Module 2 · Course notes
Reactions and load paths: where the load goes
Every load has to reach the ground. Tracing that journey — and working out which way each support pushes to make it happen — is the heart of equilibrium. The key skill is not arithmetic but a picture: imagine removing a support and watch which way the structure would move; the reaction is whatever pushes it back.
A reaction is a result, not a symbol. Its direction is decided by the movement it prevents, and it is not always upward. To find it, use notional removal: take the support away in your mind, see which way the structure moves, and the reaction is the force that would push it back to where it was.
Usually that is upward — but on an overhang the far support can be pulled down (a hold-down), and a bearing that can only push may lift off entirely.
The second idea is the load path: the load must travel through connected members to the ground, and every transfer needs a receiving member. A path that stops at a column is not finished — the column must carry the load through its foundation into the soil.
The third idea is that an offset load makes a moment. When a force misses the line that resists it, it produces a turning effect that has to be balanced too. Balancing forces is not enough; the moments must close as well.
Worked example
Worked example — which way does each support push?
A beam on two supports carries a load out on an overhang. Use notional removal to get each reaction's direction.
Step 1 — the structure
A pin and a roller with the load hanging past the roller. The roller acts as the pivot the load levers over.
Step 2 — notional removal
Remove the pin in your mind: the load levers the beam so that end springs up. The pin therefore pulls down — a hold-down. The roller, near the load, pushes up hard to carry it. Both are found from movement, not from a convention that reactions point up.
The exercises put you at each support in turn: predict which way it pushes, and whether the load path really reaches the ground.
How to read these problems
The three-step method
- 1Points of certainty. The deflected curve must pass through every support and deflect downward under the load. Mark what each support prevents before drawing anything.
- 2Deflected shape and reaction directions. Sketch the compatible deflected shape. To find a reaction's direction, imagine removing that support: the direction that pushes the structure back to its place is the reaction's sense (it may be a hold-down).
- 3Bending moment and contraflexure. Draw the bending-moment diagram on the tension side and check it against the shape: hogging where the curve is convex-up, sagging where convex-down, zero at pins and at every contraflexure.
Rules that must always hold
- 1.The bending moment is zero at a simple support and at an internal pin or hinge.
- 2.A bending-moment diagram crosses the baseline exactly at a point of contraflexure.
- 3.Under a distributed load the bending-moment diagram is curved; under point loads alone it is straight lines.
- 4.At a fully fixed support the deflected shape leaves the support with zero rotation (tangent along the member).
- 5.If a part of the structure stays straight after loading, it carries no bending moment there.
- 6.The moment is drawn on the tension side: sagging below the member, hogging above it.
Now predict for yourself
Equilibrium & load-path exercises
5 exercises on reaction directions by notional removal, uplift and hold-downs, load paths and eccentric moments. Predict, then reveal an explanation.
Start the exercises →This lesson is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions.