結(jié)構(gòu)力學(xué)位移法習(xí)題

11位移法11.1位移法的基本概念11.2等截面直桿的形常數(shù)和載常數(shù)11.3位移法的基本未知量和基本體系11.4位移法方程11.5位移法計(jì)算連續(xù)梁和無側(cè)移剛架11.6位移法計(jì)算有側(cè)移剛架和排架11.7位移法計(jì)算對(duì)稱結(jié)構(gòu)*11.8支座移動(dòng)和溫度改變時(shí)的計(jì)算*11.9用直接平衡法建立位移法方程小結(jié)一、形常數(shù)與載常數(shù)表（轉(zhuǎn)角位移方程）二、直接平衡法與基本體系法步驟（1）取位移法基本體系（2）列位移法方程（3）求系數(shù)和自由項(xiàng)（4）解方程（組）（5）疊加作彎矩圖（1）取基本未知量（2）列桿端彎矩計(jì)算式（3）建立位移法基本方程（4）解方程（組）（5）算桿端彎矩作彎矩圖三、對(duì)稱性應(yīng)用----取半邊結(jié)構(gòu)四、支座移動(dòng)和溫度變化----廣義固端彎矩五、最少基本未知量與基本結(jié)構(gòu)最少基本未知量1、去除靜定部分2、對(duì)稱性應(yīng)用3、三類基本桿件4、較多載常數(shù)類型六、位移法中求結(jié)構(gòu)位移1、結(jié)點(diǎn)位移2、由內(nèi)力圖求一般點(diǎn)的位移例：1、求結(jié)點(diǎn)C轉(zhuǎn)角2、結(jié)點(diǎn)C、D相對(duì)轉(zhuǎn)角3、求點(diǎn)E豎向位移4、求CD中點(diǎn)豎向位移力法譜、位翁移法踏對(duì)比力痰法基判本來未夜知瓜量：多犧余約擔(dān)束力基本斯結(jié)構(gòu)：仰一素般浴為也靜麗定獸結(jié)圣構(gòu)偏。作奔單聚位徐和碼外些因莊內(nèi)我力尤圖由伸內(nèi)制力浸圖物自酬乘州、鑄互拼乘場(chǎng)求騰系裝數(shù)怎，舍主瞇系兄?jǐn)?shù)察恒途正孤。建立崖力法繁方程味（協(xié)萍調(diào)）位楚移珠法基本丸未知撤量：轉(zhuǎn)結(jié)譽(yù)點(diǎn)跪獨(dú)蛛立衛(wèi)位中移基槳本辯結(jié)雪構(gòu)：?jiǎn)胃缌赫Z系作單督位和繪外因召內(nèi)力憤圖由內(nèi)屠力圖胞的結(jié)趕點(diǎn)或止隔離廳體平晴衡求雄系數(shù)完，主例系數(shù)批恒正蜘。建立咐位移妻法方糠程（筒平衡碎）解笛方勺程墊求凝多肚余擦未索知吩力迭加扯作內(nèi)盲力圖用變售形條羨件進(jìn)冶行校支核解方丑程求哥獨(dú)立賓結(jié)點(diǎn)拋位移迭屋加宅作贈(zèng)內(nèi)產(chǎn)力壺圖用平俱衡條鎖件進(jìn)旬行校罩核不普能施解罵靜輛定采結(jié)撇構(gòu)可陣以攜解夜靜拾定厭結(jié)豆構(gòu)課外纖作業(yè)P3峰4－P魂3善8第一體次1競(jìng)1思.務(wù)9（晨求吉解身畫M圖頭）、11榜.1邪1第二膝次1怒1吵.健1芒4、1蔥1搖.同1豬6第三懇次11腔.2賭3、11悠.2繞4第柳四軍次11倍.2鐘6、11旗.2卡81頌1菊.割9用位濁移法作口彎劍矩更圖犬。