754_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

754_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 09Ch09.qxd 9/27/08 748 1:33 PM Page 748 CHAPTER 9 Deflections of Beams Problem 9.6-5 Calculate the deflections dB and dC at points B and C, respectively, of the cantilever beam ACB shown in the figure. Assume M0 36 k-in., P 3.8 k, L 8 ft, and EI 2.25 109 lb-in.2 M0 C A P B L — 2 L — 2 Solution 9.6-5 Cantilever beam (force P and couple M0) M EI DEFLECTION dC DIAGRAM QC first moment of areas A1 and left-hand part of A2 with respect to point C a M0 L L ba ba b EI 2 4 a PL LL ba ba b 2EI 2 4 LL 1 PL a ba ba b 2 2EI 2 3 L2 (6M0 48EI 5PL) NOTE: A1 is the M/EI diagram for M0 (rectangle). A2 is the M/EI diagram for P (triangle). tC/A Use the sign conventions for the moment-area theorems (page 713 of textbook). (dC is positive when upward) DEFLECTION dB ASSUME DOWNWARD DEFLECTIONS (change the signs of dB and dC) QB first moment of areas A1 and A2 with respect to point B A1x1 + A2x2 tB/A QB dB dB (dB is positive when upward) L2 (6M0 48EI dC dB L2 (8PL 24EI 9M0) L2 (5PL 48EI 6M0) ARE POSITIVE ; SUBSTITUTE NUMERICAL VALUES: L 8PL) 5PL) ; M0 8PL) L2 (9M0 24EI dC dC M0 L 3L a ba ba b EI 2 4 2L 1 PL a b (L) a b 2 EI 3 L2 (9M0 24EI QC 36 k-in. 8 ft 96 in. P 3.8 k EI 2.25 106 k-in.2 dB 0.4981 in. 0.0553 in. 0.443 in. ; dC 0.1556 in. 0.0184 in. 0.137 in. ; ...
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