結(jié)構(gòu)力學(xué)大作業(yè)————多層多跨框架結(jié)構(gòu)內(nèi)力及位移計(jì)算

1、結(jié)構(gòu)力學(xué)課程大作業(yè)多層多跨框架結(jié)構(gòu)內(nèi)力及位移計(jì)算姓名：班級(jí)：學(xué)號(hào)：華中科技大學(xué)土木工程與力學(xué)學(xué)院2016年11月19日目錄任務(wù)3計(jì)算簡圖和基本數(shù)據(jù)3用分層法計(jì)算豎直荷載4二次力矩分配法計(jì)算豎直彎矩13反彎點(diǎn)法計(jì)算水平荷載16側(cè)移的計(jì)算21電算22誤差分析及心得30任務(wù)1.求解多層多跨框架結(jié)構(gòu)在豎向荷載作用下的彎矩以及水平荷載作用下的彎矩和各層的側(cè)移。2.計(jì)算方法： （1）用近似法計(jì)算：水平荷載作用用反彎點(diǎn)法計(jì)算，豎向荷載作用采用分層法和二次力矩分配法計(jì)算。 （2）用電算（結(jié)構(gòu)力學(xué)求解器）進(jìn)行復(fù)算。3. 就最大相對(duì)誤差處，說明近似法產(chǎn)生誤差的來源。4. 將手算結(jié)果寫成計(jì)算書形式。計(jì)算簡圖和基本數(shù)

2、據(jù)1. 計(jì)算簡圖：如圖1所示。L1=4.5m L2=3.0m H1=4.5m H2=3.3m2. 基本計(jì)算參數(shù)材料彈性模量：Eh=3.2×107KN/m2桿件尺寸及抗彎剛度抗拉剛度表底層柱其他層柱邊梁中間梁尺寸 b×h(mm2)550×550500×500250×450250×500抗彎剛度 EI(KNm2)244016.7166666.76075083333.3抗拉剛度 EA(KN)9680000800000036000004000000荷載列表豎向荷載g1=23KN/m2g2=20KN/m2水平荷載Fp1=32KNFp2=18KN

3、3. 荷載分組：（1）計(jì)算水平荷載（見圖2）；（2）計(jì)算豎向恒載（見圖3）；圖1 計(jì)算簡圖 圖2 水平荷載作用圖3 豎向荷載作用 用分層法計(jì)算豎直荷載按照書上的方法，將結(jié)構(gòu)分成5層，分別用力矩分配法來計(jì)算，然后疊加。其中底層以上的柱子剛度要乘折減系數(shù)0.9，傳遞系數(shù)取1/3，低層柱剛度不需要折減，傳遞系數(shù)去1/2。荷載：q1=g1×b=20×0.25=5KN/m q2=g2×b=23×0.25=5.75KN/m1.第五層計(jì)算計(jì)算簡圖線剛度：i1-4=i2-5=i3-6=166666.73.3=50505.1KNmi1-2=607504.5=13500KN

4、mi2-3=83333.33.0=27777.8KNm分配系數(shù)：結(jié)點(diǎn)1：1-2=4×135004×0.9×50505.1+13500=0.2291-4=4×0.9×50505.14×0.9×50505.1+13500=0.771結(jié)點(diǎn)2：2-1=4×135004×0.9×50505.1+13500+27777.8=0.1562-5=4×0.9×50505.14×0.9×50505.1+13500+27777.8=0.5242-3=4×27777.8

5、4×0.9×50505.1+13500+27777.8=0.320結(jié)點(diǎn)3：3-2=4×27777.84×0.9×50505.1+27777.8=0.3793-6=4×0.9×50505.14×0.9×50505.1+27777.8=0.621固端彎矩：M1-2F=-M2-1F=-112×5×4.52=-8.436KNmM2-3F=-M3-2F=-112×5×32=-3.750KN彎矩分配計(jì)算：2.第四層計(jì)算計(jì)算簡圖線剛度：i1-4=i2-5=i3-6=i4-7=i5

