Question $2$: Calculate the mid$-$span deflection in vertical direction using the principle of virtual work. Use $A=29\mathrm{.}4i{n}^2.$ Ignore the self$-$weight of the members and consider only the

In this case, we will model passenger cars with a typical weight of $4,000$ pounds $(4$ kips$)$ or $2,000(2$ kips$)$ per axle. We will represent the bridge geometry using a plane Pratt truss. The final structure and the applied external load are given below:

$\backslash$table$[[$in $$ lb$/$it$,$Area $($in $(,$d $($in$),$bf $($in$),$tf $($in$),$tw $($in$),$Ixx $($in $4),$Iyy $($in $)],[$W$16$x$100,29\mathrm{.}4,16\mathrm{.}97,10\mathrm{.}425,0\mathrm{.}985,0\mathrm{.}585,1490,186]]$

Figure $2$: Idealized Truss Geometry

The half weight of each passenger car is $P=2k.$ The member spacing is $L=20ft.$ The cross section of each truss member is constant and shown in Figure $2$ above. Each truss member is made of A$992$ steel, which has $E=29,000$ ksi.loading shown in Figure $2.(30$pts$)$