Lecture6 - Strength of Materials I EGCE201 1 Instructor: t...

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Unformatted text preview: Strength of Materials I EGCE201 1 Instructor: t . (t .t ) : 6391 3 E-mail: egwpr@mahidol.ac.th Beam Deflections As a beam is loaded, different regions are subjected to V and M the beam will deflect Recall the curvature equation x x The slope ( ) & deflection (y) at any spanwise location can be derived A cantilever with a point load The moment is M(x) = -Px The curvature equation for this case is The curvature is at A and finite at B Obviously, the curvature can be related to displacement The slope & deflection equation The following relations are established For small angles, tan ; = = dy dx ds d = = = = dy dx s x d ds d y dx M x EI ; ( ) 1 2 2 Multiply both sides of this equation by EI and integrate EI dy dx EI M x dx C x = = + ( ) 1 1 2 2 = = d y dx M x EI ( ) Where C1 is a constant of integration, Integrating again EI y M x dx C dx C dx M x dx C x C x x x x = + + = + + ( ) ( ) 1 2 1 2 Slope eqn Deflection eqn C1 and C2 must be determined from boundary conditions Double Integration method Boundary conditions Cantilever beam Overhanging beam Simply supported beam Statically indeterminate beam...
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This note was uploaded on 11/10/2010 for the course AEROSPACE AE 1202 taught by Professor Dr.adib during the Spring '10 term at Sharif University of Technology.

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Lecture6 - Strength of Materials I EGCE201 1 Instructor: t...

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