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806_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

806_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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800 CHAPTER 10 Statically Indeterminate Beams Problem 10.3-6 A propped cantilever beam of length L is loaded by a parabolically distributed load with maximum intensity q 0 at B . (a) Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B and also the equation of the deflection curve. (b) Repeat (a) if the parabolic load is replaced by q 0 sin ( x /2 L ). p A L y q 0 x B M A R A R B q 0 x 2 L 2 ( ) SOLUTION 10.3-6 (a) Parabolic load D IFFERENTIAL EQUATION (1) (2) (3) (4) (5) B . C . 1 (6) B . C . 2 B . C . 3 B . C . 4 (7) Solve Eqs. (6) and (7): S HEAR FORCE ( EQ . 2) V q 0 x 3 3 L 2 + 7 60 q 0 L C 2 1 30 q 0 L 2 C 1 7 60 q 0 L ( L ) 0 C 1 L + 3 C 2 q 0 L 2 60 (0) 0 C 4 0 ¿ (0) 0 C 3 0 ( L ) 0 C 1 L + C 2 q 0 L 2 12 + C 3 x + C 4 EI q 0 x 6 360 L 2 + C 1 x 3 6 + C 2 x 2 2 EI ¿ q 0 x 5 60 L 2 + C 1 x 2 2 + C 2 x + C 3 EI M q 0 x 4 12 L 2 + C 1 x + C 2 EI –¿ q 0 x 3 3 L 2 + C 1 EI –– q q 0 x
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