I thought I would write a post with a simple example showing the relationship between mathematics and engineering and how great mathematicians were also great engineers. Leonard Euler and Jacob Bernoulli were brilliant mathematicians more commonly known for their contributions to analysis, calculus, and probability However they were also great engineers.
Euler-Bernoulli beam theory is a great representation of that fact. Their theory of beams provided an accurate determination of the deflection deformation in beams subjected to lateral loads. This is very important when trying to build large structures to ensure that the forces within it will not deform the structure enough to initiate failure. It’s also one of the very few examples of a fourth order differential equation governing a physical process that I know of (that actually has significant physical meaning).
The accuracy of this method of beam analysis was demonstrated when it was used to construct the tallest structure in the world for that time the Eiffel Tower (1889). After completion the Euler-Bernoulli Beam theory quickly became a cornerstone of engineering and an enabler of the second industrial revolution.
Here I’ve done a pretty simple example using the theory to calculate the equation of deflection for a beam fixed to the wall on its left side and under a distributed load. In the second picture is another application of Euler-Bernoulli beam theory which allows for the determination of support forces on a beam which normally could not be determined using solely the common equations of equilibrium (statics).
complex mathematical ideas firm grounding in everyday events has always amazed and mystified me. This is a perfect example of that synergy.