6、-8=i6-9=166666.73.3=50505.1KNmi4-5=607504.5=13500KNmi5-6=83333.33.0=27777.8KNm分配系數(shù)：結(jié)點(diǎn)4：4-1=4-7=4×0.9×50505.14×0.9×50505.1×2+13500=0.4354-5=4×12656.34×0.9×46296.3×2+12656.3=0.13結(jié)點(diǎn)5：5-2=5-8=4×0.9×50505.14×0.9×50505.1×2+13500+27777.8

7、=0.3445-4=4×135004×0.9×50505.1×2+13500+27777.8=0.1025-6=4×27777.84×0.9×50505.1×2+13500+27777.8=0.21結(jié)點(diǎn)6：6-3=6-9=4×0.9×50505.14×0.9×50505.1×2+27777.8=0.3836-5=4×27777.84×0.9×50505.1×2+27777.8=0.234固端彎矩：M4-5F=-M5-4F=-1

8、12×5.75×4.52=-9.703KNmM5-6F=-M6-5F=-112×5.75×3.02=-4.313KNm彎矩分配計(jì)算：3.第三層計(jì)算：第三層與第四層除了結(jié)點(diǎn)編號(hào)改變其它相同。計(jì)算簡圖線剛度：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分配系數(shù)：結(jié)點(diǎn)7：7-4=7-10=4×0.9×50505.14×0.9×50505.1×2+135

9、00=0.4357-8=4×135004×0.9×50505.1×2+13500=0.13結(jié)點(diǎn)8：8-5=8-11=4×0.94×50505.14×0.9×50505.1×2+13500+27777.8=0.3448-7=4×135004×0.9×50505.1×2+13500+27777.8=0.1028-9=4×27777.84×0.9×50505.1×2+13500+27777.8=0.21結(jié)點(diǎn)9：9-6=9-12=4&

10、#215;0.9×50505.14×0.9×50505.1×2+27777.8=0.3839-8=4×27777.84×0.9×50505.1×2+27777.8=0.234固端彎矩：M7-8F=-M8-7F=-112×5.75×4.52=-9.703KNmM8-9F=-M9-8F=-112×5.75×3.02=-4.313KNm彎矩分配計(jì)算：4.第二層計(jì)算第二層計(jì)算也與第四層相同。計(jì)算簡圖線剛度：i7-10=i8-11=i9-12=i10-13=i11-14=i12-15=

11、166666.73.3=50505.1KNmi10-11=607504.5=13500KNmi11-12=83333.33.0=27777.8KNm分配系數(shù)：結(jié)點(diǎn)10：10-7=10-13=4×0.9×50505.14×0.9×50505.1×2+13500=0.43510-11=4×135004×0.9×50505.1×2+13500=0.13結(jié)點(diǎn)11：11-8=11-14=4×0.9×50505.14×0.9×50505.1×2+13500+27777

12、.8=0.34411-10=4×135004×0.9×50505.1×2+13500+27777.8=0.10211-12=4×27777.84×0.9×50505.1×2+13500+27777.8=0.21結(jié)點(diǎn)12：12-9=12-15=4×0.9×50505.14×0.9×50505.1×2+27777.8=0.38312-11=4×27777.84×0.9×50505.1×2+27777.8=0.234固端彎矩：M10

13、-11F=-M10-11F=-112×5.75×4.52=-9.703KNmM11-12F=-M12-11F=-112×5.75×3.02=-4.313KNm彎矩分配計(jì)算： 5.底層的計(jì)算計(jì)算簡圖線剛度：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分配系數(shù)：結(jié)點(diǎn)13：13-10=4×0.9×50505.14

14、×0.9×50505.1+54225.9+13500=0.40213-16=4×54225.94×0.9×50505.1+54225.9+13500=0.47913-14=4×135004×0.9×50505.1+54225.9+13500=0.119結(jié)點(diǎn)14：14-13=4×135004×0.9×50505.1+13500+27777.8+54225.9=0.09614-11=4×0.9×50505.14×0.9×50505.1+13500+2

15、7777.8+54225.9=0.32214-15=4×27777.84×0.9×50505.1+13500+27777.8+54225.9=0.19714-17=4×54225.94×0.9×50505.1+13500+27777.8+54225.9=0.385結(jié)點(diǎn)15：15-14=4×27777.84×0.9×50505.1+54225.9+27777.8=0.21815-12=4×0.9×50505.14×0.9×50505.1+54225.9+27777.8

