Problem $3$: A square concrete beam with a cross$-$section of $4-$in by $4-$in spans a gap of $7$ feet and is constrained on both sides $($Hin: use $13$ for concrete's thermal expansion and $10{10}^6$ for the modulus of elasticity$).$

a$.$ Find the thermal stress $({}_T)$ experienced by the beam is it is exposed to a temperature swing of $10C$ to $40C.$

b$.$ How wide would an expansion joint need to be if we wanted to reduce the thermal stress $({}_T)$ by $40\%($hint: solve for $($:$L\}?$