结构力学大作业————多层多跨框架结构内力及位移计算.docx

此文档收集于网络，如有侵权，请联系网站删除结构力学课程大作业多层多跨框架结构内力及位移计算姓名：班级：学号：华中科技大学土木工程与力学学院2016年11月19日目录任务3计算简图和基本数据3用分层法计算竖直荷载4二次力矩分配法计算竖直弯矩13反弯点法计算水平荷载16侧移的计算21电算22误差分析及心得30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。计算简图和基本数据1. 计算简图：如图1所示。L1=4.5m L2=3.0m H1=4.5m H2=3.3m2. 基本计算参数材料弹性模量：Eh=3.2107KN/m2杆件尺寸及抗弯刚度抗拉刚度表底层柱其他层柱边梁中间梁尺寸 bh(mm2)550550500500250450250500抗弯刚度 EI(KNm2)244016.7166666.76075083333.3抗拉刚度 EA(KN)9680000800000036000004000000荷载列表竖向荷载g1=23KN/m2g2=20KN/m2水平荷载Fp1=32KNFp2=18KN3. 荷载分组：（1）计算水平荷载（见图2）；（2）计算竖向恒载（见图3）；图1 计算简图 图2 水平荷载作用图3 竖向荷载作用 用分层法计算竖直荷载按照书上的方法，将结构分成5层，分别用力矩分配法来计算，然后叠加。其中底层以上的柱子刚度要乘折减系数0.9，传递系数取1/3，低层柱刚度不需要折减，传递系数去1/2。荷载：q1=g1b=200.25=5KN/m q2=g2b=230.25=5.75KN/m1.第五层计算计算简图线刚度：i1-4=i2-5=i3-6=166666.73.3=50505.1KNmi1-2=607504.5=13500KNmi2-3=83333.33.0=27777.8KNm分配系数：结点1：1-2=41350040.950505.1+13500=0.2291-4=40.950505.140.950505.1+13500=0.771结点2：2-1=41350040.950505.1+13500+27777.8=0.1562-5=40.950505.140.950505.1+13500+27777.8=0.5242-3=427777.840.950505.1+13500+27777.8=0.320结点3：3-2=427777.840.950505.1+27777.8=0.3793-6=40.950505.140.950505.1+27777.8=0.621固端弯矩：M1-2F=-M2-1F=-11254.52=-8.436KNmM2-3F=-M3-2F=-112532=-3.750KN弯矩分配计算：2.第四层计算计算简图线刚度：i1-4=i2-5=i3-6=i4-7=i5-8=i6-9=166666.73.3=50505.1KNmi4-5=607504.5=13500KNmi5-6=83333.33.0=27777.8KNm分配系数：结点4：4-1=4-7=40.950505.140.950505.12+13500=0.4354-5=412656.340.946296.32+12656.3=0.13结点5：5-2=5-8=40.950505.140.950505.12+13500+27777.8=0.3445-4=41350040.950505.12+13500+27777.8=0.1025-6=427777.840.950505.12+13500+27777.8=0.21结点6：6-3=6-9=40.950505.140.950505.12+27777.8=0.3836-5=427777.840.950505.12+27777.8=0.234固端弯矩：M4-5F=-M5-4F=-1125.754.52=-9.703KNmM5-6F=-M6-5F=-1125.753.02=-4.313KNm弯矩分配计算：3.第三层计算：第三层与第四层除了结点编号改变其它相同。计算简图线刚度：i4-7=i5-8=i6-9=i7-10=i8-11=i9-12=166666.73.3=50505.1KNmi7-8=607504.5=13500KNmi8-9=83333.33.0=27777.8KNm分配系数：结点7：7-4=7-10=40.950505.140.950505.12+13500=0.4357-8=41350040.950505.12+13500=0.13结点8：8-5=8-11=40.9450505.140.950505.12+13500+27777.8=0.3448-7=41350040.950505.12+13500+27777.8=0.1028-9=427777.840.950505.12+13500+27777.8=0.21结点9：9-6=9-12=40.950505.140.950505.12+27777.8=0.3839-8=427777.840.950505.12+27777.8=0.234固端弯矩：M7-8F=-M8-7F=-1125.754.52=-9.703KNmM8-9F=-M9-8F=-1125.753.02=-4.313KNm弯矩分配计算：4.第二层计算第二层计算也与第四层相同。计算简图线刚度：i7-10=i8-11=i9-12=i10-13=i11-14=i12-15=166666.73.3=50505.1KNmi10-11=607504.5=13500KNmi11-12=83333.33.0=27777.8KNm分配系数：结点10：10-7=10-13=40.950505.140.950505.12+13500=0.43510-11=41350040.950505.12+13500=0.13结点11：11-8=11-14=40.950505.140.950505.12+13500+27777.8=0.34411-10=41350040.950505.12+13500+27777.8=0.10211-12=427777.840.950505.12+13500+27777.8=0.21结点12：12-9=12-15=40.950505.140.950505.12+27777.8=0.38312-11=427777.840.950505.12+27777.8=0.234固端弯矩：M10-11F=-M10-11F=-1125.754.52=-9.703KNmM11-12F=-M12-11F=-1125.753.02=-4.313KNm弯矩分配计算： 5.