第六章竖向荷载作用下的内力计算

6章竖向荷载作用下内力计算§6.1框架结构的荷载计§6.1.1.板传荷载计算计算单元见下图所示因为楼板为整体现浇，本板选向板，可沿四角点沿45°线将区格分为小块，每个板上的荷载传给与之相邻的梁，板传至梁上的三角形或梯形荷载可等效为均布荷载。图61框架结构计算单元图62框架结构计算单元等效荷载B～C,(D～E)轴间框架梁：屋面板传荷载：恒载：6.09KN/m21.5m[1-2(1.5/6)2(1.5/6)2活载：2.0KN/m21.5m[1-2(1.5/6)2(1.5/6)2楼面板传荷载：恒载：3.83KN/m21.5m[1-2(1.5/6)2(1.5/6)2活载：2.0KN/m21.5m[1-2(1.5/6)2(1.5/6)2梁自重：3.95KN/mB～C,(D～E)轴间框架梁均布荷载为： 梁：恒载＝梁自重＋板传荷载＝17.128KN/m+3.95KN/m=21.103KN/m活载＝板传荷载＝5625KN楼面板传荷载：恒载＝梁自重＋板传荷载＝3.95KN/m+10.772KN/m=14.747KN/m活载＝板传荷载＝5625KN二.C～D轴间框架梁：屋面板传荷载：恒载：6.09KN/m21.2m58活载：2.0KN/m21.5m5/8楼面板传荷载：恒载：3.83KN/m21.2582=5.745KN/m活载：2.0KN/m21.2m582=3.75KN/m梁自重3.95KN/mC～D轴间框架梁均布荷载为： 梁：恒载＝梁自重＋板传荷＝2.349KN/m+9.135KN/m=11.484KN/m活载＝板传荷载＝3KN楼面板传荷载：恒载＝梁自重＋板传荷载＝2.349KN/m+5.745KN/m=8.09KN/m活载＝板传荷载＝375KN三.B轴柱纵向集中荷载计算：顶层柱：女儿墙自重：（900㎜,100㎜的混凝土压顶1.2m20.24m0.5m5.806KN/顶层柱恒载＝女儿墙＋梁自重＋板传荷载 5.806KN/m63.975KN/m(6m0.6m) 121.5/621.5/626/426.09KN/m1.5m5/832 顶层柱活载＝板传荷载 ＝2.0KN/m1.5m121.5/621.5/626/42 2.0KN/m1.5m5/832标准层柱恒载＝墙自重＋梁自重＋板荷载=7.794KN/m(60.6)3.975KN/m(60.6)3.83KN/m1.5m5/83(2.332311.52)61/422.3325KN/m61/42 3.83m1.5m121.5/621.5/626/42 标准层柱活载＝板传荷载 ＝2.0m1.5m121.5/621.5/6232.0m1.5m5/832 基础顶面荷载＝底层外纵墙自重＋基础自重＝9.738KN/m(6m0.6m)2.5KN/m(6m0.6m)四.C柱纵向集中力计算：顶层柱荷载＝梁自重＋板传梁荷载3.975KN/m(90.9)m2.349KN/m(1.20.3)m6.09KN/m1.5m5/836.09KN/m1.2m5/81.22(2.3323KN/m11.52KN/m)6m1/4顶层柱活载=板传荷载 2.0m1.5m121.5/621.5/623 2.0m1.2m121.2/621.2/623 5/81.222.0m1.5m5/832标准柱恒载=墙＋梁自重＋板传荷载＝11.52KN/m(30.6)m15.12KN/m(30.6)m15.12KN/m(30.6)m2.349KN/m(1.20.3)m3.975KN/m(60.6)m6.09KN/m1.5m5/8326.09KN/m6m1/21/22.67KN/m2.4/2m63.83KN/m23m6m标准层活载＝板传荷载＝2.0KN/m23m6m2.5KN/m21.2m6m基础顶面恒载=底层外纵墙自重＋基础自重9.738KN/m(6m0.6m)2.5KN/m(6m0.6m)（3）.框架柱自重：柱自重：底层：1.20.6m0.6m25KNm34.55m=49.14KN1.20.6m06m25KNm336m3888KN§6.2恒荷载作用下框架的内力§6.2.1.恒荷载作用下框架的弯矩计算—.恒荷载作用下框架可按下面求得 1/12ql 1/12ql

