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 27â€‰GPa , The diameter of the bar is 40â€‰mm and the torque on the solid bar is 300â€‰Nâ‹…m .

Write the expression for maximum shear in the bar.

â€ƒâ€ƒÏ„max=16TÏ€d3...... (I)

Here, the maximum shear in the bar is Ï„max , 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.

â€ƒâ€ƒÏƒt=âˆ’Ïƒc=Ï„max ...... (II)

Here, maximum tensile stress is Ïƒt and maximum compressive stress is Ïƒc .

Calculation:

Substitute 300â€‰Nâ‹…m for T , 40â€‰mm for d in Equation (I).

â€ƒâ€ƒÏ„max=16(300â€‰Nâ‹…m)Ï€( 40â€‰mm)3(480000â€‰Nâ‹…m)Ï€( 40â€‰mm( 1â€‰m1000â€‰mm ))3=(4800â€‰Nâ‹…m)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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