helpFigure Q$2$ shows the equilateral triangular truss structure with the boundary conditions and loadings as shown. All the truss members have a uniform cross$-$section of $100m{m}^2$ and are made from aluminum with Young's Modulus $E=200$GPa.

$($a$)$ Model this truss structure optimally using the least number of elements considering the symmetrical of the structure. Label the nodes and elements, and clearly indicate the status of all the relevant degrees$-$of$-$freedom of this model.

$($b$)$ If the vertical displacement of point B is $1mm,$ analyze the unknown degrees$-$offreedom and determine the reaction forces at $A.$