M1解杯：一、定取位曠移法蛛基本陡體系二犁、遲列百位鄙移密法蜻基浴本謎方宅程位盼移亮法芝基尿本悼體塑系qDllABCqll/2l/2iii三念、機(jī)計(jì)越算靜系蛋數(shù)k11和至自蹈由殖項(xiàng)F1P1DABC1=12i4i4i2i3iEk11k11DABCF1PEF1PMPiiiDABCqlq五、可作M圖四、釣解方識(shí)程得DABCMql2/(528)(×)841720(66)643410(132)9011侄.1日0畫膛出魔下齊列奮結(jié)魯構(gòu)虛的拾基貌本紐奉體慕系孫，仿并稈畫淘出緣瑞基臺(tái)本芽結(jié)黎構(gòu)絞的償單沸位顆彎拳矩赴圖分和填荷踩載立彎廁矩互圖喬。位堅(jiān)移涉法贊基劉本膚體獻(xiàn)系1解據(jù)：一縫、帶取稅位兵移合法紋基碧本問體脾系i=E/l二、茅列位德移法饑基本涉方程三、匙計(jì)算旬系數(shù)k11和自歲由項(xiàng)F1袋PDABClI＝1llEI＝1I＝2I＝4l/2DABCiEi2i8iM11=1k11DABC2iE24i2i4i2iMPF1PDABCE1肯1倒.潑1場(chǎng)1畫出咳下列栽結(jié)構(gòu)都的基稅本體角系，潑并畫危出基還本結(jié)銜構(gòu)的謝單位煙彎矩診圖和屢荷載宵彎矩加圖。DABC4mEI4m4m2.5kN/mP=10kNEIEIDABC2.薄5k行N/極mP=1晴0k廣Niii位移屋法基篇本體蒜系1解侮：一杜、材取銀位嚼移惜法淡基長(zhǎng)本財(cái)體萬系i=E太I(xiàn)/乖4二堅(jiān)、詢列險(xiǎn)位屋移殼法刑基勿本賠方猛程三只、然計(jì)網(wǎng)算戲系分?jǐn)?shù)k1鑒1和自重由項(xiàng)F1役PDABCM11=12i4i3ik115MP40(kN·m)DABCF1P1狼1熱.揭1馬4用位擇移法哪作連收續(xù)梁維及無吸側(cè)移鹿剛架熟的M圖。E測(cè)I＝臺(tái)常議數(shù)尋。DABC3m6m10kN/m10kN3m2m50kN位移法基本體系12DABC10kN/m10kN50kNiik111=1DABCk212i4i3iM1k22k122=1DABC2i4iM2解法1：一、排取位勿移法授基本叨體系i=E勞I/6三、堅(jiān)計(jì)算全系數(shù)懷和自攪由項(xiàng)二前、查列易位臭移無法旨基烈本蹈方杠程37.537.5F2PF1PDABC2045MP(kN·m)五摔、柿作M圖四起、聾解槍方生程得DABC2045.63M(kN·m)(75)(45)21.6942.19DABC3m6m10kN/m10kN3m2m50kN位村移停法仁基壇本拳體商系1ABC10kN/m50kNii10kN10kNm1=1ABCk113i3iM1解測(cè)法2：一、槍撤除夜靜定離外伸抬段，肅取位免移法份基本另體系i=EI/辭6三滑、津計(jì)利算姻系葛數(shù)塊和想自深由始項(xiàng)二、惡列位攏移法關(guān)基本殼方程46.25F1PABC2045MP(kN·m)五、夜作M圖四囑、驗(yàn)解掛方吳程得DABC2045.63M(kN·m)(75)(45)21.6942.1911莊.1談6用滾位廊移寶法貢作包連陡續(xù)捐梁道及量無她側(cè)晃移死剛忽架歡的M圖腰。E榨I＝常醉數(shù)。D15m15m20m2.4kN/mCABED2.4kN/mCABE位移暈法基圓本體飽系12iii0.75iDCABE1=1k11k212i4i3i1.5iM1DCABE2＝1k22k123i1.5i3i2i4iM2解：一磨、夢(mèng)取糖位贏移啞法稠基謝本獻(xiàn)體肚系i=EI/冠1艷5三編、言計(jì)巧算屆系響數(shù)案和欺自曬由槳項(xiàng)二慕、首列周位脫移插法奔基蝴本州方杏程DCABE80MP(kN兵·m)80F2PF1P五劇、尊作M圖四、林解方汽程組得DCABEM(kN·m)54.3227.1640.1530.1120.0870.26(120)57.711刮1鉤.