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The equivalent load (f) acting on a simply supported beam element loaded with uniformly distributed load (p) over an element of length (l) is given by which of the following expressions?

(a) f=\([\frac{pl}{2},\frac{pl^2}{12},\frac{pl}{2},-\frac{pl^2}{12}]\)

(b) f=\([\frac{pl}{2},\frac{pl^2}{12},\frac{pl}{2},\frac{pl^2}{12}]\)

(c) f=\([\frac{pl}{2},-\frac{pl^2}{12},\frac{pl}{2},-\frac{pl^2}{12}]\)

(d) f=\([\frac{pl}{2},\frac{pl^2}{12},\frac{-pl}{2},-\frac{pl^2}{12}]\)

I got this question in an interview for job.

I need to ask this question from Beams and Frames in chapter Beams and Frames of Finite Element Method

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The correct choice is (a) f=\([\frac{pl}{2},\frac{pl^2}{12},\frac{pl}{2},-\frac{pl^2}{12}]\)

The best I can explain: The value of equivalent load is given by


Here l is length of beam element, and p is the uniformly distributed load. Here \(\frac{pl}{2}\) represents the reaction force on the supports, and \(\frac{pl^2}{12}\)  represents the moment acting on the supports.

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