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Three 4cm thick and 10 cm wide boards are connected together by two parallel rows of uniformly distributed nails separated...

Three 4 cm thick and 10 cm wide boards are connected together by two parallel rows of uniformly distributed nails separated by longitude distance 5 to form a beam that is subject to constant vertical shear of 1000 N. Knowing the maximum allowed shearing force for each nail is 200 N, determine the largest longitude separation 5 between nails? P 1000 N 4 cm 4 cm 4 cm 10 cm Side view Top view

Answer:

For first moment for the section/element of interest (i.e., within red dashed rectangle) 9 Q = JA = = 160cm? Moment of inertia for the entire cross-section I 1 1440cm Cross-section view 4 cm 4 cm 4 cm 10 cm Total (horizontal) shearing force along the interface of interest for the chosen section/element must not be larger than the total shearing force that could be allowed for the two nails within the chosen section/element VQ ΔΗ- Δι 2Fallowable

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