Sign conventions and coordinate systems

Tekla Structural Designer
2021
Tekla Structural Designer

Sign conventions and coordinate systems

Tekla Structural Designer adopts the standard convention that lower case x, y, and z represent local coordinate systems, whereas upper case X, Y, and Z represent the global coordinate system. For more information on analysis result sign conventions, see the following paragraphs.

Axis systems

The following table presents the axis systems that can be used in Tekla Structural Designer:
 
Axis system name Description
Global coordinate system The global XYZ axis system within which all other systems exist.
Building directions 1 and 2 The principal axes of the building, where dir 1 is rotated at an angle to global X in the horizontal plane.
User coordinate system A local coordinate system defined by the system or the user.
1D member local coordinate system The local coordinate system that is applicable to all 1D members, such as beams, columns, and braces.
Mid-pier wall coordinate system The local coordinate system that is applicable to walls modeled using the mid-pier option.
2D member local coordinate system The local coordinate system that is applicable to all 2D members, walls, and slabs.
Result line coordinate system The local coordinate system that is applicable to result lines.
Result strip coordinate system The local coordinate system that is applicable to result strips.
Foundation reaction coordinate system The local coordinate system that is applicable to foundations.
Punching shear check axis system The local coordinate system that is applicable to punching checks.

General information

All global (XYZ) and local (xyz) axis systems follow the right-hand rule, where:
  • x axis is the pointing index finger.
  • y axis is the crooked middle finger.
  • z axis is the extended thumb.
In the directions of positive rotation:
  • About x: the y axis moves toward the z axis.
  • About y: the z axis moves toward the x axis.
  • About z: the x axis moves toward the y axis.

Diagram conventions

All arrows should point in the direction of the force or moment, as the following image illustrates:

If the arrows are reversed, they become negative forces and moments, as the following image illustrates:

Global coordinate system

The following image illustrates the global axis system and applied load directions.

The resulting deflection directions appears as follows.

Building directions 1 and 2

The principal axes of the building (Dir 1 and 2) can be specified at any angle to the global X axis in the global XY plane (positive Z vertically up).

The angle between X and direction 1 is θ, where θ is positive in right-hand rule about Z. Direction 2 is then +90 degrees from direction 1.

The following image illustrates the building directions and applied load directions.

The resulting deflection directions appear as follows.

To specify and display the building directions

  1. Go to the Project Workspace.
  2. In the Structure tree, click Structure.
  3. Go to the Properties window.
  4. Enter the Building Direction Rotation (labeled θ in the above diagram )
  5. To have the building direction axes displayed in scene views, select Show Building Direction Arrows
  6. If you prefer to label the building directions as Dir H/V or Dir X/Y you can change the Building Direction Labels.

User coordinate system

A user coordinate system can be at any angle to the global coordinate system.

The following image illustrates the axis system of a user coordinate system axis and applied load directions.

The resulting deflection directions appear as follows.

Note:
Every support is given a user coordinate system. Automatically created supports under certain objects default to the following method:
  • Support under a single column or wall rotates the foundation forces to align with the y/z-axes of the column or wall
  • Support under a mat foundation - uses the global coordinate system.

All other supports default to the global coordinate system.

1D member local coordinate system (general case)

Member orientation

Tekla Structural Designer considers member orientation when displaying analysis results. Therefore, to apply the sign convention correctly, you need to know which is end 1 and which is end 2 of the member. For beams you need to be able to identify the top flange, and for columns you also need to be able to identify the four faces: A, B, C & D.

To display the direction in a scene view select the Direction option for the member type in Scene Content.
This displays a direction arrow along the member which points from end 1 to end 2.

For beams the arrow is drawn next to the top flange. For columns the direction is always from bottom to the top and the arrow is always drawn adjacent to Face A. Looking down from the top of a column, Faces B, C, and D then follow in the clockwise direction.

Local axis system and applied load directions:

  • The local x axis along member starts at end 1 and ends at end 2
  • When gamma (γ) = 0:
    • The local z axis lies in the plane created by the local x axis and the global Z axis.
    • The global Z component of the local z axis is always negative.
    • The local y axis follows the right-hand rule.
    gamma (γ) = positive clockwise rotation of y and z axes about the x axis looking towards positive x.

Applied force directions:
  • z = Major (Fz and My):

  • y = Minor (Fy and Mz):

  • x = Axial:

Result axis system and directions

 

In the major axis:
  • Moment major = bending about the y axis
  • Shear major = shear along the z axis
In the minor axis:
  • Moment minor = bending about the z axis
  • Shear minor = shear along the y axis

In the axial direction:

Resulting member end forces and directions

Member end forces are the forces applied to the rest of the structure by the member. Based on loading applied above, the forces would be applied as follows:

1D member local coordinate system (vertical members)

Local axis system and applied load directions

Local x aligns with global Z (vertical):

  • When gamma (γ) = 0:
    • The local y axis aligns with global X.
    • The local z axis according to the right-hand rule.

    gamma (γ) = positive clockwise rotation of y and z about the x axis towards positive x.

