Choosing a Timber Beam Section
Mediumwoodflexuresection-selection
A timber beam carries a service bending moment of 60,000 lb·in. The adjusted allowable bending stress is Fb′ = 1,000 psi and all other checks are satisfied. Four candidate sections are listed in order of increasing mass: A with S = 50 in³, B with S = 65 in³, C with S = 80 in³, D with S = 95 in³. Which is the lightest section that passes the bending check (fb = M/S ≤ Fb′)?
- ASection A (S = 50 in³)
- BSection C (S = 80 in³)
- CSection B (S = 65 in³)
- DSection D (S = 95 in³)
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Answer: C. Section B (S = 65 in³)
Allowable-stress design: Srequired = M/Fb′ = 60,000/1,000 = 60 in³. A (50) fails since fb = 60,000/50 = 1,200 psi > 1,000 psi. B (65) gives fb = 923 psi, which passes and is the lightest passing section. C would be chosen only by dividing by an unnecessary φ = 0.90 (60/0.9 = 66.7 in³), which does not belong in an allowable-stress check. D passes but is heavier than needed.
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