一、任务1.求解多层多跨框架结构在竖向荷载作用下的弯矩以及水平荷载作用下的弯矩和各层的侧移。
2.计算方法：（1）用近似法计算：水平荷载作用用反弯点法计算，竖向荷载作用采用分层法和二次力矩分配法计算。
（2）用电算（结构力学求解器）进行复算。
3. 就最大相对误差处，说明近似法产生误差的来源。
4. 将手算结果写成计算书形式。
二、结构形式及各种资料1. 计算简图：如图1所示。
2. 基本计算参数底层柱bXh(mm) 其它层bXh(mm) 边梁bXh(mm) 中间梁bXh(mm) 500X500 450X450 250X450 250X450材料弹性模量：723.210/hE kN m=⨯竖向荷载：21=23/g kN m，22=20/g kN m水平荷载：=32pF kN1，2=18PF kN3. 荷载分组：（1）计算水平荷载（见图2）；（2）计算竖向恒载（见图3）；L1L2H1H2H2H2H2FFFFF图1 计算简图图2 水平荷载作用g2 g1 g1 g1 g1q2q1图3 竖向荷载作用三、计算内容➢水平荷载1、反弯点法（1）求柱的剪力由所给数据可得各层梁柱的线刚度(单位：kN·m)如下表：i底柱i其它柱i左梁i右梁34792363331270825417第五层柱；FQ14 = FQ25= FQ36= 18/3kN = 6kN第四层柱；FQ47 = FQ58= FQ69= 50/3kN第三层柱；FQ710 = FQ811= FQ912= 82/3kN第二层柱；FQ1013 = FQ1114= FQ1215= 114/3kN第一层柱；FQ1316 = FQ1417= FQ1518= 146/3kN（2）求柱的弯矩第五层柱；M14 = M41= M25= M52= M36= M63= 6×3/2 = 9kN·m第四层柱；M47 = M74= M58= M85= M69= M96= 50/3×3/2 = 25kN·m第三层柱；M710 = M107= M811= M118= M912= M129= 82/3×3/2 = 41kN·m第二层柱；M1013 = M1310= M1114= M1411= M1215= M1512= 114/3×3/2 = 57kN·m第一层柱；M1316 = M1417= M1518= 146/3×4.8/3 = 77.87kN·mM1613 = M1714= M1815= 146/3×2×4.8/3 = 155.74kN·m（3）求梁的弯矩分别取结点1、2为隔离体1M12 ∑M1=0 M12=M14=9kN·m M142M21 M23∑M2=0 M21=3kN·mM 23=2M21M23=6kN·mM25同理可得其它梁各端弯矩；M 32=9kN·m M45=34kN·m M54=11.33kN·m M56=22,67kN·m M65=34kN·mM 78=66kN·m M87=22kN·m M89=44kN·m M98=66kN·mM 1011=98kN·m M1110=32.67kN·m M1112=65.33kN·m M1211=98kN·mM 1314=134.87kN·m M1413=44.96kN·m M1415=89.91kN·m M1514=134.87kN·m弯矩图如下：（4）求每层的位移第五层；取如下基本结构图1与上图图乘得第五层水平位移；X5=3×3/2/3×（9＋25＋41＋57）/EI其它柱＋4.8×（2×16.8×155.74－2×12×77.87＋12×155.74－16.8×77.87）/6EI底柱=20.62×10-3m同理可得其它层水平位移；第四层；X4=3×3/2/3×（25＋41＋57）/EI其它柱＋4.8×16.8 （2×13.8×155.74－2×9×77.87＋9×155.74－13.8×77.87）/6EI底柱=17.14×10-3m第三层；X3=3×3/2/3×（41＋57）/EI其它柱＋4.8×（2×10.8×155.74－2×6×77.87＋6×155.74－10.8 ×77.87）/6EI底柱 =13.43×10-3m第二层：X2=3×3/2/3×57/EI其它柱＋4.8×（2×7.8×155.74－2×3×77.87＋3×155.74－7.8 ×77.87）/6EI底柱 =9.51×10-3m第一层；X1=4.8×4.8/2×155.74/2/ EI底柱=5.37×10-3m2、结构力学求解器计算参数：结点,1,0,0 结点,2,0,4.8结点,3,0,7.8 结点,4,0,10.8结点,5,0,13.8 结点,6,0,16.8结点,7,4.8,0 结点,8,4.8,4.8结点,9,4.8,7.8 结点,10,4.8,10.8 结点,11,4.8,13.8 结点,12,4.8,16.8结点,13,7.2,0 结点,14,7.2,4.8结点,15,7.2,7.8 结点,16,7.2,10.8结点,17,7.2,13.8 结点,18,7.2,16.8单元,1,2,1,1,1,1,1,1 单元,2,3,1,1,1,1,1,1单元,3,4,1,1,1,1,1,1 单元,4,5,1,1,1,1,1,1单元,5,6,1,1,1,1,1,1 单元,7,8,1,1,1,1,1,1单元,8,9,1,1,1,1,1,1 单元,9,10,1,1,1,1,1,1单元,10,11,1,1,1,1,1,1 单元,11,12,1,1,1,1,1,1单元,13,14,1,1,1,1,1,1 单元,14,15,1,1,1,1,1,1单元,15,16,1,1,1,1,1,1 单元,16,17,1,1,1,1,1,1单元,17,18,1,1,1,1,1,1 单元,2,8,1,1,1,1,1,1单元,8,14,1,1,1,1,1,1 单元,3,9,1,1,1,1,1,1单元,9,15,1,1,1,1,1,1 单元,4,10,1,1,1,1,1,1单元,10,16,1,1,1,1,1,1 