756_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

756_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 09Ch09.qxd 9/27/08 750 1:33 PM Page 750 CHAPTER 9 Deflections of Beams Solution 9.6-7 Simple beam with a uniform load DEFLECTION CURVE AND M EI DIAGRAM tB/A BB1 first moment of areas A1 and A2with respect to point B qL4 24EI L (A1 + A2) a b 2 uA BB1 L qL3 24EI ; (clockwise) DEFLECTION dmax AT THE MIDPOINT C Distance CC1 tC2/A 1 (BB1) 2 C2C1 first moment of area A1 with respect to point C qL3 3L ba b 24EI 16 A1x1 dmax maximum deflection (distance CC2) a CC2 CC1 dmax 5qL4 384EI Use absolute values of areas. ANGLE OF ROTATION AT END A 2 L qL2 a ba b 32 8EI A2 x1 3L ab 82 C2C1 qL4 48EI (downward) qL4 128EI ; qL3 24EI 3L 16 Problem 9.6-8 A simple beam AB supports two concentrated loads P at the positions shown in the figure. A support C at the midpoint of the beam is positioned at distance d below the beam before the loads are applied. Assuming that d 10 mm, L 6 m, E 200 GPa, and I 198 106 mm4, calculate the magnitude of the loads P so that the beam just touches the support at C. Solution 9.6-8 Simple beam with two equal loads DEFLECTION CURVE AND dC qL4 128EI (These results agree with Case 1 of Table G-2.) Appendix D, Case 17: A1 qL4 48EI M EI DIAGRAM deflection at the midpoint C P d A P B C L — 4 L — 4 L — 4 L — 4 ...
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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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