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736_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 736_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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730 CHAPTER 9 Deflections of Beams Method of Superposition The problems for Section 9.5 are to be solved by the method of superposition. All beams have constant flexural rigidity EI . Problem 9.5-1 A cantilever beam AB carries three equally spaced concentrated loads, as shown in the figure. Obtain formulas for the angle of rotation u B and deflection d B at the free end of the beam. A P P B P L 3 L 3 L 3 Solution 9.5-1 Cantilever beam with 3 loads Table G-1, Cases 4 and 5 u B P a L 3 b 2 2 EI + P a 2 L 3 b 2 2 EI + PL 2 2 EI 7 PL 2 9 EI ; + PL 3 3 EI 5 PL 3 9 EI ; d B P a L 3 b 2 6 EI a 3 L L 3 b + P a 2 L 3 b 2 6 EI a 3 L 2 L 3 b Problem 9.5-2 A simple beam AB supports five equally spaced loads P (see figure). (a) Determine the deflection d 1 at the midpoint of the beam.
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Unformatted text preview: P ) is distributed as a uniform load on the beam, what is the deflection d 2 at the midpoint? (c) Calculate the ratio of d 1 to d 2 . B A P P P P P L 6 — L 6 — L 6 — L 6 — L 6 — L 6 — Solution 9.5-2 Simple beam with 5 loads (a) Table G-2, Cases 4 and 6 ± 11 PL 3 144 EI ; + P a L 3 b 24 EI c 3 L 2 ² 4 a L 3 b 2 d + PL 3 48 EI d 1 ± P a L 6 b 24 EI c 3 L 2 ² 4 a L 6 b 2 d (b) Table G-2, Case 1 qL ± 5 P (c) d 1 d 2 ± 11 144 a 384 25 b ± 88 75 ± 1.173 ; d 2 ± 5 qL 4 384 EI ± 25 PL 3 384 EI ; 09Ch09.qxd 9/27/08 1:32 PM Page 730...
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