839_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

839_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

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.

Ask a homework question - tutors are online