Question $1$

$(20$ marks$)$

MARKS

a$)$ Derive an expression to determine the moment of inertia $(I_Z)$ of a section about an axis $(z)$ parallel to the axis passing through the centroid of the section, i$.$e$.$ the 'parallel axis theorem';

b$)$ Using the parallel axis theorem, determine the moment of inerta about the z axis of the timber box$-$section shown in Figure Q$1$ below. Add notes to clearly illustrate the methodology behind your calculations.

$($It can be assumed that all material in the section has the same structural properties for the purpose of this question.$)$

$6$

$10$

c$)$ Discuss why the section shown in Figure Q$1$ would be more structurally efficient than a solid section when used as a long span floor beam$/$ joist.

$4$