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 Sign conventions and coordinate systems
Sign conventions and coordinate systems
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
Axis system name  Description 

Global coordinate system  The global XYZ axis system within which all other systems exist. 
Building directions 1 and 2  The principle 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. 
Midpier wall coordinate system  The local coordinate system that is applicable to walls modeled using the midpier 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. 
General information
 x axis is the pointing index finger.
 y axis is the crooked middle finger.
 z axis is the extended thumb.
 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.
Object orientation
Tekla Structural Designer considers the orientation of the object when displaying the analysis results. Therefore, to apply the sign convention correctly, you need to know which is the end 1 and which is the end 2 of beams or walls, and which is the face A of columns.
If you select the Direction option for an element in Scene Content, Tekla Structural Designer displays an arrow on all beams, walls and columns. This arrow points from the start to the end of beams and walls, and from the bottom to the top of columns along the face A. Looking down from the top of a column, Face B, C, and D then follow in the clockwise direction.
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
Global axes (positive Z vertically up) and angle between X and direction 1 is θ, where θ is positive in righthand rule about Z.
The following image illustrates the building directions and applied load directions.
The resulting deflection directions appear as follows.
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.
 Support under a single column or wall rotates the foundation forces to align with the y/zaxes 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)
Local axis system and applied load directions:
 The local x axis along member starts from end 1 and ends in 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 righthand rule.

z = Major (Fz and My):

y = Minor (Fy and Mz):

x = Axial:
Result axis system and directions
 Moment major = bending about the y axis
 Shear major = shear along the z 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 righthand rule.
gamma (γ) = positive clockwise rotation of y and z about the x axis towards positive x.
 z = Major
 y = Minor
 x = Axial
Result axis system and directions
 Moment major = bending about the y axis
 Shear major = shear along the z axis
 Moment minor = bending about the z axis
 Shear minor = shear along the y axis
In the axial direction:
Midpier wall coordinate system
Wall axis system and applied load directions
 the x axis lies along the stem midpier 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 righthand rule and is normal to the wall.
The results from a midpier model are in the same axis system as the result line in a meshed wall.
Result axis system and direction

Moment major = bending about the y axis:

Shear major = shear along the z 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
 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 righthand rule.
Vertical and sloped panel local axis system and applied load directions
 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).
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 doublearrow convention is used for moments: the moment is around the doublearrow, 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.
 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 righthand 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.
 Outofplane 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
Result Axis System
 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 righthand rule and lies in the mesh, so x is perpendicular to the cut line.
The results from a result line are exactly like those for a midpier 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
Result axis system
 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 righthand 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.