Pretend for a minute that you were one of the fellows up there posing for the picture back in the 1930s during the construction of the Waldorf Astoria in Manhattan. You would want to make sure the engineers that designed the building had actually performed calculations of the beam you are standing on, wouldn’t you?
Engineers know how to solve beams with paper and pencil since the times of Galileo Galilei. Nowadays the Euler-Bernoulli equations are easily found on Wikipedia. But what about the hooks the beam is hanging from? A curved beam with a varying cross section? No, the answer is of course finite elements.