结构力学大作业-多层多跨框架结构内力及位移计算

1、结构力学课程大作业 结构力学课程大作业多层多跨桓架结构內力及佞移计算姓名:班级:学百：华中科技丸学土木工程与力学学院2016年11月19目目录 TOC o 1-5 h z HYPERLINK l bookmark2 o Current Document 任务3 HYPERLINK l bookmark4 o Current Document 计算简图和基本数据3 HYPERLINK l bookmark6 o Current Document 用分层法计算竖直荷载4 HYPERLINK l bookmark24 o Current Document 二次力矩分配法计算竖直弯矩13反弯点法计算水

2、平荷载16 HYPERLINK l bookmark28 o Current Document 侧移的计算21 HYPERLINK l bookmark30 o Current Document 电算22误差分析及心得30任务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。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。就最大相对误差处，说明近似法产生误差的來源。将手算结果写成计算书形式。计算简图和基本数据计算简图：如图1所示。Lx = 4.5m L2 = 3.0m

3、= 4.5m H2 = 3.3m基本计算参数材料弹性模量：Eh = 3.2 X 107KN/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b X h(mm2)550 X550500 X 500250 X 450250 X 500抗弯刚度EI（KN-m2）214016. 7166666. 76075083333. 3抗拉刚度EA（KN）9680000800000036000004000000荷载列表竖向荷载/ = 23KN/m2g2 = 2QKN/m2水平荷载Fpi = 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

4、图图2水平荷裁作用92J J J J J J J，J J JJ J J J J J,r $4J J,6Trrrrrrwg、T*C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，分别用力矩分配法來计算，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l/2o荷载：a】=6 x b = 20 X 0.25 = 5KN/mQ2 = 92 X b = 23 X 0.25 = 5.75KN/m1.第五层计算5KN/mnmnmumn1 23计算简图线刚度:166666.7飞一=50505.1幼60750=13500KN m83

5、333.33.0277778KNm分配系数:结点1：=0.2294X 135004 X (0.9 x 50505.1 + 13500)结构力学课程大作业94 X 0.9 X 50505.1n n 771I 一 4 X (0.9 X 50505.1 + 13500) - *结点2：4X 135002-丄4 X (0.9 X 50505.1 + 13500 + 27777.8)0 1 64 X 0.9 X 50505.12 0 5尸2一54 X (0.9 X 50505.1 + 13500 + 27777.8)-4 X 27777.8u 0 30血-34 X (0.9 X 50505.1 + 13

6、500 + 27777.8)结点3：4 X 27777.8M32 _ 4 X (0.9 X 50505.1 + 27777.8) - * 4x 0.9 x 50505.1u 0 6 1円-6 4 X (0.9 X 50505.1 + 27777.8)固端弯矩：M匚2 = -= 一吉 X 5 X 4.52 = -8.436KN m MJ = -ML = -x 5 x 32 = -3.750KN 弯矩分配计算:结点1. 0001235.0006. 000科端4-11-41-22-12-52-33-23-65-26-3分配系数0.771. 2290 15b0. 5240.3200 3790. 021

7、一 8 436B. 436一 3 7503. 7502.1086.5041.9320 90C-0.711-1.421一2 329-0.776一0 3B6-0.771-2. 589一1 5B1-0.791一0 B63分配与传0.0990.2980. 0880.0440.1500. 3000. 4910. 104速言矩一 0 015-0.030-0.102一 0 062-0.031-0. 0340. 0060.0120. 0030. 002 -0. 0010040. 006一 0. 003。 0120. 0190. 006最终弯矩2. 2736.814一 6 8148 64-2. 695一 3 2

8、561. 819-1.819一 0 B97一 0.6062第四层计算575KN/rp1计算简图线刚度:结构力学课程大作业 166666.7G-4 =，2-5 =，3-6 = U-7 = 5-8 =，6-9 =亍= 50505.1KN TH60750U-5 = 45 = 13500/CAf m83333.3i5-6 = 27777.8KN mO.K/分配系数:结点4：4x 0.9 x 50505.1“47 = “4-7 = 4 X (0.9 X 50505.1 X 2 + 13500) = 4354 X 12656.3“= 0 13M45 一 4 X (0.9 X 46296.3 X 2 + 1

