A horizontal shelf AD of length L=1215mm, width b=305mm, and thickness t=22mm is

Question

A horizontal shelf AD of length L=1215mm, width b=305mm, and thickness t=22mm is supported by brackets B and C (Fig A). Note that the shelf is symmetric: AB=CD. The brackets are adjustable and may be placed in any desired positions between the ends of the shelf. A uniform load of intensity q, which includes the weight of the shelf itself, acts on the shelf. (Fig B)

A) Noting x=AB, determine the internal bending moment M in the shelf. Plot the bending moment diagram (assuminga value for x). Show that the location of B for which M_max = |M_min| is:

C) The bookshelf owner decides to reinforce the shelf with a bottom wood plate (b/2)x(t/2) along its entire length (Fig C). Determine the position of the neutral axis of the new cross section (Fig C).

D) Determine the moment of inertia of the new cross section (Fig C)

Explanation / Answer

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