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813_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

813_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 10.3 Differential Equations of the Deflection Curve 807 Problem 10.3-11 A propped cantilever beam of length L is loaded by a concentrated moment M 0 at midpoint C . Use the second-order differential equa- tion of the deflection curve to solve for reactions at A and B . Draw shear-force and bending-moment diagrams for the entire beam. Also find the equations of the deflection curves for both halves find the equations of the deflection curves for both halves of the beam, and draw the deflection curve for the entire beam. At point of inflection: d d max /2 d max M 0 L 2 216 EI A L 2 L 2 y x B C M A M 0 R A R B Solution 10.3-11 E QUILIBRIUM (1) (2) B ENDING MOMENTS ( FROM EQUILIBRIUM ) D IFFERENTIAL EQUATIONS (3) (4) (5) B . C . 1 B . C . 2 D IFFERENTIAL EQUATIONS (6) EIv M R B ( L x ) ( L /2 x L ) v (0) 0 C 2 0 ¿ (0) 0 C 1 0 EIv R B x 3
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