9、2656.3)结点5：4 X 0.9 X 50505.1肉一2 = 5-8 = 4 X(0.9 X 50505.1 X 2 + 13500 + 27777.8) = 03444X13500U= = Q 1 Q2円-4 一 4 X (0.9 X 50505.1 X 2 + 13500 + 27777.8) 一 4 X 27777.8u= 0 21円一6 4 X (0.9 X 50505.1 X 2 + 13500 + 27777.8) 一 *结点6：4X0.9X50505.14x(0.9x50505.1x2+27777.8)=0.3834 X 27777.8= o 2344 X (0.9 X 5

10、0505.1 X 2 + 27777.8)固端弯矩:1一迈 X 5.75 X 4.52 9.703KNmJ = 一 m_5 =1 o-x 5.75x3.0=4313KNm弯矩分配计算:if%1 234567891 42 9S 04 ICL 4354 T0. 43S4 00.135 40.1020 20. 3449 00.215 80. S440 00.2S44 S0.3830 90. 3337 48 99 0-9. 703&.7034. M34. 3131.407a wi4 2214. ZZJL. 201a 031 O.llB0, 230-LCOZ-1.0521.407-0.551P 6770

11、 SOI-o. 602-2.031-1.24-2.03L-0.62P.677aoMo.07ea 131O.1S10. 0390.020.0730.14d0.23?0.2370.O440.0791*on0006-0. ow-0.032-0.01?-0.0320890016a coz0. 0020. 0010.002a oo30. 003at终就1.451r P. 63B-0.4724.3S44. 354r70C.743r -2.063r -5.615-2.063r S. 5 1.412-i.4121.451r P. M3-0.4T23第三层计算：第三层与第四层除了结点编号改变其它相同。75.75

12、KN/m1011 12计算简图线刚度: l4-7 =l5-8= l6-9= l7-10= l8-ll= l9-12=166666.7 = 50505.Km分配系数:结点7：60750i7_8 =45= 13500KN m.83333.3i8_9 = 27777.8KN m4 x 0.9 x50505.177 = 4 X (0.9 X 50505.1 X 2 + 13500) = 013“7-4 = “7-10 = 4 X(0.9 X 50505.1 X 2 + 13500) = 4354 X 13500结点&4X 0.94X50505.1覘一5 = Ms-ii = 4 x (0.9 x 505

13、05.1 X 2 + 13500 + 27777.8) = 3444X 13500n 1 o oA7 = 4 x(0.9 x 50505.1 X 2 + 13500 + 27777.8) = *4 X 27777.8u =021M89 _ 4X (0.9 X 50505.1 X 2 + 13500 + 27777.8) 一 结点9：4X 0.9 X 50505.1两-6 = “9-12 = 4 x (0.9 X 50505.1 X 2 + 27777.8) = 3834 X 27777.8I = 4 x (0.9 X 50505.1 X 2 + 27777.8) = *固端弯矩:M久$ = -

14、M=7 = 一寺 X 5.75 X 4.52 = 一9.703KN m 丄乙M$_9 = -Mf_8 = -寺 X 5.75 X 3.02 = -4.313KN m 丄乙弯矩分配计算:垢4507-4T 7-107-88-79358-98-119-B99-69-1210n 124-76-9LO-711-8 1 12T分瞬劉0.43S0.心50.13O.L020. 3440. 210. 3440.234asas0.3&3Pg阳f 703% 7C0-4. 3134.3131.407-0.55】4.2Z14 231I. 2610.6SJ-0.118-U236-1.652-1.652L. 7P55】分配

