719_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

719_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 1:31 PM Page 713 SECTION 9.3 Deflection Formulas Problem 9.3-7 Obtain a formula for the ratio dC /dmax of the deflection at the midpoint to the maximum deflection for a simple beam supporting a concentrated load P (see figure). From the formula, plot a graph of dC/dmax versus the ratio a/L that defines the position of the load (0.5 a/L 1). What conclusion do you draw from the graph? (Use the formulas of Example 9-3.) 713 P A B a b L Solution 9.3-7 Simple beam (concentrated load) 4b2) Pb(3L2 48EI Eq. (9-35): dC (3 13L)(3L2 Eq. (9-34): dmax dc dmax 9 13LEI Pb(L2 2 dmax 0.5 0.6 0.7 0.8 0.9 1.0 1.0 0.996 0.988 0.981 0.976 0.974 (a Ú b) (3 13L)( L2 + 8aL 4a2) a2)3/2 (3 13L) a 1 + 8 dc b 4b2) b) 16(2aL a/L b, the ratio b versus from 0.5 to 1.0. (a Ú b) Replace the distance b by the distance a by substituting L a for b: dc dmax GRAPH OF dc/dmax VERSUS b Because a b2)3/2 2 3/2 16(L (a Ú b) Divide numerator and denominator by L2: dc dmax dc dmax (3 13L) a 1 + 8 16L a 2 16 a 2 a L a L a L 4 a2 4 L2 b 3/2 a L a2 b L2 a2 b L2 a2 L2 3/2 b ; NOTE: The deflection dc at the midpoint of the beam is almost as large as the maximum deflection dmax. The greatest difference is only 2.6% and occurs when the load reaches the end of the beam (b 1). ALTERNATIVE FORM OF THE RATIO Let b dc dmax (3 13)( a L 1 + 8b 16(2 b b 2)3/2 4 b 2) ; ...
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