Exercise $8\mathrm{.}1$: Use the Virtual Displacement Method and solve the following problems:

a$)$ Determine the horizontal and vertical displacements at point A and the forces in members AC and AD for the two$-$bar truss shown in Figure $8\mathrm{.}1($a$).$

b$)$ Check the results for the forces in the members by comparing them against the forces found by the methods for joints.

c$)$ In Figure $8\mathrm{.}1($b$)$ there have been two members added: AB and AE $.$ For all four members $\backslash ((\backslash$mathrm$\{$AB$\}\backslash ),\backslash (\backslash$mathrm$\{$AC$\},\backslash$mathrm$\{$AD$\}\backslash ),$ and AE $)$ find the horizontal and vertical displacements at point A and the forces in each member.

The ratios of cross sectional area to bar length, $\backslash (\backslash$mathrm$\{$A$\}\_\{$i$\}/\backslash$mathrm$\{$L$\}\_\{\backslash$mathrm$\{$i$\}\}\backslash ),$ for each bar $"\backslash ($ i $\backslash )"$ are as follows: $0\mathrm{.}04$ for bar AB and bar $\backslash (\backslash$mathrm$\{$AD$\},0\mathrm{.}02\backslash )$ for bar AC $,$ and $0\mathrm{.}08$ for bar AE $.$ Assume the elastic modulus is $\backslash (\backslash$mathrm$\{$E$\}=200\backslash$mathrm$\{$GPa$\}\backslash ).$

$($a$)$

Figure $8\mathrm{.}1$