$($a$)$ Complete Table $1$ for the truss shown in Figure $1.$ All members have a cross sectional

area of $3{10}^{-3}{m}^2$ and a Young's modulus of $200{10}^9\frac{N}{m^2}.$

$(15\%)$

Table $1$: Member definitions, properties and orientations

$($b$)$ Sketch and state the individual stiffness matrix for a truss element expressed in terms

of the global coordinate system.

$(5\%)$

$($c$)$ Assemble the stiffness matrix for the truss shown in Figure $2.$

$(20\%)$

$($d$)$ Using a stiffness matrix approach calculate the deflections at B$.$

$(20\%)$

$($e$)$ What is the role of shape functions in the finite element analysis procedure?

$(10\%)$

$($f$)$ What are the advantages of using elements with quadratic shape functions as opposed

to those formulated with linear shape functions?

$(10\%)$

$($g$)$ Describe two approaches that could be used to check the adequacy of a finite element

mesh in capturing the stress gradient in a region of a finite element model.

$(20\%)$