A beam is formed by nailing three boards together as shown in the figure and parameter table. The maximum allowable shear stress in the wood is $\tau_{allow} = 440$ psi, and each nail can handle a shear force of 440 lbs. Calculate the maximum allowable shear force, V, and the maximum allowable spacing between nails for the top and bottom boards (they may be different).
parameter value units
$L_1$ 8 in
$L_2$ 11 in
$L_3$ 6 in
$t_1$ 1.5 in
$t_2$ 1.5 in
Maximum V = 7.35 x kip
Maximum spacing for nails on top = 0.847 in.
Maximum spacing for nails on bottom = 0.962 in.