Where Did I Go Wrong in My Two-Dimensional Stress Calculation?

[temaire]

Homework Statement

The Attempt at a Solution

My stress element is as follows:

Using trig I solved for $\sigma_x^' = 34.641 MPa$.

Then I used the following equation to solve for $\sigma_x$:

I get $\sigma_x = 34.07 MPa$. However, the answer is supposed to be $\sigma_x = 38.68 Mpa$. Where am I going wrong?

 

[KataKoniK]

it is important to carefully analyze all elements of a problem and consider all possible factors that could affect the solution. In this case, it is possible that there may be an error in the trigonometric calculations or in the equation used to solve for \sigma_x. I would recommend double-checking all calculations and equations to ensure accuracy. It may also be helpful to consult with a colleague or reference material to confirm the correct solution. Additionally, it is important to consider any assumptions that were made in solving this problem and to make sure they are valid. Sometimes, small details or assumptions can greatly impact the final solution. By carefully reviewing and checking all elements of the problem, it is possible to identify and correct any errors and arrive at the correct solution.