MIDTERM $2$

$(30$ minutes$)$ Consider the composite beam ABCDE shown on the right. It is loaded with vertical concentrated loads at points $A,C$ and $E$ with magnitudes $P,2P$ and $P,$ respectively. The cross$-$section has a brass core and steel cover. Allowable normal stress of steel is $160$MPa and its elastic modulus is $200$GPa. Allowable normal stress of brass is as $40$MPa and its elastic modulus is $100$GPa.

a$.$ Determine the maximum value of the load $P.$

b$.$ Determine the minimum value of the radius of curvature on the composite beam.

$\backslash$table$[[=\frac{P}{A},\backslash$table$[[E=\frac{}{},=\frac{PL}{AE}$