軸向拉伸和壓縮時的變形40

1、課題九 軸向拉伸和壓縮時的變形一、彈性變形與塑性變形 桿件在外力作用下會發(fā)生變形，隨著外力取消即隨之消失的變形叫做彈性變形。當(dāng)外力取消時不消失或不完全消失而殘留下來的變形叫做塑性變形。二、縱向變形和胡克定律1、縱向變形 桿件在軸向力作用下，桿的長度會發(fā)生變化，桿件長度的改變量叫做縱向變形，用l 表示。假設(shè)桿件變形前長度為l ，變形后長度為l 1見圖9-1。 圖9-1 課題九 軸向拉伸和壓縮時的變形 那么縱向變形為 l = l1 - l 拉伸時縱向變形是伸長，規(guī)定為正；壓縮時縱向變形是縮短，規(guī)定為負(fù)。2、胡克定律 在彈性受力范圍內(nèi)，桿件的縱向變形與軸力及桿長成正比，與桿件的橫截面面積成反比。 即

2、上式叫做胡克定律，式中的比例系數(shù)E為材料的彈性模量。 需特別注意：1胡克定律只適用于彈性受力范圍內(nèi)2當(dāng)用于計算變形時，在桿長l 內(nèi)，軸力N、材料的彈性模量E及截面積A均為常數(shù)。 桿件的縱向變形與桿長l 有關(guān)，在其它條件相同時，桿件愈長那么縱向變形愈大。為了消除桿長對變形的影響，常用單位長度的變形來描述桿件變形的程度。單位長度的變形叫做線應(yīng)變，用表示。課題九 軸向拉伸和壓縮時的變形 或 上式是胡克定律的的另一種形式，它說明在彈性受力范圍內(nèi)，應(yīng)力與應(yīng)變成正比。三、橫向變形 拉壓桿產(chǎn)生縱向變形時，橫向也產(chǎn)生變形。假設(shè)桿件變形前的橫向尺寸為，變形后為 ，那么橫向變形為 橫向應(yīng)變?yōu)?桿件受拉時，橫向尺寸

3、縮小，為負(fù)值；桿件受壓時橫向尺寸變大，為正值?？梢姡S向拉、壓桿的線應(yīng)變與橫向應(yīng)變的符號總是相反。課題九 軸向拉伸和壓縮時的變形 例：圖示為一兩層的木排架，作用在橫木上的荷載傳給立柱，其中一根柱的受力圖如圖b所示，P1=30KN，P2=50KN。柱子為圓截面，直徑d=150mm。木材的彈性模量E=10Gpa。求木柱的總變形。 解：木柱AB和BC兩段軸力不同，應(yīng)分別求出兩段變形，然后求其總和。1求軸力2求變形截面面積$u*x+A2D5H8KbNfQiTlXo#s%v(y0B3E6I9LdOgRjVmYp!t&w-z1C4G7JaMePhTkWnZr$u*x+A2E5H8KcNfQiUlXp#s%

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