02-03ChapGere.0008

# 02-03ChapGere.0008 - A-PDF Split DEMO Purchase from...

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SECTION 2.5 Thermal Effects 113 Solution 2.5-11 Triangular frame held by two wires F REE - BODY DIAGRAM OF FRAME B C D A P 2b b b T A T B E QUATION OF EQUILIBRIUM P (2 b ) T A (2 b ) T B ( b ) 0 or 2 T A T B 2 P (Eq. 1) D ISPLACEMENT DIAGRAM E QUATION OF COMPATIBILITY A 2 B (Eq. 2) (a) L OAD P ONLY Force-displacement relations: (Eq. 3, 4) ( L length of wires at A and B .) Substitute (3) and (4) into Eq. (2): or T A 2 T B (Eq. 5) Solve simultaneously Eqs. (1) and (5): (Eqs. 6, 7) Numerical values: T A 400 lb T B 200 lb P 500 lb T A 4 P 5 T B 2 P 5 T A L EA 2 T B L EA A T A L EA B T B L EA © M C 0 (b) L OAD P AND TEMPERATURE INCREASE T Force-displacement and temperature- displacement relations: (Eq. 8) (Eq. 9) Substitute (8) and (9) into Eq. (2): or T A 2 T B EA ( T ) (Eq. 10) Solve simultaneously Eqs. (1) and (10): (Eq. 11)
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