The forces in the given structure $($Figure $1$A$)$ due to an applied load of $35kN$ and $84kN$ are shown in

Figure $1$B$.$ Find the vertical deflection at point B due to an applied vertical load increasing from $84kN$ to

$126kN$ at joint $B$ and the horizontal load increasing from $35kN$ to $52\mathrm{.}5kN$ at joint $D.$ The directions of the

increased forces remain as those of the original forces. Assume that all the structural members obey

Hooke's law up to the load increase.

The forces in the structural members due to an applied vertical load of $1kN$ acting at joint $B$ are shown in

Figure $1$C$.$ The length, cross$-$sectional area, and modulus of elasticity of each member are provided in

Figure $1$A$.$ Use the virtual work method to find the deflection and show your work

Fig. $1A$

Fig. $1$B

Fig. $1$C