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9th Edition

Barry J. Goodno + 1 other

Publisher: Cengage Learning

ISBN: 9781337093347

Chapter 7, Problem 7.7.16P

Textbook Problem

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Solve the preceding problem if the plate is made of aluminum with *E *= 72 GPa and Poisson’s ratio *v *= 0.33. The plate is loaded in *biaxial stress *with normal stress *s _{x}*= 79 MPa, angle Ø = 18°, and the strain measured by the gage is e =

To determine

The maximum shear stress and strain in x-y plane.

The maximum shear strain in x-z plane and y-z plane.

**Given information:**

Modulus of elasticity is

Write the Equations to obtain maximum in-plane shear stress.

Here, the normal strain along x direction is

Write the expression for the strain along x direction.

Here, direct stress along x direction is

Write the expression for strain along y direction.

Here, direct stress in y direction is

Substitute value of direct stresses of x and y plane in Equation (I).

Write the expression for stress in x-y direction

Here,

Write the expression for strain in x-y direction

Write the expression for the maximum shear stress in plane x-z.

Write the expression for the maximum shear strain in x-z direction.

Write the expression for the maximum shear stress in y z direction.

**Calculation:**

Substitute

Substitute

Mechanics of Materials (MindTap Course List)

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