847_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

847_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 10.5 Temperature Effects 841 Problem 10.5-3 Solve the preceding problem by integrating the differential equation of the deflection curve. Solution 10.5-3 (a) D IFFERENTIAL EQUATION ( EQ . 10-39b) B . C . 1 B . C . 2 B . C . 3 (downward) ; R B ± a EI ( T 2 ² T 1 ) L 2 2 h a 3 k 3 EI + L 3 k b ³ ( L ) ± d B ± R B k ³ (0) ± 0 C 2 ± 0 EI ³±² R B L x 2 2 + R B x 3 6 + a EI ( T 2 ² T 1 ) 2 h x 2 + C 2 ³ ¿ (0) ± 0 C 1 ± 0 EI ³ ¿ ±² R B Lx + R B x 2 2 + a EI ( T 2 ² T 1 ) h x + C 1 EI ³ ±² R B ( L ² x ) + a EI ( T 2 ² T 1 ) h EI ³ ± M + a EI ( T 2 ² T 1 ) h F ROM EQUILIBRIUM (b) S AME REACTIONS AS IN 10.5-2(b) WHEN k : q (counter-clockwise) ; M A ± R B L ± a EI ( T 2 ² T 1 ) L 3 2 h a 3 k 3 EI + L 3 k b (upward) ; R A ±² R B ±² a EI ( T 2 ² T 1 ) L 2 2 h a 3 k 3 EI ´ L 3 k b Problem 10.5-4 A two-span beam with spans of lengths L and L/ 3 is subjected to a temperature differential with temperature
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Unformatted text preview: T 1 on its upper surface and T 2 on its lower surface (see figure). (a) Determine all reactions for this beam. Use the method of superposi-tion in the solution. Assume the spring support is unaffected by temperature. (b) What are the reactions when ? Probs. 10.5-4 and 10.5-5 k : q A h L C B R A R C T 1 T 2 L — 3 R B = k d B k y x 10Ch10.qxd 9/27/08 7:37 AM Page 841...
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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.

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