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Unformatted text preview: 09Ch09.qxd 9/27/08 754 1:35 PM Page 754 CHAPTER 9 Deflections of Beams Nonprismatic Beams
Problem 9.7-1 The cantilever beam ACB shown in the figure has moments of A inertia I2 and I1 in parts AC and CB, respectively.
(a) Using the method of superposition, determine the deflection dB at the free
end due to the load P.
(b) Determine the ratio r of the deflection dB to the deflection d1 at the free end
of a prismatic cantilever with moment of inertia I1 carrying the same load.
(c) Plot a graph of the deflection ratio r versus the ratio I2/I1 of the moments of
inertia. (Let I2 /I1 vary from 1 to 5.) I2 L
2 Solution 9.7-1 Cantilever beam (nonprismatic)
Use the method of superposition. (3) Total deflection at point B (a) DEFLECTION dB AT THE FREE END dB (dB)1 + (dB)2 (1) Part CB of the beam:
(b) PRISMATIC BEAM d1
3EI1 2 (dB)1
(2) Part AC of the beam: PL3
24EI1 Ratio: r dB
I2 ; PL3
3 EI1 7I1
I2 ; (c) GRAPH OF RATIO
I1 3 2 dC P(L/2)
2EI2 uC P(L/2)2
EI2 (dB)2 L
dC + uC a b
24EI2 3 5PL
8EI2 r 1
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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