英汉双语材料力学10PPT文件格式下载.ppt
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1).Idealcompressivecolumns:
thematerialisabsolutelyideal;
theaxisisabsolutelystraight;
thecompressiveforceisabsolutelyalongtheaxisofthecolumn.2).Stableandinstableequilibriumofcompressivecolumns:
InstableequilibriumStableequilibrium15二、压杆失稳与临界压力二、压杆失稳与临界压力:
1.理想压杆:
材料绝对理想;
轴线绝对直;
压力绝对沿轴线作用。
2.压杆的稳定平衡与不稳定平衡:
稳稳稳稳定定定定平平平平衡衡衡衡不不不不稳稳稳稳定定定定平平平平衡衡衡衡163).lossofstabilityofcompressedcolumn:
4).CriticalpressureofcompressedcolumnsStableStableequilibriumequilibriumInstableInstableequilibriumequilibriumCriticalstateCriticalpressure:
Pcrcorrespondingcorrespondingpressurepressureintermediatestateintermediatestate173.压杆失稳:
4.压杆的临界压力稳稳稳稳定定定定平平平平衡衡衡衡不不不不稳稳稳稳定定定定平平平平衡衡衡衡临界状态临界状态临界压力临界压力:
Pcr18102EULERSFORMULAOFTHECRITICALPRESSUREOFSLENDERCOMPRESSEDCOLUMNS11、Criticalpressureforthecolumnwithtwohingedends:
bendingmomentbendingmoment:
ApproximatedifferentialApproximatedifferentialequationofthedeflectioncurveequationofthedeflectioncurvePPxyPMSupposethepressurehasreachedthecriticalvalueandthecolumnhasbeenintinybendingstateasshowninthefigure.Starttodeterminethecriticalforcewiththedeflectivecurve.PxL19102细长压杆临界力的欧拉公式细长压杆临界力的欧拉公式一、两端铰支压杆的临界力一、两端铰支压杆的临界力:
假定压力已达到临界值,杆已经处于微弯状态,如图,从挠曲线入手,求临界力。
弯矩:
挠曲线近似微分方程:
PxLPxyPM20SolutionofthedifferentialequationSolutionofthedifferentialequation:
DeterminetheintegralconstantsDeterminetheintegralconstants:
ThecriticalforcePcristhesmallestpressureundertinybending,thereforeweonlytaken=1andthecolumnwillbendabouttheaxiswiththesmallestmomentofinertia.Thatis21微分方程的解:
微分方程的解:
确定积分常数:
临界力Pcr是微弯下的最小压力,故,只能取n=1;
且杆将绕惯性矩最小的轴弯曲。
222、Applicationrangeoftheformula:
3、Eulersformulaofthecriticalpressureforthecolumnwithotherendconditions:
1).Idealcompressivecolumns;
2).Inlinearelasticrange;
3).Theendsofthecolumnaresupportedbyhinges.Lengthcoefficient(orconstraintcoefficient)EulersformulaofthecriticalpressureforthecompressivecolumnwithtwohingedendsGeneralformofEulersformulaofthecriticalpressure23二、此公式的应用条件:
三、其它支承情况下,压杆临界力的欧拉公式1.理想压杆;
2.线弹性范围内;
3.两端为球铰支座。
长度系数(或约束系数)。
两端铰支压杆临界力的欧拉公式两端铰支压杆临界力的欧拉公式压杆临界力欧拉公式的一般形式压杆临界力欧拉公式的一般形式240.5lTable101EulersformulaoftheslendercompressivecolumnundervariousconstraintconditionsSupportsTwohingedendsOnefreeendandonehingedendTwofixedendsOnefixedendandonefreeendTwofixedendsbutoneofthemismovablelaterally.TheshapeofthedeflectivecurveinlostofstabilityPcrABlEulersformulaofthecriticalforcePcrLengthcoefficient=10.7=0.5=2=1PcrABlPcrABl0.7lCCDC:
InflectionpointC、D:
Inflectionpoint0.5lPcrPcrl2llC:
Inflectionpoint250.5l表101各种支承约束条件下等截面细长压杆临界力的欧拉公式支承情况两端铰支一端固定另端铰支两端固定一端固定另端自由两端固定但可沿横向相对移动失稳时挠曲线形状PcrABl临界力Pcr欧拉公式长度系数=10.7=0.5=2=1PcrABlPcrABl0.7lCCDC挠曲线拐点C、D挠曲线拐点0.5lPcrPcrl2llC挠曲线拐点26Solution:
Thedeformationofthecolumnisshowninthefigure.Theapproximatedifferentialequationofitsdeflectioncurveis:
Theboundaryconditionsare:
Example1Trytodeducethecriticalforceofthefollowingslendercolumnbytheapproximatedifferentialequationofthedeflectivecurve.PLxPM0PM0PM0xPM0Let27解:
变形如图,其挠曲线近似微分方程为:
边界条件为:
例例11试由挠曲线近似微分方程,导出下述细长压杆的临界力公式。
PLxPM0PM0PM0xPM028Inordertodeterminetheminimumcriticalpressure“k”mustbetheminimumvalueexceptzero,thatis:
Thereforethecriticalpressureis:
=0.5and29为求最小临界力,“k”应取除零以外的最小值,即取:
所以,临界力为:
=0.530CriticalpressureofthecolumnCriticalpressureofthecolumnExampleExample2Determinethecriticalpressureofthefollowingslendercompressivecolumn.=1.0,Solution:
AbouttheaxisAbouttheaxisy,twoendsarehinged:
=0.7,AbouttheaxisAbouttheaxisz,theleftendisfixedandtherightendishinged:
yzL1L2yzhbx31压杆的临界力例例2求下列细长压杆的临界力。
=1.0,解:
绕y轴,两端铰支:
=0.7,绕z轴,左端固定,右端铰支:
yzL1L2yzhbx32ExampleE