A moment is the turning or bending effect of a force about a point: the magnitude of the force multiplied by the perpendicular distance to that point. As a formula: M = F × a. The unit is the newton metre (Nm), in building work usually the kilonewton metre (kNm).
The lever arm matters at least as much as the force. The same load at twice the distance produces twice the moment. That is why a beam spanning twice as far needs not twice but considerably more material.
Types of moment
- Bending moment. The moment that tries to bend a beam. The top face goes into compression and the bottom into tension — or the other way round, depending on the sign
- Torsional moment. A twisting moment about the longitudinal axis of a member, for example a beam carrying a cantilevered floor on one side
- Overturning moment. The moment that tries to topple a wall, retaining structure or building, from wind load or earth pressure
- Torque. In fixings: the force with which a bolt is tightened, given in Nm and checked with a torque wrench
Some common formulas
For a simply supported beam of span L:
| Loading | Maximum bending moment |
|---|---|
| Uniformly distributed load q | M = q·L² / 8, at mid-span |
| Point load F at mid-span | M = F·L / 4, under the load |
| Cantilever with distributed load q | M = q·L² / 2, at the fixed end |
Note the squared term: under a uniformly distributed load the moment grows with the square of the span. Making a beam 20 per cent longer means roughly 44 per cent more moment.
Why it matters
The maximum bending moment, together with the material strength, determines which section or beam depth is needed. The section modulus has to be able to take the applied moment. That is why a beam is deeper than it is wide: depth counts squared in the resistance, width only linearly.
Deflection is a separate, second check. A beam can be strong enough and still sag too much — that is its own limit state.
Never size structure by eye. Removing a loadbearing wall, installing a steel beam or building an extension all require calculations by a structural engineer as part of the application for consent.
Related terms
- Bending moment diagram
- Bending moment
- Beam
- Shear force
- Deflection
- Span
- Section modulus
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