805_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

805_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 10Ch10.qxd 9/27/08 7:29 AM Page 799 SECTION 10.3 Differential Equations of the Deflection Curve Problem 10.3-5 A cantilever beam of length L and loaded by a triangularly q0 y distributed load of maximum intensity q0 at B. Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B and also the equation of the deflection curve. A MA 799 L x B RA RB Solution 10.3-5 Triangular load q q0 x L C2 DIFFERENTIAL EQUATION EI –– q q0 SHEAR FORCE (EQ. 2) x q0 L EI –¿ 7 q L2 120 0 x2 + C1 2L (1) (2) V q0 9 x2 + qL 2L 40 0 REACTIONS 3 EI – M EI ¿ EI q0 q0 q0 x + C1x + C2 6L x3 x2 x5 + C1 + C2 + C3 x + C4 120L 6 2 1 – (L) 0 ‹ C1L + C2 B.C. 2 ¿ (0) 0 ‹ C3 B.C. 3 (0) 4 (L) 0 0 ‹ C4 ‹ C1 Solve Eqs. (6) and (7): C1 9 qL 40 0 RA (4) x4 x2 + C1 + C2 x + C3 24L 2 B.C. B.C. (3) RB (5) (6) 11 qL 40 0 ; 7 q L2 120 0 ; DEFLECTION CURVE (EQ. 5) 0 0 L + C2 3 V(L) ; FROM EQUILIBRIUM MA L2 q0 6 9 qL 40 0 V(0) EI 2 q0 L 60 (7) q0 x5 9 x3 + q0 L 120L 40 6 1 ( 2 q0 x 5 240LEI 9q0 Lx 3 7 x2 q0 L2 20 2 or 7q0 L2 x 2) ; ...
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