I got an onsite interview for a structures engineer position shortly after college. The interview started with me presenting a short technical presentation on something I had done. From there, I was led to a room to interview one-on-one with whoever was interested.

The first interview was basically a quiz of some basic statics problems you should remember from school: shear and moment diagrams, free body diagrams, and similar concepts. These then evolved into more complicated thought experiments, like how to design the optimum beam for a certain load, including what material and shape it should be. It's not so much about getting the right answer but how you arrived at it.

The interview continued with several short, approximately 20-minute, one-on-one interviews from a number of different people. Everyone had their one or two trick questions to ask, covering everything from vibration modes to computer programming. They then asked about your experience and what you've done in the past, pretty much whatever you put on your resume.

By the end of the day, you might have had zero interviews or you might have had ten. You interview with whoever is interested in talking to you, and it takes as long as it takes; mine took over 7 hours total.

In the end, you're exhausted, but you get a very good feeling about how the company operates and if it's something you are interested in.

If you had a simply supported rectangular beam with a single load in the middle, how would you optimize its thickness to minimize weight?

What material would you make it out of to maximize stiffness for the same mass?

What about if it was a circular tube, or if it was in just compression or tension? How does that change your answer?