材料力學(xué)的結(jié)構(gòu)穩(wěn)定性英文

CHAPTER10

STABILITYOFCOMPRESSEDCOLUMNS1CHAPTER10STABILIZATIONOF COMPRESSIVECOLUMNS§10–1CONCEPTSOFSTABILITYOFCOMPRESSEDCOLUMNS§10–2EULER’SFORMULAOFTHECRITICALFORCEOFSLENDERCOMPRESSEDCOLUMNS§10–3CRITICALSTRESSOFCOMPRESSEDCOLUMNSASSTRESSEXCEEDSPROPORTIONALLIMIT

§10-4STABILITYCHECKANDREASONABLESECTIONOFCOMPRESSEDCOLUMNS2§10–1

CONCEPTSOFSTABILITYOFCOMPRESSEDCOLUMNSTheload-carryingcapacityofstructuremembers：①Strength②Rigidity③Stability

Somestructuremembersinengineeringhaveenoughstrengthandrigiditybuttheyareunabletoworksafelyandreliably.STABILITYOFCOMPRESSEDCOLUMN3PSTABILITYOFCOMPRESSEDCOLUMN41、Stableandinstableequilibrium：1).instableequilibrium

STABILITYOFCOMPRESSEDCOLUMN52).StableequilibriumSTABILITYOFCOMPRESSEDCOLUMN63).Stableandinstableequilibrium

STABILITYOFCOMPRESSEDCOLUMN72、Lossofstabilityandthecriticalpressureofthecolumn：1).Idealcompressivecolumns：thematerialisabsolutelyideal；theaxisisabsolutelystraight；thecompressiveforceisabsolutelyalongtheaxisofthecolumn.2).Stableandinstableequilibriumofcompressivecolumns：STABILITYOFCOMPRESSEDCOLUMNInstableequilibriumStableequilibrium83).lossofstabilityofcompressedcolumn：4).CriticalpressureofcompressedcolumnsStableequilibriumInstableequilibriumCriticalstateCriticalpressure:Pcr

correspondingpressureSTABILITYOFCOMPRESSEDCOLUMNintermediatestate9

§10–2

EULER’SFORMULAOFTHECRITICALPRESSUREOF SLENDERCOMPRESSEDCOLUMNS

1、Criticalpressureforthecolumnwithtwohingedends:①bendingmoment：②ApproximatedifferentialequationofthedeflectioncurvePPxyPMSTABILITYOFCOMPRESSEDCOLUMNSupposethepressurehasreachedthecriticalvalueandthecolumnhasbeenintinybendingstateasshowninthefigure.Starttodeterminethecriticalforcewiththedeflectivecurve.PxL10③Solutionofthedifferentialequation：④Determinetheintegralconstants：

ThecriticalforcePcr

isthesmallestpressureundertinybending，thereforeweonlytaken=1andthecolumnwillbendabouttheaxiswiththesmallestmomentofinertia.STABILITYOFCOMPRESSEDCOLUMNThatis112、Applicationrangeoftheformula：3、Euler’sformulaofthecriticalpressureforthecolumnwithotherendconditions:1).Idealcompressivecolumns；2).Inlinearelasticrange；3).Theendsofthecolumnaresupportedbyhinges.—Lengthcoefficient（orconstraintcoefficient）Euler’sformulaofthecriticalpressureforthecompressivecolumnwithtwohingedends

GeneralformofEuler’sformulaofthecriticalpressureSTABILITYOFCOMPRESSEDCOLUMN120.5lTable10–1Euler’sformulaoftheslendercompressivecolumnundervariousconstraintconditionsSupportsTwohingedendsOnefreeendandonehingedendTwofixedendsOnefixedendandonefreeendTwofixedendsbutoneofthemismovablelaterally.

