846_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 846_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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840 CHAPTER 10 Statically Indeterminate Beams Problem 10.5-2 A propped cantilever beam, fixed at the left-hand end A and simply supported at the right-hand end B , is subjected to a temperature differential with temperature T 1 on its upper surface and T 2 on its lower surface (see figure). (a) Find all reactions for this beam. Use the method of superposition in the solution. Assume the spring support is unaffected by temperature. (b) What are the reactions when ? Probs. 10.5-2 and 10.5-3 k : q A h L M A R A R B = k d B T 1 T 2 y x k B Solution 10.5-2 (a) R EACTIONS ASSUMING AN ELASTIC SPRING AT B Use the method of superposition. Select R B as the redundant. R ELEASED STRUCTURE F ROM EQUILIBRIUM (b) R EACTIONS ASSUMING AN SPRING AT
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Unformatted text preview: B IS RIGID (counter-clockwise) ; M A ± R B L ± 3 EI a ( T 2 ² T 1 ) 2 h R A ± ² R B ± ² 3 EI a ( T 2 ² T 1 ) 2 hL (upward) R B ± 3 EI a ( T 2 ² T 1 ) 2 hL (downward) (counter-clockwise) ; M A ± R B L ± a ( T 2 ² T 1 ) L 3 2 h a 3 EIk 3 EI + L 3 k b R A ± ² R B ± ² a ( T 2 ² T 1 ) L 2 2 h a 3 EIk 3 EI + L 3 k b (upward) R B ± a ( T 2 ² T 1 ) L 2 2 h a 3 EIk 3 EI + L 3 k b (downward) ( δ B ) 1 ( δ B ) 2 ( δ B ) 3 R B L R B R B Δ T = T 2 – T 1 ( d B ) 3 ± ( d B ) 1 ² ( d B ) 2 ± R B k ( d B ) 2 ± R B L 3 3 EI ( d B ) 1 ± a ( T 2 ² T 1 ) L 2 2 h 10Ch10.qxd 9/27/08 7:37 AM Page 840...
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