Maximum Shear Stress in a Wood Beam
Mediumwoodshearrectangular-section
An unnotched rectangular wood beam has actual dimensions b = 3.5 in wide and d = 9.25 in deep and carries a service shear V = 3,000 lb. What is the maximum shear stress in the rectangular section?
- A92.7 psi
- B278.0 psi
- C139.0 psi
- D112.5 psi
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Answer: C. 139.0 psi
For a rectangle the peak shear stress is 1.5 times the average: τmax = 3V/(2bd) = 3(3,000)/(2 · 3.5 · 9.25) = 9,000/64.75 = 139.0 psi. 92.7 psi is the average V/A = 3,000/32.375, which is not the maximum. 278.0 psi uses 3V/(bd), dropping the factor 2. 112.5 psi uses nominal 4 × 10 dimensions (4 × 10 = 40 in²) instead of actual dimensions.
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