Question $2(25$ Marks$)$

Figure $2$ shows the cross$-$section of a thin$-$walled beam. The thickness $t$ of the walls is constant throughout.

Figure $2$: cross$-$section of a thin$-$walled beam.

$($a$)$ Calculate the position of the shear centre from wall $3-4($i$.$e$.)$ of the thin$-$

MARKS

walled section shown in Fig. $2.$

$20$

$($b$)$ Give the definition of shear centre.

Total

$5$

$25$

To calculate the second moments of area of the inclined walls, use the following expressions.

$I_{}=\frac{a^{3}tSi{n}^2}{12},I_{yy}=\frac{a^{3}tCo{s}^2}{12},I_{xy}=2\frac{t^3\text{S}\text{i}\text{n}2}{24}$