Question $1(34$ marks$)$

The figure below shows a $2$D truss structure where the cross$-$sectional area of each member is $0\mathrm{.}03m^2$ and the structure is made of steel $($modulus$,E=200$GPa $).$

a$)$ Detemine the global stiffiness matrix, Kglobal, for the structure.

$(15$ marks$)$

b$)$ A force of $3$ kN is applied at node $3$ in the direction shown. Determine the horizontal and vertical displacements at node $3$ of the truss structure.

$(8$ marks$)$

c$)$ Determine the horizontal and vertical reaction forces at node $4.$

$(6$ marks$)$

d$)$ Determine the axial stress of the element located between nodes $2$ & $3.$

$(5$ marks$)$

Figure Q$1$