839_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 839_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 833 SECTION 10.4 Method of Superposition Problem 10.4-23 A wide-flange beam ABC rests on three P identical spring supports A, B and C (see figure). The flexural rigidity of the beam is EI 6912 106 1b-in.2 and each spring has stiffness k 62,500 1b/in. The length of the beam is L 16 ft. If the load P is 6000 1b, what are the reactions RA, RB, and RC? Also, draw the shear-force and bending-moment diagrams for the beam, labeling all critical ordinates. C A B k k L — 4 RA L — 4 k L — 2 RB Solution 10.4-23 Beam on three springs (Case 5, Table G-2) (dB)1 11PL3 P + 2k 768EI (dA)2 RB 2k (dC)2 RB 2k (dB) 2 RBL3 1 [(dA) 2 + (dC) 2 ] + 2 48EI Select RB as the redundant. EQUILIBRIUM RA 3P 4 RB 2 RC P 4 RB 2 RELEASED STRUCTURE AND FORCE-DISPL. EQS. RBL3 RB + 2k 48EI COMPATIBILITY (dB)1 (downward) (upward) (dB)2 RB k Substitute and solve: RB Pa (dA)1 3P 4k Let k * (dC)1 P 4k RB (dB)1 1 [(d ) + (dC)1 ] + 2 A1 L P a b c 3L2 4 48EI L2 4a b d 4 833 384 EI + 11kL3 b 1152 EI + 16 kL kL3 EI (nondimensional) P 384 + 11 k * a b 16 72 + k * ; ; RC ...
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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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