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724_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 724_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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718 CHAPTER 9 Deflections of Beams Solution 9.3-14 Cantilever beam (partial uniform load) B ENDING - MOMENT EQUATION (E Q . 9-12a) B . C . 1 n (0) 0 C 1 0 M 0 ( a x L ) C 2 ( a x L ) B . C . (0 x a ) EI q 2 a a 2 x 2 2 ax 3 3 + x 4 12 b + C 3 2 ( v ¿ ) Left ( v ¿ ) Right at x a C 2 qa 3 6 EI ¿ EI ¿¿ (0 x a ) EI ¿ q 2 a a 2 x ax 2 + x 3 3 b + C 1 (0 x a ) EI M q 2 ( a x ) 2 q 2 ( a 2 2 ax + x 2 ) B . C . 3 n (0) 0 C 3 0 B . C . 4 ( n ) Left ( n ) Right at x a (These results agree with Case 2, Table G-1.) d B ( L ) qa 3 24 EI (4 L a ) ; qa 3 24 EI (4 x a ) ( a x L ) ; qx 2 24 EI (6 a 2 4 ax + x 2 ) (0 x a ) ; C 4 qa 4 24 EI C 2 x + C 4 qa 3 x 6 + C 4 ( a x L ) Problem 9.3-15 Derive the equations of the deflection curve for a cantilever beam AB supporting a distributed load of peak intensity q 0 acting over one-half of the length (see figure). Also, obtain formulas for the deflections d B and d C at points B and C , respectively. ( Note : Use the second-order differential equation of

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