底层的计算计算简图线刚度：i10-13=i11-14=i12-15=166666.73.3=50505.1KNmi13-16=i14-17=i15-18=244016.74.5=54225.9KNmi13-14=607504.5=13500KNmi14-15=83333.33.0=27777.8KNm分配系数：结点13：13-10=40.950505.140.950505.1+54225.9+13500=0.40213-16=454225.940.950505.1+54225.9+13500=0.47913-14=41350040.950505.1+54225.9+13500=0.119结点14：14-13=41350040.950505.1+13500+27777.8+54225.9=0.09614-11=40.950505.140.950505.1+13500+27777.8+54225.9=0.32214-15=427777.840.950505.1+13500+27777.8+54225.9=0.19714-17=454225.940.950505.1+13500+27777.8+54225.9=0.385结点15：15-14=427777.840.950505.1+54225.9+27777.8=0.21815-12=40.950505.140.950505.1+54225.9+27777.8=0.35715-18=454225.940.950505.1+54225.9+27777.8=0.425固端弯矩：M13-14F=-M14-13F=-1125.754.52=-9.703KNmM14-15F=-M15-14F=-1125.753.02=-4.313KNm弯矩分配计算：柱子杆端弯矩叠加 杆端最终弯矩弯矩图二次力矩分配法计算竖直弯矩计算简图线刚度：底层以上柱=16666.73.3=50505.1KNm底层柱=244016.74.5=54225.9KNm边梁=607504.5=13500KNm中间梁=83333.33.0=27777.8KNm计算相对转动刚度：构件名称转动刚度S相对转动刚度S框架梁边跨4i=540001.000中跨4i=111111.22.058框架柱底层4i=216903.64.017其他层4i=202020.43.741计算分配系数：结点Si左梁上柱下柱右梁11.000+3.741=4.7410.0000.0000.7890.21121.000+3.741+2.058=6.7990.1470.0000.550.30332.058+3.741=5.7990.3550.0000.6450.000423.741+1.000=8.4820.0000.4410.4410.118523.741+1.000+2.058=10.540.0950.3550.3550.195623.741+2.058=9.540.2160.3980.3980.000723.741+1.000=8.4820.0000.4410.4410118823.741+1.000+2.058=10.540.0950.3550.3550195923.741+2.058=9.540.2160.3920.3920.0001023.741+1.000=8.4820.0000.4410.4410.1181123.741+1.000+2.058=10.540.0950.3550.3550.1951223.741+2.058=9.540.2160.3920.3920.000131.000+4.017+3.741=8.7580.0000.4270.4590.114141.000+4.017+3.741+2.058=10.8160.0920.3460.3710.190152.058+4.017+3.741=9.8160.2100.3810.4090.000 荷载列表：固端弯矩顶层边梁顶层中间梁其他层边梁其他层中间梁MF 844Nm3.75 KNm 9.7KNm 4.31KNm 分配与最终弯矩：弯矩图:反弯点法计算水平荷载1.计算柱的剪力因为每一排柱的线刚度都相等，每根柱的剪力相等。第五层柱：FQ14=FQ25=FQ36=183=6KN第四层柱：FQ47=FQ58=FQ69=18+323=503KN第三层住：FQ710=FQ811=FQ912=18+32+323=823KN第二层柱： FQ1013=FQ1114=FQ1215=18+3233=38KN 底层柱：FQ1316=FQ1417=FQ1518=18+3243=1463KN2.计算柱的弯矩 因为每一排柱的线刚度都相等，每根柱的弯矩相等。第五层柱：M14=M41=M25=M52=M36=M63=63.32=-9.9KNm第四层柱：M47=M74=M58=M85=M69=M96=5033.32=-27.5KNm第三层住：M710=M107=M811=M118=M912=M129=8233.32=-45.1KNm第二层住；M1013=M1310=M1114=M1411=M1215=M1512=383.32=-62.7KNm底层柱：反弯点在柱2/3高处M1316=M1417=M1518=14634.53=-73KNmM1613=M1714=M1815=146324.53=-146KNm3.计算梁的弯矩取出结点为隔离体说明：边梁与中间梁线刚度不一样所以边梁按照0.313分配，中间梁按照0.687分配。