758_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

758_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 09Ch09.qxd 9/27/08 752 1:33 PM Page 752 CHAPTER 9 Deflections of Beams DEFLECTION d AT THE MIDPOINT C Distance CC1 tC2/A C2C1 1 (BB1) 2 2 M0 L 12EI first moment of area between A and C with respect to C 1 M0 LL a ba ba b 2 2EI 2 6 d M0 L2 12EI CC1 C2C1 M0 L2 16EI (Downward) M0 L2 48EI ; (These results agree with Case 7 of Table G-2.) M0 L2 48EI Problem 9.6-10 The simple beam AB shown in the figure supports two P P equal concentrated loads P, one acting downward and the other upward. Determine the angle of rotation uA at the left-hand end, the deflection d1 under the downward load, and the deflection d2 at the midpoint of the beam. A B a a L Solution 9.6-10 Simple beam with two loads Because the beam is symmetric and the load is antisymmetric, the deflection at the midpoint is zero. ‹ d2 0 ; ANGLE OF ROTATION uA AT END A tC/A CC1 A1 a first moment of area between A and C with respect to C L 2 a+ a 2L b + A2 a b a 3 3 2 Pa(L uA a)(L 12EI 2a) CC1 L/2 Pa(L a)(L 6LEI ab 2a) (clockwise) DEFLECTION d1 UNDER THE DOWNWARD LOAD Distance a DD1 a b (CC1) L/2 Pa2(L M1 EI A1 1 M1 a b (a) 2 EI A2 1 M1 L a ba 2 EI 2 tD2/A Pa(L 2a) LEI 2a) Pa2(L 2LEI ab Pa(L 2a)2 4LEI D2D1 DD1 2a) first moment of area between A and D with respect to D a A1 a b 3 d1 a)(L 6LEI 2a) Pa3(L 6LEI D2D1 2 2a)2 Pa (L 6LEI (Downward) ; ; ...
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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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