A specimen used in a coupon test is shown in the figure. The stresses on element A are known to be s y = -1500 psi. Use Mohr’s circle to: (a) Find the stresses acting on the element oriented at an angle ?? = -35°. (b) Find maximum normal and shear stresses and show them on sketches of properly oriented elements.

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 7, Problem 7.4.9P
Textbook Problem

A specimen used in a coupon test is shown in the figure. The stresses on element A are known to be sy= -1500 psi. Use Mohr’s circle to: (a) Find the stresses acting on the element oriented at an angle ?? = -35°. (b) Find maximum normal and shear stresses and show them on sketches of properly oriented elements.

Expert Solution

(a)

To determine

The state of stress on the element oriented at angle 35°.

Explanation of Solution

Given information:

The normal stress at point A along y-axis is 1500psiand orientation of element is 35°.

Write the expression for average stress.

σavg=σx+σy2(I)

Here, average stress is σavg, normal stress along x-direction is σx, and normal stress along y-direction is σy.

Write the expression for the radius of Mohrs circle.

R=(σx+σy2)2+τxy(II)

Here, the radius of the Mohrs circle is Rand shear stress along xy-plane is τxy.

Write the expression for the normal stress on element along x-direction.

σx1=σavg+Rcos(2θ)(III)

Here, normal stress on element along x-direction is σx1and orientation of the element is θ.

Write the expression for the normal stress on element along y-direction.

σy1=σavgRcos(2θ)(IV)

Here, normal stress on element along y-direction is σy1.

Write the expression for shear stress on the element.

τx1y1=Rsin(2θ)(V)

Here, shear stress on oriented element is τx1y1.

Calculation:

Substitute 0for σxand 1500psifor σyin equation (I).

σavg=0psi+(1500)psi2=1500psi2=750psi

Substitute 0for σx, 1500psifor σy, and 0for τxyin equation (II).

R=(0psi+(1500psi)2)2+(0psi)2=(750psi)2=750psi

Substitute 750psifor σavg, 750psifor Rand 35°for θin equation (III)

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