结点1：M1=0 M12=-M14=9.9KNm结点2：M2=0 M21+M23=-M25=9.9KNm M21=9.90.313=3.24KNm M23=9.90.687=6.66KNm结点3：M3=0 M32=-M36=9.9KNm结点4:M4=0 M45=-（M41+M47）=9.9+27.5=37.4KNm结点5：M5=0 M54+M56=-（M52+M58）=27.5+9.9=37.4KNm M54=37.40.313=12.25KNm M56=37.40.687=25.15KNm结点6：M6=0 M65=-（M63+M69）=9.9+27.5=37.4KNm结点7：M7=0 M78=-（M74+M710）=45.1+27.5=72.6KNm结点8：M8=0 M89+M87=M85+M811=27.5+45.1=72.6KNm M87=72.60.313=23.78KNm M89=72.60.687=48.82KNm结点9：M9=0 M98=-（M96+M912）=45.1+27.5KNm=72.6kNm结点10：M10=0 M1011=-(M107+M1013)=45.1+62.7=107.8KNm结点11：M11=0 M1110+M1112=-(M118+M1114)=62.7+45.1 =107.8KNm M1110=117.60.313=35.31KNm M1112=117.60.687=72.49KNm结点12：M12=0 M1211=-(M129+M1215)=45.1+62.7=107.8KNm结点13：M13=0 M1314=-(M1310+M1316)=62.7+73=135.7KNm结点14：M14=0 M1413+M1415=-(M1411+M1417)=62.7+73=135.7KNm M1413=135.70.313=44.45KNm M1415=135.70.687=91.25KNm结点15：M15=0 M1514=-(M1512+M911518)=62.7+73=135.7KNm最终弯矩图：侧移的计算根据课本265页公式3=Fp12h32i3i算得每一层相对于下一层的侧移。5=18123.3250505.13=0.108mm4=18+32123.3250505.13=0.299mm3=18+322123.3250505.13=0.431mm2=18+323123.3250505.13=0.743mm1=18+324124.5254225.93=1.514mm则第i层的侧移为1ii第五层侧移:3.095mm第四层侧移:2.987mm第三层侧移:2.688mm第二层侧移:2.257mm第一层侧移:1.514mm电算1.竖直荷载结点,1,0,0结点,2,0,4.5结点,3,0,7.8结点,4,0,11.1结点,5,0,14.4结点,6,0,17.7结点,7,4.5,17.7结点,8,4.5,14.4结点,9,4.5,11.1结点,10,4.5,7.8结点,11,4.5,4.5结点,12,4.5,0结点,13,7.5,0结点,14,7.5,4.5结点,15,7.5,7.8结点,16,7.5,11.1结点,17,7.5,14.4结点,18,7.5,17.7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,6,7,1,1,1,1,1,1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,18,7,1,1,1,1,1,1单元,5,8,1,1,1,1,1,1单元,4,9,1,1,1,1,1,1单元,3,10,1,1,1,1,1,1单元,2,11,1,1,1,1,1,1单元,8,17,1,1,1,1,1,1单元,9,16,1,1,1,1,1,1单元,10,15,1,1,1,1,1,1单元,11,14,1,1,1,1,1,1结点支承,1,6,0,0,0,0结点支承,12,6,0,0,0,0结点支承,13,6,0,0,0,0单元材料性质,1,1,9680000,244016.7,0,0,-1单元材料性质,11,11,9680000,244016.7,0,0,-1单元材料性质,12,12,9680000,244016.7,0,0,-1单元材料性质,2,5,8000000,166666.7,0,0,-1单元材料性质,7,10,8000000,166666.7,0,0,-1单元材料性质,13,16,8000000,166666.7,0,0,-1单元材料性质,6,6,3600000,60750,0,0,-1单元材料性质,17,17,4000000,83333.3,0,0,-1单元材料性质,18,21,3600000,60750,0,0,-1单元材料性质,22,25,4000000,83333.3,0,0,-1单元荷载,6,3,5,0,1,90单元荷载,17,3,5,0,1,-90单元荷载,18,3,5.75,0,1,90单元荷载,19,3,5.75,0,1,90单元荷载,20,3,5.75,0,1,90单元荷载,21,3,5.75,0,1,90单元荷载,22,3,5.75,0,1,90单元荷载,23,3,5.75,0,1,90单元荷载,24,3,5.75,0,1,90单元荷载,25,3,5.75,0,1,90弯矩图 位移图2.水平荷载：结点,1,0,0结点,2,0,4.5结点,3,0,7.8结点,4,0,11.1结点,5,0,14.4结点,6,0,17.7结点,7,4.5,17.7结点,8,4.5,14.4结点,9,4.5,11.1结点,10,4.5,7.8结点,11,4.5,4.5结点,12,4.5,0结点,13,7.5,0结点,14,7.5,4.5结点,15,7.5,7.8结点,16,7.5,11.1结点,17,7.5,14.4结点,18,7.5,17.7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,6,7,1,1,1,1,1,1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,18,7,1,1,1,1,1,1单元,5,8,1,1,1,1,1,1单元,4,9,1,1,1,1,1,1单元,3,10,1,1,1,1,1,1单元,2,11,1,1,1,1,1,1单元,8,17,1,1,1,1,1,1单元,9,16,1,1,1,1,1,1单元,10,15,1,1,1,1,1,1单元,11,14,1,1,1,1,1,1结点支承,1,6,0,0,0,0结点支承,12,6,0,0,0,0结点支承,13,6,0,0,0,0单元材料性质,1,1,9680000,244016.7,0,0,-1单元材料性质,11,11,9680000,244016.7,0,0,-1单元材料性质,12,12,9680000,244016.7,0,0,-1单元材料性质,2,5,8000000,166666.7,0,0,-1单元材料性质,7,10,8000000,166666.7,0,0,-1单元材料性质,13,16,8000000,166666.7,0,0,-1单元材料性质,6