A simple truss structure is shown in Figure Q$3.$ All joints can be considered as

fully pinned for buckling in any direction. Truss members' elastic modulus $(E)$

and yield strength $({}_y)$ are $70$GPa and $215$MPa, respectively. Assume that the

joint $B$ is restrained moving in to the out of plane direction.

I. Show that the compressive force in member $AB$ is $\frac{\sqrt[\phantom{2}]{5}P}{2}.$

$[4/20$ marks$]$

II$.$ Determine the maximum $P$ load that can be applied at $B$ if a tube section as

shown in figure is used.

$[8/20$ marks$]$

III. The tube section is to be replaced with a rectangular solid section as shown in

figure. What is the required minimum $b(mm)$ if the applied $P$ load is

$240kN.$

$[8/20$ marks$]$

Tube section

Rectangular section

Figure Q$3.$