# Complex stress problem

1. Apr 10, 2009

### rock.freak667

1. The problem statement, all variables and given/known data

In an element of material, subjected to general two-dimensional stress one axial stress is 66N/mm2 (tensile) and the shear stress is 48N/mm2. Calculate the values and directions of the principal stresses and the normal and shear stresses on planes equally inclined to the axes if the other axial stress of 22N/mm2 is a) tensile and b)compressive.

2. Relevant equations

$$\sigma_n=\frac{1}{2}(\sigma_x+\sigma_y)+\frac{1}{2}(\sigma_x-\sigma_y)cos2\theta+\tau_{xy}sin2\theta$$

$$\tau_n= \frac{1}{2}(\sigma_x-\sigma_y)sin 2\theta-\tau_{xy}cos2\theta$$

3. The attempt at a solution

Well I used the fact that the principal stresses are given by

$$\sigma_1,\sigma_2=\frac{1}{2}(\sigma_x+\sigma_y) \pm \sqrt{(\sigma_x-\sigma_y)^2+4\tau_{xy}^2$$

and got the values to be 96.8 N/mm2 and -8.80N/mm2

Then I used the fact that

$$tan2\theta=\frac{2\tau_{xy}}{\sigma_x-\sigma_y}$$

and got $\theta=32.69$. That part I got out, but I don't know how to get the normal and shear stresses on planes equally inclined to the axes.

I am not sure about what the question means by equally inclinded to the axes.

EDIT:solved.

Last edited: Apr 10, 2009