760_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

760_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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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 P C I1 B 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 P L3 ab 3EI1 2 (dB)1 (2) Part AC of the beam: PL3 24EI1 Ratio: r dB d1 7I1 PL3 a1 + b 24EI1 I2 ; PL3 3 EI1 7I1 1 a1 + b 8 I2 ; (c) GRAPH OF RATIO I2 I1 3 2 dC P(L/2) (PL/2)(L/2) + 3EI2 2EI2 uC P(L/2)2 (PL/2)(L/2) + 2EI2 EI2 (dB)2 L dC + uC a b 2 7PL3 24EI2 3 5PL 48EI2 3PL2 8EI2 r 1 2 3 4 5 1.00 0.56 0.42 0.34 0.30 ...
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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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