Problem $3)$

$(20$ points$)$

Consider a composite bimetallic bar with a section consisting of aluminum and steel as shown

below. The modulus of elasticity $E$ of the aluminum is $10,000$ kips per square inch and the

modulus of elasticity $E$ of the steel is $30,000$ kips per square inch $($recall $1$ kip $=1000$ pounds$).$

The bar has cross$-$sectional dimensions indicated on the sketch at the left. The bar is

compressed by forces $P=50$ kips acting through rigid end plates which causes a uniform

compressive stress in each bar. The line of action of the loads has an eccentricity e with the

middle of the bar. Determine:

a$)$ The axial force in the aluminum bar and the axial force in the steel bar.

$(10$ points$)$

b$)$ The eccentricity $e$ of the loads.

$(10$ points$)$