1、1第五章 竖向荷载作用下横向框架(KJ-3)内力计算由于结构基本对称，在竖向荷载作用下的框架侧移可略去不计。其内力分析采用弯矩分配法，在竖向荷载作用下梁端可以考虑塑性内力重分布，取弯矩调幅系数 0.8，楼面的竖向荷载分别按恒载及满跨活载计算。5.1 竖向恒载作用下内力计算5.1.1 恒荷载计算：（1）计算单元：计算单元宽度为 3.9m，如图所示。直接传给框架的楼面荷载如图中水平阴影所示，计算单元范围内的楼面荷载则直接通过次梁以集中力的形式传给横向框架梁，作用在各结点上。由于纵向框架梁与柱轴线不重合，因此在框架结点上还作用有集中力矩。390270270210302702（2）荷载计算 A D C
2、P1F2PF3PM M2q1q1均布荷载：在上图中 =4.125/m 代表横梁自重。顶层：A、 D 柱集中力=（2.256+2.187+4.11.35）3.9=38.92KNC 柱集中力=（2.187+4.12.55）3.9=49.30KNF1 处集中力=（1+4.12.7）3.9=47.10KNF2 处集中力=（1+4.12.4）3.9=42.28KNF3 处集中力=（1+4.12.85）3.9=49.47KN附加节点弯矩：38.920.18=7 mkN14 层：A、 D 柱集中力=（3.83.15+2.187+3.91.35）3.9+3.65.625=96.0KNC 柱集中力=（3.83.
3、15+2.187+3.92.55）3.9+3.66.75=118.30KNF1 处集中力=（1+3.92.7）3.9=44.97KNF2 处集中力=（3.83.15+1+3.92.4）3.9=87.09KNF3 处集中力=（1+3.92.85）3.9=47.25KN附加节点弯矩：96.00.18=17.28 mkN即，5 层边柱附加弯矩：38.92/20.42+96/20.18=16.81 k4 层边柱附加弯矩：96/20.42+96/20.18=28.82-3 层边柱附加弯矩：96/21.0+96/20.18=56.64 1 层边柱附加弯矩：960.18=17.28 mkN35.1.2 活荷
4、载计算活荷载布置：办公室： 2.0 kN/m2走廊、楼梯、卫生间： 2.5 kN/m2不上人屋面： 0.5 kN/m2活载作用在次梁上，次梁作用在主梁上，故考虑框架时，活载按集中力布置。活荷载作用下框架梁梁上的荷载分布如下： ACDP1P2P3FFqq1屋面：P1=0.53.91.35=2.63KN ; F1=0.53.92.7=5.27KNF2=0.53.92.4=4.68KN P2=0.53.92.55=4.97KNF3=0.53.92.85=5.56KN P3=0.53.91.35=2.63KN露面：P1=23.91.35=10.53KN ; F1=23.92.7=21.06KNF2=2
5、3.91.35+2.53.91.05=20.77KN P2=2.53.91.05+23.91.5=21.94KNF3=23.92.85=22.23KN P3=23.91.35=10.53KN一层：P2=2.51.952.55+21.951.5+2.51.951.05=23.4KNF3=2.51.952.85+21.952.85=25.01KNP3=2.51.951.35+21.951.35=11.85KN 42.63594.68975.623102011010.53260.72345.018.536.7942.351 38.92471.28493.71602528. 17.89618.3546
6、.91728 389696918.3.74.7909472541.872511251525活荷载满跨布置图（单位: ）kN恒荷载布置图单位(单位 : ）kN2.635294.689721.942310.510.532106.723410.532106.7219421.942310.5 4.97562.310.53260.7219423.4501.8521.942310.510.53260.72194活载各层隔跨布置-工况(单位: )kN活载各层隔跨布置-工况 (单位: )kN55.1.3 恒载作用下固端弯矩计算均布荷载：4.125750 4.12570=4.1257.5/12= -19.34
7、=4.1255.7/12= -11.17左MmkN左MmkN=4.1257.5/12=19.34 =4.1255.7/12=11.17右 右集中力作用下：27014.849.13027=-（47.12.74.8+42.285.42.1）/7.5=-70.21 左M mkN=(47.14.82.7+42.282.15.4)=75.89右 =-49.4732.7/5.7=-33.3 左 mkN=49.472.73/5.7=37右2702104.9847.2530=-（44.972.74.8+87.095.42.1）/7.5=-91.83 左M mkN=(44.974.82.7+87.092.15.
