> For the complete documentation index, see [llms.txt](https://tlcfem.gitbook.io/suanpan-manual/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://tlcfem.gitbook.io/suanpan-manual/element/beam/f31.md).

# F31

3D Displacement Based Bernoulli Beam

* Number of Nodes: 2
* Number of DoFs: 6 (Translation, Translation, Translation, Rotation, Rotation, Rotation)
* DoF Label: U1, U2, U3, UR1, UR2, UR3

## References

1. [10.1016/0045-7949(95)00103-N](https://doi.org/10.1016/0045-7949\(95\)00103-N)

## Syntax

```
element F31 (1) (2) (3) (4) (5) [6] [7]
# (1) int, unique element tag
# (2) int, node i
# (3) int, node j
# (4) int, section tag
# (5) int, orientation tag
# [6] int, number of integration points, default: 5
# [7] int, nonlinear geometry switch, default: false
```

## Remarks

1. The Lobatto integration is used by default. The number of integration points ranges from 3 to 20.
2. Please check [`orientation`](/suanpan-manual/element/beam/orientation.md) for its definition.
3. To use the corotational formulation for nonlinearity, please attach a corotational formulation enabled `orientation`.

## Output Type

This model supports the following additional history variables to be recorded.

| variable label | physical meaning          |
| -------------- | ------------------------- |
| BEAME          | local element deformation |
| BEAMS          | local element resistance  |

For example,

```
hdf5recorder (1) Element BEAME (2...)
hdf5recorder (1) Element BEAMS (2...)
# (1) int, unique recorder tag
# (2...) int, tags of elements to record
```


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