The big idea: A structure is in equilibrium when the forces on it sum to zero AND the moments sum to zero.
The second condition is the one students leave out — and a bracket with perfectly balanced vertical forces still rotates off a wall.
Both conditions drawn, then the three ways a structure leaves equilibrium — only one of which is about strength.
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| Condition | What it means | What it looks like when it fails |
|---|---|---|
| Forces balance | Up equals down and left equals right: the weight is matched by the reactions, and any sideways push by friction or a fixing | The whole structure accelerates — it falls, or it slides |
| Moments balance | The turning effects sum to zero. A moment is a force multiplied by its perpendicular distance from the pivot | It rotates: a bracket peels off a wall, a shelf tips, a ladder swings out |
Moment = force × perpendicular distance: Doubling the distance doubles the turning effect for the same force.
That is why a load at the front of a shelf is far worse than the same load at the back, why a long spanner undoes a tight nut, and why the top fixing of a bracket is the one that pulls out.
The shelf-bracket example: A book at the front edge of a shelf tries to rotate the bracket about its lowest fixing. The upper screws resist that rotation in tension, the lower ones in compression and shear.
So the top screw is the critical one — and it is the one that appears in a wall as a little cone of crumbled plaster.
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How structures actually fail
Tipping
The line of action of the weight falls outside the support base. Nothing broke — the geometry stopped working. Fixed by a wider base, a lower centre of mass, or ballast.
Sliding
A horizontal force exceeds what friction or the fixings can resist. The failure mode of ladders, of unfixed furniture, and of anything on a wet floor.
Material failure
A member yields, fractures, shears at a joint, or a slender column buckles. Only this one is about how strong the material is.
So check stability first
Two of the three have nothing to do with strength, and no amount of stronger material fixes either. Stability is geometry, and it is checked before anything is sized.
The tipping test: Drop a vertical line from the centre of mass. If it lands inside the support base, the structure stands; if it lands outside, it tips.
That single test explains a wide-based lamp, a weighted umbrella stand, a wheelchair's anti-tip castors and why a tall bookcase is strapped to a wall.
How this is tested — describing equilibrium and identifying the conditions where a structure fails. It comes up two ways:
Paper 1 — multiple choice
- Identify which equilibrium condition a described failure breaks.
- Pick the change that prevents tipping.
Paper 2 — analysing a product
- Explain why a named product is or is not in equilibrium.
- Analyse the failure modes of a structure and how to prevent each.
The trap: Answering "the forces are balanced" and stopping. The moment condition is the other half, and it is the one that explains brackets, shelves, ladders and tipping.
A tall, narrow bookcase is loaded with heavy books on its top shelf. Analyse the ways it could fail and how each could be prevented.
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