劉2快1用真位衡移賠法派作扮圖冶示爭(zhēng)剛針架受的M圖營(yíng)。D4m4m6mCABE8kNEI＝常數(shù)DCABE8kN12位手移啟法棟基藏本允體扇系解睡：一、恭取位訊移法經(jīng)基本宴體系i=EI/4三脾、流計(jì)負(fù)算趙系紫數(shù)士和榮自背由集項(xiàng)二、臺(tái)列位郵移法永基本池方程2i/3iiiDCABE1＝1k11k21M13i2i2i4iCk112i4i3iDCk21k12DCk22k222＝1DCABEM23i/46i/43i/46i/4Ck126i/43i/4CF1PDCF2P8kNDCABEF1PF2PMP8kN五王、書作M圖四、粒解方并程組得DCABEM7.538.785.6510.041.25(kN·m)1劇1憲.慕2沒3用頭位糊移習(xí)法臟計(jì)往算艇圖開示睛排筒架釣和護(hù)剛慰架舟，泡作M、Q和N圖吐。12m6mABCDABCD1位左移廉法饅基姑本候體括系解誼：一稻、阻取幟位殊移掩法撞基基本態(tài)體痛系i=EI/鍛6三來、慢計(jì)言算朗系謹(jǐn)數(shù)歲和頁自沾由稼項(xiàng)二、妙列位跨移法煎基本揉方程CDk11ABCDk111＝13i/63i/6M19郵0CDF1PABCDF1PMP(kN·m)五、耽作M圖四姥、站解答方陰程得ABCD225135(kN·m)(90)22.5ABCD22.5六、芳作Q、N圖22.5CABD97.522.511違.2海4用智位護(hù)移席法肯計(jì)須算朝圖逃示浸排時(shí)架懸和溪?jiǎng)偲＜苡?jì)，映作M、Q和N圖測(cè)。解：一、灘取位裁移法氣基本似體系三、鄭計(jì)算篇系數(shù)典和自截由項(xiàng)二、投列位隱移法畝基本島方程位移釣法基亞本體甚系2m4mDCABi=640kN/m2mi=4i=3DCABi=640kN/mi=4i=312k11k211＝1Ck111816DCk21816M1DCAB18k12k222＝1Ck126DCAB6M29/46DCk22四、鵲解方內(nèi)程組F1PF2PMP(k盞Nm)DCAB8皇0101包0CF1P8010DCF2P得七、驗(yàn)校核五州、抖作M圖六、作Q、N圖816M1DCAB18MP(kNm)DCAB801010DCAB6M29/46N(kN)DCAB76.355.0283.65M(kNm)DCAB34.5014.5914.5820.09(20)(80)72.714.54Q(kN)DCAB14.9876.355.0283.655.021森1鳥.大2流6利用信對(duì)稱級(jí)性，猾作圖茄示結(jié)造構(gòu)M圖。6呈m6島m6m4秀m2踏0務(wù)k顯N熊/籠mABCDEFG6m1解：一、氧取半瓜邊結(jié)渣構(gòu)和穿位移柱法基座本體楚系。i=EI/6二、然列位呀移法扁基本寬方程6m6m20kN/mACDE4mii1.5iACDEM14i1=13ik116i2i三、吵計(jì)算加系數(shù)睜和自酒由項(xiàng)ACDE6060F1P360MP(kN·m)半鳴邊盲結(jié)們構(gòu)府和位移聰法基按本體英系五、糾作M圖得ABCDEFG180360(9090)18090(kN·m)四瀉、業(yè)解抵方峰程11陰.2姻8利用淡對(duì)稱罷性，踩作圖暮示結(jié)詳構(gòu)M、Q和N圖。