797_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

797_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 09Ch09.qxd 9/27/08 1:37 PM Page 791 791 SECTION 9.11 Temperature Effects Solution 9.11-1 Simple beam with temperature differential d2 Eq. (9-147): – v¿ B.C. dx a(T2 2 a(T2 T1)x h dv dx h T1)x 2 v(0) 2x) aL(T2 T1) 2h v ¿ (0) ; T1) aL(T2 2h aL2(T2 8h L ab 2 dmax T1) ; (positive dmax is downward deflection) T1)x aL(T2 + C2 2h 2h B.C. T1)(L 2h (positive uA is clockwise rotation) 0 ‹ C1 a(T2 a(T2 v¿ uA C1 L 1 (Symmetry) v ¿ a b 2 2 T1) 0 C2 0 a(T2 T1)(x)(L x) ; 2h (positive n is upward deflection) Problem 9.11-2 A cantilever beam AB of length L and height h (see figure) is subjected to a temperature change such that the temperature at the top is T1 and at the bottom is T2. Determine the equation of the deflection curve of the beam, the angle of rotation uB at end B, and the deflection dB at end B. y T1 A T2 L Solution 9.11-2 Cantilever beam with temperature differential Eq. (9-147): – v¿ B.C. v¿ dv dx d2 dx a(T2 2 a(T2 T1) x h 1 n (0) 0 B.C. 2 n(0) a(T2 0 T1)x C2 0 2 ; 2h C1 (positive n is upward deflection) C1 a(T2 T1) x h a(T2 T1) h T1) x 2 a b + C2 h 2 0 uB v ¿ (L) aL(T2 T1) h ; (positive uB is counterclockwise rotation) dB (L) aL2(T2 2h T1) ; (positive dB is upward deflection) h B x ...
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