The figure below shows a planar truss

$($a$)$ Find out the displacement at 'node $2\text{'}$ marked in the figure by using the Direct

Stiffness Method & also find out the reaction forces & member forces $($analytic hand

calculation$)$

$($b$)$ Following this, develop a 'MATLAB program' for the planar truss problem as given

in the figure below and carry out the following tasks: $($i$)$ Assembly of element

stiffness matrices $($ii$)$ Application of boundary conditions $($iii$)$ Solution for nodal or

joint displacements $($iv$)$ reaction forces & $($v$)$ member forces

$A_1=A_2=1\mathrm{.}5c{m}^2$

$E=2{10}^7\frac{N}{c}{m}^2$