Determine the moments of inertia and radii of gyration of the circular area. Determine the moments of inertia Ix and Iy for the anular ring.

2) The box beam is constructed from four boards that are fastened together using nails spaced along the beam every 2 inches. The beam is subjected to a maximum internal shear force of 475 lb. a) Locate the neutral axis and compute the moment of inertia for the cross-section in in*. [Ans. to check: 1 = 197.7 in¹] b) Calculate the first moment of area in in³ at each of the two connection interfaces (i.e. once for the top flange and once for the bottom board). Draw a clear sketch of the cross-section showing the neutral axis and the necessary dimensions to calculate the first moment of area. [Ans. to Check: Qtop = 31.2 in³] c) Compute the shear flow occurring between the wood and the nails at each of the two connection interfaces in lb/in. [Ans. to Check: qbottom = 49.0 lb/in] d) Design the section by choosing the required shear strength of the nails (in lb). Check both interfaces but choose only one assuming you would like to use the same nails for the entire beam. [Ans. to check: 75 lb…

Deteemine the moment of inertia of the area with respect to the centroidal axis

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