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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
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).
M1 M2 qL2
RA a b
(L a)2 qL
8 L) L(2a L) x1 (2
2 22) q
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.
- Fall '11