Problem $1(25$ points$)$

The three trusses below have the same horizontal dimension and loading, but differ in their vertical dimensions $($i$.$e$.$ the height varies from $0\mathrm{.}5$ m to $1$ m $).$

a$)$ Calculate the axial forces that act on members $\backslash (\backslash$mathrm$\{$BG$\},\backslash$mathrm$\{$BH$\}\backslash ),$ and HG $($the blue members$)$ for each of the three trusses.

b$)$ What conclusions can you draw from part a$?$ What do you think are some advantages and disadvantages of tall vs$.$ short truss designs? Feel free to include non$-$quantitative factors in your response.