4m4mii4i4iD4m4m6mCABEIF40kN/mIII3I3I3mCAE40kN/m解紫：一橋、燒取鴿半槍邊捎結(jié)彩構(gòu)貧和求位較移掠法園基行本容體炎系消。i=E項(xiàng)I/蟻4二、幸列位學(xué)移法灰基本抖方程三至、貫計(jì)戲算疾系葬數(shù)剛和腦自摔由券項(xiàng)半咸邊攏結(jié)普構(gòu)滔和位移很法基忍本體縮慧系1=1k11k21M14i2i4i2=1k12k22M24i2i4i2i4i12五廢、刑作M圖四、多解方役程組得六降、梯作Q、N圖57.395.22DCABE57.3920.8720.8710.4310.435.22(180)122.61F10.43(kN·m)1迫9愧.此5值7DCABE1203.9119.57F(kN)1203.91DCABEF23.48(kN)12012019.57F1PF2P12060MP(kN·m)2灘0槳1拴1年專王升本頑試卷、三慘、12、試位用位涉移法肯計(jì)算原圖示撿連續(xù)益梁，幸并繪補(bǔ)制彎脖矩圖密和剪諸力圖畏。E彼I＝返常舊數(shù)沈。3m6m3mABC10kN/m60kN位戒移介法釀基薯本敵體理系1解：一、贈(zèng)取位襪移法薦基本豆體系i=EI/蓄6三估、閱計(jì)燈算壘系口數(shù)續(xù)和晌自辱由蕉項(xiàng)二、場(chǎng)列位臘移法尾基本銜方程五謀、忌作M圖四答、繭解撐方染程得ABC10kN/m60kNii1=1k114i3iM1ABC2i45F1P45MP(kN·m)ABC45六犬、包作Q圖22.5Q(kN)37.5ABC303022.5M(kN·m)(45)45(90)45ABC45ABC6m6m20kNq=10kN/m2殘0刺0吊9年專杜升本可試卷長(zhǎng)、三薪、1乒2、用秀位移罵法求掠解圖倉示超分靜定殿結(jié)構(gòu)赤，并源繪結(jié)嚇構(gòu)的睬彎矩窮圖。欣（EI為常背數(shù)）r11Z1=13iM12i4i解：一免、喇取勻位串移劉法橫基徐本雪體母系i=EI/也6三娘、剛計(jì)示算病系賣數(shù)r11和烘自杯由翠項(xiàng)R1P二扯、負(fù)列礦位緩移末法欄基唉本雹方繁程Cr11CR1P位移法基本體系20kNABCq=10kN/mZ1ii30MP2i30R1P(kN·m)12.9M

38.6(kN·m)12.9(45)19.3五份、荷作M圖四密、狡解賭方斗程得20鑒08年專升內(nèi)本試站卷爹、役三周、12、用自位移嫌法求塘解圖鳴示超科靜定攔結(jié)構(gòu)佩，列臂出位傍移法柱基本喉方程膝，求婆出方島程的逃系數(shù)拴和自兵由項(xiàng)診（不鐵必求潔方程惠）。柿（各進(jìn)桿E哈I為常勝數(shù)）D6m6m6mq=10kN/mGABEDiq=10kN/mGABEZ2Z1基本體系iiiGr11r11Z1=1M12i4ir214i2iZ2=1r12M22ir224i2i4i3iEr21Gr12Er22解否：一、爭(zhēng)取位迷移法寄基本絨體系i=EI/員6三、語計(jì)算冤系數(shù)稿和自婦由項(xiàng)二、枯列位揮移法某基本山方程ER2PGR1P30MP30R1PR2P(kN·m)四、蘆解方衫程組20許07年專制升劇本試迷卷吧、棄三嶼、1板2、膀?qū)€圖炸示價(jià)超爸靜從定辛結(jié)軍構(gòu)覆，籮先賭進(jìn)債行慮對(duì)蠅稱朗簡(jiǎn)脂化嶺，尿再