单元,5,11,1,1,1,1,1,1单元,11,17,1,1,1,1,1,1 单元,6,12,1,1,1,1,1,1单元,12,18,1,1,1,1,1,1 结点支承,7,6,0,0,0,0结点支承,1,6,0,0,0,0结点支承,13,6,0,0,0,0结点荷载,2,1,32,0结点荷载,3,1,32,0结点荷载,4,1,32,0结点荷载,5,1,32,0结点荷载,6,1,18,0单元材料性质,1,1,8E6,1.67E5,0,0,-1单元材料性质,6,6,8E6,1.67E5,0,0,-1单元材料性质,11,11,8E6,1.67E5,0,0,-1单元材料性质,2,5,6.48E6,1.09E5,0,0,-1单元材料性质,7,10,6.48E6,1.09E5,0,0,-1单元材料性质,12,15,6.48E6,1.09E5,0,0,-1单元材料性质,16,25,3.6E6,0.61E5,0,0,-1内力计算杆端内力值 ( 乘子 = 1)----------------------------------------------------------------------------------------------- 杆端 1 杆端 2--------------------------------------- ------------------------------------------ 单元码轴力剪力弯矩轴力剪力弯矩-----------------------------------------------------------------------------------------------1 91.6477957 41.5868667 -139.956636 91.6477957 41.5868667 59.66032412 60.2178903 20.9136559 -20.1687023 60.2178903 20.9136559 42.57226553 35.6974411 17.9393052 -18.4335661 35.6974411 17.9393052 35.38434964 17.7785994 11.8540971 -9.13693405 17.7785994 11.8540971 26.42535745 6.31520023 5.62088082 -1.70037808 6.31520023 5.62088082 15.16226436 158.182837 56.3611802 -163.376605 158.182837 56.3611802 107.1570597 87.9743752 57.2464693 -81.0735487 87.9743752 57.2464693 90.66585938 38.5163078 39.1415323 -52.0686505 38.5163078 39.1415323 65.35594659 9.67843568 24.0410138 -29.9975315 9.67843568 24.0410138 42.125510010 -0.93769305 10.0271528 -10.0474779 -0.93769305 10.0271528 20.033980511 -249.830632 48.0519530 -149.963820 -249.830632 48.0519530 80.685554512 -148.192265 35.8398747 -46.0504376 -148.192265 35.8398747 61.469186413 -74.2137490 24.9191623 -30.0370679 -74.2137490 24.9191623 44.720419114 -27.4570351 14.1048889 -13.6313729 -27.4570351 14.1048889 28.683293915 -5.37750718 2.35196635 0.96683431 -5.37750718 2.35196635 8.0227333616 -11.3267892 -31.4299053 79.8290265 -11.3267892 -31.4299053 -71.034519117 -12.2120783 -101.638367 117.196089 -12.2120783 -101.638367 -126.73599218 -29.0256493 -24.5204491 61.0058316 -29.0256493 -24.5204491 -56.692324319 -10.9207123 -73.9785166 86.0421854 -10.9207123 -73.9785166 -91.506254420 -25.9147918 -17.9188417 44.5212837 -25.9147918 -17.9188417 -41.489156721 -10.8142733 -46.7567139 53.8643213 -10.8142733 -46.7567139 -58.351792022 -25.7667836 -11.4633991 28.1257354 -25.7667836 -11.4633991 -26.898580623 -11.7529226 -22.0795279 25.2744073 -11.7529226 -22.0795279 -27.716459624 -12.3791191 -6.31520023 15.1622643 -12.3791191 -6.31520023 -15.150696725 -2.35196635 -5.37750718 4.88328387 -2.35196635 -5.37750718 -8.02273336-----------------------------------------------------------------------------------------------电算弯矩图59.66-139.9642.57-20.1735.38-18.4326.43-9.1415.16-1.70107.16-163.3890.67-81.0765.36-52.0742.13-30.0020.03-10.0580.69-149.9661.47-46.0544.72-30.0428.68-13.638.020.97-71.0379.83-126.74117.20-56.6961.01-91.5186.04-41.4944.52-58.3553.86-26.9028.13-27.7225.27-15.1515.16-8.024.88位移计算杆端位移值 ( 乘子 = 1)-----------------------------------------------------------------------------------------------杆端 1杆端 2---------------------------------------- ------------------------------------------ 单元码水平位移竖直位移转角水平位移竖直位移转角-----------------------------------------------------------------------------------------------1 0.00000000 0.00000000 0.00000000 0.00506450 0.00005499 -0.001153962 0.00506450 0.00005499 -0.00115396 0.00849562 0.00008287 -0.000845653 0.00849562 0.00008287 -0.00084565 0.01105299 0.00009939 -0.000612394 0.01105299 0.00009939 -0.00061239 0.01277797 0.00010762 -0.000374475 0.01277797 0.00010762 -0.00037447 0.01373952 0.00011055 -0.000189226 0.00000000 0.00000000 0.00000000 0.00504940 0.00009491 -0.000807957 0.00504940 0.00009491 -0.00080795 0.00845692 0.00013564 -0.000675948 0.00845692 0.00013564 -0.00067594 0.01101843 0.00015347 -0.000493099 0.01101843 0.00015347 -0.00049309 0.01274361 0.00015795 -0.0003261910 0.01274361 0.00015795 -0.00032619 0.01372302 0.00015752 -0.0001887611 0.00000000 0.00000000 0.00000000 0.00504126 -0.00014990 -0.0009956212 0.00504126 -0.00014990 -0.00099562 0.00844964 -0.00021851 -0.0007834313 0.00844964 -0.00021851 -0.00078343 0.01101122 -0.00025286 -0.0005813714 0.01101122 -0.00025286 -0.00058137 0.01273577 -0.00026558 -0.0003742315 0.01273577 -0.00026558 -0.00037423 0.01372145 -0.00026807 -0.0002505216 0.00506450 0.00005499 -0.00115396 0.00504940 0.00009491 -0.0008079517 0.00504940 0.00009491 -0.00080795 0.00504126 -0.00014990 -0.0009956218 0.00849562 0.00008287 -0.00084565 0.00845692 0.00013564 -0.0006759419 0.00845692 0.00013564 -0.00067594 0.00844964 -0.00021851 -0.0007834320 0.01105299 0.00009939 -0.00061239 0.01101843 0.00015347 -0.0004930921 0.01101843 0.00015347 -0.00049309 0.01101122 -0.00025286 -0.0005813722 0.01277797 0.00010762 -0.00037447 0.01274361 0.00015795 -0.0003261923 0.01274361 0.00015795 -0.00032619 0.01273577 -0.00026558 -0.0003742324 0.01373952 0.00011055 -0.00018922 0.01372302 0.00015752 -0.0001887625 0.01372302 0.00015752 -0.00018876 0.01372145 -0.00026807 -0.00025052-----------------------------------------------------------------------------------------------电算位移图➢竖向恒载1.分层法（1）确定计算简图。