结构力学大作业(华科)

1、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H1=4.8m H2=3m L1=4.8m L2=2.4m底层柱bXh(mm)其它层bXh(mm)边梁bXh(mm)中间梁bXh(mm)500X500450X450250X450250X450材料弹性模量

2、： 竖向荷载： ， 水平荷载： ，3. 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 竖向荷载作用三、计算内容Ø 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 = F

3、Q1114 = 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 =

4、M1114 = M1411 = M1215 = M1512 = 114/3×3/2 = 57kN·m第一层柱；M1316 = M1417 = M1518 = 146/3×4.8/3 = 77.87kN·m M1613 = 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 1 M12 M1=0 M12=M14=9kN·m M14 2M21 M23 M2=0 M21=3kN·m M23=2M21 M23=6kN·m M25

5、同理可得其它梁各端弯矩；M32=9kN·m M45=34kN·m M54=11.33kN·m M56=22,67kN·m M65=34kN·mM78=66kN·m M87=22kN·m M89=44kN·m M98=66kN·mM1011=98kN·m M1110=32.67kN·m M1112=65.33kN·m M1211=98kN·mM1314=134.87kN·m M1413=44.96kN·m M1415=89.91kN·m

6、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×（9254157）/EI其它柱4.8× （2×16.8×155.742×12×77.8712×155.7416.8 ×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×（254157）/EI其它柱4.8× 16.8 （2×13.8×15

7、5.742×9×77.879×155.7413.8 ×77.87）/6EI底柱 =17.14×10-3m第三层；X3=3×3/2/3×（4157）/EI其它柱4.8× （2×10.8×155.742×6×77.876×155.7410.8 ×77.87）/6EI底柱 =13.43×10-3m第二层：X2=3×3/2/3×57/EI其它柱4.8× （2×7.8×155.742×3×

8、;77.873×155.747.8 ×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,

9、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,

10、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,

11、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

12、)- 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 59.6603241 2 60.2178903 20.9136559 -20.1687023 60.2178903 20.9136559 42.5722655 3 35.6974411 17.9393052 -18.4335661 35.6974411 17.9393052 35.3843496 4 17.7785994 11.8540971 -9.13693405 17.7785994 11.854

13、0971 26.4253574 5 6.31520023 5.62088082 -1.70037808 6.31520023 5.62088082 15.1622643 6 158.182837 56.3611802 -163.376605 158.182837 56.3611802 107.157059 7 87.9743752 57.2464693 -81.0735487 87.9743752 57.2464693 90.6658593 8 38.5163078 39.1415323 -52.0686505 38.5163078 39.1415323 65.3559465 9 9.6784

14、3568 24.0410138 -29.9975315 9.67843568 24.0410138 42.1255100 10 -0.93769305 10.0271528 -10.0474779 -0.93769305 10.0271528 20.0339805 11 -249.830632 48.0519530 -149.963820 -249.830632 48.0519530 80.6855545 12 -148.192265 35.8398747 -46.0504376 -148.192265 35.8398747 61.4691864 13 -74.2137490 24.91916

15、23 -30.0370679 -74.2137490 24.9191623 44.7204191 14 -27.4570351 14.1048889 -13.6313729 -27.4570351 14.1048889 28.6832939 15 -5.37750718 2.35196635 0.96683431 -5.37750718 2.35196635 8.02273336 16 -11.3267892 -31.4299053 79.8290265 -11.3267892 -31.4299053 -71.0345191 17 -12.2120783 -101.638367 117.196

16、089 -12.2120783 -101.638367 -126.735992 18 -29.0256493 -24.5204491 61.0058316 -29.0256493 -24.5204491 -56.6923243 19 -10.9207123 -73.9785166 86.0421854 -10.9207123 -73.9785166 -91.5062544 20 -25.9147918 -17.9188417 44.5212837 -25.9147918 -17.9188417 -41.4891567 21 -10.8142733 -46.7567139 53.8643213

17、-10.8142733 -46.7567139 -58.3517920 22 -25.7667836 -11.4633991 28.1257354 -25.7667836 -11.4633991 -26.8985806 23 -11.7529226 -22.0795279 25.2744073 -11.7529226 -22.0795279 -27.7164596 24 -12.3791191 -6.31520023 15.1622643 -12.3791191 -6.31520023 -15.1506967 25 -2.35196635 -5.37750718 4.88328387 -2.3

