Wood Bearing Length Across the Grain

Mediumwoodbearingcompression-perpendicular
A wood beam delivers a service reaction of 8,000 lb through a bearing contact 5.5 in wide (across the beam), compressing the wood perpendicular to the grain. The adjusted bearing stress is Fc⊥′ = 400 psi (all adjustments already included). What is the minimum theoretical bearing length along the beam?
  1. A20.00 in
  2. B4.55 in
  3. C2.91 in
  4. D3.64 in
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Answer: D. 3.64 in

Required area = P/Fc⊥′ = 8,000/400 = 20.0 in². Length = area/width = 20.0/5.5 = 3.64 in. 20.00 in forgets to divide by the 5.5 in width. 4.55 in and 2.91 in apply an extra 0.80 factor (dividing by it or multiplying by it), even though Fc⊥′ is already adjusted.
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