A horizontal shelf AD of length L = 1215 mm, width b = 305 mm, and thickness t = 22 mm is supported by brackets at B and C (see part a of the figure). The brackets are adjustable and may be placed in...

A horizontal shelf AD of length L = 1215 mm, width b = 305 mm, and thickness t = 22 mm is supported by brackets at B and C (see part a of the figure). 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 (see part b of the figure).

(a) Determine the maximum permissible value of the load q if the allowable bending stress in the shelf is

_allow
= 8.5 MPa and the position of the supports is adjusted for maximum load carrying capacity

(b) The bookshelf owner decides to reinforce the shelf with a bottom wood plate b/2 t/2 along its entire length (see figure part c). Find the new maximum permissible value of the load q if the allowable bending stress in the shelf remains at

_allow
= 8.5 MPa.