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Unformatted text preview: Chapter 9 Deflection of Beams 9.1 Introduction  Concerning about the deflection of a beam Special interest: the maximum deflection Design: to meet design criteria 1 M EI = 1 ( ) M x EI = 2 2 ( ) d y M x d x EI = 9.1 Introduction (4.21) M = bending moment E = modulus I = moment of inertia If M is not a constant, i.e. M=M(x) (9.1) or will be explained in Sec. 9.3 dy dx = 2 2 ( ) d y M x d x EI = y = y(x) 1 Px EI =  (9.1) (9.2) 9.2 Deformation of a Beam under Transverse Loading 1 ( ) M x EI = Since M(x) = Px Example: a beam subjected to transverse loads Moment Diagram and the Deformed Configuration: M max occurs at C In addition to M(x) and 1/ , we need further information on: 1. Slope at various locations 2. Max deflection of a beam 3. Elastic curve : y = y(x) 9.3 Equation of the Elastic Curve 1 ( ) x dy EI M x dx C dx = + 2 2 ( ) d y M x d x EI = (9.4) (9.5) 2 2 3 2 2 1 [1 ( ) ] d y d x dy dx = + 2 2 1 d y d x = 2 2 ( ) d y M x d x EI = 9.3 Equation of the Elastic Curve9....
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 Fall '11
 Wu

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