結(jié)構(gòu)力學(xué)課程大作業(yè)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(jiǎn)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(jiǎn)圖和基本數(shù)據(jù)1.計(jì)算簡(jiǎn)圖：如圖1所示。L2.基本計(jì)算參數(shù)材料彈性模量：E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550×550500×500250×450250×500抗彎剛度244016.7166666.76075083333.3抗拉剛度9680000800000036000004000000荷載列表豎向荷載gg水平荷載FF3.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(jiǎn)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：qq1.第五層計(jì)算計(jì)算簡(jiǎn)圖線剛度：iii分配系數(shù)：結(jié)點(diǎn)1：μμ結(jié)點(diǎn)2：μμμ結(jié)點(diǎn)3：μμ固端彎矩：MM彎矩分配計(jì)算：2.第四層計(jì)算計(jì)算簡(jiǎn)圖線剛度：iii分配系數(shù)：結(jié)點(diǎn)4：μμ結(jié)點(diǎn)5：μμμ結(jié)點(diǎn)6：μ6-3μ固端彎矩：MM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(jiǎn)圖線剛度：iii分配系數(shù)： 結(jié)點(diǎn)7：μμ結(jié)點(diǎn)8：μμμ結(jié)點(diǎn)9：μμ固端彎矩：MM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(jiǎn)圖線剛度：iii分配系數(shù)：結(jié)點(diǎn)10：μμ結(jié)點(diǎn)11：μμμ結(jié)點(diǎn)12：μμ固端彎矩：MM彎矩分配計(jì)算：5.底層的計(jì)算計(jì)算簡(jiǎn)圖線剛度：iiii分配系數(shù)： 結(jié)點(diǎn)13：μμμ結(jié)點(diǎn)14：μμμμ結(jié)點(diǎn)15：μμμ固端彎矩：MM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(jiǎn)圖線剛度：底層以上柱=底層柱=邊梁=中間梁=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)Sμμμμ11.000+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=8.4820.0000.4410.4410.11852×3.741+1.000+2.058=10.540.0950.3550.3550.19562×3.741+2.058=9.540.2160.3980.3980.00072×3.741+1.000=8.4820.0000.4410.4410．11882×3.741+1.000+2.058=10.540.0950.3550.3550．19592×3.741+2.058=9.540.2160.3920.3920.000102×3.741+1.000=8.4820.0000.4410.4410.118112×3.741+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M8．44N?m3.75KN?m9.7KN?m4.31KN?m分配與最終彎矩：彎矩圖:反彎點(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：F第四層柱：F第三層?。篎第二層柱：F底層柱：F2.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：M第四層柱：M第三層?。篗第二層?。籑底層柱：反彎點(diǎn)在柱2/3高處MM3.計(jì)算梁的彎矩取出結(jié)點(diǎn)為隔離體說明：邊梁與中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：M結(jié)點(diǎn)2：MMM結(jié)點(diǎn)3：M結(jié)點(diǎn)4:M結(jié)點(diǎn)5：MMM結(jié)點(diǎn)6：M結(jié)點(diǎn)7：M結(jié)點(diǎn)8：MMM結(jié)點(diǎn)9：M結(jié)點(diǎn)10：M結(jié)點(diǎn)11：MMM結(jié)點(diǎn)12：M結(jié)點(diǎn)13：M結(jié)點(diǎn)14：MMM結(jié)點(diǎn)15：M最終彎矩圖：側(cè)移的計(jì)算根據(jù)課本265頁公式?3?????則第i層的側(cè)移為1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),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,15,16,1,1,1,1,1,1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),2,5,8000000,166666.7,0,0,-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),22,25,4000000,83333.3,0,0,-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),7,4.5,17.7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,9,10,1,1,1,1,1,1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),2,5,8000000,166666.7,0,0,-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),22,25,4000000,83333.3,0,0,-1結(jié)點(diǎn)荷載,6,1,18,0結(jié)點(diǎn)荷載,5,1,32,0結(jié)點(diǎn)荷載,4,1,32,0結(jié)點(diǎn)荷載,3,1,32,0結(jié)點(diǎn)荷載,2,1,32,0 彎矩圖位移圖誤差分析1.分層法：在第二跨柱子的彎矩與電算的結(jié)果相差最大，再次就是梁的彎矩。分層法是采用的力矩分配法，力矩分配法只適用于無線位移的結(jié)構(gòu)，在這里忽略了線位移，這是誤差的來源之一。另外對(duì)于多節(jié)點(diǎn)的力矩分配法也只是近似的，需要迭代無數(shù)次才能夠逼近原結(jié)構(gòu)，分層法對(duì)于底層以上的柱的剛度取0.9倍，傳遞系數(shù)取