817_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

817_Mechanics - 10Ch10.qxd 7:32 AM Page 811 811 SECTION 10.4 Method of Superposition Another solution by the 2nd order differential equation

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SECTION 10.4 Method of Superposition 811 Another solution by the order differential equation. D IFFERENTIAL EQUATIONS B . C . 1 B . C . 2 B . C . 3 v ¿ ( L ) ± 0 M A L ± qL L 2 2 ² qL 3 6 ± qL 3 3 v ¿ (0) ± 0 C 2 ± 0 v ¿ (0) ± 0 C 1 ± 0 EIv ± R A x 3 6 ² M A x 2 2 ² qx 4 24 + C 1 x + C 2 EIv ¿ ± R A x 2 2 ² M A x ² qx 3 6 + C 1 EIv ± M ± R A x ² M A ² qx 2 2 2 nd D EFLECTION CURVE or v ± q 24 EI ( ² x 4 + 4 Lx 3 ² 4 L 2 x 2 ) ; EIv ± R A x 3 6 ² M A x 2 2 ² qx 4 24 ± qL x 3 6 ² qL 2 3 x 2 2 ² qx 4 24 M B ± qL 2 2 ² qL 2 3 ± qL 2 6 ; M A ± qL 2 3 ; Problem 10.4-3 A propped cantilever beam of length 2 L with support at B is loaded by a uniformly distributed load with intensity q . Use the method of superposition to solve for all reactions. Also draw shear-force and bending- moment diagrams, labeling all critical ordinates. A B LL x y C M A R A R B q Solution 10.4-3
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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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