(a)
Find the orientation and magnitude of the principal strains in the plane.
(a)
Answer to Problem 149P
The orientation of the principal strains is
The in-plane maximum principal strain is
The in-plane minimum principal strain is
Explanation of Solution
Given information:
The normal strain in Rosette 1 is
The Rosette 1 makes an angle with the x-axis is
The normal strain in Rosette 2 is
The Rosette 2 makes an angle with the x-axis is
The normal strain in Rosette 3 is
The Rosette 3 makes an angle with the x-axis is
Calculation:
Write the equation for the normal strain 1 as follows;
Substitute
Write the equation for the normal strain 2 as follows;
Substitute
Write the equation for the normal strain 3 as follows;
Substitute
Add equation (1) and (2).
Substitute
Substitute
Find the orientation
Substitute
Therefore, the orientation of the principal strains is
Find the average normal strain
Substitute
Find the radius of the Mohr’s circle (R) using the equation.
Substitute
Find the in-plane maximum principal strain
Substitute
Find the in-plane minimum principal strain
Substitute
Therefore,
The in-plane maximum principal strain is
The in-plane minimum principal strain is
(b)
Find the in-plane maximum shearing strain.
(b)
Answer to Problem 149P
The in-plane maximum shearing strain is
Explanation of Solution
Refer to part (a);
The radius of the Mohr’s circle is
Find the in-plane maximum shearing strain
Substitute
Therefore, the in-plane maximum shearing strain is
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Chapter 7 Solutions
EBK MECHANICS OF MATERIALS
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