The big idea: A force diagram shows every force acting on a structure as an arrow, at the point where it acts, pointing the way it pushes.
Read one in four steps: the loads, the reactions that balance them, the moments, and then what each member is doing.
The same beam with the arrows added one stage at a time — loads, then reactions, then moments.
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Finding the reactions
Up must equal down
The reactions together balance the loads. An 800 N load on a beam means the two supports carry 800 N between them, whatever the split.
Symmetrical load, equal reactions
A load at mid-span gives 400 N at each support. No calculation is needed, and saying so is a legitimate answer.
Off-centre load, take moments
Moment = force × perpendicular distance. Take moments about one support so that reaction drops out, then solve for the other.
Check both conditions
The forces balance AND the moments balance. If either fails, a force has been missed or placed wrongly.
A worked pair: An 800 N load sits 1 m from the left end of a 4 m simply supported beam.
Moments about the left support: 800 × 1 = R₂ × 4, so R₂ = 200 N. Forces up equal forces down, so R₁ = 800 − 200 = 600 N. The support nearer the load carries more, which is the check that the answer is the right way round.
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| On the diagram | What it means | What the designer must then check |
|---|---|---|
| Arrows pointing AWAY from each other along a member | The member is being stretched — tension | The material's tensile strength, and the joints at each end, which are usually the weak point |
| Arrows pointing TOWARDS each other | The member is being squashed — compression | BUCKLING before crushing, if it is at all slender — the effective length is what matters, not the strength |
| Arrows offset across a member | It is being cut across — shear | The shear area: a bolt, a pin or a weld throat |
| A load across a member with supports elsewhere | It is bending | Where the bending moment is largest, and the depth of the section there |
The notation is the whole point: Arrows apart means tension. Arrows together means compression.
That is the entire convention, and it is what lets one drawing tell a reader in another country which members need to be thin cables and which need to be fat tubes.
How this is tested — interpreting simple force diagrams for a given structure. It comes up two ways:
Paper 1 — multiple choice
- Read a reaction off a symmetrical beam.
- Identify whether a labelled member is in tension or compression.
Paper 2 — analysing a product
- Calculate the reactions for a loaded beam.
- Interpret a force diagram and say which members carry what.
The trap: Assuming the reactions are always equal. They are only equal when the load is symmetrical — otherwise you must take moments.
A 3 m shelf rests on two brackets at its ends. A 240 N load sits 0.5 m from the left bracket. Apply the conditions of equilibrium to find both reactions, and state where the shelf is most likely to fail.
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