381_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

381_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 04Ch04.qxd 9/25/08 12:43 PM Page 375 375 SECTION 4.5 Shear-Force and Bending-Moment Diagrams Problem 4.5-29 A beam of length L is being designed to support a uniform load q 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 condition. A a L 22) L Solution 4.5-29 Beam with overhangs a Solve for a: M1 M2 The maximum bending moment is smallest when M1 M2 (numerically). a)2 q(L 8 M2 M1 M2 qL2 8 a RA a b 2 (L a)2 qL (2a 8 L) L(2a L) x1 (2 2 22) q (L 8 qL2 (3 8 M1 B 0.3536 a 0.2071 L 0.5858L a)2 0.02145qL2 ; ; ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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