801_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 801_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Differential Equations of the Deflection Curve The problems for Section 10.3 are to be solved by integrating the differential equations of the deflection curve. All beams have constant flexural rigidity EI. When drawing shear-force and bending-moment diagrams, be sure to label all critical ordinates, including maximum and minimum values . Problem 10.3-1 A propped cantilever beam AB of length L is loaded by a counterclockwise moment M 0 acting at support (see figure). Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), obtain the reactions, shear forces, bending moments, slopes, and deflections of the beam. Construct the shear-force and bending-moment diagrams, labeling all critical ordinates. B 10 Statically Indeterminate Beams
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Unformatted text preview: 795 Solution 10.3-1 Propped cantilever beam applied load Select M A as the redundant reaction. R EACTIONS ( FROM EQUILIBRIUM ) (1) (2) B ENDING MOMENT ( FROM EQUILIBRIUM ) (3) D IFFERENTIAL EQUATIONS EI ± – ² M ² M A L ( x ³ L ) + M x L M ² R A x ³ M A ² M A L ( x ³ L ) + M x L R B ² ³ R A R A ² M A L + M L M ² (4) B . C . 1 (5) B . C . 2 B . C . 3 R EACTIONS ( SEE EQS . 1 AND 2) M A ² M 2 R A ² 3 M 2 L R B ² ³ 3 M 2 L ; ± ( L ) ² ‹ M A ² M 2 ± (0) ² ‹ C 2 ² 0 EI ± ² M A L a x 3 6 ³ Lx 2 2 b + M 0 x 3 6 L + C 2 ± ¿ (0) ² ‹ C 1 ² EI ± ¿ ² M A L a x 2 2 ³ Lx b + M 0 x 2 2 L + C 1 A L y x B M M A R A R B 10Ch10.qxd 9/27/08 7:29 AM Page 795...
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