For concentrated load

*P* at midspan of a simply supported beam of span

*L* = 12 ft.

$V_{max} = \frac{1}{2}P$

$M_{max} = \frac{1}{4}PL = \frac{1}{4}P(12) = 3P$

From the cross section shown:

$I =\dfrac{8(8^3)}{12} - \dfrac{4(4^3)}{12} = 320 \, \text{ in}^4$

$Q_{NA} = 4(2)(2) + 6(2)(3) + 2(2)(1) = 56 \, \text{ in}^3$

From bending stress

$f_b = \dfrac{Mc}{I}$

$1400 = \dfrac{3P(12)(4)}{320}$

$P = 3111.11 \, \text{ lb}$

Maximum shear stress

$f_v = \dfrac{VQ_{NA}}{Ib} = \dfrac{\frac{1}{2}(3111.11)(56)}{320(4)}$

$f_v = 68.06 \, \text{ psi}$ *answer*

Spacing (or pitch) of screws, *s*

From Strength of Screws

$s = \dfrac{RI}{VQ_\text{screws}}$

For Horizontal Bolts

$Q_h = 4(2)(3) = 24 ~ \text{in.}^3$

$s_h = \dfrac{2(200)(320)}{(3111.11/2)(24)} = 3.42 ~ \text{in.}$ *answer*

For Vertical Bolts

$Q_v = 8(2)(3) = 48 ~ \text{in.}^3$

$s_v = \dfrac{2(200)(320)}{(3111.11/2)(48)} = 1.734 ~ \text{in.}$ *answer*