752_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

752_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 09Ch09.qxd 9/27/08 746 1:33 PM Page 746 CHAPTER 9 Deflections of Beams Problem 9.6-2 The load on a cantilever beam AB has a triangular distribution q0 with maximum intensity q0 (see figure). Determine the angle of rotation uB and the deflection dB at the free end. B A L Solution 9.6-2 Cantilever beam (triangular load) M EI x DIAGRAM b(n + 1) n+2 uB uB/A uA 0 4L 5 uA q0 L3 24EI A1 q0 L3 24EI uB ; (clockwise) DEFLECTION ANGLE OF ROTATION Q1 First moment of area A1 with respect to B Q1 A1x dB Q1 Use absolute values of areas. Appendix D, Case 20: A1 bh n+1 q0 L2 1 (L) a b 4 6EI q0 L3 24EI a q0 L3 4L ba b 24EI 5 q0 L4 30EI q0 L4 30EI ; (Downward) (These results agree with Case 8, Table G-1.) Problem 9.6-3 A cantilever beam AB is subjected to a concentrated load P and P a couple M0 acting at the free end (see figure). Obtain formulas for the angle of rotation uB and the deflection dB at end B. A B M0 L Solution 9.6-3 Cantilever beam (force P and couple M0) M EI DIAGRAM NOTE: A1 is the M/EI diagram for M0 (rectangle). A2 is the M/EI diagram for P (triangle). ANGLE OF ROTATION Use the sign conventions for the moment-area theorems (page 713 of textbook). A1 M0 L EI x1 L 2 A2 PL2 2EI x2 2L 3 ...
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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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