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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Unformatted text preview: 09Ch09.qxd 9/27/08 1:30 PM Page 709 SECTION 9.2 Differential Equations of the Deflection Curve 709 Solution 9.2-3 Cantilever beam q0x2 (10L3 120LEI 10L2x + 5Lx2 x3) Take four consecutive derivatives and obtain: q0 (L LEI –– x) From Eq. (9-12c): q q0 a 1 EI –– x b L ; The load is a downward triangular load of maximum ; intensity q0. Problem 9.2-4 The deflection curve for a cantilever beam AB (see figure) is given by the following equation: q0 x2 360L2EI (45L4 40L3x + 15L2x2 x4) (a) Describe the load acting on the beam. (b) Determine the reactions RA and MA at the support. Solution 9.2-4 Cantilever beam q0x2 (45L4 40L3x + 15L2x2 x4) 360L2EI q0 (15L4x 20L3x2 + 10L2x2 x5) 60L2EI q0 (3L4 8 L3x + 6 L2x2 x4) 12L2EI q0 ( 2 L3 + 3L2x x3) 3L2EI q0 (L2 x2) L2EI – – –¿ –– (a) LOAD (EQ. 9-12c) q EI –– q0 a 1 (b) REACTIONS RA AND MA (EQ. 9-12b AND EQ. 9-12a) V At x M 2 x L2 b EI –¿ 0: V EI – q0 3L2 RA q0 12L2 ; The load is a downward parabolic load of maximum intensity q0. ; At x 0: M ( MA 2L3 + 3L2x 2q0 L 3 (3L4 q0 L2 4 x3) ; 8L3x + 6L2x2 x4) ; NOTE: Reaction RA is positive upward. Reaction MA is positive clockwise (minus means MA is counterclockwise). ...
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