Question $1$: A square $10$ inch by $10$ inch plate with a $\frac{1}{2}$ inch thickness is subjected to the forces as shown. The plate is welded at an angle of $40$ degrees to the horizontal axis and the forees are assumed to be distributed uniformly to all four sides of the plate.

$[20$ marks$]$ Use the Mohr's cincle solution $($not the Iransformation equations$)$ to determine the following:

$($a$)$ stresses acting on a weld orientated $40$ degrees to the horizontal. Show your answer on a properly orientated element.

$($b$)$ the maximum in$-$plane shear stress $($and associated normal stresses$)$ and orientation of the corresponding planes. Once again, show your answer on a sketch of a properly oriented element.

Note that credit will only be given for a solution using Mohr's circle. This means that you need to draw a Mohr's circle based on the stress components given in this problem. Remember to show numbers on your circle. Your calculations must be based on the geometry of your circle. So use your calculator. In other words, you are expected to use trigonometry to construct your Mohr's circle. Do not give a graphical solution that is scaled off! The stress transformation equations can only be used to check your answer.

CE $2023$: Mechanics of Materials

April $14,2008$

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