# A propeller shaft subjected to combined torsion and axial thrust is designed to resist a shear stress of 57 MPa and a compressive stress of 105 MPa (see figure). (a) Determine the principal stresses and show them on a sketch of a properly oriented element. (b) Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element.

### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 7, Problem 7.3.16P
Textbook Problem
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## A propeller shaft subjected to combined torsion and axial thrust is designed to resist a shear stress of 57 MPa and a compressive stress of 105 MPa (see figure). (a) Determine the principal stresses and show them on a sketch of a properly oriented element. (b) Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element.

(a)

To determine

The principal stresses and sketch the orientation of element

### Explanation of Solution

Given information:

The normal stress along x-axis is 105MPathe normal stress along y-axis is 0MPathe shear stress along x-y plane is 57MPa

Write the expression of the principal stresses

σ1,2=σx+σy2±(σxσy2)2+τxy2        …… (I)

Here, the normal stresses along the x-axis is σxthe normal stresses along the y-axis is σythe shear stress along x-y plane is τxythe maximum principal stress is σ1the minimum principal stress is σ2

Write the expression of the inclination of principal stresses:

tan2θ=2τxyσxσy        …… (II)

Here, the angle of orientation of the principal stress plane is θ

Calculation:

Substitute 105MPafor σx

0MPafor σyand τxy=57MPain Equation (I).

σ1,2=(105MPa)+0MPa2±(105MPa0MPa2)2+(57MPa)2=52

(b)

To determine

The maximum shear stress and sketch the orientation of element.

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