Chapter 1. Free Body Diagram
Higher category : 【Solid Mechanics】 Solid Mechanics Index
Problem. Equilibrium of Force and Moment
The simply-supported beam ABCD is loaded by a weight W = 27 kN through the arrangement shown in the figure. The cable passes over a small frictionless pulley at B and is attached at E to the end of the vertical arm. Calculate the axial force N, shear stress V, and bending moment M at section C, which is just to the left of the vertical arm. (Note: Disregard the widths of the beam and vertical arm and use centerline dimensions when making calculations.)
Solution.
⑴ OK, let’s get started to understand all of the factors. Note that every partitions can be expressed as Free Body Diagram and ΣF = 0, ΣM = O due to equilibrium state.
⑵ Free Body Diagram of the Cable.
⑶ at B. Keep in mind that there was no friction around points, so the point B is in equilibrium state of moment. Thus, two non-orthogonal lines are the same in the size of force.
⑷ And the reaction forces at B and E(oriented bottom-right and bottom-left, respectively.) would act toward the ‘⊥’ shaped things. So we can consider Free Body Diagram shown in the figure.
⑸ Then you should consider equilibrium of force and moment both. If you calculate two equations, you will get the unknown values of two reaction forces at the end of the bar.
Input: 2016.04.25 14:03