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Unformatted text preview: 09Ch09.qxd 9/27/08 746 1:33 PM Page 746 CHAPTER 9 Deflections of Beams Problem 9.6-2 The load on a cantilever beam AB has a triangular distribution q0 with maximum intensity q0 (see figure).
Determine the angle of rotation uB and the deflection dB at the free end.
L Solution 9.6-2 Cantilever beam (triangular load)
EI x DIAGRAM b(n + 1)
uA 0 4L
5 uA q0 L3
24EI uB ; (clockwise) DEFLECTION
ANGLE OF ROTATION Q1 First moment of area A1 with respect to B Q1 A1x dB Q1 Use absolute values of areas.
Appendix D, Case 20:
n+1 q0 L2
6EI q0 L3
24EI a q0 L3
5 q0 L4
30EI q0 L4
; (Downward) (These results agree with Case 8, Table G-1.) Problem 9.6-3 A cantilever beam AB is subjected to a concentrated load P and P a couple M0 acting at the free end (see figure).
Obtain formulas for the angle of rotation uB and the deflection dB at end B. A B M0 L Solution 9.6-3 Cantilever beam (force P and couple M0)
EI DIAGRAM NOTE: A1 is the M/EI diagram for M0 (rectangle). A2 is
the M/EI diagram for P (triangle).
ANGLE OF ROTATION
Use the sign conventions for the moment-area theorems
(page 713 of textbook).
A1 M0 L
EI x1 L
2 A2 PL2
2EI x2 2L
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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