04-01ChapGere.0023

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SECTION 4.5 Shear-Force and Bending-Moment Diagrams 281 B A 3.0 kN/m 1.0 kN/m 2.4 m R A = 2.0 kN R B = 2.8 kN Set V 5 0: x 1 5 1.2980 m V 5 2.0 2 x 2 x 2 2.4 Ê ( x 5 meters; V 5 kN) M (kN . m) 2 2.8 2.0 0 0 M max = 1.450 x 1 = 1.2980 m x V (kN) Problem 4.5-25 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 qL 2 /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
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