762_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 762_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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*Problem 9.7-3 Beam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses k 1 and k 2 and the beam has flexural rigidity EI . (a) What is the downward displacement of point C , which is at the midpoint of the beam, when the moment M 0 is applied? Data for the structure are as follows: M 0 ± 7.5 k-ft, L ± 6 ft, EI ± 520 k-ft 2 , k 1 ± 17 k/ft, and k 2 ± 11 k/ft. (b) Repeat (a) but remove M 0 and, instead, apply uniform load q over the entire beam. 756 CHAPTER 9 Deflections of Beams B B C A k 1 R A = k 1 d A M 0 R B = k 2 d B k 2 L /2 2 EI EI L /2 q = 250 lb/ft (for Part (b) only) *Solution 9.7-3 M 0 ± 7.5 kip/ft L ± 6ft EI ± 520 kip/ft 2 (a) B ENDING - MOMENT EQUATIONS - MOMENT M 0 AT C B . C . B . C . (1) B . C . (2) B . C . (3) ² L a L 2 b ±² R a L 2 b 1 2 J M 0 a L 2 b 3 6 L + C 1 L 2 K ±³ M 0 a L 2 b 2 2 + M 0 a L 2 b 3 6 L + C 3 L 2 + C 4 ² ¿ L a L 2 b ±² ¿ R a L 2 b 1 2 J M 0 a L 2 b 2 2 L + C 1 K ±³ M 0 L 2 + M 0 a L 2 b 2 2 L + C 3 ² ( L ) ± 0 ³ M 0 L 2 2 +
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Unformatted text preview: M L 3 6 L + C 3 L + C 4 ± EI ² ± ³ M x 2 2 + M x 3 6 L + C 3 x + C 4 a L 2 … x … L b EI ² ¿ ± ³ M x + M x 2 2 L + C 3 a L 2 … x … L b EI ² – ±³ M 2 + M a x ³ L 2 b L ±³ M + M x L a L 2 … x … L b ² (0) ± C 2 ± 2 EI ² ± M x 3 6 L + C 1 x a … x … L 2 b 2 EI ² ± M x 3 6 L + C 1 x + C 2 a … x … L 2 b 2 EI ² ¿ ± M x 2 2 L ´ C 1 a … x … L 2 b 2 EI ² – ± M ± M x L a … x … L 2 b q ± 250 lb/ft k 1 ± 17 kip/ft k 2 ± 11 kip/ft 09Ch09.qxd 9/27/08 1:35 PM Page 756...
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