(6(6B7C故： 1/1221.0362B7CMC7B7C7 1/1211.48462C7MC7D7B6C 1/1214.74762B6CMC6B6C6 1/128.0962C6MD6C6恒荷载作用下框架的受荷简图如图63所示: 图63竖向受荷总图：1.图中各值的单位为KN图中数值均为标准值图中括号数值为活荷载图64：恒载作用下的受荷简图(2).根据梁，柱相对线刚度，算出各节点的弯矩分配系数ijiji/(icib分配系数如图65,图66所示

(6B柱：

图6- B柱弯矩各层分配系数简底层：i下柱＝0.801/(0.8010.6091.0))标准层：i上柱＝1.00.6091.01.0))i左梁＝0.6090.6091.01.0顶层：

C柱：

图6－ C柱弯矩各层分配系数简标准层：i下柱＝1.00.6091.00.2110.801))顶层：

三.恒荷载作用下的弯矩剪力计算，根据简图（64梁：M

MM1/2ql2Q.lAMB柱：MCMD

QBMAMB/l1/ MM1/2ql2Q.l QAMAMB/l1/MCMDQD.hQD(MCMD)/MCMDQC.hQC(MCMD)/

（6－4（6－5四.恒荷载作用下的边跨框架的轴力计算，包括连梁传来的荷载及柱自重.N7123.24721.1036/2N6N7124.17214.7476/238.88N5N6124.17214.7476/238.88601.142KNN4N5124.17214.7476/238.88808.435KNN3N4124.17214.7476/238.881015.728KNN2N3124.17214.7476/238.881223.021KNN1N2124.17214.7476/238.88恒荷载作用下的中跨框架的轴力计算：N7154.31811.4842.4/2N6N7200.1738.092.4/238.88416.88KNN5N6200.1738.092.4/238.88665.621KNN4N5200.1738.092.4/238.88808.435KNN1N2200.1738.092.4/238.88图65恒荷载作用下的计算简图五.弯矩分配及传递弯矩二次分配法比分层法作了更进一步的简化。在分层法中，用弯矩分配法计算分层单元的杆端弯矩一节点的不平衡弯矩都将影响到节点所在单元中的所有杆弯矩二次分配法假定任一节点的不平衡弯矩只影响至与该节点相交的各杆件的远此可将弯矩分配法的循环次数简化到一次分配、一次传递、再一次分配。所以本框架设计采用弯矩分配法计算框架内力，传递系数为1/2各节点分配两次即可。如表61所示：表6－ 恒载作用下的框架弯矩内力二次分配上柱下 左

右 上柱下柱左

右梁下柱

左 右

下柱上

-4379 62.57 1571 18.78 1878 18.78 1878 18.78 1878 18.59 1913 22.56 1233图6－5恒荷载作用下的弯矩 单位（KN.m）六.恒载作用下的的框架弯矩图对于无荷载直接作用的杆件（，将其柱端的弯矩连以直线，即为该杆件的弯矩图；对于有荷载作用的杆件（如梁，则以杆端弯矩的连线为基线。叠加相应简支梁的弯矩图，即为该杆件的弯矩图。弯矩图如上图65所示181211812MFMB7C7

21.103KN/m62m2 (48.22KN.m53.02KN.m)MFMC7D7

11.484KN/m62m2 (9.79KN.m9.79KN.m)18121812MB6C6

14.747KN/m62m2 (43.29KN.m44.22KN.m)18121812MC6D6

11.484KN/m62m2 (4.16KN.m4.16KN.m)18121812MB5C5

21.103KN/m62m2 (41.18KN.m42.35KN.m)18121812MC5D5

11.484KN/m62m2 (4.8KN.m4.8KN.m)18121812MB5C5

B4C

B2C

MFM12C5D512

18C418

C3D

1.02KN/MFMC2D2

11.484KN/m62m2 (4.5KN.m4.5KN.m)18M18M

21.103KN/m62m2 (38.69KN.m40.5KN.m)1218M1218M

11.484KN/m62m2 (4.5KN.m4.5KN.m)12七恒载作用下剪力计算121梁端剪力：QA7(MAMB)/L1/2ql(48.4453.02)/61/221.03662.327KNQB7(MAMB)/L1/2ql(48.4453.02)/61/221.036Q`QQ`Q

AA

)/L1/2ql)/L1/2qlQB6(MAMB)/L1/2ql(43.7953.02)/61/221.03644.169KNQB6(MAMB)/L1/2ql(48.4453.02)/61/221.03644.313KNQ`QQ`Q

AA

)/L1/2ql)/L1/2qlQB5(MAMB)/L1/2ql(41.1842.35)/61/221.03644.046KNQB5(MAMB)/L1/2ql(41.1842.35)/61/221.03644.436KNQ`QQ`Q

