1-24. An element is subject to a normal stress and a shear stress  as shown in the figure. If the element is oriented  clockwise from its current position, determine the distribution of the equivalent state of stress. Assume  and  are independent.

Solution:

According to the stress diagram, we have

, , ,

Thus,   follows .

,   

Thus,   follows .

Thus,   follows .                                                                            Ans.