How do I interpret 2D Results (FE Contour Forces) and what are the Sign Conventions?

Tekla Structural Designer
Not version-specific
Tekla Structural Designer
FE
Finite element
Contours
2D results
conventions
sign conventions
axis system
axes
surface
Environment
Not environment-specific

Questions

Typical questions we receive on understanding 2D results are:

  • I have a hard time understanding these different stresses, what are they?
  • Is there some where that explains what the forces are, Fx vs Fxz...etc?
  • What is Mdx top vs Mdx bottom for a wall?  Which surface represents which face?
  • What about the signs of forces - how do I interpret these?

Answers

These questions are answered in order below.  Firstly however, we recommend you consider attending TSD Training as this is probably be the most efficient way of learning about this and many other fundamentals of using TSD and understanding its results.  Details on Training and how to arrange it can be found on your regional Tekla website.

  

I have a hard time understanding these different stresses, what are they?

The 2D (Finite Element (FE) ) contour results Mx, My, Fx and Fy...etc are actually in terms of force not stress (2D stress results denoted by the sigma symbol are also now available) - they display the instantaneous force at a point of a constantly varying distribution over the extent of the FE mesh.  The (metric) units are kN/m and kNm/m, in which the “/m” term is a unit width perpendicular to the force direction.  To produce an absolute force (in units of kN or kNm ir kips or kip_ft), contour values must be integrated over a finite width in this direction.  A simple example of this is shown below.  Note that  Tekla Structural Designer does this automatically for meshed Wall Line Results and those of manually applied Result Lines.  Contour values are used directly for slab design since this design is for a unit width requiring force/unit width.

Image
TSD 2D results.png

 


To interpret 2D element Contour results, one must understand the axis system and the force result conventions used.  These are essentially the same for both slabs and walls.  The axis system for "2D members" (i.e. wall and slab panels) is given in the Help topic Sign conventions and coordinate systems here.

 

Image
TSD-panel_axis


From this we see that wall (vertical panel) axes directions are fixed - Y is always vertical and X is always horizontal.  For slab panels the X and Y axes directions are controlled by the panel’s rotation angle.  The panel X axis is indicated by the blue span arrow and the Y axis by the green.  The X axis is horizontal on plan for a rotation angle = 0°.  2D Results are always reported w.r.t. the panel axis directions (not the global axis directions).

 

 

Image
Slab panel axes.png

Is there some where that goes over what the forces are, Fx vs Fxz...etc?

Yes there are descriptions in this Help Topic Display 2D results :

 

Image
TSD FE Forces Sign Conventions - Help 1.png



The diagram below illustrates these forces and the panel and 2D element axis system (for results).  

 

 

 

Image
TSD FE Forces Sign Conventions - new 2017 - small.png

 



The arrows 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 ‘face’ cut (anywhere) in the FE mesh perpendicular to the force direction.  Thus for example; Mx acts on the X-face which 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 suffix 'd', act in the same manner as the unprocessed moments without this suffix; thus Mdx acts in the same manner as Mx and so on.  The design moments are further classified into top and bottom components (hogging and sagging respectively - see below) for the slab design process.
 
You may note that the positive Z-axis direction (up) follows the right-hand rule and is not the same as that shown in Help diagram (above).  The reason for this apparent contradiction is that the Help diagram shows the positive applied load direction convention which - for Z only - is opposite to that of the Global and 2D element axes.
 

 


What is Mdx top vs Mdx bottom for a meshed wall?  Which surface represents which face?

The only difference between a slab and a wall panel (for understanding contour results) is that the wall Y axis is always vertical and the X axis horizontal.  Just as for slabs the Z axis is orthogonal to these and normal to the wall surface.


Regarding wall top and bottom surfaces – this can be identified by looking at the 2D element local axes in the Solver View (activated via Scene Content as shown below).  Again the convention is exactly the same as for slabs.  The axis arrow colors follow the same convention as for the global axes; blue = X and green = Y.  The local Z axis is not displayed, but it follows the right-hand rule.  For a horizontal slab logically the Z axis direction is up and the top of the slab panel is the top surface - i.e. the face in the +ve local Z axis direction.  The same rule applies to slabs and walls of any orientation. 

The axes are drawn and labelled in the picture below to make this clear.  A quick way to identify the 'top' wall surfaces is to open a 2D Frame view of the Frame the wall is in (walls are always in a Frame) - in this 2D view you will be looking at the "top" surface of the wall.  If you look at a solver view of the Frame and activate the 2D element Local Axes in Scene Contents, you will see that the X-axis (blue arrow) of the wall 2D elements is always horizontal and pointing from Left to Right.  This is because the local axis system of the 2D elements always follows that of the Frame, which is positive left to right.  The 2D element Y axis (green) is vertical and the Z axis points out of the screen towards you.

It is worth noting also that the direction of a Frame is dictated by the grid line that it is created on (where a grid line lies along the Frame line).  If you wish to control the orientation of the 'top' surface of walls, you need to be aware of this and create grid lines with the appropriate direction.  If you create a wall where no gridline exists along the wall insertion line, this will create a grid line and a frame in the wall direction - i.e. with the positive direction from the start to the end of the wall insertion line.  This in turn will dictate the direction of the 2D elements' X-axis - they will be aligned with the frame direction which in this case follows the wall direction - and hence the wall 'top' surface.

 

Image
Meshed wall 2D element axes

 


What about the sign of forces - how do I interpret these?

The final information required to interpret 2D results is the sign convention for forces – beware this is not the same as that of 1D elements.  

  • For moments; a positive moment creates tension in the Top surface of the shell.  Hence ‘hogging’ moment for a slab (e.g. moment over a supporting column) is positive while ‘sagging’ (span) moment is negative.  As stated before, the conventions for wall results are exactly the same, so understanding the axis directions they can be interpreted in the same way. 

  • For axial load (Fx and Fy); compression is negative. 

  • We are not usually concerned about the sign of shear, however, for completeness;  out-of-plane shear (Fxz and Fyz) is positive when shear is such that moment is increasing in the positive X or Y direction.

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