18、5196635 -5.37750718 -8.02273336-电算弯矩图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 -0.00115396 2 0.00506450 0.00005499 -0.00115396 0.00849562 0.00008287 -0.00084565 3 0.00849562 0.00008287 -0.00084565 0.01105299 0.00009939

19、-0.00061239 4 0.01105299 0.00009939 -0.00061239 0.01277797 0.00010762 -0.00037447 5 0.01277797 0.00010762 -0.00037447 0.01373952 0.00011055 -0.00018922 6 0.00000000 0.00000000 0.00000000 0.00504940 0.00009491 -0.00080795 7 0.00504940 0.00009491 -0.00080795 0.00845692 0.00013564 -0.00067594 8 0.00845

20、692 0.00013564 -0.00067594 0.01101843 0.00015347 -0.00049309 9 0.01101843 0.00015347 -0.00049309 0.01274361 0.00015795 -0.00032619 10 0.01274361 0.00015795 -0.00032619 0.01372302 0.00015752 -0.00018876 11 0.00000000 0.00000000 0.00000000 0.00504126 -0.00014990 -0.00099562 12 0.00504126 -0.00014990 -

21、0.00099562 0.00844964 -0.00021851 -0.00078343 13 0.00844964 -0.00021851 -0.00078343 0.01101122 -0.00025286 -0.00058137 14 0.01101122 -0.00025286 -0.00058137 0.01273577 -0.00026558 -0.00037423 15 0.01273577 -0.00026558 -0.00037423 0.01372145 -0.00026807 -0.00025052 16 0.00506450 0.00005499 -0.0011539

22、6 0.00504940 0.00009491 -0.00080795 17 0.00504940 0.00009491 -0.00080795 0.00504126 -0.00014990 -0.00099562 18 0.00849562 0.00008287 -0.00084565 0.00845692 0.00013564 -0.00067594 19 0.00845692 0.00013564 -0.00067594 0.00844964 -0.00021851 -0.00078343 20 0.01105299 0.00009939 -0.00061239 0.01101843 0

23、.00015347 -0.00049309 21 0.01101843 0.00015347 -0.00049309 0.01101122 -0.00025286 -0.00058137 22 0.01277797 0.00010762 -0.00037447 0.01274361 0.00015795 -0.00032619 23 0.01274361 0.00015795 -0.00032619 0.01273577 -0.00026558 -0.00037423 24 0.01373952 0.00011055 -0.00018922 0.01372302 0.00015752 -0.0

24、0018876 25 0.01372302 0.00015752 -0.00018876 0.01372145 -0.00026807 -0.00025052-电算位移图Ø 竖向恒载1.分层法（1）确定计算简图。本结构可分为顶层、中间层、底层三部分进行计算，然后再叠加即可。该结构顶层、中间层、底层的计算简图分别如下图所示 1 2 3 20kN/m 23kN/m 1 2 3 4 5 6 4 5 6 7 8 9 顶层 中间层 10 11 12 20kN/m 13 14 15 16 17 18 底层（2）顶层弯矩计算计算分配系数注意柱的线刚度应乘折减系数0.9对于结点1有12=4×

25、;12708/(4×(0.9×36333+12708)=0.2814=4×0.9×36333/(4×(0.9×36333+12708)=0.72对于结点2有21=4×12708/(4×(0.9×363331270825417)=0.1825=4×0.9×36333/(4×(0.9×363331270825417)=0.4623=4×25417/(4×(0.9×363331270825417)=0.36对于结点3有32=4×25

26、417/(4×(0.9×36333+25417)=0.4436=4×0.9×36333/(4×(0.9×36333+25417)=0.56计算固端弯矩MF21=-MF12=ql2/12=20×4.82 /12=38.4kN·mMF32=-MF23=ql2/12=20×2.42 /12=9.6kN·m弯矩分配计算顶层弯矩计算过程如下表所示结点编号412356杆端编号4-11-41-22-12-52-33-23-65-26-3分配系数0.720.280.180.460.360.440.56固端弯矩-