15、与传-0.C77-o.am-0. 602-2 031L 24-2.031-0. 62-0.6770. 044UOT9O.L310.131Ct 0330.02acn30.140UZ370. Z370.0440.0H 0.011-c. 0C6P Q09aras -o. 017P 0327 0090 0160.0020. 002a ooi0. S020.003o.aaa1.451-0.4724. 3Xr -e.F 9. 743乙(XZ roe-2. 0033. 390 1.412-1.4121.401r -0.W37歹24.第二层计算第二层计算也与第四层相同。线刚度:计算简图 7-10 =l8-ll

16、= S -12= 110-13= 111-14= 112-15= 166666.7 = 50505.1KN m60750_iio-ii = - = 13500KN - m83333.3=27777.8KN m11 123.0分配系数:结点10：4 X 0.9 X 50505.1冷0-7 = Mio-13 = 4 x(0.9x 50505.1 x 2 + 13500) = 4354X 13500= 4 x (0.9 X 50505.1 X 2 + 13500) = 0 13结点11：4 X 0.9 X 50505.1心丄-8 = 4 x(0.9 X 50505.1 X 2 + 13500 + 2

17、7777.8) = ，3444X 13500u= 0 102- 4 X (0.9 X 50505.1 X 2 + 13500 + 27777.8) 一 *4 x 27777.8= 4 x (0.9 X 50505.1 x 2 + 13500 + 27777.8) = 0 21结点12：4 X 0.9 X 50505.112-9 = /zi2-i5 = 4 x (0.9 X 50505.1 X 2 + 27777.8) = 3834 X 27777.8”一0 2344 X (0.9 X 50505.1 X 2 + 27777.8)*固端弯矩：Mfo_n = -“爲一口 = - 寺 X 5.75

18、X 4.52 = -9.703KN m 丄乙-5.75 X 3.02 = -4.313KN m丄乙弯矩分配计算:嗨5i7-108 e-ii99-1210-71010 1310-1L11-101111-2 11-1211-1412-111212-912-15】31S-101414-1L1 !O.30. 4330.130.1020. 3440. 21a 3440.2M0 3830. 3539 T039. 703 4.3134.3131.40?-a 55i4 2214. 2211.2&10.631-0.118-0.23-1.652-I. W0-BS3-2.427J.734-6.708-QOS農743

19、0.161仇9044.1996曲 -L2CT-2.751(LB羽7肿2.W一九咖-8- T08 Y.ftU -9.003S.TU0.1414.546&81 抽4.5M也7E1 a晶-taw2.7W电T(B-0.368&6S8 DO4.48B.441-o.satt47ms1.4294.75A-0,690TW-e.79-ALTl-RM1-2.143.8771.BL9Q.69953*1$ 3.596-fi.2S-.15 0阳 -R3WJ.A36-2.42-tais.3L127439苑 r-2.-2.11-5.413.41f-1.5C-1. 530. 4410.4410.1 LB 10. 0950.

20、3550. 3550.1956 2160. 3920. 392 |T709.70-4.314.314.23龟281.14T. 51-1.91-1.91-1.05H 93-i.es-1.692.142.14T26.5TP梵-0.96P. 47T 53-0.5-0.34-1. 77-1.77-0. 470.1?0.&40U0. 350.4S0.870.974.644.MT. 239.虻 r -2.23-2. 23-5 473.33 r-1.671.6C0. 4410.4410.118 J|0. 0950. 35S0. 3550.1350.2160. 3920. 332T709.70-4 314.

21、314. 234.281. 14-0.51-1.91-1. 91L 05-o. w j -i.es692.142. 07P. 260. 57P我-0. 93-0. 47-0.53-0.S4P. 82-1. 74-1.74T. 470.170. 630 630. 350.470.860.S64. 674. 61TZ89. W r -2.24-Z. 21-5.453.33 f-1.65-1.650.4270.4390. 1L40. OS20. 340. 3710.190.210. 3810.409T. ?09.70-4. 314. 314144. 451. 11-0.50-l.B2.00-1.02

