755_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

755_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 09Ch09.qxd 9/27/08 1:33 PM Page 749 749 SECTION 9.6 Moment-Area Method Problem 9.6-6 A cantilever beam ACB supports two concentrated loads P1 and P2 P1 as shown in the figure. Calculate the deflections dB and dC at points B and C, respectively. Assume P1 10 kN, P2 5 kN, L 2.6 m, E 200 GPa, and I 20.1 106 mm4. C A P2 B L — 2 L — 2 Solution 9.6-6 Cantilever beam (forces P1 and P2) M EI dB DIAGRAMS 1 P1L L L L 1 P2L 2L a ba ba + b + a b (L) a b 2 2EI 2 2 3 2 EI 3 P2L3 5P1L3 + 48EI 3EI ; (downward) DEFLECTION dC dC tC/A QC first moment of areas to the left of point C with respect to point C dc P2 L L L 1 P1L L L a ba ba b + a ba ba b 2 2EI 2 3 2EI 2 4 + P1 E 10 kN P2 200 GPa I 5 kN L 20.1 6 Use absolute values of areas. tB/A QB ; (downward) SUBSTITUTE NUMERICAL VALUES: first moment of areas with respect dB 4.554 mm + 7.287 mm 11.84 mm dC DEFLECTION dB dB 5P2L3 P1L3 + 24EI 48EI 2.6 m 10 mm4 1 P2L L L a ba ba b 2 2EI 2 3 1.822 mm + 2.277 mm 4.10 mm ; ; (deflections are downward) to point B Problem 9.6-7 Obtain formulas for the angle of rotation uA at support A and the deflection dmax at the midpoint for a simple beam AB with a uniform load of intensity q (see figure). q A B L ...
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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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