轴向拉伸和压缩时的变形40

1、课题九 轴向拉伸和压缩时的变形一、弹性变形与塑性变形 杆件在外力作用下会发生变形，随着外力取消即随之消失的变形叫做弹性变形。当外力取消时不消失或不完全消失而残留下来的变形叫做塑性变形。二、纵向变形和胡克定律1、纵向变形 杆件在轴向力作用下，杆的长度会发生变化，杆件长度的改变量叫做纵向变形，用l 表示。假设杆件变形前长度为l ，变形后长度为l 1见图9-1。 图9-1 课题九 轴向拉伸和压缩时的变形 那么纵向变形为 l = l1 - l 拉伸时纵向变形是伸长，规定为正；压缩时纵向变形是缩短，规定为负。2、胡克定律 在弹性受力范围内，杆件的纵向变形与轴力及杆长成正比，与杆件的横截面面积成反比。 即

2、上式叫做胡克定律，式中的比例系数E为材料的弹性模量。 需特别注意：1胡克定律只适用于弹性受力范围内2当用于计算变形时，在杆长l 内，轴力N、材料的弹性模量E及截面积A均为常数。 杆件的纵向变形与杆长l 有关，在其它条件相同时，杆件愈长那么纵向变形愈大。为了消除杆长对变形的影响，常用单位长度的变形来描述杆件变形的程度。单位长度的变形叫做线应变，用表示。课题九 轴向拉伸和压缩时的变形 或 上式是胡克定律的的另一种形式，它说明在弹性受力范围内，应力与应变成正比。三、横向变形 拉压杆产生纵向变形时，横向也产生变形。假设杆件变形前的横向尺寸为，变形后为 ，那么横向变形为 横向应变为 杆件受拉时，横向尺寸

3、缩小，为负值；杆件受压时横向尺寸变大，为正值。可见，轴向拉、压杆的线应变与横向应变的符号总是相反。课题九 轴向拉伸和压缩时的变形 例：图示为一两层的木排架，作用在横木上的荷载传给立柱，其中一根柱的受力图如图b所示，P1=30KN，P2=50KN。柱子为圆截面，直径d=150mm。木材的弹性模量E=10Gpa。求木柱的总变形。 解：木柱AB和BC两段轴力不同，应分别求出两段变形，然后求其总和。1求轴力2求变形截面面积$u*x+A2D5H8KbNfQiTlXo#s%v(y0B3E6I9LdOgRjVmYp!t&w-z1C4G7JaMePhTkWnZr$u*x+A2E5H8KcNfQiUlXp#s%

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