Simply supported beam—conjugate beam method

[Equations in this post may not look right (or appear at all) in your RSS reader. Go to the original article to see them rendered properly.] The fourth way we’re going to derive the formula for the center deflection of a simply supported beam with a uniform load is the conjugate beam method. This is probably tied with the moment-area method for the simplest and fastest way to get the formula—at least if you’ve memorized the properties of parabolas. I wrote about the conjugate beam method last year. In a nutshell, it takes advantage of the similarity of the relationships between bending moment and distributed load, M″=−q and between displacement and bending moment, y″=−MEI To get the deflection of the beam, we construct a conjugate beam that’s loaded by the M/EI diagram of the real beam. Calculating the moment at a point of the conjugate beam gives us the deflection at the corresponding point in the real beam. For our problem, the conjugate beam looks like this: The supports of the…