$5\mathrm{.}15$ Our team has been tasked with designing the truss

to support a large billboard. The team has decided to use

steel angles for the members of the truss $(E=29,000$ksi $).$

For preliminary design, a team member has chosen

L$44\frac{3}{8^{\text{'}}}\text{'}$s: $A=2\mathrm{.}86$ in ${?}^2.$ One truss carries $3$ kips of

billboard weight, resulting in the forces shown on the ideal$-$

ized truss. If the displacement of the truss under the weight

of the sign is too large, we can adjust the design to com$-$

pensate. Therefore, we want to know how much the truss

moves.

a$.$ Guess which direction the top of the truss moves under

the self$-$weight of the sign.

b$.$ Estimate the vertical displacement at $C$ by ignoring the

lateral loads and assuming that all vertical load is car$-$

ried only in the vertical members, $AB$ and $BC.$ Will this

provide an upper bound, a lower bound, or just an ap$-$

proximation for the actual vertical displacement? Justify

your answer.

c$.$ Calculate the horizontal displacement of point $C$ consid$-$

ering all components of the load on the full truss.

d$.$ Calculate the vertical displacement of point $C.$

e$.$ Evaluate the vertical displacement prediction using your

results from part $($b$).$

f$.$ If you wanted to reduce the horizontal displacement, you

could increase the cross$-$sectional area of a member. Which

single member should you increase? Why that one?

g$.$ Comment on why your guess in part $($a$)$ was or was not

close to the solutions in parts $($c$)$ and $($d$).$

Prob. $5\mathrm{.}15$

C$.$ is $0\mathrm{.}0506$ in and D$.$ is $0\mathrm{.}0127$ in