720_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

720_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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714 CHAPTER 9 Deflections of Beams Deflections by Integration of the Bending-Moment Equation Problems 9.3-8 through 9.3-16 are to be solved by integrating the second-order differential equation of the deflection curve (the bending-moment equation). The origin of coordinates is at the left-hand end of each beam, and all beams have constant flexural rigidity EI . Problem 9.3-8 Derive the equation of the deflection curve for a cantilever beam AB supporting a load P at the free end (see figure). Also, determine the deflection d B and angle of rotation u B at the free end. ( Note : Use the second-order differential equation of the deflection curve.) y B A P L Solution 9.3-8 Cantilever beam (concentrated load) B ENDING - MOMENT EQUATION (E Q . 9-12a) B . C . n ± (0) ² 0 ± C 1 ² 0 B . C . n (0) ² 0 ± C 2 ² 0 ³²´ Px 2 6 EI (3 L ´ x ) ; EI ³²´ PLx 2 2 + Px 3 6 + C 2 EI ³ ¿ ²´ PLx + Px 2 2 + C 1 EI ³ ² M ²´ P ( L ´ x ) (These results agree with Case 4, Table G-1.)
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Unformatted text preview: u B ² ´³ ¿ ( L ) ² PL 2 2 EI ; d B ² ´³ ( L ) ² PL 3 3 EI ; ³ ¿ ² ´ Px 2 EI (2 L ´ x ) Problem 9.3-9 Derive the equation of the deflection curve for a simple beam AB loaded by a couple M at the left-hand support (see figure). Also, determine the maximum deflection d max . ( Note : Use the second-order differential equation of the deflection curve.) y x A M B L Solution 9.3-9 Simple beam (couple M ) B ENDING-MOMENT EQUATION (E Q . 9-12a) EI ³ ² M a x 2 2 ´ x 3 6 L b + C 1 x + C 2 EI ³ ¿ ² M a x ´ x 2 2 L b + C 1 EI ³ – ² M ² M a 1 ´ x L b B . C . n (0) ² ± C 2 ² B . C . n ( L ) ² ³ ² ´ M x 6 LEI (2 L 2 ´ 3 Lx + x 2 ) ; ‹ C 1 ² ´ M L 3 09Ch09.qxd 9/27/08 1:31 PM Page 714...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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