Applied force directions as displayed in the previous image:
  • z = Major
  • y = Minor
  • x = Axial

Result axis system and directions

In the major axis:
  • Moment major = bending about the y axis
  • Shear major = shear along the z axis

In the minor axis:
  • Moment minor = bending about the z axis
  • Shear minor = shear along the y axis

In the axial direction:

Mid-pier wall coordinate system

Wall axis system and applied load directions

As the following image illustrates, centered on the centroid of the cut section:
  • the x axis lies along the stem mid-pier element (positive lowest to highest)
  • the z axis lies along the plane of the wall (positive end 2 to end 1)
  • the y axis follows the right-hand rule and is normal to the wall.

The results from a mid-pier model are in the same axis system as the result line in a meshed wall.

Result axis system and direction

In the major axis:
  • Moment major = bending about the y axis:

  • Shear major = shear along the z axis:

In the minor axis:
  • Moment minor = bending about the z axis:

  • Shear minor = shear along the y axis:

In axial and torsion, force is in the x axis and torsion about the x axis:

2D member local coordinate system

Horizontal panel local axis system and applied load directions

Horizontal panel local axes are the following:
  • The local z axis is normal to the plane of the panel
  • When θ = 0:
    • The local x axis plane is in the plane of the panel, aligned with the global X axis and positive in the positive global X direction.
    • The local y axis is in the plane of the panel and follows the right-hand rule.
    θ = positive clockwise rotation of the x and y axis about the z axis looking towards positive z.

Vertical and sloped panel local axis system and applied load directions

Vertical and sloped panel local axes are the following:
  • The local z axis is normal to the plane of the panel.
  • When θ = 0:
    • The local x axis plane is in the plane of the panel and in a horizontal plane.
    • The local y axis is in the plane of the panel and follows the line of greatest slope of the plane (positive in the direction of positive global).
    θ = positive clockwise rotation of x and y about z looking towards positive x.

Sloped panel (axes at θ):

Vertical panel (axes when θ = 0):

2D member forces sign convention

The sign convention for 2D member forces is not the same as that of 1D elements. The following diagram illustrates the forces and the panel and 2D element axis system (for results):

  • The arrows in the diagram show positive force directions.
    • The double-arrow convention is used for moments: the moment is around the double-arrow, positive being clockwise when looking in the arrow direction.
    • The forces act on a member face cut anywhere in the FE mesh, perpendicular to the force direction.
    Thus, for example, Mx acts on the X face that is perpendicular to the X axis and is moment resulting from spanning in the X direction, Fxz is the out-of-plane shear force acting on the X face, and so on.
  • The wood armer design moments (denoted by the d suffix) act in the same manner as the unprocessed moments without the d suffix. Thus, Mdx acts in the same manner as Mx, and so on.
  • The design moments are further classified into top and bottom components for the slab design process.
  • The positive Z axis direction (up) follows the right-hand rule and, therefore, is not the same as that for the 2D member local coordinate system. This is because the 2D member local coordinate system for the applied load directions displays the positive applied load direction convention that, for Z only, is opposite to the convention of the global and 2D element axes.
  • A positive moment creates tension in the top surface of the shell. Therefore, the moment over a supporting column is positive, whereas the span moment is negative.
  • The conventions for wall results are exactly the same as conventions for columns, so they can be interpreted in the same way.
  • The compression of axial loads (Fx and Fy) is negative.
  • Out-of-plane shear (Fxz and Fyz) is positive when shear is such that moment is increasing in the positive X or Y direction.

Result line coordinate system

Centered on the centroid of the cut section:
  • The z axis lies along the result line (positive end 2 to end 1).
  • The y axis normal to plane of mesh (generally positive in the positive Z direction, in special cases positive x towards positive Z).
  • The x axis follows the right-hand rule and lies in the mesh, so x is perpendicular to the cut line.
Note:

The results from a result line are exactly like those for a mid-pier model when the cut is horizontal and the cut direction matches the direction required.

  • In the major axis: bending about the y axis and shear along the z axis
  • In the minor axis: bending about the z axis and shear along the y axis
  • Axial and torsion: force in x and bending about the x axis

General case:

Special case:

Result strip coordinate system

Centered at each station along the strip center line, whether there is a single or several continuous strips:
  • The z axis is normal to plane of mesh (generally positive in the negative Z direction, in special cases positive x towards positive Z).
  • The x axis lies along the result strip (positive end 1 to end 2)
  • The y axis lies along the transverse line to the result strips and follows the right-hand rule, so the y axis is perpendicular to the strip line.
  • Deflection in the z direction
  • Out of plane moment about the y axis
  • Shear in the z direction

General case:

Special case:

Foundation reaction coordinate system

As the following image illustrates, the foundation reaction coordinate system is aligned with the coordinate system for the support node, whether that is the global coordinate system or a user coordinate system.

Reactions are the forces applied to the structure by the foundation. They appear as follows.

Punching shear check axis system

For all punching checks, the YZ plane is in the slab plane. Using the YZ system in the slab plane coherently assumes that the vertical force is positive upwards following the right hand rule.
  • Punching checks applied to point loads - by default the check Y and Z axes default to align with global X and Y. The Loaded Area Orientation angle can then be used to rotate these in relation to the global Y axis.

    Punching checks applied to columns - as the following image illustrates, the check Y and Z axes are aligned and locked to the local axis system for the column elements so it is easier to relate forces in both objects.


  •  
    - Global coordinate system
    - Punching shear check axis system
    Note: The two axis systems are locked together, so if the column is rotated, the punching check axes also rotate.
    - Column 1D member local coordinate system
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