765_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

765_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: 09Ch09.qxd 9/27/08 1:35 PM Page 759 759 SECTION 9.7 Nonprismatic Beams Problem 9.7-4 A simple beam ABCD has moment of inertia I near the supports q and moment of inertia 2I in the middle region, as shown in the figure. A uniform load of intensity q acts over the entire length of the beam. Determine the equations of the deflection curve for the left-hand half of the beam. Also, find the angle of rotation uA at the left-hand support and the deflection dmax at the midpoint. A B C I D I 2I L — 4 L — 4 L Solution 9.7-4 Simple beam (nonprismatic) Use the bending-moment equation (Eq. 9-12a). B.C. 1 Symmetry: ¿ L ab 2 REACTIONS, BENDING MOMENT, AND DEFLECTION CURVE qL3 24 From Eq. (4): C2 2EI ¿ qL x2 4 0 qx3 6 qL3 24 a L L …x… b 4 2 (5) SLOPE AT POINT B (FROM THE RIGHT) RA 2 qL 2 RB M qx 2 Rx qLx 2 Substitute x 2 qx 2 EI ¿ B B.C. L into Eq. (5): 4 11qL3 768 (6) 2 CONTINUITY OF SLOPES AT POINT B ¿ (vB)Left ¿ (vB)Right From Eqs. (3) and (6): BENDING-MOMENT EQUATIONS FOR THE LEFT-HAND HALF qL L 2 q L 3 ab a b + C1 44 64 11qL3 768 ‹ C1 7qL3 256 L b 4 (7) OF THE BEAM EI – qx2 2 qLx 2 M a0 … x … L b 4 (1) SLOPE OF THE BEAM (FROM EQS. 3 AND 5) M qx 2 L L a …x… b 4 2 EI ¿ qL x2 4 qx3 6 7qL3 256 EI ¿ E(2I ) – qLx 2 2 qL x2 8 qx3 12 qL3 48 (2) INTEGRATE EACH EQUATION EI ¿ qL x2 4 qx3 + C1 6 2 2EI ¿ qL x 4 3 qx + C2 6 a0 … x … a L b 4 L L …x… b 4 2 (3) a L L …x… b 4 3 (8) ANGLE OF ROTATION uA (FROM EQ. 7) uA (4) a0 … x … v ¿ (0) 7qL3 (positive clockwise) 256EI ; ...
View Full Document

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.

Ask a homework question - tutors are online