材料力學(xué)課件13組合變形.ppt

1、5 . 組合變形的 應(yīng)力與強度計算,The stresses and strength of combined deformations,In engenering the strength of combined deformations often need to be calculated . The steps are as follows :,(1) 確定危險截面 , 用截面法計算危險截面上的內(nèi)力 .,組合變形桿件強度計算的步驟 :,(2) 確定危險截面上的危險點 , 分析危險點的應(yīng)力狀態(tài) .,Determine the dangerous cross section of the

2、bar , and using section method to get the internal forces on this section .,Determine the dangerous point on the cross section , and analysis the state of stress at this point .,(3) 根據(jù)適當(dāng)?shù)膹姸葴?zhǔn)則計算組合變形桿件的強度 .,強度計算包含三個方面的內(nèi)容 (The calculation of strength for a bar involes three parts ) :,a. 校核強度 (Examine t

3、he strength of the bar ),b. 計算許可載荷 (Determine the maximum laodings acted on the bar ),c. 計算許可截面尺寸 (Determine the minimum cross section of the bar ),Calculate the strength of the bar acoording to certain strength criterion .,5.1 拉彎扭組合變形 (Generially combined deformations ),Suppose the internal forces

4、on the dangerious section are N T M . The dangerious point will be point A or B . Its state of stress is shown in follows figure .,For the ductile materials :,Very important formulas,If the cross section of the bar is not circular .,5.2 拉彎組合變形 (Combined deformation of tension and bending ),T = 0,The

5、 dangerious point is a simple state of stress .,拉彎組合中的最大正應(yīng)力的計算,T = 0,The dangerious point is a simple state of stress .,(2) 強度準(zhǔn)則 ( Strength criterion ),如圖的集中荷載 P 可在立柱端面中線上移動，要使立柱橫截面上不產(chǎn)生拉應(yīng)力，偏心量 e 允許的最大值為多少？,Example :,5.4 彎扭組合變形 (Combined deformations of bending and torsion),N = 0,The dangerious point

6、 is a plane state of stress .,強度準(zhǔn)則 ( Strength criterion ),For the circular section , we can get :,AB 段承受彎扭組合變形,最大彎矩,扭矩,故軸徑 d 應(yīng)滿足,Example : Determine the diameter of bar AB using the fourth criterion . Known the allowed stress of the material .,5.5 斜 彎 曲 ( Skew bending ),The dangerious section is A .

7、 The moments on section A are :,(1) 斜彎曲概念 ( Concept of skew bending ),For example , a beam acted by a force P shown in right figur . The beam will be bending along two directions y and z . This bending is called skew bending .,The dangerious points are C and D . The stresses at C and D are :,Tension

8、 stress,compression stress,斜彎曲問題一般出現(xiàn)在矩形、工字形等截面的梁中。,(3) Circular and regular-polygon cross section,For the circular and regular-polygon cross section , there is no skew bending . The bending is plane bending !,(a) Circular cross section,Especially for two moments on the cross section shown follows ,

9、the result will be attained :,(b) Regular-polygon cross section,Dangerious point is A or B .,Especially for two moments on the cross section shown follows , the result will be attained :,平移 P1 到 B， A 截面承受彎扭組合荷載：,平移 P2 到 B， A 截面承受拉彎組合荷載：,P1 = 2 kN,P2 = 3 kN,L = 400 mm,a = 300 mm,d = 50 mm,危險點應(yīng)力狀態(tài),扭轉(zhuǎn)切

10、應(yīng)力,例 求圖示結(jié)構(gòu) A 截面危險點的第三強度相當(dāng)應(yīng)力。,拉伸正應(yīng)力,P1 = 2 kN,P2 = 3 kN,L = 400 mm,a = 300 mm,d = 50 mm,彎曲正應(yīng)力,例 求圖示結(jié)構(gòu) A 截面危險點的第三強度相當(dāng)應(yīng)力。,5.6 斜彎曲和基本變形的組合問題 ( Combined deformations of Skew bending and other basic deformations ),For example , deformation of the column shown follows is combined with skew bending and comp

11、ression .,例 如圖的集中荷載 P 可在立柱端面上平行移動，要使立柱橫截面上不產(chǎn)生拉應(yīng)力， P 應(yīng)該限制在什么樣的區(qū)域內(nèi)？,壓縮正應(yīng)力,最大彎曲拉應(yīng)力,不產(chǎn)生拉應(yīng)力的條件,截面核心 ( kern of cross-section ),特別注意: 圓形截面和正多邊形梁斜彎曲問題如何處理？,結(jié)論 圓形截面和正多邊形梁問題不能按斜彎曲方式處理。,5.7 桿件彎曲的一般情況,正多邊形的橫向荷載通過截面形心，則總是產(chǎn)生平面彎曲。,(1) 平面彎曲,實體桿件的橫向荷載通過截面形心，并沿形心慣性主軸方向，則產(chǎn)生平面彎曲。,薄壁桿件的橫向荷載通過彎曲中心，并沿形心慣性主軸方向，則產(chǎn)生平面彎曲。,(2) 斜彎曲,桿件的橫向荷載通過彎曲中心，但不沿形心慣性主軸方向，則將產(chǎn)生斜彎曲。,(3) 彎扭