> For the complete documentation index, see [llms.txt](https://docs.enercalc.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.enercalc.com/e3d-user-manual/model-entities/toc161394014/toc161394017.md).

# Member Local Coordinate System

How the local coordinate system of a member is defined from its start node, end node, and local angle.

The local coordinate system of a member is determined by the start and end nodes, and an element local angle. The default (local angle equals 0 degrees) local coordinate system of a member is defined using the following procedures:

![](https://560001759-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWNe8U6EBBBdUJHdb2X9G%2Fuploads%2Fgit-blob-ad8c302103938c3b0801d3c32948b217bcebec89%2FFASTFR~1_img222.png?alt=media)

| Steps | Description                                                                                                      | Mathematical Notations                                                    |
| ----- | ---------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------- |
| A     | **V\*\*\*\*x** points from node 1 (N1) to node 2 (N2)                                                            | **V\*\*\*\*x** **=** N2 **–** N1                                          |
| B1    | For vertical members: **V\*\*\*\*z** is always parallel to **V\*\*\*\*Z**                                        | For vertical members **V\*\*\*\*z** **= V\*\*\*\*Z**                      |
| B2    | For non-vertical members: **V\*\*\*\*z** is perpendicular to a plane formed by **V\*\*\*\*x** and **V\*\*\*\*Y** | For non-vertical members **V\*\*\*\*z** **= V\*\*\*\*x** x **V\*\*\*\*Y** |
| C     | **V\*\*\*\*y** is determined based on **V\*\*\*\*x** and **V\*\*\*\*z** and the right-hand rule                  | **V\*\*\*\*y** **= V\*\*\*\*z** x **V\*\*\*\*x**                          |

For a member with a non-zero local angle (γ), first follow the procedures above that determine the default local coordinate system. Then rotate the default system a γ angle about its local x vector **V\*\*\*\*x**. The rotated **Vx, V\*\*\*\*y** and **V\*\*\*\*z** define the local coordinate system. The figure below shows the local coordinate systems of some members with different local angles (γ).

| ![](https://560001759-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWNe8U6EBBBdUJHdb2X9G%2Fuploads%2Fgit-blob-b4ae7c491ee4a14d9d7e454c4e67f962ff0e03ca%2FFASTFR~1_img223.png?alt=media) Local coordinate systems for members with different local angles |
| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |


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