英汉双语材料力学10PPT文件格式下载.ppt

1、1）.Ideal compressive columns：the material is absolutely ideal；the axis is absolutely straight；the compressive force is absolutely along the axis of the column.2）.Stable and instable equilibrium of compressive columns：Instable equilibriumStable equilibrium15二、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

2、；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）.loss of stability of compressed column：4）.Critical pressure of compressed columnsStable Stable equilibriumequilibriumInstable Instable equilibriumequilibriumCritical stateCritical pressure:Pcr correspondingcorrespondingpressurepress

3、ureintermediate stateintermediate state173.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:Pcr18102 EULERS FORMULA OF THE CRITICAL PRESSURE OF SLENDER COMPRESSED COLUMNS1 1、Critical pressure for the column with two hinged ends:bending momentbending moment：Approximate differentialA

4、pproximate differential equation of the deflection curve equation of the deflection curvePPxyPM Suppose the pressure has reached the critical value and the column has been in tiny bending state as shown in the figure.Start to determine the critical force with the deflective curve.PxL19102 细长压杆临界力的欧拉

5、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：PxLPxyPM20Solution of the differential equationSolution of the differential equation：Determine the integral constantsDetermine the integral constants：The critical force Pcr is the smallest pressure under tiny ben

6、ding，therefore we only take n=1 and the column will bend about the axis with the smallest moment of inertia.That is21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、Application range of the formula：3、Eulers formula of the critical pressure for the column with other end conditions:1

7、）.Ideal compressive columns；2）.In linear elastic range；3）.The ends of the column are supported by hinges.Length coefficient（or constraint coefficient）Eulers formula of the critical pressure for the compressive column with two hinged ends General form of Eulers formula of the critical pressure23二、此公式

8、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240.5lTable101 Eulers formula of the slender compressive column under various constraint conditionsSupportsTwo hinged endsOne free end and one hinged endTwo fixed endsOne fixed en

9、d and one free endTwo fixed ends but one of them is movable laterally.The shape of the deflective curve in lost of stabilityPcrABlEulers formula of the critical forcePcr Length coefficient=10.7=0.5=2=1PcrABlPcrABl0.7lCCDC:Inflection point C、D:Inflection point 0.5lPcrPcrl2llC:Inflection point 250.5l表

10、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：The deformation of the column is shown in the figure.The approximate differential equation of its deflection curve is:The b

11、oundary conditions are:Example 1 Try to deduce the critical force of the following slender column by the approximate differential equation of the deflective curve.PLxPM0PM0PM0 xPM0Let27解：变形如图，其挠曲线近似微分方程为：边界条件为:例例1 1 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。PLxPM0PM0PM0 xPM028In order to determine the minimum cri

12、tical pressure“k”must be the minimum value except zero,that is：Therefore the critical pressure is：=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：=0.530Critical pressure of the columnCritical pressure of the column Example Example 2 Determine the critical pressure of the following slender compressive column.=1.0，Solution：About the axisAbout the axis y，two ends are hinged：=0.7，About the axisAbout the axis z，the left end is fixed and the right end is hinged：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：yzL1L2yzhbx32Example E