The Bernoulli Bunch

I had thought I was done referencing new material I had covered in class, as I prefer to cover topics that aren’t solely just definitions, but I had to note this because it is quite interesting. Every engineer and engineering student (provided you pay attention to the minute details in the textbooks you skim), can relate to finding the developers of a specific mathematical concept interesting. In specific, when a given mathematician or physicist is known to have developed several principles in different fields.

Tacking on to the twenty different ways to find deflection and slope of a beam, I had studied the Principle of Virtual Work introduced by “John Bernoulli” in 1717. The principle equates the work done on a beam to the product of the force and its deflection. It equates the angular work done on the bean to the product of a couple and the angular displacement. The entire process involves the application of unit loads and unit couples to a virtual structure and the evaluation of specific integrals to find deflection or slope at a specific point. Figuring I took Fluid Mechanics last year, I would have had to not pay attention the entire semester to not recognize the last name Bernoulli. Assuming it was the same guy, I was at first impressed that the same person had worked in both fields and developed extremely useful principles for both. Upon doing some research, the Bernoulli family was, to keep it short, smarter than your average household.

Johann Bernoulli was the man responsible for the virtual work method for beams. Oddly, the book for my Structural Analysis class states his first name as John, which doesn’t make sense. The man responsible for the all famous and “commonly misused Bernoulli equation” for Fluid mechanics was Daniel Bernoulli. As it turns out, Daniel was the son of Johann. Daniel had two brothers named Niklaus and Johann II who were both renowned mathematicians. If somehow anyone has ever felt the pressure to live up to the expectations of their parents and older siblings, just remind yourself you aren’t growing up in the Bernoulli house.