A built-up plywood box beam with 2 × 4 S4S top and bottom flanges is held together by nails. Determine the pitch (spacing) of the nails if the beam supports a uniform load of 200 #/ft. along the 26 foot span. Assume the nails have a shear capacity of 80# each.

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Accepted Answer

Construct the shear diagram to obtain the critical shear condition and its location.

Note that the condition of shear is critical at the supports and that the shear intensity decreases as you approach the centerline of the beam. This would indicate that the nail spacing P varies from the support to midspan. Nails are closely spaced at the support, but increasing spacing occurs toward midspan, following the shear diagram.

[latex] f_{ v }=\frac{V Q}{I b} [/latex]

[latex] I_{x}=\frac{\left(4.5^{\prime \prime} ight)\left(18^{\prime \prime} ight)^{3}}{12}-\frac{\left(3.5^{\prime \prime} ight)\left(15^{\prime \prime} ight)^{3}}{12}=1,202.6 in .^{4} [/latex]

Q=A [latex]\bar{y}[/latex] = (5.25 in.² )(8.25")= 43.3 in.³

Shear force = [latex]f_{ v } imes A_{ v }[/latex]

where

[latex]A_{ v }[/latex] =shear area

Assume the following:

F = capacity of two nails (one each side) at the flange, representing two shear surfaces

[latex] F=f_{ v } imes b imes p=\frac{V Q}{I b} imes b p [/latex]

[latex] herefore F=p imes \frac{V Q}{I} \quad p=\frac{F I_{x}}{V Q} [/latex]

At the maximum shear location (support)

V = 2,600#,

[latex] p=\frac{(2 ext { nails } imes 80 \# / ext { nail })\left(1,202.6 ext { in. }^{4} ight)}{(2,600 \#)\left(43.3 in .^{3} ight)}=1.71^{\prime \prime} [/latex]

Checking the spacing requirement p at different locations along the beam, we obtain a graphical plot (like the s diagram) of the spacing requirements.

At the support,

[latex]V_{0}=2,600 \#, p_{0}=1.36^{\prime \prime} [/latex]

[latex]V_{2}=2,200 \# ; p_{2}=\frac{(2 imes 80 \# / ext { nail })\left(1,202.6 in .^{4} ight)}{(2,200 \#)\left(43.3 in .^{3} ight)} [/latex]=2.02"

[latex]V_{4}=1,800 \# ; p_{4}=\frac{(2 imes 80 \# / ext { nail })\left(1,202.6 ext { in. }^{4} ight)}{(1,800 \#)\left(43.3 in .^{3} ight)}[/latex]=2.47"

[latex]V_{6}=1,400 \# ; p_{6}=\frac{(2 imes 80 \# / ext { nail })\left(1,202.6 in .^{4} ight)}{(1,400 \#)\left(43.3 in .^{3} ight)}=3.17^{\prime \prime} [/latex]

[latex] V_{8}=1,000 \# ; p_{8}=\frac{(2 imes 80 \# / ext { nail })\left(1,202.6 in .^{4} ight)}{(1,000 \#)\left(43.3 in .^{3} ight)}=4.44^{\prime \prime} [/latex]

[latex] V_{10}=600 \# ; p_{10}=\frac{(2 imes 80 \# / ext { nail })\left(1,202.6 in .^{4} ight)}{(600 \#)\left(43.3 in .^{3} ight)}=7.04^{\prime \prime}[/latex]

In practical nail spacing, increments of half an inch or one inch should be used.

Question 8.11: A built-up plywood box beam with 2 × 4 S4S top and bottom fl...

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