27、38.438.4-9.69.6分配与传递弯矩9.2227.6510.755.38-2.11-4.22-5.38-1.79-2.89-5.77-14.75-11.55-5.78-4.920.692.080.810.411.272.543.241.08-0.15-0.30-0.78-0.60-0.30-0.260.040.110.040.020.070.130.170.06-0.02-0.04-0.03最终弯矩9.9529.84-29.8438.12-15.57-22.551.97-1.97-5.18-0.65（3）中间层弯矩计算计算分配系数同样，柱的线刚度应乘折减系数0.9对于结点4有47=41

28、=4×0.9×36333/(4×(0.9×36333×2+12708)=0.4245=4×12708/(4×(0.9×36333×2+12708)=0.16对于结点5有52=58=4×0.9×36333 /(4×(0.9×36333×2+1270825417)=0.3254=4×12708/(4×(0.9×36333×2+1270825417)=0.1256=4×25417/(4×(0.9

29、5;36333×2+1270825417)=0.24对于结点6有63=69=4×0.9×36333/(4×(0.9×36333×2+25417)=0.3665=4×25417/(4×(0.9×36333×2+25417)=0.28计算固端弯矩MF54=-MF45=ql2/12=23×4.82 /12=44.16kN·mMF65=-MF56=ql2/12=23×2.42 /12=11.04kN·m弯矩分配计算中间层弯矩计算过程如下表所示（4）底层弯矩计算计算

30、分配系数上层柱的线刚度应乘折减系数0.9，底层柱的线刚度不用折减。对于结点13有1310=4×0.9×36333/(4×(0.9×3633334792+12708)=0.411316=34792×4/(4×(0.9×3633334792+12708)=0.43 1314=4×12708/(4×(0.9×3633334792+12708)=0.16对于结点14有1413=4×12708/(4×(0.9×3633334792+1270825417)=0.121411=4

31、×0.9×36333/(4×(0.9×3633334792+1270825417)=0.311417=34792×4/(4×(0.9×3633334792+1270825417)=0.331415=4×25417/(4×(0.9×3633334792+1270825417)=0.24对于结点15有1512=4×0.9×36333/(4×(0.9×363333479225417) =0.361514=4×25417/(4×(0.9

32、5;363333479225417) =0.271518=34792×4/(4×(0.9×363333479225417) =0.37 计算固端弯矩MF1413=-MF1314=ql2/12=44.16kN·mMF1514=-MF1415=ql2/12=11.04kN·m弯矩分配计算底层弯矩计算过程如下表所示各杆端弯矩叠加、结点不平衡力矩一次分配及杆端最终弯矩如下列各表所示结点编号123杆端编号1-41-22-12-32-53-23-6分配系数0.720.280.180.360.460.440.56不平衡力矩一次分配29.84-29.8438.

33、12-22.55-15.571.97-1.976.48-3.82-0.81-4.67-1.810.691.371.760.360.45最终弯矩31.65-31.6538.81-21.18-17.632.33-2.33结点编号456杆端编号4-14-54-75-45-25-85-66-36-56-9分配系数0.420.160.420.120.320.320.240.360.280.36不平衡力矩一次分配9.95-5.18-0.6519.46-38.9219.4643.56-11.47-11.47-20.62-2.414.82-2.416.48-3.82-0.81-6.90-2.63-6.901.

34、082.882.882.160.530.40.53最终弯矩22.51-41.5519.0444.64-13.77-12.41-18.46-2.535.22-2.69结点编号789杆端编号7-47-87-108-78-58-118-99-69-89-12分配系数0.420.160.420.120.320.320.240.360.280.36不平衡力矩一次分配6.48-3.82-0.8119.46-38.9219.4643.56-11.47-11.47-20.62-2.414.82-2.416.48-3.82-0.81-5.44-2.08-5.440.922.442.441.840.580.460

35、.58最终弯矩20.5-4120.544.48-12.85-12.85-18.78-2.645.28-2.64结点编号101112杆端编号10-710-1110-1311-1011-811-1411-1212-912-1112-15分配系数0.420.160.420.120.320.320.240.360.280.36不平衡力矩一次分配6.48-3.82-0.8119.46-38.9219.4643.56-11.47-11.47-20.62-2.414.82-2.416.33-3.71-0.81-5.38-2.05-5.380.92.412.411.810.580.460.58最终弯矩20.5