TheshapeofthedeflectivecurveinlostofstabilityPcrABlEuler’sformulaofthecriticalforcePcr

Lengthcoefficientμμ=1μ0.7μ=0.5μ=2μ=1PcrABlPcrABl0.7lCCDC:InflectionpointC、D:Inflectionpoint0.5lPcrPcrl2llC:InflectionpointSTABILITYOFCOMPRESSEDCOLUMN13Solution：Thedeformationofthecolumnisshowninthefigure.Theapproximatedifferentialequationofitsdeflectioncurveis:Theboundaryconditionsare:

Example1

Trytodeducethecriticalforceofthefollowingslendercolumnbytheapproximatedifferentialequationofthedeflectivecurve.PLxPM0PM0PM0xPM0STABILITYOFCOMPRESSEDCOLUMNLet14Inordertodeterminetheminimumcriticalpressure“k”mustbetheminimumvalueexceptzero,thatis：Thereforethecriticalpressureis：=0.5STABILITYOFCOMPRESSEDCOLUMNand15③CriticalpressureofthecolumnExample2

Determinethecriticalpressureofthefollowingslendercompressive column.=1.0，Solution：①Abouttheaxis

y，

twoendsarehinged：=0.7，②Abouttheaxis

z，theleftendisfixedandtherightendishinged：yzL1L2yzhbxSTABILITYOFCOMPRESSEDCOLUMN16Ex忍am悟pl填e3De樹te袋rm帆in弄e危th笑e閉cr瞇it主ic蛛al憤p旨re濫ss更ur符e朱of屈t波he揪f販ol利lo腐wi摔ng饅s口le宰nd急er喝c文om桂pr紀(jì)es毀si勾ve嗽c潑ol哥um狹ns烤.K屈no違wi術(shù)ng讀:L爺=0董.5佩m輩a旗nd嗎E擁=2漂00足GP稼a.So擦lu棒ti族on：Fi啊g.恥(a)Fi是g.痛(b)Fig.(a)Fig.(b)5010PLPL(45456)Equal-leganglesteelyzST蠅AB童IL灰IT短Y材OF第C蒸OM漏PR白ES等SE禮D剖CO揚(yáng)LU語(yǔ)MN17§1筆0–嚴(yán)3CR旬IT編IC顧AL做S維TR萌ES倉(cāng)S若OF尊C氧OM惰PR舒ES屆SE席D固CO骨LU命MN蜂S堅(jiān)AS牲S丙TR腔ES畜S持E淚XC盾EE篩DS后T趴HE鍋P芝RO絨PO后RT候IO萬(wàn)NA慈L絕LI五MI溪T1、Ba鼓si揚(yáng)c屯co段nc乓ep妨ts1)剖.C析ri專ti招ca陜l忘st微re闊ss：Me茅an絹s墳tr類es飯s兄in板t歸he批c確ro乞ss爺s猛ec云ti宋on直o亂f伐th繡e棉co派mp推re怠ss涼iv液e弱co倡lu體mn刪i薪n掏th暈e摩cr鍛it撤ic批al犧s位ta絨te瞧.3)尿.F斥le瓦xi咳bi踏li閥ty：2)各.C仇ri墊ti掠ca纏l墾st短re褲ss斯f霜or基s勉le剖nd企erco恩mp冬re棗ss不ed讓c思o(jì)l休um侵ns：22lpsEcr=Th季at焦i俊s:ST什AB尿IL各IT妄Y扎OF址C怒OM批PR觸ES嬸SE氏D選CO曬LU宴MNRadiusofinertiaFl儲(chǔ)ex拌ib層il景it肥y概(o鍵r筑sl錢en缺de嘴rn址es嫂s哀ra米ti旺o)鳳o歲f訂th凈e各co攤lu夾mn184)追.D云iv對(duì)is醒io芒n懲of待l嘉ar章ge隔f嚇le廁xi撤bi雞li砍ty必c閘ol裙um嫂n：2、Ca昌lc釀ul爽at吊io脆n騙of雙t險(xiǎn)he伍c蔽ri桑ti終ca壤l汁st銹re和ss游f需or碧t國(guó)he究c判ol利um賠ns高w刮it杏h靠mi挨dd屯le借o皂r陽(yáng)sm榜al葡l缸fl健ex扯ib架il威it關(guān)y1)腳.虛Em社pi富ri由ca蔬l贏fo軟rm財(cái)ul營(yíng)a免wi挎th伍t扮he柿l荷in竊ea萍r業(yè)va譽(yù)ri心at逮io賠n①A慰sP<<S：ST饑AB穴IL絡(luò)IT鹽Y旨OF拿C圾OM州PR菊ES姜SE磚D億CO腐LU吸MNisoneofthemiddleflexibilitycolumn.ThecolumnwithItscriticalstressmaybedeterminedbytheempiricalformula.Thecolumnswithiscalledthelargeflexibilitycolumn(orslenderclumn).ThecriticalpressureofthiskindofcolumniscalculatedbyEuler’sformula.Thecolumnswithiscalledmiddleorsmallflexibilitycolumn.ItscriticalpressureofthiskindofcolumncannotbecalculatedbyEuler’sformula.19③To梯ta俱l階fi猜gu方re赴o禾f斯th尺e溪cr第it梨ic口al洗s回tr浸es扁s②A素sS<：bss=a-sl

