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723_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

723_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 9.3 Deflections by Integration of the Bending-Moment Equation 717 Problem 9.3-13 Derive the equations of the deflection curve for a simple beam AB loaded by a couple M 0 acting at distance a from the left-hand support (see figure). Also, determine the deflection d 0 at the point where the load is applied. ( Note : Use the second-order differential equation of the deflection curve.) y x A B M 0 a b L Solution 9.3-13 Simple beam (couple M 0 ) B ENDING - MOMENT EQUATION (E Q . 9-12a) B . C . 1 ( n ) Left ( n ) Right at x a B . C . 2 n (0) 0 C 3 0 B . C . 3 n ( L ) 0 C 4 M 0 L a a L 3 b C 1 L ( a x L ) EI M 0 x 2 2 + M 0 x 3 6 L + C 1 x + M 0 ax + C 4 EI M 0 x 3 6 L + C 1 x + C 3 (0 x a ) C 2 C 1 + M 0 a EI ¿ M 0 L a Lx x 2 2 b + C 2 ( a x L ) EI M M 0 L ( L x ) ( a x L ) EI ¿ M 0 x 2 2 L + C 1 (0 x a ) EI M M 0 x L (0 x a ) B . C . 4 ( n ) Left ( n ) Right at x a N OTE : d 0 is positive downward. The preceding results agree with Case 9, Table G-2. M 0 ab (2 a L ) 3 LEI ; d 0 ( a ) M 0 a (
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Unformatted text preview: L ³ a )(2 a ³ L ) 3 LEI ( a … x … L ) ; ´ ² ³ M 6 LEI (3 a 2 L ³ 3 a 2 x ³ 2 L 2 x + 3 Lx 2 ³ x 3 ) (0 … x … a ) ; ´ ² ³ M 0 x 6 LEI (6 aL ³ 3 a 2 ³ 2 L 2 ³ x 2 ) C 1 ² M 6 L (2 L 2 ³ 6 aL + 3 a 2 ) ‹ C 4 ² ³ M a 2 2 Problem 9.3-14 Derive the equations of the deflection curve for a cantilever beam AB carrying a uniform load of intensity q over part of the span (see figure). Also, determine the deflection d B at the end of the beam. ( Note: Use the second-order differential equation of the deflection curve.) A B q y x L a b 09Ch09.qxd 9/27/08 1:31 PM Page 717...
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