Figure $4\backslash$table$[[$L$\_($AB$)($m$),$L$\_($BC$)($m$),$F$\_($x$)($kN$),$F$\_($y$)($kN$),$A$($mm$^(2)),$E$($N$/$mm$^(2))],[4,2\mathrm{.}5,35,0,200,210000]]$ a$)$ Using a stiffness matrix approach, calculate the displacements $($x and y$)$ of the loaded Figure $4$

joint of the truss arrangement shown in Figure $4.$ Each member has a cross$-$sectional

area of A mm$2$

and Young$$s modulus of E N$/$mm$2$

$.$ The values of A$,$ E$,$ LAB, LBC$,$ Fx

and Fy are given in Table $2$ and are different for each student.

Note: Only hand calculations will be accepted. $(60\%)$

Figure $4$

b$)$ Calculate the stress and strain in member AC and state whether it is in tension or

compression. $(10\%)$

c$)$ Explain the differences between four noded quadrilateral elements and eight noded

quadrilateral elements. $(15\%)$

d$)$ Explain the difference between the nodal solution and the element solution for an

element using linear shape functions.