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715_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

715_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 9.2 Differential Equations of the Deflection Curve 709 Solution 9.2-3 Cantilever beam Take four consecutive derivatives and obtain: From Eq. (9-12c): The load is a downward triangular load of maximum intensity q 0 . ; q EI –– q 0 a 1 x L b ; –– q 0 LEI ( L x ) q 0 x 2 120 LEI (10 L 3 10 L 2 x + 5 Lx 2 x 3 ) Problem 9.2-4 The deflection curve for a cantilever beam AB (see figure) is given by the following equation: (a) Describe the load acting on the beam. (b) Determine the reactions R A and M A at the support. q 0 x 2 360 L 2 EI (45 L 4 40 L 3 x + 15 L 2 x 2 x 4 ) Solution 9.2-4 Cantilever beam (a) L OAD (E Q . 9-12c) The load is a downward parabolic load of maximum intensity q 0 . ; q EI –– q 0 a 1 x 2 L 2 b ; –– q 0 L 2 EI ( L 2 x 2 ) –¿ q 0 3 L 2 EI ( 2 L 3 + 3 L 2 x x 3
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