799_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 799_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 9.11 Temperature Effects 793 M AXIMUM DEFLECTION Set n ( x ) 0 and solve for x (b) ( T 2 T 1 ) T 0 x 2 B . C . n (0) 0 C 2 0 B . C . n ( L ) 0 C 1 a T 0 L 3 12 h a T 0 x 4 12 h + C 1 x + C 2 v ¿ a T 0 x 3 3 h C 1 d 2 dx 2 a T 0 x 2 h d max a T 0 L 3 9 1 3 h Downward ; a T 0 c a L 1 3 b 3 L 2 L 1 3 d 6 h d max a L 1 3 b 0 a T 0 2 h a x 2 L 2 3 b x L 1 3 M AXIMUM DEFLECTION Set n ( x ) 0 and solve for x Downward d max a T 0 L 4 48 h (2 1 2 1) ; a T 0 c a L 1 2 b 4 L 3 L 1 2 d 12 h d max a L 1 2 b 0 a T 0 3 h a x 3 L 3 4 b x L 1 2 v ¿ ( x ) a T 0 3 h a x 3 L 3 4 b ( x ) a T 0 ( x 4 L 3 x ) 12 h Problem 9.11-5 Beam AB , with elastic support k R at A and pin support at B , 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 linearly along the beam:
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