803_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

803_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 10Ch10.qxd 9/27/08 7:29 AM Page 797 797 SECTION 10.3 Differential Equations of the Deflection Curve SHEAR-FORCE AND BENDING-MOMENT DIAGRAMS BENDING MOMENT (FROM EQ. 1) q2 (L 12 M 6Lx + 6x 2) ; SLOPE (FROM EQ. 2) qx (L2 12EI ¿ 3Lx + 2x 2) ; DEFLECTION (FROM EQ. 3) qx 2 (L 24EI x)2 L ab 2 dmax ; qL4 384EI Problem 10.3-3 A cantilever beam AB of length L has a fixed support at A and y a roller support at B (see figure). The support at B is moved downward through a distance dB. Using the fourth-order differential equation of the deflection curve (the load equation), determine the reactions of the beam and the equation of the deflection curve. (Note: Express all results in terms of the imposed displacement dB .) x A dB MA B RA RB L Solution 10.3-3 Cantilever beam with imposed displacement dB REACTIONS (FROM EQUILIBRIUM) RA (1) RB B.C. MA RBL (2) EI –¿ q V 0 (3) (4) C1 EI – M EI ¿ (5) C1x 2/2 + C2x + C3 EI C1x + C2 3 (6) 2 C1x /6 + C2x /2 + C3x + C4 B.C. 1 (0) B.C. 2 ¿ (0) 0 0 ‹ C4 ‹ C3 B.C. 0 4 (L) ‹ C1L + C2 6EIdB/L2 0 0 (7) 3EIdB 3 L C2 3EIdB L2 SHEAR FORCE (EQ. 4) V 3EIdB 3 L (8) (9) SOLVE EQUATIONS (8) AND (9): C1 0 dB ‹ C1L + 3C2 DIFFERENTIAL EQUATIONS EI –– 3 – (L) RA V(0) 3EIdB L3 ...
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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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