8535.090.41913.630.6214.93-10.8534.710.162-86.6911.84-4.35-4.19-83.390.13886.69-8.705.922.0685.970.36018.72-22.70-11.355.38-28.670.360-22.70-9.525.382.12-26.83-11.750.142-4.92-8.950.4199.314.65-3.2210.740.4193.6519.314.30-3.2210.380.162-25.863.60-1.27-1.24-24.770.13825.86-2.541.800.5725.690.365.432-6.62-3.311.49-8.430.36-6.62-2.641.49-7.760.142-2.05-2.610.59-4.070.38729.8615.31-7.8137.360.38713.629.8610.45-7.8132.490.226-90.7517.44-5.57-4.56-83.450.1680.2870.2870.25890.7518.72-5.72-11.14-19.03-19.03-17.118.72-11.35-6.811.592.712.712.4389.91-27.67-23.13-20.390.3878.594.65-2.3710.880.3873.6518.593.02-2.379.240.226-25.865.02-1.54-1.38-23.770.16825.86-3.092.510.4525.730.2875.432-5.27-3.310.77-7.820.287-5.27-1.870.77-6.380.258-2.05-4.740.69-6.100.29120.9014.93-8.4127.410.53918.9438.7117.95-15.5841.080.170-90.7512.21-3.98-4.91-87.430.13590.75-7.966.102.0690.960.23126.10-13.61-9.523.52-19.600.4270.2070.2916.044.30-2.447.890.5395.11211.185.19-4.5211.850.170-25.863.53-1.09-1.43-24.850.13525.86-2.191.760.5625.990.2317.592-3.75-2.640.95-5.430.427-6.93-3.261.76-8.420.207-2.05-3.360.86-4.55-5.72-25.16-12.20-11.843.166.51-30.49-14.760.50035.9119.35-7.8147.450.34318.9424.63-5.3519.280.157-90.7511.27-3.74-2.450.12790.75-7.485.640.8889.780.2760.1950.402-5.7226.10-23.69-16.26-11.49-12.581.921.352.79-33.48-14.35-15.860.50010.375.59-2.2813.680.3435.1127.12-1.565.550.157-25.863.26-1.03-0.72-24.350.12725.86-2.061.630.2325.660.4027.592-6.52-3.460.74-9.240.276-4.480.51-3.970.195-2.05-3.160.36-4.859.64-7.172.78-1.99（a）恒载作用下（b）活载作用下kN·m）图2.9 横向框架弯矩的二次分配法（M单位：