827_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

827_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 10Ch10.qxd 9/27/08 7:36 AM Page 821 821 SECTION 10.4 Method of Superposition Problem 10.4-12 The figure shows a nonprismatic, propped cantilever beam AB with flexural rigidity 2EI from A to C and EI from C to B. Determine all reactions of the beam due to the uniform load of intensity q. (Hint: Use the results of Problems 9.7-1 and 9.7-2.) q MA RA B EI C 2EI A L 2 L 2 RB Solution 10.4-12 Nonprismatic beam Select RB as the redundant. FORCE-DISPLACEMENT RELATIONS RELEASED STRUCTURE From Prob. 9.7-2: dB I1 : I I2 : 2I qL4 a1 128EI1 ‹ (dB)1 I1 15 b I2 17qL4 256EI From Prob. 9.7-1: dB (dB)1 downward deflection of end B due to load q PL3 a1 24EI1 I1 7b I2 ‹ (dB) 2 3RBL3 16EI COMPATIBILITY dB (dB)1 (dB) 2 0 or (dB) 2 upward deflection due to reaction RB 17qL4 256EI 3RBL3 16EI RB 0 17qL 48 ; EQUILIBRIUM RA qL MA qL2 2 31qL 48 7qL 2 RB L 48 RB Problem 10.4-13 A beam ABC is fixed at end A and supported by beam DE at point B (see figure). Both beams have the same cross section and are made of the same material. (a) Determine all reactions due to the load P. (b) What is the numerically largest bending moment in either beam? ; P A B C E D MA RA L 4 RD L 4 L 4 RE 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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