反弯点法及D值法设计题

1、土木1204班组员:卢焕然邵明明胡伟卢鼎刘杰张辉周敏题目：试分别用反弯点法和 力、轴力)和水平位移 8 kMD值法计算下图1-1所示框架结构的内力(弯矩、剪图中在各杆件旁标出了线刚度，其中i =2600kN?m。17kNG(12)H(15)(2)0(15)(12)DEE在II 匚3,6m(4)4.5m图 1-1 :精选范本，供参考!(1)反弯点法:解：顶层柱反弯点位于柱中点M底层柱的反弯点位于柱高1%处，在反 弯点处将柱切开，脱离体如图2、图3所示。8kN图1-2顶层脱离体:EFg图1-3底层脱离体:(1)求各柱剪力分配系数 = “ K顶层:2-EHE-=0.4282 2 3底层:DA C =

2、3 =0.33 2 4= 0.4(2)计算各柱剪力:Fqgd =Fqif =0.286 8kN = 2.29kNFQHE =0.428 8kN = 3.42kNFQAD =Fqcf =0.3 25kN = 7.5kNFqbe =0.4 25kN = 10kN(3)计算杆端弯矩，以节点E为例说明杆端弯矩的计算杆端弯矩：Meh =Fqhe M，= T.42kN M33m = 5.64 kN m (反弯点位于 h2 处)hi3.6，2Meb=-FqbeM = -10kNK m=-12 kN m (反弯点位于柱 2h1 处)333 1计算梁端弯矩时，先求出节点柱端弯矩之和为：M =Meh Meb =

3、T7.64 kN m按梁刚度分配：一12,八八 MED 17.64 =7.84 kN mED 27MEF =15 17.64 =9.8 kN m 27图1-4是刚架弯矩图：2.513.785.643.133.783.7817129.812.7818245.647.843.783.7812.7893.7818图1-4弯矩图（单位kN m ）：(2) D值法:求各柱的剪力值:/12+12 公K = =62. 2ac = -6=0.752+612 2D = 0.75?h 1.653.321.65V =？ 8 2.16 6.1=12+15+12 + 15 门K =92 3ac =0.822+912 3

4、D = 0.82?2.713.322.71V =? 8 3.556.1/15+15 二K =7.52. 27.5 八会ac =0.792+7.512 2D = 0.79?升 1.743.321.74V =? 8 2.286.112K = =430.5+4 八”ac =0.752+412 3D = 0.75?丁 2.083.62V = 28? 25 7.087.3412+15 K =6.7540.5+6.75 八会 ac =0.832+6.7512 4 D = 0.83?乞3.073.623.07 -V =? 25 10.467.34k_15_. K = =530.5+5 C rc ac =0.

5、792+512 3D = 0.79?52.193.622.19V =? 25 7.467.34求个柱反弯点高度yhK=6 , y0 =0.45*1 , y1=0 y2=0K=9 , y0 =0.4512+黑1 , y1=0, y2=013 = 12 = 1 , 丫3=012y = 0.45 +0 + 0 = 0.4513y =1 , y3=012y = 0.45 +0+ 0 = 0.45K = 4 , y0=0.5511 = = 0.92 , y( =0 , y2 = 03.6I3 = H = 1 , y3=0y = 0.55 + 0 + 0 = 0.55K =6.75 , y0 =0.5011 = 12 = 1 , yl=0, y2 =012I3=11|=1 , y3=0y = 0.50 +0 + 0 = 0.50求各柱的杆端弯矩：第二层：M上=2.161-0.45) 3.3=3.78 M上=3.5劭(1-0.45) 3.3=5.64M下=2.辍 0. 4 3.3 = 3 M下=3.550.45 3.3=5.64第一层：.55 3.6=24.0M上=7.08?(1 0.6)?3.6 9.0 M上=10.4?(1 0.55?3.6 12.0M下=7.0的0.6 3.6=18.0绘制各横梁与柱的弯矩图：3.783.788 M3.783.133.7812.78