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9th Edition

Barry J. Goodno + 1 other

Publisher: Cengage Learning

ISBN: 9781337093347

Chapter 7, Problem 7.7.7P

Textbook Problem

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A thin square plate in *biaxial stress *is subjected to stresses *?? *and *??., *as shown in part a of the figure. The width of the plate is *h *= 12.0 in. Measurements show that the normal strains in the *x *and *v *directions are s = 427 **× 10-6 **and s = **113 **× l0-6, respectively.

With reference to part b of the figure. which shows a Iwo-dimensional view of the plate. determine the following quantities.

(a) The increase *.d *in the length of diagonal *Oil. *

(b) The change . in the angle between diagonal *Oti *and the *x *axis,

(c) The shear strain y associated with diagonals * Oil *and cf(that is. find the decrease in angle

** (a)**

To determine

The increase in the length of the diagonal.

** Given information:**

The width of the square plate is

** Explanation:**

Write the expression for the length of the diagonal.

Write the expression for strain along

Write the expression for change in diameter.

** Calculation:**

Substitute,

Substitute,

(b)

To determine

The change in the angle between diagonal Od and the x-axis.

(c)

To determine

The shear strain associated with the diagonals.

Mechanics of Materials (MindTap Course List)

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