A wooden beam is fabricated by nailing together three boards as shown. The boards have dimensions of b1 = 20 in., d1 = 1.2 in., b2 = 1.2 in., d2 = 19 in., b3 = 10 in., and d3 = 1.2 in. The vertical distance from the bottom edge of the section to the centroid is 12.761 in. The moment of inertia of the section about the z axis is 4113 in.4. Determine the maximum shear stress in the cross section if the internal shear force is V = 440 lb. Assume that the shear force V acts in the y direction.The maximum shear stress will occur at the centroid. Cut a cross section along the centroidal z axis and calculate the first moment of area at this section. b1Nail Adid2b2dzNail Bb3

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Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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A wooden beam is fabricated by nailing together three boards as shown. The boards have dimensions of b₁ = 20 in., d₁ = 1.2 in., b₂ = 1.2 in., d₂ = 19 in., b₃ = 10 in., and d₃ = 1.2 in. The vertical distance from the bottom edge of the section to the centroid is 12.761 in. The moment of inertia of the section about the z axis is 4113 in.⁴. Determine the maximum shear stress in the cross section if the internal shear force is V = 440 lb. Assume that the shear force V acts in the y direction.

The maximum shear stress will occur at the centroid. Cut a cross section along the centroidal z axis and calculate the first moment of area at this section.

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