02-03ChapGere.0008

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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 ) 2 T A (2 b ) 2 T B ( b ) 5 0o r2 T A 1 T B 5 2 P (Eq. 1) D ISPLACEMENT DIAGRAM E QUATION OF COMPATIBILITY d A 5 2 d B (Eq. 2) (a) L OAD P ONLY Force-displacement relations: (Eq. 3, 4) ( L 5 length of wires at A and B .) Substitute (3) and (4) into Eq. (2): or T A 5 2 T B (Eq. 5) Solve simultaneously Eqs. (1) and (5): (Eqs. 6, 7) Numerical values: T A 5 400 lb T B 5 200 lb P 5 500 lb T A 5 4 P 5 Ê T B 5 2 P 5 T A L EA 5 2 T B L EA d A 5 T A L EA Ê d B 5 T B L EA © M C 5 0 `~ (b) L OAD P AND TEMPERATURE INCREASE D T Force-displacement and temperature- displacement relations: (Eq. 8) (Eq. 9) Substitute (8) and (9) into Eq. (2): or T A 2 2 T B 5 EA a ( D T ) (Eq. 10) Solve simultaneously Eqs. (1) and (10): (Eq. 11) (Eq. 12) Substitute numerical values: P 5 500 lb EA
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