16、=0.35715-18=4×54225.94×0.9×50505.1+54225.9+27777.8=0.425固端彎矩：M13-14F=-M14-13F=-112×5.75×4.52=-9.703KNmM14-15F=-M15-14F=-112×5.75×3.02=-4.313KNm彎矩分配計(jì)算：柱子桿端彎矩疊加 桿端最終彎矩彎矩圖二次力矩分配法計(jì)算豎直彎矩計(jì)算簡圖線剛度：底層以上柱=16666.73.3=50505.1KNm底層柱=244016.74.5=54225.9KNm邊梁=607504.5=13500KNm中間梁

17、=83333.33.0=27777.8KNm計(jì)算相對(duì)轉(zhuǎn)動(dòng)剛度：構(gòu)件名稱轉(zhuǎn)動(dòng)剛度S相對(duì)轉(zhuǎn)動(dòng)剛度S框架梁邊跨4i=540001.000中跨4i=111111.22.058框架柱底層4i=216903.64.017其他層4i=202020.43.741計(jì)算分配系數(shù)：結(jié)點(diǎn)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=5.7990.3550.0000.6450.00042×3.741+1.000=8.4820.0000.4410.44

18、10.11852×3.741+1.000+2.058=10.540.0950.3550.3550.19562×3.741+2.058=9.540.2160.3980.3980.00072×3.741+1.000=8.4820.0000.4410.441011882×3.741+1.000+2.058=10.540.0950.3550.355019592×3.741+2.058=9.540.2160.3920.3920.000102×3.741+1.000=8.4820.0000.4410.4410.118112×3.741+

19、1.000+2.058=10.540.0950.3550.3550.195122×3.741+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 荷載列表：固端彎矩頂層邊梁頂層中間梁其他層邊梁其他層中間梁MF 844Nm3.75 KNm 9.7KNm 4.31KNm 分配與最終彎矩：彎矩圖:反彎

20、點(diǎn)法計(jì)算水平荷載1.計(jì)算柱的剪力因?yàn)槊恳慌胖木€剛度都相等，每根柱的剪力相等。第五層柱：FQ14=FQ25=FQ36=183=6KN第四層柱：FQ47=FQ58=FQ69=18+323=503KN第三層住：FQ710=FQ811=FQ912=18+32+323=823KN第二層柱： FQ1013=FQ1114=FQ1215=18+32×33=38KN 底層柱：FQ1316=FQ1417=FQ1518=18+32×43=1463KN2.計(jì)算柱的彎矩 因?yàn)槊恳慌胖木€剛度都相等，每根柱的彎矩相等。第五層柱：M14=M41=M25=M52=M36=M63=6×3.32=

21、-9.9KNm第四層柱：M47=M74=M58=M85=M69=M96=503×3.32=-27.5KNm第三層?。篗710=M107=M811=M118=M912=M129=823×3.32=-45.1KNm第二層??；M1013=M1310=M1114=M1411=M1215=M1512=38×3.32=-62.7KNm底層柱：反彎點(diǎn)在柱2/3高處M1316=M1417=M1518=1463×4.53=-73KNmM1613=M1714=M1815=1463×2×4.53=-146KNm3.計(jì)算梁的彎矩取出結(jié)點(diǎn)為隔離體說明：邊梁與中

22、間梁線剛度不一樣所以邊梁按照0.313分配，中間梁按照0.687分配。結(jié)點(diǎn)1：M1=0 M12=-M14=9.9KNm結(jié)點(diǎn)2：M2=0 M21+M23=-M25=9.9KNm M21=9.9×0.313=3.24KNm M23=9.9×0.687=6.66KNm結(jié)點(diǎn)3：M3=0 M32=-M36=9.9KNm結(jié)點(diǎn)4:M4=0 M45=-（M41+M47）=9.9+27.5=37.4KNm結(jié)點(diǎn)5：M5=0 M54+M56=-（M52+M58）=27.5+9.9=37.4KNm M54=37.4×0.313=12.25KNm M56=37.4×0.687=2

