813_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

813_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 10Ch10.qxd 9/27/08 7:29 AM Page 807 807 SECTION 10.3 Differential Equations of the Deflection Curve dmax M 0 L2 216EI At point of inflection: d Problem 10.3-11 A propped cantilever beam of length L is loaded by a concentrated moment M0 at midpoint C. Use the second-order differential equation of the deflection curve to solve for reactions at A and B. Draw shear-force and bending-moment diagrams for the entire beam. Also find the equations of the deflection curves for both halves find the equations of the deflection curves for both halves of the beam, and draw the deflection curve for the entire beam. dmax/2 y L — 2 MA A M0 L — 2 C x B RA RB Solution 10.3-11 EQUILIBRIUM RA RB MA M0 (1) (2) RBL EIv ¿ RB Lx RB EIv RB L x2 2 x2 + C3 2 RB (7) x3 + C3 x + C4 6 BENDING MOMENTS (FROM EQUILIBRIUM) RA x M MA a0 … x … RB (L M x) B.C. L b 2 3 v(L) 4 continuity condition at point C At x L a … x … Lb 2 DIFFERENTIAL EQUATIONS (0 … x … L/2) M EIv ¿ RB x + M 0 + RBL RB EIv RB x2 + M 0 x + RBL x + C1 2 x3 x2 x2 + M0 + RBL + C1 x + C2 6 2 2 B.C. 1 ¿ (0) 0 ‹ C1 2 v(0) 0 ‹ C2 RB L C3 M0 From eq. (9): C4 B.C. EIv – M RB (L x) (6) RB L2 + C3 8 RB L3 3 M0 L2 2 5 continuity condition at point C At x DIFFERENTIAL EQUATIONS (L/2 … x … L) L 2 L 2 (5) 0 ( ¿ )right L2 L L + M 0 + RB L 8 2 2 0 B.C. (3) (4) ‹ C3 L + C4 L : ( ¿ )left 2 RB EIv – RB L3 3 B.C. RB x + M 0 + RBL 0 L : (v )left 2 (v )right (8) (9) ...
View Full Document

Ask a homework question - tutors are online