Question $4[10$ marks$]$

A beam is made of four equal planks connected by $\backslash (12-\backslash$mathrm$\{$mm$\}\backslash )$ diameter bolts and spaced at equal intervals along the longitudinal axis of the beam, as shown.

a$)$ Draw the shear$-$force diagram of the beam and determine its maximum absolute value.

b$)$ If the allowable average shearing stress in the bolts is of $60$ MPa $,$ determine the maximum allowable spacing $\backslash ($ s $\backslash )$ of the bolts.