Exercise $1$

$($a$)$ For the simply supported beam shown in the figure below, $($i$)$ calculate the support reactions and

$($iii$)$ determine the shear force diagram.

$($b$)$ For the section indicated at $(1),$ which is located $2m$ from the support on the left hand side,

identify the shear force, $V,$ in $kN.$ Then, using the cross$-$sectional geometry shown below for the

$T$ section, at the same section $(1)$:

$($i$)$ determine the location of the centroid $($neutral axis$)$

$($ii$)$ Evaluate the moment of inertia of the cross section

$($iii$)$ Calculate the maximum shear stress

$($iv$)$ Calculate the shear stress at point $B$

$($v$)$ Calculate the shear flow at point B

$($vi$)$ If nails are used to fasten the two boards at point $B,$ and the spacing of the nails is $s=50$

$mm,$ what is the shear force per nail?

Figure: Exercise $1$ beam and cross$-$section