Analysis: Conventional Interactions

In most of our free-body diagrams so far, forces have been applied by strings, so it was easy to know which direction they go in. You can work it out by geometry. It’s not always so easy. We need to be able to represent many different loading situations. Here are some common ones and their conventional representations. The left hand figure shows a heavy beam supported by a roller at one end and a pin joint at the other. The right hand figure shows a free-body diagram. It’s a heavy beam so we’ve included the weight. Can you see that the rollers applies a force perpendicular to the surface it rolls against? And of course it can only push upwards in this case.

The pin joint can push and pull and it can go sideways too. You can represent its effect by components as shown or by a result and at an angle to some datum. In either case, it requires two quantities. We often neglect friction in the pin joint but if you can’t, you’ll need to add a couple. Here’s another common situation, a built-in end. Common terms are encastre and cantilever. It’s like a pin joint with a lot of friction. The free-body diagram has force components in two directions and an end-fixing moment. The weight of the beam has been neglected in this case.

If you’re not sure of the sense of force components up or down, left or right, then don’t worry about it too much. If you get it wrong, it generally just comes out negative. There are exceptions. For example, a roller can only push and fix and forces must oppose motion. We’ll see that in week five. Common sense and intuition can help. Check your intuition on this one. If you have a pin joint instruct when the weight can be neglected, then the forces at each end must be equal, opposite, and in the same line. You’ll see the reason in week four.

If you just show pin joints with two force components at each end, it’s not wrong and you’ll get the right answer, but you are missing out on insights. You’re not exercising your engineers’ eyes. Now you are ready for some tutorial problems and then some design.