To figure out if a structure will work, an engineer needs to model the structure in a way that can be analyzed. One of the most important steps in modeling is to decide on the structure’s supports.
I’m not talking about concrete blocks versus postholes. I’m talking about something more abstract: what types of movement are prevented because of the support? Think of all the different ways an object (a donut, say) can move. If you drop a donut from shoulder height, it moves vertically. If you push the donut across some ice, it moves horizontally. And if you thread a stick through the donut hole and spin, the donut rotates.
These three movements – rotation, horizontal translation, and vertical translation – cover all possible types of motion in 2D. (“Translation” in this case means movement in a straight line.) You don’t typically want a building or a bridge to move at all, so somehow your supports need to prevent all three. In engineer speak, a 2D structure has three degrees of freedom (DOF) and requires three restraints.
Now here’s an important point. Your model assumes the structure is rigid, meaning if one part moves, the whole thing moves. That means you could restrain horizontal translation in one corner, vertical translation in another corner, and rotation in the middle.
But some supports are easier to build than others. The most common types are as follows. A fixed support allows no movement or rotation at all, like a pole embedded in concrete. A pin support allows rotation but no translation, like a door hinge. And a roller support allows rotation and horizontal translation but no vertical translation, like a unicycle wheel on pavement. You could probably rig up another combination – you could use two parallel plates to allow translation but no rotation, for instance – but you’d need a good reason. The three most common types suffice for most purposes.
If you have more DOF than restraints, then your structure is unstable – very bad! If you have more restraints than DOF, then your structure is stable, but it’s hard to figure out how the forces distribute. So engineers like to model structures with restraints equal to DOF. We’ll model the supports for a simple bridge next month.