A beam carries a point load at midspan. Choose a support type at each end — the reactions update instantly.
In structural engineering, a beam is a horizontal member that carries load perpendicular to its own axis — meaning loads push down on it, and it resists by bending. The beam itself doesn't float. Something has to hold it up at its ends (or somewhere along its length). Those somethings are supports.
The support type determines everything: how many reaction forces exist, in which directions they act, and how you solve for them. Get the support wrong in your model and your entire analysis is wrong — even if the math is perfect.
Every support prevents certain movements. If a support prevents vertical movement, it generates a vertical reaction force. If it prevents horizontal movement, it generates a horizontal reaction force. If it prevents rotation, it generates a moment reaction.
The number of reaction components a support provides equals the number of movements it prevents. That's not a coincidence — it's Newton's third law applied to structural connections. The support pushes back with exactly as many forces as it takes to stop the motion you're trying to prevent.
A steel bridge beam resting on a bearing pad. The beam end can slide horizontally as it expands and contracts with temperature. The pad only pushes up.
A bolted connection at the end of a truss. The bolt holds the member in place but lets it rotate slightly as loads shift. It pushes back both vertically and horizontally.
A cantilevered canopy bolted into a concrete wall. The wall grabs the beam end completely — it can't slide, it can't rotate. The wall has to push back in every direction including resisting the tendency to rotate.
Static equilibrium gives you three equations for a 2D problem:
That means you can solve for at most three unknowns. If your support configuration produces more than three unknown reaction components, the structure is statically indeterminate — and you need more advanced methods to solve it.
This is why the roller + pin combination is so common in introductory problems. A roller gives one unknown (vertical reaction). A pin gives two (vertical and horizontal). Total: three unknowns, three equations. Solvable. Clean. That's not an accident — it's deliberate problem design.
In the node module, all forces acted at the same point. Distance didn't matter. On a beam, forces act at different positions — and that changes everything. A force applied far from a support creates a larger rotational tendency than the same force applied close to it. That tendency is called a moment.
Moment = Force x perpendicular distance.
If you push down at the midpoint of a 20-foot beam with 10 kips, you're creating a moment of 10 x 10 = 100 kip-feet about the left support. For the beam to stay still — not rotate — the right support has to push back with enough force to cancel that rotational tendency.
That's SM = 0. The sum of all moments about any point must equal zero. And the powerful thing: if you take moments about one support, that support's own reaction disappears from the equation — leaving you with one equation and one unknown. That's how you solve for reactions on a beam.
You'll work through this fully in the statics module. For now, the important thing is the concept: distance matters, and SM = 0 is what keeps the beam from rotating.
A pin and a roller both allow the beam end to rotate freely. Under load, the beam bends — and the ends tilt slightly. Pin and roller supports accommodate that tilt without resisting it. They generate force reactions only, not moment reactions.
A fixed support is different. It grabs the beam end completely and holds it level — no tilt allowed. To do that, the wall has to exert a moment reaction in addition to the vertical and horizontal forces. That moment reaction is real — it shows up as stress in the connection, bending in the wall, tension in the anchor bolts.
This is why cantilevered structures — balconies, canopies, overhead signs — depend so heavily on their connection to the supporting wall or column. That connection is doing three jobs at once: holding the beam up, holding it in, and holding it from rotating. All three have to be designed for.
The fixed connection at the wall resists vertical force, horizontal force, and the rotational moment from the overhanging load. The further the load is from the wall, the larger the moment — and the harder the wall has to work.
A beam is a member loaded perpendicular to its axis. The transverse loads create internal shear forces (trying to slide sections apart) and bending moments (trying to curve the beam). The beam resists by developing internal stresses — compression on one face, tension on the other. The deeper the beam, the more lever arm between the compression and tension forces, and the more moment it can resist. This is why beams are deep relative to their width.
How a beam is supported changes everything. A simply supported beam (pin + roller) is statically determinate — reactions are easily found from equilibrium, and the beam is free to rotate at both ends. A cantilever (fixed at one end, free at the other) develops maximum moment at the wall. A fixed-fixed beam has zero rotation at both ends and develops smaller midspan moments but larger support moments. Same beam, same load, completely different behavior.