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Lab Report

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City University of Hong Kong

Dept. of Physics & Materials Science

AP2104 Mechanics of Solids

Laboratory Manual

Experiment 1Pure Bending of a Beam

Experiment 2Torsional Deformations

Experiment 3Yield Criteria for Ductile Materials under Plane Stresses

Experiment 1

Pure Bending of a Beam

Objective

1. To examine the stresses at various positions of the beam under a constant load of pure bending.

2. To determine the curvature of deflection of the beam.

Introduction

1. Pure Bending and Nonuniform Bending

When analyzing beams, it is often necessary to distinguish between pure bending and nonuniform bending. Pure bending refers to flexure of a beam under a constant bending moment. Therefore, pure bending occurs only in regions of a beam where the shear force is zero ( because V = dM/dx ). In contrast, nonuniform bending refers to flexure in the presence of shear forces, which means that the bending moment changes as we move along the axis of the beam. As an example of pure bending, consider a simple beam AB loaded by two couples M1| having the same magnitude hut acting in opposite directions (Fig. 1a). These loads produce a constant bending moment M = M1 throughout the length of the beam. Note that the shear force V is zero at all cross sections of the beam. [pic]

[pic]
Fig. 1 (a) Simple beam in pure bending. (b) Cantilever beam in pure bending

Another illustration of pure bending is given in Fig. 1b, where the cantilever beam AB is subjected to a clockwise couple M2 at the free end. There are no shear forces in this beam, and the bending moment M is constant throughout its length. The bending moment is negative (M = - M2). The symmetrically loaded simple beam of Fig. 2a is an example of a beam that is partly in pure bending and partly in nonuniform bending, as seen from the shear-force and bending-moment diagrams (Figs. 2b and c). The central...