# L20 - Chapter 9 Deflection of Beams What is the elastic...

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Chapter 9 Deflection of Beams •What is the elastic curve ? (describe the deformed beam shape using equations) •What are the slope and deflection at point B or C?

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Deformation of a Beam Under Transverse Loading Bending under general transverse loadings. EI x M ) ( 1 = ρ Cantilever beam subjected to concentrated load at the free end, EI Px = ρ 1 Curvature varies linearly with x At the free end A , 1 ρ A = 0, ρ A = At the support B , PL EI B B = ρ ρ , 0 1 1/ =curvature at location x ρ
Deformation of a Beam Under Transverse Loading M=0 -> Curvature is zero i.e., at each end and at E . EI x M ) ( 1 = ρ M>0 concave upwards M<0 concave downwards Maximum curvature occurs where the moment magnitude is a maximum. determine maximum deflection and slope.

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Equation of the Elastic Curve From elementary calculus, simplified for beam parameters, 2 2 2 3 2 2 2 1 1 dx y d dx dy dx y d + = ρ Substituting and integrating, ( ) ( ) ( ) 2 1 0 0 1 0
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