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# Lecture6 - Strength of Materials I EGCE201 1 Instructor...

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Strength of Materials I EGCE201 1 Instructor: t . 0 (t .t ) 0 : 6391 3 À E-mail: [email protected] 3 : 66(0) 2889-2138 t

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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 ( θ ) & 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

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The slope & deflection equation The following relations are established For small angles, t a n ; θ ρ θ = = d y d x d s d θ ρ θ = = = = d y d x s x d d s d y d x M x E I ; ( ) 1 2 2
• Multiply both sides of this equation by EI and  integrate E I d y d x E I M x d x C x = = + θ ( ) 1 0 1 2 2 ρ = = d y d x M x E I ( ) • Where C1 is a constant of integration, Integrating  again E I y M x d x C d x C d x M x d x C x C x x x x = + + = + + ( ) ( ) 1 0 0 2 0 1 0 2 Slope eqn Deflection eqn C1 and C2 must be determined from boundary conditions Double Integration method

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Boundary conditions Cantilever beam Overhanging beam Simply supported beam
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Lecture6 - Strength of Materials I EGCE201 1 Instructor...

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