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Wood Beam Deflection Limit Check

Mediumwooddeflectionserviceability
A simply supported wood beam spans L = 14 ft and carries a uniform service load of 100 lb/ft including self-weight. E = 1.6×10⁶ psi and I = 100 in⁴. Using Δ = 5wL⁴/(384EI) for immediate elastic deflection with a limit of L/360, what is the deflection and does it satisfy the limit?
  1. A6.48 in; fails the L/360 limit
  2. B0.540 in; passes (limit taken as L/240 = 0.700 in)
  3. C0.636 in; fails the L/360 limit
  4. D0.540 in; fails the L/360 limit of 0.467 in
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Answer: D. 0.540 in; fails the L/360 limit of 0.467 in

Convert to inches first: w = 100/12 = 8.333 lb/in, L = 14(12) = 168 in. Δ = 5(8.333)(168)⁴/(384 · 1.6×10⁶ · 100) = 3.319×10¹⁰/6.144×10¹⁰ = 0.540 in. The limit is 168/360 = 0.467 in, so 0.540 > 0.467 and the beam fails. 6.48 in leaves w as 100 lb/in without converting from lb/ft. 'Passes' results from using a looser L/240 limit instead of L/360. 0.636 in divides by 0.85 as if a wet-service factor reduced E, but stiffness adjustments are not part of this given check.
in in
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