$[2]$ Problem $2$:

A $4$ noded scaffolding truss has been setup to support a load $($P$)$ in $-$ve $y-$direction as shown in the figure. The

coordinates of the nodes are as follows

Figure $2$: Scaffolding Truss $($in $3$D$)$

Material Properties and Cross$-$sectional Area:

$E=210$GPa

$A=0\mathrm{.}002m^2$

Loads:

$P=20kN$

Nodal Coordinates: $($All dimensions are in m$.)$

$1-=(0,4\mathrm{.}2,0),2-=(0,0,4\mathrm{.}2),3-=(4\mathrm{.}2,0,0),4-=(0,0,0)$

NOTE: Nodes $2,3$ and $4$ are pinned to the ground

a$)$ Construct the System Free Body Diagram for the truss $(2$ pts$)$

b$)$ Find unknown displacements $(3$ pts$)$

c$)$ Find Reaction forces at nodes $2\mathrm{.}3$ and $4(3$ pts$)$

d$)$ Find stress in element $2(2$ pts$)$