Is the Maximum Shear Strain Direction Always 45 Degrees?

[temaire]

Homework Statement

Homework Equations

$$\gamma_{max} = {\left|{\epsilon_1} - {\epsilon_2} \right|}$$

The Attempt at a Solution

I calculated the maximum shear strain to be $200 \mu$.

For the angle, I don't know exactly how to go about finding it. However, the solution says that the angle is $45^{\circ}$. Does this mean that all they were asking was to state the angle between the maximum shear plane and the principal plane, which is always $45^{\circ}$? Or am I supposed to solve for the maximum shear plane angle by first finding the principal plane angle and subtracting $45^{\circ}$ from it?

 

[CJSGrailKnigh]

You need to get chummy with your buddy the Mohr stress/strain circle... although just looking at the question you could solve it purely from math. I assume you have a solid mechanics or mechanics of materials textbook you could easily find it in there.

 

[temaire]

You need to get chummy with your buddy the Mohr stress/strain circle... although just looking at the question you could solve it purely from math. I assume you have a solid mechanics or mechanics of materials textbook you could easily find it in there.

Our professor explicitly told us not to use Mohr's circle for this question.

I have tried looking through my mechanics of materials textbook, but couldn't find a way of solving for the direction angle of the maximum shear strain, just with having the principal strains and the maximum shear strain.

I want to know whether the question was supposed to ask you to state the angle between the maximum shear strain and the angle and the principal plane angle. I know this sounds trivial, but the answer to this problem does say $45^{\circ}$.

 

[nvn]

temaire: I currently think you worked the problem correctly. I currently think all they were asking for was to state the angle between the maximum shear plane and principal planes, which is always 45 deg.

 

[temaire]

temaire: I currently think you worked the problem correctly. I currently think all they were asking for was to state the angle between the maximum shear plane and principal planes, which is always 45 deg.

Thank you nvn. That's what I was thinking as well.

 

[Kaycee92]

Always 45 deg. You're right.