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9th Edition

Barry J. Goodno + 1 other

Publisher: Cengage Learning

ISBN: 9781337093347

Chapter 7, Problem 7.5.4P

Textbook Problem

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An element of a material is subjected to plane stresses as shown in the figure. The stresses *o, cry., *and are 10 MPa, *—15 *MPa, and *5 *MPa. respectively. Assume *E *= 200 GPa and v = 0.3.

(a) Calculate the normal strain in the *x, *v. and *z *directions and the shear strain.

(b) Calculate the strain-energy density of the element.

** (a)**

To determine

The normal strain in the

The normal strain in the

The normal strain in the

** Given information:**

The normal stress in the

** Explanation:**

Write the expression for the modulus of rigidity.

Here, the modulus of Rigidity is

Write the expression for the strain in

Here, the normal stress in

Write the expression for the strain in

Write the expression for strain in the

Write the expression for the shear strain in

Here, the shear stress in the

** Calculation:**

Substitute

Substitute

Substitute

** (b)**

To determine

The strain energy density of the element.

Mechanics of Materials (MindTap Course List)

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