AA

)/L1/2ql)/L1/2qlQB4(MAMB)/L1/2ql(41.1842.35)/61/221.03644.046KNQB4(MAMB)/L1/2ql(41.1842.35)/61/221.03644.436KNQ`QQB`QB

AA

)/L1/2ql)/L1/2qlQB3(MAMB)/L1/2ql(41.3542.47)/61/221.03644.054KNQB3(MAMB)/L1/2ql(41.3542.47)/61/221.03644.428KNQ`QQ`Q

AA

)/L1/2ql)/L1/2qlQB2(MAMB)/L1/2ql(38.6940.496)/61/221.03643.94KNQB2(MAMB)/L1/2ql(38.6940.496)/61/221.03644.542KNQ`Q

A

)/L1/2qlQB`QB

A

)/L1/2ql2柱端剪力：Q7(48.44427.47)/3.676Q`(43.2924.35)/3.618.79KNQ6(16.3220.59)/3.610.25KNQ`(15.7118.78)/3.69.58KN763 Q`Q`(18.7818.78)/3.610.43KNQ3(20.5920.32)/3.611.36KNQ`(12.3296.16)/3.63 21Q2(21.0325.26)/3.612.86KNQ`(19.1322.563)/3.611.58KNQ1(13.436.72)/4.554.43KNQ`(12.3296.16)/4.554.06KN21图66恒载作用下的剪力图注：由于该框架结构左右对称，所以竖向荷载作用下框架剪力 称§63活荷载作用下框架的内力§6.3.1活载作用下的框架内力同恒载作用下用弯矩分配法计算框架内力，折减系数为1/2节点分配两次即可。活荷载作用下框架内力如表62所示：§6.32活荷载作用下框架的内力计—.梁端的固端弯矩可按下面的方法求得； 1/12ql 1/12ql故：Mab1/125.6256616.875Mba1/125.6256616.875MCD1/1232.42.41.44MDC1/1232.42.41.44

(6(6M 1/123.752.42.4MM`1/123.752.42.4M 图67恒载作用下的轴力图（KN）代表压力，BC轴与DE轴对称。

10 13.14 图68活荷载作用下的弯矩图表62上柱下柱

左 右

上柱下柱左

右梁下柱上柱左

右 下柱上.线（，则以杆件65所示1811812MFMB7C7

5.625KN/m62m2 (13.328KN.m15.025KN.m)MFMC7D7

3KN/m62m2 (0.5KN.m0.5KN.m)18121812MB6C6

5.625KN/m62m2 (16.154KN.m16.544KN.m)18121812MC6D6

3KN/m62m2 (2.308KN.m2.308KN.m)18121812MB5C5

5.625KN/m62m2 (15.684KN.m16.204KN.m)18121812MC5D5

3.75KN/m62m2 (0.938KN.m0.938KN.m)18121812MB5C5

B4C

B2C

MFM12C5D512

18C418

C3D

1.762KN/MFMC2D2

3.75KN/m62m2 (2.138KN.m2.138KN.m)18M18M

5.625KN/m62m2 (14.73KN.m14.73KN.m)1218M1218M

3.75KN/m62m2 (3.55KN.m3.55KN.m)1212根据简图（6－4）和推导计算其活荷载作用下的剪如图（69）QA7(MAMB)/L1/2ql(13.32815.025)/61/25.625616.592KNQB7(MAMB)/L1/2ql(13.32815.025)/61/25.625617.158KNQ`QQ`Q

AA

)/L1/2ql1/232.4)/L1/2ql1/232.4QB6(MAMB)/L1/2ql(16.15416.544)/61/25.625616.81KNQB6(MAMB)/L1/2ql(16.15416.544)/61/25.625616.94KNQ`QQ`Q

AA

)/L1/2ql1/22.43.75)/L1/2ql1/22.43.75QB5(MAMB)/L1/2ql(15.68416.204)/61/25.625616.788KNQB5(MAMB)/L1/2ql(15.68416.204)/61/25.6256Q`QQ`Q

AA

)/L1/2ql1/23.752.4)/L1/2ql1/23.752.4QB4(MAMB)/L1/2ql(15.68416.204)/61/25.625616.788KNQB4(MAMB)/L1/2ql(15.68416.204)/61/25.6256Q`QQB`QB

AA

)/L1/2ql1/23.752.4)/L1/2ql1/23.752.4QB3(MAMB)/L1/2ql(15.68416.204)/61/25.625616.792KNQB3(MAMB)/L1/2ql(15.68416.204)/61/25.625616.958KNQ`QQ`Q

AA

)/L1/2ql1/23.752.4)/L1/2ql1/23.752.4QB2(M