22、Y 1-1.64-1. 762. 140.00-0. 250. 55-O.0C0 00-0. 45Y 51-0.E40.00-0. 81-O.B7-0 220.080.30a 12o. ie0.280. 520. 555. 473.58T.069.84F -2.53-L.68-5. 23.18r-1.97-1.21结构力学课程大作业反弯点法计算水平荷载1计算杆的剪力FPi=32KN256因为每一排柱的线刚度都相等，每根柱的剪 力和等。第五层柱：甩二32蚀8918A?L4 = Fq25 = Fq36 =亍= 6KNFPi=32KN121112第四层柱：厂厂厂18 + 32Fq47 心58 F 6

23、93FPi=32KNu14155016161718电三I8KN结构力学课程大作业 第三层住:_ 18 + 32 +32 _ 82Fq710 = Q811 = Fqx2 =2=可 KN第二层柱：18 + 32x3Fqi013 = 21114 = FQ121S = 38KN底层柱：厂厂厂18 + 32 X4 146F 1316 = F 1417 =心1518 =2= 一一KN2.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：3.3503.3= M96 = Tx =-27.5KNmMg = M41 = M25 = M52 = M36 = M&3 = 6 X - = 9.9KN

24、m 第四层柱：M47 = M74 = M58 = M&5 = M&9第三层住：823.3M710 = Mj.07 = 811 = Mug = M912 = Ml29 =45.1KNm第二层住：33 M1013 = M3io = Mun = M1411 = M12is = M1512 = 38 X=-62.7KN m底层柱：反弯点在柱2/3高处1464.5M6 = Mi4i7 = Mi5i8 = X = 73KN m1462 X 4.5M1613 = Mi7i4 = M1815 = 3 X g = 46KN m3 计算梁的弯矩 取出结点为隔离体4 MttM i厂、MP厂、MoolA?zOMMlC

25、7 厂1：Mie：-Mr2磺厂、14M*c*s4 KU明照点说按结M12 = -M14 = 9.9KN m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 .687分配。结点2：结点3：结点4:M32 = M36 = 9.9KN m乂“： = 0结点8：丹8 = 0乂 M2 = 0M21 + M23 = -M25 = 9.9KN mM2l = 9.9 X 0.313 = 3.24KN mM23 = 9.9 X 0.687 = 6.66KN m乂 “4 = 0M45 = - (M41 + M47 丿=9.9 + 27.5 = 37.4KN m结点5：M5 = 0M54 + M56 =

26、 - (M52 + M58 丿=27.5 + 9.9= 37.4KN mM54 = 37.4 X 0.313 = 12.25KN - mM56 = 37.4 X 0.687 = 25.15KN -in结点6：M6 = 0 M6S = 一 (M63 + “69 丿=9.9 + 27.5 = 37.4KN m结点7：M78 = 一(M74 + M710)= 45.1 + 27.5 = 72.6KN mM89 + M87 = M8S + M811 = 27.5 + 45.1 = 72.6KN mMQ7 = 72.6 X 0.313 = 23.78KN m“89 = 72.6 X 0.687 = 48

27、.82KN m结点9：2M9 = 0“98 = -(M36 + Af912 ； = 45.1 + 27.5KNm=72.6kNm结点10：Mio = 0M1011 = -(M107 + M1013) = 45.1 + 62.7=107.8KNm结点11：工 Mu = 0 M1110 + M1112 = -(Mug + Mum) = 62.7 + 45.1=107.8KN mMlll0 = 117.6 X 0.313 = 3531KN mM1112 = 117.6 X 0.687 = 72.49KN m 结点12：M2 = 0 M12h = (M29 + M2i5)= 45.1 + 62.7=l

28、Q7.8KNm结点13：工 M3 = 0M1314 = -(M1310 + M1316) = 62.7 + 73 = 135.7KN m结点14：Mu = 0 Mm3 + Muis = (Mun + Mui?) = 62.7 + 73=135.7KN mM1413 = 135.7 X 0.313 = 44.45KN mM1415 = 135.7 X 0.687 = 91.25KN m 结点15：M5 = 0 M5i4 = (M5i2 + 911518)= 62.7 + 73 = 135.7KN m最终弯矩图：侧移的计算根据课本265页公式人3= 皐算得每一层和对于下一层的侧移。0108mmAs

