Name:

CCE $203-$ HW $7\mathrm{.}1-7\mathrm{.}3$

Date:

You suffer from sleepwalking, and sometimes you sleepwalk so far away that you can't find your way back home. This morning you woke up on the ground of a truck stop right under a fuel tanker$.$ Because you are still groggy from just waking up$,$ you had the "amazing" idea to calculate the stresses acting on a rotated stress element on the bottom of a fuel tanker at a unique angle. From a late$-$night scrolling through YouTube, you know that the stresses acting on the bottom surface of a fuel tanker are ${}_x=7750,{}_Y=1175$ psi $,$ and ${}_{xY}=940$ as shown in figure. If you rotate the stress element at an angle $=55$ from the x $-$axis $($where a positive angle denotes counterclockwise rotation$),$ what are the new stresses acting on the element?

Draw these stresses on a sketch of an element oriented at the angle $.$