The cantilevered beam: an analytical solution for general deflections of linear-elastic materials

Honestly, I was scared! How do you boy dare to disagree with the great Richard Feynmann? That was the first thing that came to my mind when I saw how he was computing the bending moment at a point $x$ on a cantilever beam (after eq. 38.39 in his famous Lecture notes).

Fig. 1: Computing the bending moment in a cantilever beam.

The main observation giving birth to my little baby — my first paper — is that the bending moment has to be calculated when the beam is at equilibrium, at which point the force perpendicular to the arm is $F_{\perp}=F\cos\theta$ (with $\theta$ being the angle between the tip and the vertical) instead of the vertically applied force $F$ on the tip, as shown in Fig 1. I could demonstrate that correcting the formulation with this observation gives results more in agreement with the experiments.

That was really exciting when I was just beginning to crawl!