Solving Strain in a Box on the X-Y Axis: A Homework Problem

[Bradracer18]

Homework Statement

I've got a problem that I can't figure out. It deals with strain.

I've got a box, sitting on the x-y axis(like normal x-y axis's are). The box extends 4 inches from the origin in the x direction, and 2 inches up. Going clockwise(starting at origin) the corners are labeled A, D, C, B.

epsilon(or strain) in the x direction is = + 880 u in/in.
strain in y direction = + 960 u in/in
and finally, the shear(or gamma) strain in the xy direction is = -750 u radians.

Need to determine the normal strain Eac along the diagonal AC(there is a line from A to C).

u is micro...so x10^-6.

Homework Equations

strain(E) = (Ex +Ey)/2 + (Ex - Ey)/2 *cos2(theta) + gamma(xy)*sin2(theta)

The Attempt at a Solution

Sorry for so many words, I don't know how to make symbols. I hope you get the picture of how I explained it. Basically, I think this box is stretching upwards and to the right(slanted to the right and to the "up", from the origin).

My question is, what is theta...the rest is pretty obvious...I can not find theta.

My answer sheet say the answer is 596 u in/in. And, using that equation, I put in theta's and found about 60.15 degrees to work. I can't for the life of me, find how 60 degrees works though.

I appreciate you help.

Brad

 

[Bradracer18]

Is this not understandable?

 

[radou]

Theta is the angle between the x-axis and the AC diagonal.