Simply supported beam—moment-area 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.] Continuing our odyssey through various ways of calculating the deflection at the center of a simply supported beam with a uniform load, today we use the moment-area method. There are two moment-area theorems used to calculate the slopes and deflections of a beam. Here’s how they’re given in the textbook I used as an undergrad, the 3rd edition of Elementary Structural Analysis by Norris, Wilbur, and Utku.1 The first theorem is The change in the slope of the tangents of the elastic curve between two points A and B is equal to the area under the M/EI diagram between these two points. The second theorem is The deflection of point B on the elastic curve from the tangent to this curve at point A is equal to the static moment about an axis through B of the area under the M/EI diagram between points A and B. The “elastic curve” is the curve made by the…