Chap_4(材料力学课件)讲解.ppt

Chapter 4 Internal Forces In Bending 1 2 §4–3 梁的剪力和弯矩 一、弯曲内力： [举例]已知：如图，P，a，l。 求：距A端x处截面上内力。 P a P l YA XA RB A A B B 解：①求外力 A B P YA XA RB m m x ②Determine internal forces— method of section A YA Q M RB P M Q Internal forces of the beam in bending Shearing force Bending moment 1). Bending moment：M Moment of the internal force couple with the acting plane in the cross-section perpendicular to the section when the beam is bending. C C A B P YA XA RB m m x ②求内力——截面法 A YA Q M RB P M Q ∴ 弯曲构件内力 剪力 弯矩 1. 弯矩：M 构件受弯时，横截面上其作用面垂直于截面的内力偶矩。 C C 2). Shearing force：Q Internal force which the acting line in the cross-section parallel to the section, when the beam is bending. 3).Sign conventions for the internal forces: ① Shearing force Q: It is positive when it results in a clockwise rotation with respect to the object under consideration, otherwise it is negative. ②Bending moment M：It is positive when it tends to bend the portion concave upwards, otherwise it is negative. Q(+) Q(–) Q(–) Q(+) M(+) M(+) M(–) M(–) 2. 剪力：Q 构件受弯时，横截面上其作用线平行于截面的内力。 3.内力的正负规定: ①剪力Q: 绕研究对象顺时针转为正剪力；反之为负。 ②弯矩M：使梁变成凹形的为正弯矩；使梁变成凸形的为负弯矩。 Q(+) Q(–) Q(–) Q(+) M(+) M(+) M(–) M(–) Example 2：Determine the internal forces acting on sections 1—1 and 2—2 section as shown in fig.(a). Solution：Determine internal forces by the method of section. Free body diagram of the left portion of section 1—1 is shown in fig.（b）. Fig.（a） 2、Examples q qL a b 1 1 2 2 qL Q1 A M1 Fig. （b） x1 [例2]：求图（a）所示梁1--1、2--2截面处的内力。 x y 解：截面法求内力。 1--1截面处截取的分离体 如图（b）示。 图（a） 二、例题 q qL a b 1 1 2 2 qL Q1 A M1 图（b） x1 Free body diagram of the left portion of  section 2—2 is shown in fig.（b）. x y 图（a） q qL a b 1 1 2 2 qL Q2 B M2 x2 图（c） 2--2截面处截取的分离体如图（c） x y 图（a） q qL a b 1 1 2 2 qL Q2 B M2 x2 图（c） 1. Internal-force equations: Expressions that show the internal forces as functions of the position x of the section.. 2. The shearing-force and bending-moment diagrams: ) ( x Q Q = Shearing force equation )