2016工程力学-材料力学（高教版）教案：第十章 压杆稳定.docVIP

第十章 压杆稳定 1M e c h a n i c s o f M a t e r i a l s23CHAPTER 10 STABILIZATION OFCOMPRESSIVE COLUMNS§ 10–1 CONCEPTS OF STABILITY OF COMPRESSED COLUMNS§ 10–2 EULER’S FORMULA OF THE CRITICAL FORCE OF SLENDERCOMPRESSED COLUMNS§ 10–3 CRITICAL STRESS OF COMPRESSED COLUMNS AS STRESSEXCEEDS PROPORTIONAL LIMIT§ 10-4 STABILITY CHECK AND REASONABLE SECTION OFCOMPRESSED COLUMNS4第十章 压杆稳定§ 10–1 压杆稳定性的概念§ 10–2 细长压杆临界力的欧拉公式§ 10–3 超过比例极限时压杆的临界应力§ 10-4 压杆的稳定校核及其合理截面5§ 10–1 CONCEPTS OF STABILITY OF COMPRESSED COLUMNSThe load-carryingcapacity of structuremembers,① Strength② Rigidity③ StabilitySome structure membersin engineering have enoughstrength and rigidity butthey are unable to worksafely and reliably,6§ 10–1 压杆稳定性的概念构件的承载能力,① 强度②刚度③稳定性工程中有些构件具有足够的强度、刚度，却不一定能安全可靠地工作。7P8P91,Stable and instable equilibrium,1),instable equilibrium10一、稳定平衡与不稳定平衡,1,不稳定平衡112),Stable equilibrium122,稳定平衡133),Stable and instable equilibrium143,稳定平衡和不稳定平衡152,Loss of stability and the critical pressure of the column,1).Ideal compressive columns,the material is absolutely ideal； the axis is absolutelystraight； the compressive force is absolutely along the axis of the column,2),Stable and instable equilibrium of compressive columns,InstableequilibriumStableequilibrium16二、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,稳定平衡不稳定平衡173).loss of stability of compressedcolumn,4).Critical pressure of compressed columnsStableequilibriumInstableequilibriumCritical stateCritical pressure,Pcrcorrespondingpressureintermediate state183.压杆失稳,4.压杆的临界压力稳定平衡不稳定平衡临界状态临界压力, Pcr过 度对 应 的压力19§ 10–2 EULER’S FORMULA OF THE CRITICAL PRESSURE OFSLENDER COMPRESSED COLUMNS1,Critical pressure for the column with two hinged ends,PyyxM ?),(yEIPEIMy ??????① bending moment,② Approximate differentialequation of the deflection curve,02 ???????? ykyyEIPyEIPk ?2:w h e r ePPxyPMSuppose the pressure has reached