09-01ChapGere.0003

09-01ChapGere.0003 - M A(E Q 9-12b AND E Q 9-12a At x 5 0...

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Problem 9.2-4 The deflection curve for a cantilever beam AB (see figure) is given by the following equation: v 52 (45 L 4 2 40 L 3 x 1 15 L 2 x 2 2 x 4 ) (a) Describe the load acting on the beam. (b) Determine the reactions R A and M A at the support. Solution 9.2-4 Cantilever beam q 0 x 2 } 360 L 2 EI SECTION 9.2 Differential Equations of the Deflection Curve 549 (a) L OAD (E Q . 9-12c) The load is a downward parabolic load of maximum intensity q 0 . q 52 EIv –– 5 q 0 ¢ 1 2 x 2 L 2 v ‡¿ 52 q 0 L 2 EI ( L 2 2 x 2 ) v 52 q 0 3 L 2 EI ( 2 2 L 3 1 3 L 2 x 2 x 3 ) v 52 q 0 12 L 2 EI (3 L 4 2 8 L 3 x 1 6 L 2 x 2 2 x 4 ) v ¿ 52 q 0 60 L 2 EI (15 L 4 x 2 20 L 3 x 2 1 10 L 2 x 3 2 x 5 ) v 52 q 0 x 2 360 L 2 EI (45 L 4 2 40 L 3 x 1 15 L 2 x 2 2 x 4 ) (b) R EACTIONS R A AND
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Unformatted text preview: M A (E Q . 9-12b AND E Q . 9-12a) At x 5 0: At x 5 0: N OTE : Reaction R A is positive upward. Reaction M A is positive clockwise (minus means M A is counterclockwise). M 5 M A 5 2 q L 2 4 M 5 EIv – 5 2 q 12 L 2 (3 L 4 2 8 L 3 x 1 6 L 2 x 2 2 x 4 ) V 5 R A 5 2 q L 3 V 5 EIv ‡ 5 2 q 3 L 2 ( 2 2 L 3 1 3 L 2 x 2 x 3 ) L q A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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