166_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

166_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: Sec_2.5.qxd 9/25/08 160 3:00 PM Page 160 CHAPTER 2 Axially Loaded Members Solution 2.5-11 Triangular frame held by two wires FREE-BODY DIAGRAM OF FRAME (b) LOAD P AND TEMPERATURE INCREASE T Force-displacement and temperature-displacement relations: TAL + a( ¢ T)L (Eq. 8) dA EA TBL + a( ¢ T)L EA Substitute (8) and (9) into Eq. (2): TAL 2TBL + a( ¢ T)L + 2a( ¢ T)L EA EA dB or EQUATION OF EQUILIBRIUM MC 2TB EA ( T) (Eq. 10) Solve simultaneously Eqs. (1) and (10): 0 P(2b) TA (Eq. 9) TA(2b) TB(b) 0 or 2TA TB 2P (Eq. 1) TA DISPLACEMENT DIAGRAM TB 1 [4P + EAa( ¢ T)] 5 2 [P EAa( ¢ T)] 5 (Eq. 11) (Eq. 12) Substitute numerical values: P 500 lb EA T 180°F 12.5 2 (Eq. 2) B (a) LOAD P ONLY Force-displacement relations: (Eq. 3, 4) TB 2 (500 lb 5 Set TB P 270 lb) ; 454 lb 92 lb ; ¢T or TA 2TB Solve simultaneously Eqs. (1) and (5): TA 0 in Eq. (12): EA ( T) or 2TBL EA 4P 2P TB 5 5 Numerical values: P 500 lb TA 400 lb TB 200 lb 1 (2000 lb + 270 lb) 5 (c) WIRE B BECOMES SLACK TAL TBL dB dA EA EA (L length of wires at A and B.) Substitute (3) and (4) into Eq. (2): TAL EA 10 6/°F TA EQUATION OF COMPATIBILITY A 120,000 lb P EAa (120,000 lb)(12.5 * 10 333.3°F (Eq. 5) Further increase in temperature: (Eqs. 6, 7) T 333.3°F 153°F ; 500 lb 180°F ; 6 /°F) ...
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