Problem $1$:

Determine the stresses at point $m,$ and show the results in an element located at this point.

Problem $2$

Draw Mohr's Circle for the element in the figure and find the following using the mohr's circle:

a$)$ Orientation of Principal Planes and Principal Stresses.

b$)$ Magnitude and direction of shear stresses on Principal Planes.

c$)$ Maximum In$-$plane Shear Stress and the orientation of the plane subjected to Maximum In$-$plane Shear Stress.

d$)$ Magnitude and direction of normal stresses on the plane subjected to maximum shear stress

e$)$ The state of stress on a plane rotated $30$ degrees counter clockwise.

Problem $3$:

For the beam and cross section in problem $1,$ design the spacing of the nails connecting the two webs to the flange. Each nail can resist the shear force of $600lbf.$ Use two different spacing for economy.