29、=x 50505.1 X318 18 + 32卜 4= Tn= 0299mm50505.1 X 318 + 32 X 2A3= ry= 0.431mm蒜 x 50505.1 x 318 + 32x3A2= -5= 0 743mm芳 x 50505.1 x 318 + 32 X 4Ax= = 1.514mm总 X 54225.9 X3则第i层的侧移为丫也第五层侧移:3.095mm第四层侧移:2.987mm第三层侧移:2.688mm第二层侧移:2.257mm笫一层侧移:1.514mm电算uunmnuiIS67uiuunnuiuunmuiu1649uunmnui1015uumiimn111 竖直荷栽

30、 结点,1,0,0结点20,4.5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,167.5,11.1结点,17,7.5,14.4结点,1&7.5J7.7单元,1,2,1,单九231,1单元,3,4,1,1,1,1,1,1单元,4,5,1,1,1,1,1,1 单尤 5,6,1,1 单元,6,7,1,1,1,1,1,1 单元,7,

31、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 单丿匚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,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,

32、1,1 单元,9,16, 单元,10,15,1,1,1,1,1,1 单元,11,11 结点支承,160,0,0,0 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,14,9680000,244016.7,0,0,-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,2,5,8000000,166666.7,0,0,4 单元材料性质,740,8000000,166666.7,0,0,-1 单元材料性质,13,16,8000000,166666.7,

33、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 单元荷栽,17,3,5,0,1,-90 单元荷我,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 单元荷我,22,3,5.75,0,1,90 单元荷戦,23,3

34、,5.75,0,1,90 单元荷執24,3,5.75,0,1,90单元荷载,2535.75,0190內力计篇用端内力值（乗子=1）单元码杆漏1杆端2轴力剪力弯逅轴力剪力弯矩1-4. 2770165-1.371590182. 13343091-64.2770165-1.37159018-4 038724892-51.3272264-3. 060641925.31307434-51.3272264-3.06064192-4 787043993-38. 1662293-3. 063291295. 09344768-381662293-3. 06329129-5.015413584-24. 87255

35、66-2.9孑2245565,13692171-24.8725566-2.972245567 671488635-11 4596506-4.249156085.81790386T1.4596506-4.24915608-6.204311226-4 2491560811 4596506-6 20431122-4 24915608-11 0403493-7 260883477-18. 3539 口92.09885278-3.03030606-16.35397392.080652793.062906118-38. 52787741.44611293-2.36148096-38.52787741.44

36、6112932.410691729-59. 16493251.53979039-2.67947053-69.16493251.539790392.4018377710-60. 12478921 6139369272594911-B0. 12478921 613936922 6000427311-101.7701610.72592971-2 20295122-101. 7701610. 725929711.0637324812-43.952821?0. 64566047-1 96780775-43 务 282170. 6456604?1 9476643613-35. 42298431.44670

37、500-2 26034795-35.42298431.446705002.5137785414-26. 41883801.52350090-2.37062776-26.41883801 523500902. 6569252015-17.22456591.52613262-2.51028722-17.22456591.526132622 5259504416-7.686375482. 16030331-3. 13929906-7. 686375482.160303313.9897018517-2.16030531-7. 686375483 98970185-2.160303317.3136245

38、23 43057541181.2769105313.4129060-10.4893924L27691053-12. 4620939-6.3500652719-0.0910457313.29 茜 726-10.152需5Z-0.09104573-12.5813273-9.54955819200.0026493713.1609971-9.880491670.00264937-12. 7140028-6.87475452211.6890517412.9497900-9 351 79923L 68905174-12. 9252099-9 29649384220.634170687.71180957-2.925678200.63417068-9.53819043-5 66524949230.002631 728. 05572784-3 459395940.00263172-9.19427216-5.1