A beam of length L is being designed to support a uniform load of intensity q (see figure). If the supports of the beam are placed at the ends, creating a simple beam, the maximum bending moment in the beam is ql2/8. However, if the supports of the beam are moved symmetrically toward the middle of the beam (as pictured), the maximum bending moment is reduced.
Determine the distance a between the supports so that the maximum bending moment in the beam has the smallest possible numerical value.
Draw the shear-force and bending-moment diagrams for this condition.

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