   Chapter 3, Problem 3.5.12P Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347 Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347
Textbook Problem

A solid aluminum bar (G = 27 GPa ) of diameter d = 40 mm is subjected to torques T = 300 N - m acting in the directions shown in the figure, Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements. (a)

To determine

The maximum shear stress.

The maximum tensile stress.

The maximum compressive stress.

The stresses on the element in diagrammatically form.

Explanation

Given information:

The shear modulus of solid bar is 27GPa , The diameter of the bar is 40mm and the torque on the solid bar is 300Nm .

Write the expression for maximum shear in the bar.

τmax=16Tπd3...... (I)

Here, the maximum shear in the bar is τmax , the torque is T and the diameter of the bar is d .

Since the maximum tensile and compressive stress are equal to shear stress on the plane of maximum shear stress.

σt=σc=τmax ...... (II)

Here, maximum tensile stress is σt and maximum compressive stress is σc .

Calculation:

Substitute 300Nm for T , 40mm for d in Equation (I).

τmax=16(300Nm)π( 40mm)3(480000Nm)π( 40mm( 1m1000mm ))3=(4800Nm)2

(b)

To determine

The maximum shear strain.

The maximum tensile strain.

The maximum compressive strain.

The strains on the deformed element in diagrammatically form.

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