802_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

802_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 10Ch10.qxd 9/27/08 796 7:29 AM Page 796 CHAPTER 10 Statically Indeterminate Beams SHEAR FORCE (FROM EQUILIBRIUM) V 3M 0 2L RA SHEAR-FORCE AND BENDING-MOMENT DIAGRAMS ; BENDING MOMENT (FROM EQ. 3) M M0 (3x 2L ; L) SLOPE (FROM EQ. 4) ¿ M0 x (2L 4LEI ; 3x) DEFLECTION (FROM EQ. 5) M0 x 2 (L 4LEI ; x) Problem 10.3-2 A fixed-end beam AB of length L supports a y uniform load of intensity q (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. q A MA x B MB L RA RB Solution 10.3-2 Fixed-end beam (uniform load) Select MA as the redundant reaction. B.C. REACTIONS (FROM SYMMETRY AND EQUILIBRIUM) EI RA RB qL 2 MB RAx qx 2 2 MA EI ¿ M MA + M Ax + q (Lx 2 q Lx 2 a 22 ‹ C1 MA + q (Lx 2 x 2) (1) x4 b + C2 12 2 (0) 0 ‹ C2 3 (L) 0 ‹ MA x3 b + C1 3 0 qL2 12 RB qL 2 MA qL2 12 MB SHEAR FORCE (FROM EQUILIBRIUM) (2) (3) REACTIONS RA x 2) 0 q Lx 3 M Ax 2 +a 2 26 B.C. DIFFERENTIAL EQUATIONS EI – 0 B.C. MA BENDING MOMENT (FROM EQUILIBRIUM) M 1 ¿ (0) V RA qx q (L 2 2x) ; ; ...
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