   # Repeat the preceding problem using s x = 5.5 MPa. ?? y = 4 MPa. and t x y = 3.2 MPa. ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 7, Problem 7.3.2P
Textbook Problem
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## Repeat the preceding problem using sx= 5.5 MPa. ??y= 4 MPa. and txy= 3.2 MPa. To determine

The principal stresses acting on the body.

### Explanation of Solution

Given information:

The normal stress acting on the element in x-direction is 5.5MPa , the normal stress acting on the element in y-direction is 4MPa and the shear stress acting on the element is 3.2MPa .

Write the expression for average stress acting on the body.

σavg=σx+σy2 ...... (I)

Here, the normal stresses acting along x and y direction is σx and σy , average stress acting on the body is σavg .

Write the expression for radius of Mohr’s circle.

R=( σ x σ y 2)2+τxy2 ...... (II)

Here, shear stress along the xy plane is τxy , radius of the Mohr’s circle is R .

Write the expression for maximum and minimum principal stress acting on the body.

σ1=σavg±R ...... (III)

Here, maximum principal stress is σ1 .

Write the expression for maximum shear stress.

τmax=R ...... (IV)

Here, maximum shear stress is τmax .

Write the expression for principal angle.

θp1=12tan1(2τxyσxσy)...... (V)

Here, principal angle is θp1 .

Write the expression for shear angle.

θx1=θp145° ...... (VI)

Here, shear angle is θx1 .

Calculation:

Substitute 750psi for σx and 600psi for σy .in Equation (I).

σavg=750psi( 0.00689MPa 1psi)+600psi( 0.00689MPa 1psi)2=5.1675MPa+4.134MPa2=9.3015MPa2=4.65MPa

Substitute 750psi for σx , 600psi for σy and 400psi for τxy in Equation (II).

R=( { 750psi( 0.00689MPa1psi )}{ 600psi( 0.00689MPa1psi )}2 +{400psi( 0

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