A bending moment diagram is the graphical representation of the bending moment along the length of a beam, joist or column. The horizontal axis gives the position along the member, the vertical axis the magnitude of the moment. At a glance you can see where the structure is worked hardest and how large the moment is there.
The diagram is the key tool in sizing a structural member. Where the curve reaches its extreme value, the section has to take the most.
Shapes worth recognising
| Situation | Shape of the diagram |
|---|---|
| Simply supported beam, distributed load | Parabola, peak at mid-span |
| Simply supported beam, point load at mid-span | Triangle, apex under the load |
| Cantilever, distributed load | Parabola with its peak at the fixed end, zero at the free end |
| Continuous beam over several supports | Alternating span and support moments with zero points in between |
On a simply supported beam the moment at both supports is always zero — a pinned support cannot take a moment. At a fixed end the opposite is true: that is exactly where the moment is largest.
Why the diagram is so useful
- Governing section. The peak value determines which section or beam depth is required
- Placing reinforcement. In reinforced concrete the sign of the moment tells you where the tension zone is: at a span moment it is at the bottom, at a support moment at the top. The main reinforcement has to sit in the tension zone. Steel in the wrong place does almost nothing
- Zero points and points of contraflexure. The places where the curve crosses zero are the sensible points at which to curtail reinforcement, place a splice or make an assembly connection
- Openings. A hole through a beam costs most capacity where the moment is large. At or near a zero point it is far less critical
- Understanding the structure. A continuous beam over two spans has a substantial negative moment over the middle support — a detail easily missed if you only look at one span
The bending moment diagram is always drawn together with the shear force diagram. Both belong in any structural calculation and form part of what is submitted with an application for consent.
Related terms
- Moment
- Bending moment
- Shear force
- Beam
- Reinforcement
- Deflection
- Structural calculation
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