英汉双语材料力学5.pptVIP

Example 4 Try to determine the ratio of the elastic limit bending moment M max to the plastic one Mjx of the beam with rectangular sections. [例4] 试求矩形截面梁的弹性极限弯矩M max与塑性极限弯矩 Mjx之 比。 （三）采用变截面梁 ，如下图： 最好是等强度梁，即 若为等强度矩形截面，则高为 同时 P x §5-5 PLANAR BENDING OF THE UNSYMMETRIC BEAM?BENDING CENTER OF THE OPENED THIN-WALLED SECTION The geometric equation and physical equation are not changed. P x y z O (neutral) axis z is through the center of the section. Axes y and z must be the principal axes of inertia of the section and the acting lines of external forces must coincide with the principal axes of inertia of the section §5-5 非对称截面梁的平面弯曲 ? 开口薄壁截面的弯曲中心 几何方程与物理方程不变。 P x y z O Use this expression to determine the formula of the normal stress. The method to study the shearing stress and the formula of the shearing stress are not changed. Bending center(center of the shearing force)：Acting point of the lateral force not to make the rod produce torsion.（such as the preceding origin O of the coordinates.） P x y z O Use this expression to determine the distance e from axis x to the axis of the rod. 依此确定正应力计算公式。 剪应力研究方法与公式形式不变。 弯曲中心(剪力中心)：使杆不发生扭转的横向力作用点。 （如前述坐标原点O） P x y z O Channel steel： P Q e On the web On the flange Resultant H Resultant R, R ≈ Q e x y z P s M Conditions for the unsymmetrical beam to produce planar bending：Acting lines of external forces must lie in the principle plane of inertia and the neutral axis is the centroid principal axis. Lateral forces must be through the bending center. 槽钢： 非对称截面梁发生平面弯曲的条件：外力必须作用在主惯性面内，中性轴为形心主轴，,若是横向力，还必须过弯曲中心。 e x y z P P s M Q e Determination of the bending center: (1)For the section with double symmetric axes its cencroid is the bending center. (2)For the section of antisymmetry the antisymmetric center of the section is the bending center. (3)If the section consists of two narrow and long rectangles, the intersection of longitudinal lines of the two rectangles is the bending center