A wooden beam is fabricated from one 2 × 12 and two 2 × 12 dimension...

A wooden beam is fabricated from one 2 × 12 and two 2 × 12 dimension lumber boards to form the double-tee cross section shown. The beam flange is fastened to the stem with nails. Each nail can safely transmit a force of 160 lb in direct shear. The allowable shear stress of the wood is 84 psi. Assume b₁ = 12 in., b₂ = 2 in., d₁ = 2 in., d₂ = 12 in.
(a) If the nails are uniformly spaced at an interval of s = 2.4 in. along the span, what is the maximum internal shear force V that can be supported by the double-tee cross section?
(b) What nail spacing s would be necessary to develop the full strength of the double-tee shape in shear? (Full strength means that the maximum horizontal shear stress in the double-tee shape equals the allowable shear stress of the wood.)

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Ally Wells answered 6 months ago

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