Module 1 · Course notes
A drawing is a structural claim
Before you can predict a structure, you have to learn to read one. Every symbol on a structural drawing — a support, a hinge, an arrow, a shaded diagram — is a claim about what the structure does. This module builds the habit that runs through the whole course: read the movement, the reactions and the internal forces as three descriptions of one response, and check that they agree.
A deflected shape, a set of reactions and a bending-moment diagram are not three separate facts. They are three views of the same event — the structure responding to its load. If they are all correct, they tell exactly the same story: where the beam sags, the moment is sagging; where a support pushes up, the beam is held up; where there is a hinge, the moment is zero.
That is the coherence check, and it is the most powerful hand tool you have. A result that looks polished but fails it is wrong, however it was produced.
The second habit is to predict before you calculate. Numbers tell you how much; they do not tell you whether the answer is even possible. If you have already pictured the response, a wrong analysis stands out immediately — a moment appearing at a pin, a reaction pointing the wrong way, a span deflecting upward under downward load.
The third habit follows from it: a converged solver is not a validated model. A program can solve the wrong structure perfectly. Convergence means the arithmetic is consistent, not that the topology, supports and releases are what you intended.
Worked example
Worked example — is this a coherent set?
A beam with an internal hinge is offered with a deflected shape and a moment diagram. Read them together and check the hinge.
Step 1 — read the symbols
A beam fixed at the left, propped at the right, with an internal hinge at mid-span carrying a uniform load. The fixing prevents rotation; the hinge releases moment. Those two facts constrain everything.
Step 2 — the moment must be zero at the hinge
A genuine hinge cannot transfer bending moment. So a coherent bending-moment diagram must pass through zero exactly at the hinge — hogging towards the fixing, sagging towards the prop. Any diagram showing moment at the hinge fails the coherence check and must be rejected, no matter how neat.
The exercises below give you sets of claims — some coherent, some not. Your job is not to calculate, but to read them and decide whether the movement, the reactions and the internal forces can all be true at once.
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
Visual-language exercises
5 exercises on reading structures and checking that a set of diagrams is coherent — including a converged software result you should not trust.
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.