PPEspl2

=ST辯AB筍IL際IT秀Y散OF顫C眨OM全PR雁ES轉(zhuǎn)SE攜D掙CO集LU獸MNTh抹e耳cr暮it箱ic輪al貝s工tr湯es論s則of尾t君hi烘s竊co螞lu思mn亞i港s疊it紗s蝦yi棍el杠d味li托mi適t.isoneofthesmallflexibilityThecolumnwithcolumn.

202)仍Em屢pi化ri蒸ca寇l惑fo綠rm梨ul敗a旗wi友th腦t飽he否p的ar紫ab鼠ol肺ic數(shù)v岔ar線ia躺ti準(zhǔn)onTh且e撫co本mm畢on逗f快or除m憲in投t變hest李ru膀ct遠(yuǎn)ur雅al悅e綿ng辦in尼ee紐奉ri砌ng蹲i首s：①AsP<<s：②Ass<：ST援AB拔IL濱IT績(jī)Y艙OF凍C蘭OM百PR唱ES典SE奴D席CO智LU俘MNFo恢rA3st扒ee挺l,A5st鎮(zhèn)ee潔l爸an歸d貼16粱Mn圓s征te惡el害,AsTh惱is主f休or應(yīng)mu誤la亞i假s凡us烘ed六t貨o跑de確te案rm顆in躍e越th待e及cr溝it袋ic晨al叔s魂tr隊(duì)es封s.21So廣lu疫ti史on：Fo叢r眾on按e亂pi鄙ec兔e徒of混a嫌ng眉le杰s蛛te火el：Af韻te構(gòu)r暢tw改o睛pi悲ec艷es笑o忠f孔an其gl泊e日st聽(tīng)ee甚l喂is跡c卡om互bi改ne辟d轉(zhuǎn)as哈s上ho您wn燙i斯n懷th擔(dān)e寒fi臥gu輩re脂,Th什er線ef床or終e譯th凡e霸cr醒it畢ic宅al助p冊(cè)re種ss企ur忽e竭sh桃ou堤ld灶b憐e減de振te鬧rm骨in手ed羞b順y鴉t燙he紙e峽mp施ir用ic褲al通f扛or恐mu歌layzST嘆AB克IL群IT灶Y紀(jì)OF仙C棉OM養(yǎng)PR臟ES蘿SE賤D霞CO茂LU徒MNEx遺am倘pl選e4A捎co潑mp多re已ss孕iv喬e蟲co厭lu下mn腳i枕s菊ma信de圓f爛ro萬(wàn)m役tw棗o狂eq戲ua耐l-雄l星eg戶a魯ng罪le授s磨te獄el炸o席f捕565貞68.護(hù)I以ts恒t壓wo豎e屢nd始s節(jié)ar覺(jué)e箏bo糾th同h兼in車ge蕩d.坡I汪ts婆l著en邀gt駛h甩isL=1激.5芝m.鹿T硬he伍p昨re幅ss也ur興e賣isP=1菠50緞kN可.控Th仇e織an師gl輩e溪st快ee奧l售is凱A3st涂ee萌l.桂T長(zhǎng)ry春t醉o垃de營(yíng)te識(shí)rm庭in亭e盞th厭e企cr好it叮ic糖al犧p優(yōu)re學(xué)ss扭ur賴e謙an漂d耍th藥e包sa尖fe仆ty良c姐oe番ff騾ic治ie島nt膽o絕f每st桑ab濟(jì)il暴it豪y縫nstby這E群ul杏er騰’s葬f滑or脂mu碎la煙o(wú)舒r悼th隱e攪em蹲pi道ri拘ca宋l狹fo電rm應(yīng)ul鴨a葵wi兵th斬t針he碧p夏ar泥ab牙ol曉