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09-01ChapGere.0010 - 556 A-PDF Deflections of Beams CHAPTER...

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556 CHAPTER 9 Deflections of Beams 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 0 at the point where the load is applied. ( Note: Use the second-order differential equation of the deflection curve.) Solution 9.3-13 Simple beam (couple M 0 ) y x A B M 0 a b L B ENDING - MOMENT EQUATION (E Q . 9-12a) (0 x a ) (0 x a ) (a x L ) (a x L ) B . C . 1 ( ) Left ( ) Right at x a C 2 C 1 M 0 a (0 x a ) B . C . 2 v (0) 0 C 3 0 (a x L ) EIv M 0 x 2 2 M 0 x 3 6 L C 1 x M 0 ax C 4 EIv M 0 x 3 6 L C 1 x C 3 v ¿ v ¿ EIv ¿ M 0 L ¢ Lx x 2 2 C 2 EIv M M 0 L ( L x ) EIv ¿ M 0 x 2 2 L C 1 EIv M M 0 x L B . C . 3 v ( L ) 0 B . C . 4 ( v ) Left ( v ) Right at x a (0 x a ) ( a x L ) N OTE : 0 is positive downward. The pending results agree with Case 9, Table G-2. M 0 ab (2 a L ) 3 LEI 0 v ( a ) M 0 a ( L a )(2 a L ) 3 LEI v M 0 6 LEI (3 a 2 L 3 a 2 x 2 L 2 x 3 Lx 2 x 3 ) v M 0 x 6 LEI (6 aL
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