> 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/results/shell-forces.md).

# Shell Forces

The stress resultants on every shell element: membrane forces, bending moments and transverse shears, all per unit width.

## 🔧 Grasshopper component

`Shell Forces (Alpaca4d)` — **Alpaca4d ▸ 08\_NumericalOutput**

### Inputs

| Name        | Nick          | Type    | Default | Description                                                                                               |
| ----------- | ------------- | ------- | ------- | --------------------------------------------------------------------------------------------------------- |
| AlpacaModel | `AlpacaModel` | Model   | —       | The analysed model.                                                                                       |
| History     | `History`     | Boolean | `false` | Read every recorded step instead of one. The outputs become trees `{step; element}`. **Step** is ignored. |
| Step        | `Step`        | Integer | `0`     | Analysis step.                                                                                            |

### Outputs

One branch per shell element, values at the element's integration points.

| Name | Nick  | Type          | Description                                  |
| ---- | ----- | ------------- | -------------------------------------------- |
| pxx  | `pxx` | Number (tree) | Membrane force along local *x*, in `kN/m`.   |
| pyy  | `pyy` | Number (tree) | Membrane force along local *y*, in `kN/m`.   |
| pxy  | `pxy` | Number (tree) | In-plane shear, in `kN/m`.                   |
| mxx  | `mxx` | Number (tree) | Bending moment about local *x*, in `kN·m/m`. |
| myy  | `myy` | Number (tree) | Bending moment about local *y*, in `kN·m/m`. |
| mxy  | `mxy` | Number (tree) | Twisting moment, in `kN·m/m`.                |
| vxz  | `vxz` | Number (tree) | Transverse shear on the *x* face, in `kN/m`. |
| vyz  | `vyz` | Number (tree) | Transverse shear on the *y* face, in `kN/m`. |

## 📈 When to use it

**Use it when**

* You are designing slab or wall reinforcement — `mxx`, `myy` and `mxy` are what go into a Wood–Armer calculation.
* You need membrane forces in a shear wall or a tank.

**Do not use it when**

* You want a contour → [Shell Forces View](/docs/basics/visualisation/shell-forces-view.md).
* You want the principal directions → [Principal Stress Lines](/docs/basics/visualisation/principal-stress-lines.md) traces them as curves.

{% hint style="warning" %}
**These are local-axis results, and the local axes are per face** unless you set them. Two adjacent faces of the same slab can report `mxx` about different directions, which makes the numbers meaningless to compare or to contour.

Set **Local X Axis** on the [ASD Shell](/docs/basics/elements/shell.md) component for any model whose shell results you intend to read.
{% endhint %}

## 💡 Sign convention

All quantities are **per unit width**. Positive membrane force is tension. A positive `mxx` puts the bottom face — the face on the negative local *z* side — in tension.