Classical Structural Analysis (2nd verse) Dec 2025

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I consider next a simple beam subject to a triangular load (aka uniformly varying load).

I derived the formulas for shear, moment, rotation, and deflection.

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I noticed a couple interesting things:

• the slopes at each end of the beam are interesting (take a look at the PDF below)
• the moment diagram due to a triangle load is exactly like the deflection diagram due to a moment load
  
  this, of course, is not a coincidence; rather it is a nice example of the conjugate beam method (reference 1 and reference 2), developed by Muller-Breslau.

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