材料力-杆件的弯曲内力分析.ppt

CHAPTER 4 shearing and moment in beams 机械系 Shear and Moment in Beams 梁的剪（切）力与弯曲 Beam梁 The term beam is reserved for a slender bar that carries transverse横向 loading载荷 (the applied forces are perpendicular垂直于 to the bar) In this text, we consider only loadings that are also coplanar共面, that is, all the external forces lie in the symmetry对称面 xy-plane, where the x-axis coincides一致 with the centroidal axis of the bar. If the force are understood to act perpendicular to the longitudinal经度的axis, the only nonzero components of the internal force system acting on any cross section—for example, section m-m—are the shear force V (this cause shear stress) and the bending moment M (this cause normal stress) Support 1. Simply supported beam简支梁 Supports and Loads Support 2. Cantilever beam 悬臂梁 Supports and Loads Support 3.Overhanging beam外伸梁 Supports and Loads Loads 1. Concentrated load 集中力 Supports and Loads Loads 2. Distributed load 分布力 Supports and Loads Loads 3. Couple力偶 By plotting these expressions to scale, we obtain the shear force and bending moment diagrams剪力和弯矩图 for the beam. Analysis of Internal Forces free from section A support, FBD 解除A截面约 束, 受力分析. 解 according to FBD，establish equilibrium equation 根据受力图，建立平衡方程 according to equilibrium equation 根据平衡方程 解 according to FBD，establish equilibrium equation 根据受力图，建立平衡方程 according to equilibrium equation 根据平衡方程 The couple M is called the resisting moment抵抗力矩at section m-m. The magnitude of M may be found by use of a statics equation which states that the sum of the moments of all forces about an axis through m-m and perpendicular to the plane of the page is zero. ∑Mm-m =0, - FAyx + F1(x - a) +M= 0 or M = FAyx - F1(x - a) The vertical force V is called the resisting shear at section m-m. For equilibrium of forces in the vertical direction, ∑Fy =0, FAy - F1 - V= 0 or V =FAy - F1 The customary习惯的 sign conventions惯例 for shearing force and bending moment are represented