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805_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

805_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 10.3 Differential Equations of the Deflection Curve 799 Problem 10.3-5 A cantilever beam of length L and loaded by a triangularly distributed load of maximum intensity q 0 at B . 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. A L y q 0 x B M A R A R B Solution 10.3-5 Triangular 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): C 1 9 40 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 6 EI q 0 x 5 120 L + C 1 x 3 6 + C 2 x 2 2 + C 3 x + C 4 EI ¿ q 0 x 4 24 L + C 1 x 2 2 + C 2 x + C 3 EI M q 0 x 3
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