> For the complete documentation index, see [llms.txt](https://alpaca4d.gitbook.io/docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://alpaca4d.gitbook.io/docs/examples/moment-curvature.md).

# Moment Curvature

Computes the moment–curvature response of a reinforced-concrete section: a [Patch](/docs/basics/moment-curvature/patch.md) of [Concrete01](/docs/basics/moment-curvature/concrete01.md) for the concrete, a [Layer Fiber](/docs/basics/moment-curvature/layer.md) of [ReinforcingSteel](/docs/basics/moment-curvature/reinforcing-steel.md) for the bars, collected into a [Fiber Section](/docs/basics/moment-curvature/fiber-section.md) and pushed by [Moment Curvature](/docs/basics/moment-curvature/moment-curvature.md).

Use it to see how the materials and the reinforcement layout drive stiffness, yield strength and post-yield behaviour, and as a starting point for section-level studies — M–N interaction, effective cracked stiffness, ductility.

The section is 300 × 500 mm with φ24 bars 30 mm in from its faces, 8 along one and 3 along the other, under 400 kN of compression. Its sizes are typed in millimetres and turned into metres on the way in, since a fibre section is in metres and its materials in kN/m²; a size left in millimetres, or an area in mm², gives moments thousands of times too large.

## What to try

* **Read the ductility.** The curve stops where the first fibre reaches its ultimate strain; **κYield**, **κUltimate** and **Ductility** give the section's curvature ductility, and **Failure** says which material failed, and where.
* **Sweep the axial force.** Feed a range into **Axial** (negative for compression) and watch the ductility fall as the compression grows. For the whole M–N interaction at the ultimate limit state use [Interaction Domain](/docs/basics/moment-curvature/interaction-domain.md) instead.
* **Bend it off its axes.** Give **Direction** an angle, `30` say: the moment holds that direction and the neutral axis turns as it needs to.
* **Change the bar count.** `NumberOfFibers` on the Layer Fiber, and watch where the curve flattens.
* **Refine the patch mesh.** Each face is one fibre, so the mesh density is the fibre density. Compare a coarse and a fine mesh near the neutral axis.
* **Draw the curves.** [Moment Curvature Diagram](/docs/basics/moment-curvature/moment-curvature-diagram.md) draws them, with first yield and the ultimate state marked; wire it several results to compare.
* **Unpack the fibres.** [Fiber Stress Strain](/docs/basics/moment-curvature/fiber-stress-strain.md) gives the stress and strain history of every fibre.

See [Moment Curvature](/docs/basics/moment-curvature.md) for the reference documentation on each component.

{% hint style="info" %}
Running the definition writes `MomentCurvature.tcl` and a `FiberResults` folder next to the Grasshopper file, and the materials' curves in `AlpacaResults`. They are analysis artefacts and can be deleted between runs. The definition was made with the earlier Moment Curvature: upgrade it with Grasshopper's **Upgrade Components…** for the yield and ultimate outputs above. `MaxPhi` is given as 0.04 rad/m, past the ultimate state, so the upgraded component stops there; empty it to have it taken from the section's ultimate state instead.
{% endhint %}

## Download

[moment-curvature](https://raw.githubusercontent.com/Alpaca4d/alpaca4d.github.io/main/doc/examples/moment-curvature/moment-curvature.gh)