ic仍v醫(yī)ar賽ia教ti勺o(hù)n丹.wi查th屠t蘿he薪p霧ar倡ab恨ol狠ic獄v鄭ar泄ia懲ti詢on集.22Sa冒fe斧ty爹c億oe帽ff奸ic圓ie億ntST叛AB牙IL役IT餡Y乎OF李C株OM桃PR腸ES娘SE拜D理CO雁LU團(tuán)MN23§1識(shí)0–踏4ST云AB蹤蝶IL坊IT享Y逮CH晝EC著K額AN忙D里RE唱AS期ON暮AB握LE諷S管EC派TI礙ON杏S地OF土C告OM爺PR幟ES兩SE摧D隔CO交LU尺M(jìn)N施S1、Pe鼠rm顛is臂si餐bl序e弱st忍re樓ss愿f鴉or訓(xùn)t費(fèi)he弱c堂om繡pr暮es畢se京d拾co掠lu場(chǎng)mn憑s駝in墨s虜ta徑bi莊li艷za摟ti注on吵:1)哨.De企te欠rm浮in形e慈th占e東pe撒rm顆is泰si建bl逮e直st球re蔽ss館b貸y辯th鬼e覺(jué)me懲th純od嘆o機(jī)f濃th墓e秋sa餡fe覺(jué)ty吼c鑄oe揚(yáng)ff設(shè)ic吃ie楚nt捆:2)糊.De倡te鑄rm織in甩e礙th傻e腿pe置rm加is懷si蛇bl奮e竊st深re粥ss冠b繼y專th加e炸me逝th鋒od涉o透f即th廉e貨re精du買ct先io犧n筐co湊ef搭fi哥ci苗en計(jì)t:2、St唱ab壟il核it享y硬co詢nd嶺it付io農(nóng)n周of柿t予he勸c技o(jì)m準(zhǔn)pr令es涼se悼d緊co威lu陰mn從s:ST惹AB之IL諸IT悄Y套OF季C吹OM踐PR忽ES權(quán)SE手D上CO吉LU毯MNReductioncoefficient.Itisrelatedtomaterialpropertiesandtheflexibilityofcolumns,and.24Ex鋒am率pl無(wú)e構(gòu)5Th賴e革co誦lu絲式mnABin伏t秤he雖s鋸im紫pl棟e場(chǎng)cr酬an勁e秤sh傅ow討n燭in刷t待he過(guò)f濃ig斜ur鋒eis益m差ad換e字fr至om愉c償ir色cu長(zhǎng)la露r疼de劉al鞭.待It策s遵le浙ng葛th中i史sL=只6m禽a難nd送i槳ts左d圾ia左me枯te滴r協(xié)isd=蘿0.敞3m組.[]皆=1達(dá)1M因Pa繪.鐘Tr摔y鍵to袖d攀et暈er擾mi違ne把t戚he通p月er笛mi榴ss緩ib旺le磚p肚re祝ss執(zhí)ur剖e容of駱t房誠(chéng)he投c旋ol抽um定n.So潛lu淺ti劍on：Ap不pl世y估th才e跑me炮th響od脈o捏fre躍du垂ct講io階n昂co寨ef速fi薦ci鞋en勝t.①M(fèi)擱ax劣im斧um則f帶le鵝xi度bi降li黃tyIn遙p齊la架nexy，=1彼.0In具p予la享nezy，=2很.0T1ABWT2xyzOST柴AB屈IL駱I(yè)T澇Y營(yíng)OF王C被OM螞PR混ES茶SE忍D瘡CO查L(zhǎng)U酬MN25②D揪et縮慧er匙mi貍ne捉t快he陰r礎(chǔ)ed戒uc姑ti承on役c乓oe泛ff風(fēng)ic切ie患nt③D挑et悔er軌mi棵ne拴t季he昆p失er革mi液ss沉ib用le附p量re吉ss怒ur趁eST污AB在IL葡IT邀Y拳OF酬C匆OM瓦PR瘦ES剃SE武D嘗CO技LU殺MNFo卸r忍wo鏟od待en區(qū)c稿ol充um篇n:忽as263、Re槳as始o(jì)n蕩ab彼le跟s較ec掛ti薯on材o茶f見(jiàn)th走e終co趨lu粗mn忙:It胞i六s尋re輔as衫on刊ab醉le扣.ST睬AB醋IL堆IT喚Y召OF咳C宰OM擠PR狀ES鏡SE訂D味CO銀LU年MN保國(guó)寺大殿的拼柱形式SakyamniwoodenpagodaYingzhouwoodenpagodaIt倍w冠as司b龜ui亭lt冷i拒n寒10撤56賣w峰it哄h類th抱e涌do器ub寸le琴-s村le鼠ev冊(cè)e瘡st肉ru計(jì)ct共ur頃e.占Th眨e篩pa雞go株da偵p犁la并ne瓜i鐵s紙oc墾ta伯go享n.租It兄u積nd舍er災(zāi)we另nt貓t鏟he旺l睡ev灰el管8侍e茫ar東th汁qu飼ak斗e蟲of創(chuàng)1纖30率5.27So減lu選ti李on：Fo糞r焰ea先ch吳c臨ha喂nn胸el乞s簽te攪el必o伴f啞nu逗mb備er招1稻0,賭th虎e磨ce雷nt嬸ro注id字i甚s吳a政t驚th蜂e詞po歲in糕tC1.Af撇te邀r遺tw棟o奶ch謠an扣ne振l繳st匆ee警ls掠a剩re盛c飲om家bi府ne蝴d，PLz0yy1z1C1aST腥AB吹IL訂IT賠Y豆OF急C異OM抄PR朽ES驢SE蛋D側(cè)CO販LU躲MNEx蝦am攜pl逐e份6Th焦e夫up炒ri穴gh顏t刊co魄lu鍬mn菠s稍ho全wn偏i中n吃th膝e明fi增gu財(cái)re代i寨s灰ma簡(jiǎn)de日f(shuō)跳ro膚m臭tw孫o樸ch蔑an虛ne戰(zhàn)l催s揭te耗el肝s.It隔s全le累ng柏th漂i議sL=6網(wǎng)m.衡K惱no嘴wi己ng劉th撈e吩ma闊te籍ri卡al握i修s襲A3st乎ee罷l,惡E呆=2膽00恨GP滑a讀a正nd.I裁ts揀l醋o(hù)w掏er呢e皺nd禾i早s腰fi坑xe痕d日an凱d名it推s符up仇pe融r堪en鹽d脾is燒s插up孝po爐rt漲ed脅b臥y墓a書sp糖he急ri穗ca羨l刊hi斬ng奴e.嫌H餓ow寺m酒uc頂h緒is殃t原h(huán)e壺v嶄al暢ue寨o哀fawh醫(yī)en呈t永he枯c隨ri批ti非ca滴l肝pr舅es弱su口re索o旨f染th芳e膽up注ri煮gh之t輕co暴lu葉mn秀i初s搭th惑e紫ma駐xi諷mu刊m?Th松at辰i尼s欄it稈i良s粗re壘as堤on沖ab梨le假a滲sso28De謎te寸rm佳in勿e恐th神e幸cr認(rèn)it睡ic咸al葛f晚or芳ce：It婦i逗s絕a犯la塔rg棄e尋fl翻ex回ib壇il緊it遠(yuǎn)y毫ro漫d它.T劍