8、4)=125.73右 =-47.2532.7/5.7=-31.81 左 mkN=47.252.73/5.7=35.34右6故竖向恒载作用下，待分配弯矩为：MA5=70.21+19.34-16.81=72.74 mkNMA4=91.83+19.34-28.8=82.37MA3=MA2=91.83+19.34-56.64=54.53kMA1=91.83+19.34-17.28=93.89 mNMc5 左 =-(75.89+19.34)=-95.23kMc5 右 =(33.3+11.17)=44.47MC4 左 =MC3 左 =MC2 左 =MC1 左 =-(125.73+19.34)=-145.0
9、7 mkNMC4 右 =MC3 右 =MC2 右 =MC1 右 =(31.81+11.17)=42.98MD5=-(35.34+11.7+7)=-54.04 mkNMD4=MD3=MD2=MD1=-(35.34+11.7+17.28)=-64.32kN5.1.4 活荷载作用下固端弯矩计算27015.4685.63027=-（5.272.74.8+4.685.42.1）/7.5=-7.81 左M mkN=(5.274.82.7+4.682.15.4)=8.37右 =-5.5632.7/5.7=-3.74 左 mkN=5.562.73/5.7=4.16右2701.62.3077=-（21.062.
10、74.8+20.775.42.1）/7.5=-32.08 左M mkN=(21.064.82.7+20.772.15.4)=35.71右 =-22.2332.7/5.7=-14.96 左 mkN=22.232.73/5.7=16.63右 25.0137=-25.0132.7/5.7=-16.84 左MmkN=25.012.73/5.7=18.71右85.2 弯矩分配由于结构基本对称，在竖向荷载作用下的框架侧移可忽略不计，其内力分析采用弯矩分配法，在竖向荷载作用下，楼面竖向荷载分别按恒载满布置，活载满跨布置，活载不利布置 1，活载不利布置 2 计算。恒荷载作用下 KJ-2 梁内力计算（弯矩分配）
11、 （单位：kNm）A 轴 C 轴 D 轴上柱 下柱 右梁 左梁 上柱 下柱 右梁 左梁 上柱 下柱0.000 0.415 0.585 0.282 0.000 0.346 0.372 0.650 0.000 0.350 -72.740 95.230 -44.470 54.040 0.000 30.187 42.553 -16.288 -19.985 -21.487 -35.126 -18.914 -8.144 21.276 -17.563 -10.743 3.380 4.764 -1.047 -1.285 -1.381 6.983 3.760 33.567 -33.567 99.171 -21.
12、270 -84.901 15.154 -15.154 0.293 0.293 0.413 0.210 0.257 0.257 0.276 0.481 0.260 0.260 -82.370 145.070 -42.980 64.320 0.000 24.174 24.174 34.022 -21.433 -26.228 -26.228 -28.202 -30.923 -16.698 -16.698 -10.717 17.011 -15.462 -14.101 3.145 3.145 4.426 -0.325 -0.398 -0.398 -0.428 6.779 3.661 3.661 27.3
13、19 27.319 -54.638 140.323 -26.626 -26.626 -87.071 26.075 -13.038 -13.038 0.293 0.293 0.413 0.210 0.257 0.257 0.276 0.481 0.260 0.260 -54.530 145.070 -42.980 64.320 16.003 16.003 22.523 -21.433 -26.228 -26.228 -28.202 -30.923 -16.698 -16.698 -10.717 11.262 -15.462 -14.101 3.145 3.145 4.426 0.882 1.07
14、9 1.079 1.160 6.779 3.661 3.661 19.148 19.148 -38.297 135.780 -25.149 -25.149 -85.483 26.075 -13.038 -13.038 0.293 0.293 0.413 0.210 0.257 0.257 0.276 0.481 0.260 0.260 -54.530 145.070 -42.980 64.320 16.003 16.003 22.523 -21.433 -26.228 -26.228 -28.202 -30.923 -16.698 -16.698 -10.717 11.262 -15.462
15、-14.101 3.145 3.145 4.426 0.882 1.079 1.079 1.160 6.779 3.661 3.661 19.148 19.148 -38.297 135.780 -25.149 -25.149 -85.483 26.075 -13.038 -13.038 0.293 0.293 0.413 0.210 0.257 0.257 0.276 0.481 0.260 0.260 -93.890 145.070 -42.980 64.320 27.555 27.555 38.781 -21.433 -26.228 -26.228 -28.202 -30.923 -16
16、.698 -16.698 -10.717 19.390 -15.462 -14.101 3.145 3.145 4.426 -0.825 -1.009 -1.009 -1.085 6.779 3.661 3.661 30.700 30.700 -61.400 142.202 -27.237 -27.237 -87.728 26.075 -13.038 -13.038 9活荷载满布作用下 KJ-2 梁内力计算（弯矩分配） （单位：kNm）A 轴 C 轴 D 轴上柱 下柱 右梁 左梁 上柱 下柱 右梁 左梁 上柱 下柱0.000 0.415 0.585 0.282 0.000 0.346 0.37
17、2 0.650 0.000 0.350 -7.810 8.370 -3.740 4.160 0.000 3.241 4.569 -1.306 -1.602 -1.722 -2.704 -1.456 -0.653 2.284 -1.352 -0.861 0.271 0.382 -0.263 -0.323 -0.347 0.560 0.301 3.512 -3.512 9.086 -1.925 -7.161 1.155 -1.155 0.293 0.293 0.413 0.210 0.257 0.257 0.276 0.481 0.260 0.260 -32.080 35.710 -14.960
