> 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/basics/moment-curvature.md).

# Moment Curvature

A **fibre section** divides a cross-section into many small areas, gives each one a uniaxial material, and integrates their response. It is how a section's real non-linear behaviour — concrete crushing, reinforcement yielding, the loss of stiffness after cracking — comes out of the material laws rather than being assumed.

The **Moment Curvature** component then pushes such a section to a given curvature under a held axial force and returns the full curve.

{% hint style="info" %}
This tab is marked **βeta** in Grasshopper (`MomentCurvature_βeta`). It works as a section-level tool. Fibre sections cannot yet be assigned to a [ForceBeamColumn](/docs/basics/elements/force-beam-column.md), which takes an [elastic section](/docs/basics/sections.md).
{% endhint %}

## Components in this tab

**Materials** — non-linear uniaxial laws, for fibres.

| Component                                                              | Nickname           | Models                                           |
| ---------------------------------------------------------------------- | ------------------ | ------------------------------------------------ |
| [Concrete01](/docs/basics/moment-curvature/concrete01.md)              | `Concrete`         | Concrete with zero tensile strength.             |
| [Steel01](/docs/basics/moment-curvature/steel01.md)                    | `Steel01`          | Bilinear steel with kinematic hardening.         |
| [ReinforcingSteel](/docs/basics/moment-curvature/reinforcing-steel.md) | `ReinforcingSteel` | Reinforcing bar, with a strain-hardening branch. |

**Fibres** — the pieces a section is made of.

| Component                                                       | Nickname       | Builds                                              |
| --------------------------------------------------------------- | -------------- | --------------------------------------------------- |
| [Fiber Point](/docs/basics/moment-curvature/fiber-point.md)     | `Fiber Point`  | One fibre: a point, an area, a material.            |
| [Layer Fiber](/docs/basics/moment-curvature/layer.md)           | `Layer Fiber`  | A row of equally spaced fibres along a curve.       |
| [Patch](/docs/basics/moment-curvature/patch.md)                 | `Patch`        | An area filled with fibres, one per mesh face.      |
| [Fiber Section](/docs/basics/moment-curvature/fiber-section.md) | `FiberSection` | Collects points, layers and patches into a section. |

**Analysis**

| Component                                                                   | Nickname | Does                                                            |
| --------------------------------------------------------------------------- | -------- | --------------------------------------------------------------- |
| [Moment Curvature](/docs/basics/moment-curvature/moment-curvature.md)       | `MC`     | Runs the section analysis.                                      |
| [Fiber Stress Strain](/docs/basics/moment-curvature/fiber-stress-strain.md) | `FBS`    | Splits the per-fibre history into fibres, stresses and strains. |

## Local axes and units

Fibre geometry is drawn in the **world XY plane** and read as the section's local *yz* plane:

| Drawn in    | Is the section's              |
| ----------- | ----------------------------- |
| World **X** | Local **y** — the green arrow |
| World **Y** | Local **z** — the blue arrow  |

This is the order OpenSees writes a fibre in. [Fiber Section](/docs/basics/moment-curvature/fiber-section.md) draws both arrows so you can see which is which.

Everything is in **metres** and **kN**: coordinates in `m`, fibre areas in `m²`, stresses in `kN/m²`, curvature in `rad/m`, moments in `kN·m`. Strains are dimensionless.

## A typical definition

```
Concrete01 ──► Patch  ─┐
                       ├──► Fiber Section ──► Moment Curvature ──► M, κ
ReinforcingSteel ──► Layer Fiber ─┘                            └──► Fiber Stress Strain
```

1. Mesh the concrete outline and give it to a [Patch](/docs/basics/moment-curvature/patch.md) with a [Concrete01](/docs/basics/moment-curvature/concrete01.md) material — the mesh density is the fibre density.
2. Draw the bar positions as a curve and give it to a [Layer Fiber](/docs/basics/moment-curvature/layer.md) with a [ReinforcingSteel](/docs/basics/moment-curvature/reinforcing-steel.md) material.
3. Collect both in a [Fiber Section](/docs/basics/moment-curvature/fiber-section.md).
4. Push it with [Moment Curvature](/docs/basics/moment-curvature/moment-curvature.md).