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Unformatted text preview: 09Ch09.qxd 9/27/08 750 1:33 PM Page 750 CHAPTER 9 Deflections of Beams Solution 9.6-7 Simple beam with a uniform load
DEFLECTION CURVE AND M
EI DIAGRAM tB/A BB1 first moment of areas A1 and A2with
respect to point B
(A1 + A2) a b
24EI ; (clockwise) DEFLECTION dmax AT THE MIDPOINT C
2 C2C1 first moment of area A1 with respect
to point C
dmax maximum deflection (distance CC2) a CC2 CC1 dmax 5qL4
384EI Use absolute values of areas.
ANGLE OF ROTATION AT END A
2 L qL2
8EI A2 x1 3L
82 C2C1 qL4
48EI (downward) qL4
128EI ; qL3
16 Problem 9.6-8 A simple beam AB supports two concentrated loads P at
the positions shown in the figure. A support C at the midpoint of the beam is
positioned at distance d below the beam before the loads are applied.
Assuming that d 10 mm, L 6 m, E 200 GPa, and
I 198 106 mm4, calculate the magnitude of the loads P so that the beam
just touches the support at C. Solution 9.6-8 Simple beam with two equal loads
DEFLECTION CURVE AND dC qL4
128EI (These results agree with Case 1 of Table G-2.) Appendix D, Case 17:
EI DIAGRAM deflection at the midpoint C P d A P
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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