18、16.630 0.000 9.415 9.415 13.250 -4.356 -5.331 -5.331 -5.732 -7.995 -4.317 -4.317 -2.178 6.625 -3.998 -2.866 0.639 0.639 0.900 -0.552 -0.675 -0.675 -0.726 1.378 0.744 0.744 10.054 10.054 -20.108 37.427 -6.006 -6.006 -25.416 7.147 -3.573 -3.573 0.293 0.293 0.413 0.210 0.257 0.257 0.276 0.481 0.260 0.2
19、60 -32.080 35.710 -14.960 16.630 0.000 9.415 9.415 13.250 -4.356 -5.331 -5.331 -5.732 -7.995 -4.317 -4.317 -2.178 6.625 -3.998 -2.866 0.639 0.639 0.900 -0.552 -0.675 -0.675 -0.726 1.378 0.744 0.744 10.054 10.054 -20.108 37.427 -6.006 -6.006 -25.416 7.147 -3.573 -3.573 0.293 0.293 0.413 0.210 0.257 0
20、.257 0.276 0.481 0.260 0.260 -32.080 35.710 -14.960 16.630 0.000 9.415 9.415 13.250 -4.356 -5.331 -5.331 -5.732 -7.995 -4.317 -4.317 -2.178 6.625 -3.998 -2.866 0.639 0.639 0.900 -0.552 -0.675 -0.675 -0.726 1.378 0.744 0.744 10.054 10.054 -20.108 37.427 -6.006 -6.006 -25.416 7.147 -3.573 -3.573 0.293
21、 0.293 0.413 0.210 0.257 0.257 0.276 0.481 0.260 0.260 -32.080 35.710 -16.840 18.710 9.415 9.415 13.250 -3.962 -4.848 -4.848 -5.213 -8.995 -4.857 -4.857 -1.981 6.625 -4.498 -2.606 0.581 0.581 0.818 -0.447 -0.547 -0.547 -0.588 1.253 0.677 0.677 9.996 9.996 -19.992 37.927 -5.394 -5.394 -27.138 8.362 -
22、4.181 -4.181 10活荷载隔层隔跨-作用下 KJ-2 梁内力计算（弯矩分配） （单位：kNm）A 轴 C 轴 D 轴上柱 下柱 右梁 左梁 上柱 下柱 右梁 左梁 上柱 下柱0.000 0.415 0.585 0.282 0.000 0.346 0.372 0.650 0.000 0.350 -7.810 8.370 0.000 0.000 0.000 3.241 4.569 -2.360 -2.896 -3.114 0.000 0.000 -1.180 2.284 0.000 -1.557 0.490 0.690 -0.644 -0.790 -0.850 1.012 0.545 3
23、.731 -3.731 7.650 -3.686 -3.963 -0.545 0.545 0.293 0.293 0.413 0.210 0.257 0.257 0.276 0.481 0.260 0.260 0.000 0.000 -14.960 16.630 0.000 0.000 0.000 0.000 3.141 3.843 3.843 4.133 -7.995 -4.317 -4.317 1.570 0.000 -3.998 2.066 -0.461 -0.461 -0.649 0.839 1.027 1.027 1.104 -0.993 -0.536 -0.536 -0.461 -
24、0.461 0.922 3.980 4.870 4.870 -13.721 9.708 -4.854 -4.854 0.293 0.293 0.413 0.210 0.257 0.257 0.276 0.481 0.260 0.260 -32.080 35.710 0.000 0.000 9.415 9.415 13.250 -7.497 -9.174 -9.174 -9.865 0.000 0.000 0.000 -3.749 6.625 0.000 -4.932 1.100 1.100 1.548 -1.391 -1.702 -1.702 -1.830 2.371 1.281 1.281
25、10.515 10.515 -21.030 33.447 -10.876 -10.876 -11.695 -2.561 1.281 1.281 0.293 0.293 0.413 0.210 0.257 0.257 0.276 0.481 0.260 0.260 0.000 0.000 -14.960 16.630 0.000 0.000 0.000 3.141 3.843 3.843 4.133 -7.995 -4.317 -4.317 1.570 0.000 -3.998 2.066 -0.461 -0.461 -0.649 0.839 1.027 1.027 1.104 -0.993 -
26、0.536 -0.536 -0.461 -0.461 0.922 3.980 4.870 4.870 -13.721 9.708 -4.854 -4.854 0.293 0.293 0.413 0.210 0.257 0.257 0.276 0.481 0.260 0.260 -32.080 35.710 0.000 0.000 9.415 9.415 13.250 -7.497 -9.174 -9.174 -9.865 0.000 0.000 0.000 -3.749 6.625 0.000 -4.932 1.100 1.100 1.548 -1.391 -1.702 -1.702 -1.830 2.371 1.281 1.281 10.515 10.515 -21.030 33.447 -10.876 -10.876 -11.695 -2.561 1.281 1.281
