PART I

The cantilever beam supports a constant distributed load of $10$kips$/$foot and a point load of P$.$

A$)$ Draw the shear force and bending moment diagrams for the beam. Indicate the critical points $($i$.$e$.,$ maximum values$)$

B$)$ If sigma allowable is $30$ ksi $,$ tau allowable is $6$ ksi $,$ the nail shear strength is $20$ kips $,$ and the nail spacing is $2$ inches, what is the maximum allowable force P on the beam?

$-$Note: The moment of inertia is $264\mathrm{.}6$in$^(4),$ the location of the neutral axis is $4\mathrm{.}5$ inches from the top of the cross section.

PART II

Let P$=10$kips.

ybar $=4\mathrm{.}5$ inches from top of cross section

I$=264\mathrm{.}6$in$^(4)$

A$)$ What is the principal stress in the beam at point A$.$ Draw these stresses on a stress block.

B$)$ Construct Mohr's Circle for the stress block you determined in part A and indicate all critical points $($i$.$e$.,$ center, point A$,$ radius$)$

C$)$ What are the in$-$plane principal stresses $($sigma $1$ and sigma $2)?$

D$)$ What angle does the major principal stress $($sigma $1)$ act at$?$

E$)$ Draw the stress block for the in$-$plane principal stresses calculated in part C$.$