Problem $1(5$ points$)$

Using the Double$-$Integration Method, compute the equation$($s$)$ for the deflected shape of the beam shown below. Assume that $E,$I, and $L$ are known. The left support is a pin and the right support is a roller.

Hint: You will have two equations that express the deflection: one from $0$ to $\frac{L}{2},$ and the other from $\frac{L}{2}$ to $L.$ There will be four constants of integration that you need to find. Two of our conditions are that displacement at A and B are zero. The other two conditions come from the fact that the beam is continuous at midspan $)=(\frac{L}{2}.$ Continuity means that slope and displacement should be the same for the two different equations when both are evaluated at $x=\frac{L}{2}.$

Problem $2(5$ points$)$

Using the Method of Virtual Work, find the vertical displacement at Point A on the truss to the right. Assume that $E=200$GPa and that cross$-$sectional area $A=300m{m}^2.$

$C=$ Pin

$D=$ Pin

$($Despite the two pins, this is determinate $-$ you can solve this. We know that the vertical reaction force at $D$ must be zero by taking the method of joints at location D$.)$

Warning $-$ Units for E and I are very important! Be careful and make sure they match with the units for the loads and lengths given in the problem.

$1$GPa$={10}^9\frac{N}{m^2}=1k\frac{N}{m}{m}^2.$ I find this problem is easier if you convert everything to millimeters and kilo$-$Newtons, but Newtons and meters is fine too.