> 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/b21e.md).

# B21E

2D Displacement Based Bernoulli Beam With End Moment Release

* Number of Nodes: 2
* Number of DoFs: 3 (Translation, Translation, Rotation)
* DoF Label: U1, U2, UR3

## Syntax

```
element B21EL (1) (2) (3) (4) [5] [6]
element B21EH (1) (2) (3) (4) [5] [6]
# (1) int, unique element tag
# (2) int, node i
# (3) int, node j
# (4) int, section tag
# [5] int, number of integration points, default: 6
# [6] bool string, 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. To use the corotational formulation for nonlinearity, please turn on the switch.
3. To release end moment at node `(2)`, use element `B21EL` in which `L` stands for low.
4. To release end moment at node `(3)`, use element `B21EH` in which `H` stands for high.
5. Analysts shall ensure the node with moment released must be connected to other elements that have in-plane rotational DoF.
6. Local iterations are performed to achieve a tolerance of `1E-13`.
7. Since additional rotation is involved to achieve a pinned connection, visualisation is not available.
8. Unlike 3D beam elements, there is no need to attach an `orientation` to 2D beam elements.


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation by asking a question.

Perform an HTTP GET request on the following URL with the `ask` and `goal` query parameters:

```
GET https://tlcfem.gitbook.io/suanpan-manual/element/beam/b21e.md?ask=<question>&goal=<user_goal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is what the user is ultimately trying to achieve, the reason they need the answer. Sharing it helps GitBook give you a better, more relevant answer. A goal is most helpful when it describes the outcome the user wants rather than restating the question. For example, with `ask=how do I create an API token`, a goal like `automate deployments from our CI pipeline` lets GitBook tailor the answer to that use case.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.