798_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

798_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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792 CHAPTER 9 Deflections of Beams Problem 9.11-3 An overhanging beam ABC of height h has a guided support at A and a roller at B . The beam is heated to a temperature T 1 on the top and T 2 on the bottom (see figure). Determine the equation of the deflection curve of the beam, the angle of rotation u C at end C , and the deflection d C at end C . x y A L BC T 1 T 2 T 1 T 2 a h Solution 9.11-3 B . C . n ± (0) ² 0 C 1 ² 0 B . C . n ( L ) ² 0 ³ ( x ) ² a ( T 2 ´ T 1 )( x 2 ´ L 2 ) 2 h C 2 ²´ a ( T 2 ´ T 1 ) L 2 2 h ³² a ( T 2 ´ T 1 ) x 2 2 h + C 1 x + C 2 v ¿ ² a ( T 2 ´ T 1 ) x h µ C 1 ³ ² d 2 dx 2 a ( T 2 ´ T 1 ) h Upward Counter Clockwise u C ² v ¿ ( L µ a ) ² a ( T 2 ´ T 1 L µ a ) h ; ² a ( T 2 ´ T 1 )(2 La + a 2 ) 2 h ; d C ²³ ( L + a ) ² a ( T 2 ´ T 1 )[( L + a ) 2 ´ L 2 ] 2 h Problem 9.11-4 A simple beam AB of length L and height h (see figure) is heated in such a manner that the temperature difference T 2 ´ T 1 between the bottom and top of the beam is proportional to the distance from support A ; that is, assume the temperature difference varies
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