MATERIALS SCI + ENGR: INT W/ACCESS
MATERIALS SCI + ENGR: INT W/ACCESS
10th Edition
ISBN: 9781119808084
Author: Callister
Publisher: WILEY
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Chapter 6, Problem 28QAP

a)

To determine

The magnitude of load to produce an elongation of δl=0.45mm .

b)

To determine

The deformation after the load released.

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An elastic bar of the length L and cross section area A is rigidly attached to the ceiling of a room, and it supports a mass M. Due to the acceleration of gravity g the rod deforms vertically. The deformation of the rod is measured by the vertical displacement u(x) governed by the following equations: dx (σ(x)) + b(x) = 0 PDE σ(x) = Edx du Hooke's law (1) b(x) = gp= body force per unit volume where E is the constant Young's modulus, p is the density, and σ(x) the axial stress in the rod. g * I u(x) L 2
An elastic bar of the length L and cross section area A is rigidly attached to the ceiling of a room, and it supports a mass M. Due to the acceleration of gravity g the rod deforms vertically. The deformation of the rod is measured by the vertical displacement u(x) governed by the following equations: dx (σ(x)) + b(x) = 0 PDE σ(x) = Edx du Hooke's law (1) b(x) = gp= body force per unit volume where E is the constant Young's modulus, p is the density, and σ(x) the axial stress in the rod. g * I u(x) L 2
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