第十章 压杆稳定.pptVIP

③压杆的临界力 [例2] 求下列细长压杆的临界力。 ?=1.0， 解：①绕 y 轴，两端铰支： ?=0.7， ②绕 z 轴，左端固定，右端铰支： y z L1 L2 y z h b x Example 3 Determine the critical pressure of the following slender compressive columns.Knowing:L=0.5m and E=200GPa. Solution：Fig.(a) Fig.(b) Fig.(a) Fig.(b) 50 10 P L P L (45?45? 6) Equal-leg angle steel y z [例3] 求下列细长压杆的临界力。已知： L=0.5m ， E=200GPa. 图(a) 图(b) 解：图(a) 图(b) 50 10 P L P L (45?45? 6) 等边角钢 y z §10–3 CRITICAL STRESS OF COMPRESSED COLUMNS AS STRESS EXCEEDS THE PROPORTIONAL LIMIT  1、 Basic concepts 1).Critical stress：Mean stress in the cross section of the compressive column in the critical state. 3).Flexibility： 2).Critical stress for slender compressed columns： 2 2 l p s E cr = That is: Radius of inertia Flexibility (or slenderness ratio) of the column §10–3 超过比例极限时压杆的临界应力 一、 基本概念 1.临界应力：压杆处于临界状态时横截面上的平均应力。 3.柔度： 2.细长压杆的临界应力： 4).Division of large flexibility column： 2、Calculation of the critical stress for the columns with middle or small flexibility 1). Empirical formula with the linear variation ①As?P??S ： is one of the middle flexibility column . The column with Its critical stress may be determined by the empirical formula. The columns with is called the large flexibility column(or slender clumn). The critical pressure of this kind of column is calculated by Euler’s formula. The columns with is called middle or small flexibility column. Its critical pressure of this kind of column can not be calculated by Euler’s formula. 4.大柔度杆的分界： 二、中小柔度杆的临界应力计算 1.直线型经验公式 ①?P??S 时： ③Total figure of the critical stress ②As ?S? ： b s s = a -s l P P E s p l 2 = The critical stress of this column is its yield limit. is one of the small flexibility The column with column. ③临界应力总图 ②?S? 时： s b a s - = s l P P E s p l 2 = 2)Empirical formula with the parabolic variation The common form in the structural engineering is： ①As ?P??s ： ②As ?s? ： For A3steel, A5steel and 16Mn steel, As This formula is used to determine the critic