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730_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 730_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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724 CHAPTER 9 Deflections of Beams Problem 9.4-4 A beam with a uniform load has a guided support at one end and spring support at the other. The spring has stiffness k 48EI/ L 3 . Derive the equation of the deflection curve by starting with the third-order differential equation (the shear-force equation). Also, determine the angle of rotation u B at support B . R B = k d B M A k = 48 EI / L 3 A B q y x L Solution 9.4-4 S HEAR - FORCE EQUATION B . C . n ( L ) M ( L ) 0 EI qL 2 x 2 4 qx 4 24 + C 2 x + C 3 EI ¿ qL 2 x 2 qx 3 6 + C 2 EI qL 2 2 qx 2 2 C 1 qL 2 2 EI qx 2 2 + C 1 EI –¿ V qx B . C . n (0) 0 C 2 0 B . C . u B ¿ ( L ) qL 3 3 EI (Counterclockwise) ; (2 x 4 12 x 2 L 2 11 L 4 ) ; ( x ) q 48 EI C 3 11 qL 4 48 ( L ) qL k qL 4 48 EI Problem 9.4-5
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