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Member Local Coordinate System

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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:

 

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Steps

Description

Mathematical Notations

A

Vx points from node 1 (N1) to node 2 (N2)

Vx = N2 – N1

B1

For vertical members:

Vz is always parallel to VZ

For vertical members

Vz = VZ

B2

For non-vertical members:

Vz is perpendicular to a plane formed by Vx and VY

For non-vertical members

Vz = Vx x VY

C

Vy is determined based on Vx and Vz and the right-hand rule

Vy = Vz x Vx

 

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 Vx.  The rotated Vx, Vy and Vz define the local coordinate system. The figure below shows the local coordinate systems of some members with different local angles (γ).

 

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Local coordinate systems for members with different local angles
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