36、6-40.9720.4144.46-12.88-12.77-18.81-2.645.28-2.64结点编号131415杆端编号13-1013-1413-1614-1314-1114-1714-1515-1215-1415-18分配系数0.410.160.430.120.310.330.240.360.270.37不平衡力矩一次分配6.48-3.82-0.8118.99-38.9119.9243.55-11.13-11.84-20.58-2.424.91-2.49-2.66-1.04-2.780.461.181.260.920.290.220.3最终弯矩22.81-39.9517.1444.01

37、-13.77-10.58-19.66-2.945.13-2.19结点编号161718杆端编号16-1317-1418-15最终弯矩9.96-5.92-1.27最终弯矩图如图所示2二次力矩分配法计算框架各杆的线刚度及分配系数结果如下表所示构件名称转动刚度S相对转动刚度S框架梁左跨4i=4×12708 =508321.000右跨4i=4×25417=1016682.000框架柱底层4i=4×34792=1391682.738其它层4i=4×36333=1453322.859结点S左梁右梁上柱下柱11.0002.859=3.8590.260.7421.0002

38、.0002.859=5.8590.170.340.4932.0002.859=4.8590.410.5942.859×21.000=6.7180.140.430.4352.859×21.0002.000=8.7180.110.230.330.3362.859×22.000=7.7180.260.370.3772.859×21.000=6.7180.140.430.4382.859×21.0002.000=8.7180.110.230.330.3392.859×22.000=7.7180.260.370.37102.859×2

39、1.000=6.7180.140.430.43112.859×21.0002.000=8.7180.110.230.330.33122.859×22.000=7.7180.260.370.37132.8592.7381.000=6.5970.150.430.42142.8592.7381.0002.000=8.5970.120.230.330.32152.8592.7382.000=9.5970.260.380.36计算梁端固端弯矩 顶层左跨梁：MF=ql2/12=20×4.82/12=38.4kN·m右跨梁；MF=ql2/12=20×2.42

40、/12=9.6kN·m右跨梁； 其它层左跨梁；MF=ql2/12=23×4.82/12=44.16kN·m右跨梁；MF=ql2/12=23×2.42/12=11.04kN·m弯矩分配与传递具体过程如下列各表所示结点编号123杆端编号1-41-22-12-32-53-23-6分配系数0.740.260.170.340.490.410.59固端弯矩-38.438.4-9.69.6二次力矩分配28.429.98-4.9-9.79-14.11-3.94-5.669.5-2.454.99-1.97-5.47-4.9-2.04-5.22-1.830.420

41、.831.22.854.09最终弯矩32.7-32.738.91-20.53-18.383.61-3.61结点编号456杆端编号4-14-54-75-45-25-85-66-36-56-9分配系数0.430.140.430.110.330.330.230.370.260.37固端弯矩-44.1644.16-11.0411.04二次力矩分配18.996.1818.99-3.64-10.93-10.93-7.62-4.08-2.88-4.0814.21-1.829.53.09-7.06-5.47-1.44-2.83-3.81-2.04-9.41-3.07-9.411.23.593.592.53.2

42、12.263.21最终弯矩23.79-42.8719.0844.81-14.4-12.81-17.6-3.76.61-2.91结点编号789杆端编号7-47-87-108-78-58-118-99-69-89-12分配系数0.430.140.430.110.330.330.230.370.260.37固端弯矩-44.1644.16-11.0411.04二次力矩分配18.996.1818.99-3.64-10.93-10.93-7.62-4.08-2.88-4.089.5-1.829.53.09-5.47-5.47-1.44-2.04-3.81-2.04-7.39-2.4-7.391.023.073.072.132.922.052.92最终弯矩21.1-42.221.144.63-13.33-13.33-17.97-3.26.4-3.2结点编号101112杆端编号10-710-1110-1311-1011-811-1411-1212-912-1112-15分配系数0.430.140.430.110.330.330.230.370.260.37固端弯矩-44.1644.16-11.0411.04二次力矩分配18.996.1818.99-3.64-10.93-10.93-7.62-4.08-2.88-4.089.5-1.829.53.09-5.47-5