Determine the centroidal moments of inertia for the following structural shapes: 2x4 joist, 2x6 joist, 2x8 joist, 2x12 joist, 3x12 joist, 4x6 joist, 4x8 joist, 4x12 joist. Please show work.

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Sizing Joists and Rafters

In civil engineering and building construction, joists and rafters are the major components including beams and columns. Almost every structural construction including buildings, skyscrapers, bridges, commercial complexes, and so on makes use of joists and rafters to provide structural integrity to the building. Joists are primarily thick long pieces of metals, concrete, or wood that are used to support the floor and ceiling. On the other hand, rafters form the major component of pitched roofs, which are a series of sloped long pieces extending from a ridged area that makes contact with the plane area of the wall. They account for the load-bearing of the building along with the beams.