Assume any missing data.

Problem $1(40$ points$)$:

The following rolled$-$steel shape with yield strength $210$ MPa and Young's modulus $200$ GPa is selected to support a given loading at a minimal cost and a safety factor of $1\mathrm{.}3.$

a$)$ Select the most economical wide$-$flanged beam to support the loading shown,

b$)$ Determine the actual value of ${}_m$ in the beam,

c$)$ Determine the principal stress ${}_{\text{m}\text{a}\text{x}}$ at the junction of a flange and the web,

d$)$ Calculate the deflection at point $C,$ and the slope at point $A.$