Beam Theory

Fri Sep 16 2022

You might have done an experiment in school with a spring, some weights and a ruler. You would’ve measured the length of the spring, then measured its length with some amount of weight hanging from it. If you did, you would have found that not only did the spring increase in length whenever another weight was added, but the increase in length was in proportion to the increase in weight, and when you unloaded the spring it would return to its original length. Replace the spring with a steel bar, or a concrete block, or a length of wood, and the experiment works the same (although you might need something more precise than a ruler). This is called elastic deformation, on the atomic scale you are stretching the bonds between atoms. Plastic deformation occurs when the material is loaded to the point the atoms begin to slide past each other, we want to avoid this because the material is permernantly altered.

This is a very simple problem to analyse because it is 1-dimensional and linear. You can analyse a relatively complex arrangement of these springs without needing to reach for a computer. And it doesn’t need to literally be a spring, you could look at the compression of a concrete block, or the extension of a fishing line, as long as the thing is elastic and the line of action of the load is along its neutral axis (i.e. it isn’t being bent or buckled).

What about things that bend sideways?