23、5.15KNm結(jié)點(diǎn)6：M6=0 M65=-（M63+M69）=9.9+27.5=37.4KNm結(jié)點(diǎn)7：M7=0 M78=-（M74+M710）=45.1+27.5=72.6KNm結(jié)點(diǎn)8：M8=0 M89+M87=M85+M811=27.5+45.1=72.6KNm M87=72.6×0.313=23.78KNm M89=72.6×0.687=48.82KNm結(jié)點(diǎn)9：M9=0 M98=-（M96+M912）=45.1+27.5KNm=72.6kNm結(jié)點(diǎn)10：M10=0 M1011=-(M107+M1013)=45.1+62.7=107.8KNm結(jié)點(diǎn)11：M11=0 M1110

24、+M1112=-(M118+M1114)=62.7+45.1 =107.8KNm M1110=117.6×0.313=35.31KNm M1112=117.6×0.687=72.49KNm結(jié)點(diǎn)12：M12=0 M1211=-(M129+M1215)=45.1+62.7=107.8KNm結(jié)點(diǎn)13：M13=0 M1314=-(M1310+M1316)=62.7+73=135.7KNm結(jié)點(diǎn)14：M14=0 M1413+M1415=-(M1411+M1417)=62.7+73=135.7KNm M1413=135.7×0.313=44.45KNm M1415=135.7&

25、#215;0.687=91.25KNm結(jié)點(diǎn)15：M15=0 M1514=-(M1512+M911518)=62.7+73=135.7KNm最終彎矩圖：側(cè)移的計(jì)算根據(jù)課本265頁公式3=Fp12h32i3i算得每一層相對(duì)于下一層的側(cè)移。5=18123.32×50505.1×3=0.108mm4=18+32123.32×50505.1×3=0.299mm3=18+32×2123.32×50505.1×3=0.431mm2=18+32×3123.32×50505.1×3=0.743mm1=18+32&

26、#215;4124.52×54225.9×3=1.514mm則第i層的側(cè)移為1ii第五層側(cè)移:3.095mm第四層側(cè)移:2.987mm第三層側(cè)移:2.688mm第二層側(cè)移:2.257mm第一層側(cè)移:1.514mm電算1.豎直荷載結(jié)點(diǎn),1,0,0結(jié)點(diǎn),2,0,4.5結(jié)點(diǎn),3,0,7.8結(jié)點(diǎn),4,0,11.1結(jié)點(diǎn),5,0,14.4結(jié)點(diǎn),6,0,17.7結(jié)點(diǎn),7,4.5,17.7結(jié)點(diǎn),8,4.5,14.4結(jié)點(diǎn),9,4.5,11.1結(jié)點(diǎn),10,4.5,7.8結(jié)點(diǎn),11,4.5,4.5結(jié)點(diǎn),12,4.5,0結(jié)點(diǎn),13,7.5,0結(jié)點(diǎn),14,7.5,4.5結(jié)點(diǎn),15,7.5,7.8結(jié)點(diǎn)

27、,16,7.5,11.1結(jié)點(diǎn),17,7.5,14.4結(jié)點(diǎn),18,7.5,17.7單元,1,2,1,1,1,1,1,1單元,2,3,1,1,1,1,1,1單元,3,4,1,1,1,1,1,1單元,4,5,1,1,1,1,1,1單元,5,6,1,1,1,1,1,1單元,6,7,1,1,1,1,1,1單元,7,8,1,1,1,1,1,1單元,8,9,1,1,1,1,1,1單元,9,10,1,1,1,1,1,1單元,10,11,1,1,1,1,1,1單元,11,12,1,1,1,1,1,1單元,13,14,1,1,1,1,1,1單元,14,15,1,1,1,1,1,1單元,15,16,1,1,1,1,

28、1,1單元,16,17,1,1,1,1,1,1單元,17,18,1,1,1,1,1,1單元,18,7,1,1,1,1,1,1單元,5,8,1,1,1,1,1,1單元,4,9,1,1,1,1,1,1單元,3,10,1,1,1,1,1,1單元,2,11,1,1,1,1,1,1單元,8,17,1,1,1,1,1,1單元,9,16,1,1,1,1,1,1單元,10,15,1,1,1,1,1,1單元,11,14,1,1,1,1,1,1結(jié)點(diǎn)支承,1,6,0,0,0,0結(jié)點(diǎn)支承,12,6,0,0,0,0結(jié)點(diǎn)支承,13,6,0,0,0,0單元材料性質(zhì),1,1,9680000,244016.7,0,0,-1單元

29、材料性質(zhì),11,11,9680000,244016.7,0,0,-1單元材料性質(zhì),12,12,9680000,244016.7,0,0,-1單元材料性質(zhì),2,5,8000000,166666.7,0,0,-1單元材料性質(zhì),7,10,8000000,166666.7,0,0,-1單元材料性質(zhì),13,16,8000000,166666.7,0,0,-1單元材料性質(zhì),6,6,3600000,60750,0,0,-1單元材料性質(zhì),17,17,4000000,83333.3,0,0,-1單元材料性質(zhì),18,21,3600000,60750,0,0,-1單元材料性質(zhì),22,25,4000000,83333

30、.3,0,0,-1單元荷載,6,3,5,0,1,90單元荷載,17,3,5,0,1,-90單元荷載,18,3,5.75,0,1,90單元荷載,19,3,5.75,0,1,90單元荷載,20,3,5.75,0,1,90單元荷載,21,3,5.75,0,1,90單元荷載,22,3,5.75,0,1,90單元荷載,23,3,5.75,0,1,90單元荷載,24,3,5.75,0,1,90單元荷載,25,3,5.75,0,1,90彎矩圖 位移圖2.水平荷載：結(jié)點(diǎn),1,0,0結(jié)點(diǎn),2,0,4.5結(jié)點(diǎn),3,0,7.8結(jié)點(diǎn),4,0,11.1結(jié)點(diǎn),5,0,14.4結(jié)點(diǎn),6,0,17.7結(jié)點(diǎn),7,4.5,17.

31、7結(jié)點(diǎn),8,4.5,14.4結(jié)點(diǎn),9,4.5,11.1結(jié)點(diǎn),10,4.5,7.8結(jié)點(diǎn),11,4.5,4.5結(jié)點(diǎn),12,4.5,0結(jié)點(diǎn),13,7.5,0結(jié)點(diǎn),14,7.5,4.5結(jié)點(diǎn),15,7.5,7.8結(jié)點(diǎn),16,7.5,11.1結(jié)點(diǎn),17,7.5,14.4結(jié)點(diǎn),18,7.5,17.7單元,1,2,1,1,1,1,1,1單元,2,3,1,1,1,1,1,1單元,3,4,1,1,1,1,1,1單元,4,5,1,1,1,1,1,1單元,5,6,1,1,1,1,1,1單元,6,7,1,1,1,1,1,1單元,7,8,1,1,1,1,1,1單元,8,9,1,1,1,1,1,1單元,9,10,1,1,1

32、,1,1,1單元,10,11,1,1,1,1,1,1單元,11,12,1,1,1,1,1,1單元,13,14,1,1,1,1,1,1單元,14,15,1,1,1,1,1,1單元,15,16,1,1,1,1,1,1單元,16,17,1,1,1,1,1,1單元,17,18,1,1,1,1,1,1單元,18,7,1,1,1,1,1,1單元,5,8,1,1,1,1,1,1單元,4,9,1,1,1,1,1,1單元,3,10,1,1,1,1,1,1單元,2,11,1,1,1,1,1,1單元,8,17,1,1,1,1,1,1單元,9,16,1,1,1,1,1,1單元,10,15,1,1,1,1,1,1單元,11,14,1,1,1,1,1,1結(jié)點(diǎn)支承,1,6,0,0,0,0結(jié)點(diǎn)支承,12,6,0,0,0,0結(jié)點(diǎn)支承,13,6,0,0,0,0單元材料性質(zhì),1,1,9680000,244016.7,0,0,-1單元材料性質(zhì),11,11,9680000,244016.7,0,0,-1單元材料性質(zhì),12,12,9680000,244016.7,0,0,-1單元材料性質(zhì),2,5,