Stresses in 2D elements

Tekla Structural Designer
2020
Tekla Structural Designer

Stresses in 2D elements

Which stresses can be displayed?

You can view the stresses on the outer faces of 2D elements for both slabs and walls by selecting the required result from droplist beneath Results in the 2D Results group.

The first 6 values are calculated directly from the forces and moments:
  1. σx top - in-plane axial stress in the x direction, top surface
  2. σy top - in-plane axial stress in the y direction, top surface
  3. τxy top - in-plane shear stress in xy direction, top surface
  4. σx bottom - in-plane axial stress in the x direction, bottom surface
  5. σy bottom - in-plane axial stress in the y direction, bottom surface
  6. τxy bottom - in-plane shear stress in xy direction, bottom surface
Note: The above 6 values are available for loadcases & combinations, but not envelopes
The next 4 values are determined from the first 6 values:
  1. σx max tension - maximum tension stress in the x direction for both surfaces
  2. σy max tension - maximum tension stress in the y direction for both surfaces
  3. σx max compression - maximum compression stress in the x direction for both surfaces
  4. σy max compression - maximum compression stress in the y direction for both surfaces
Note: The above 4 values are available for loadcases, combination & envelopes.
The center stress values are calculated directly from the forces and moments:
  1. σx in-plane - in-plane axial stress in the x direction, center
  2. σy in-plane - in-plane axial stress in the y direction, center
The last 4 values are determined from the above 2 values:
  1. σx in-plane tension - maximum tension stress in the x direction center
  2. σy in-plane tension - maximum tension stress in the y direction center
  3. σx in-plane compression - maximum compression stress in the x direction center
  4. σy in-plane compression - maximum compression stress in the y direction center

How might these results be used?

Users performing the design of structures with concrete core walls are interested to know which panels within the walls are cracked. Which panels are cracked can be determined by comparing the maximum tensile stress in each panel to the concrete tensile strength.

Tekla Structural Designer calculates stress values from the gross section properties (ignoring the reinforcement). To determine cracked panels, you can see the maximum tension (and compression) stress in each direction for each panel, across loadcases, combinations and envelopes.

Calculation of in-plane axial and shear stress

For loadcases and combinations, by using the 2D element thickness, stresses (based on the gross section properties) can be calculated from the forces at the nodes:

σxtop = Fx / t + 6Mx / t2

σytop = Fy / t + 6My / t2

τxytop = Fxy / t + 6Mxy / t2

σxbottom = Fx / t - 6Mx / t2

σybottom = Fy / t - 6My / t2

τxybottom = Fxy / t - 6Mxy / t2

σxin-plane = Fx / t

σyin-plane = Fy / t

Note:
  • Tension stresses are positive
  • Compression stresses are negative

The process for enveloping the above values is the same as that used for other envelopes. For each of the items, a pair of values is found, these are the minimum & maximum values across all loadcases and combinations.

Calculation of maximum tension and compression stress for loadcases and combinations

For loadcases and combinations, the maximum tension and compression values are determined for a specific direction by finding the maximum or minimum of the top and bottom stresses in that direction:

σx max tension = Max ( σxtop, σxbottom, 0.0 )

σy max tension = Max ( σytop, σybottom, 0.0 )

σx max compression = Min ( σxtop, σxbottom, 0.0 )

σy max compression = Min ( σytop, σybottom, 0.0 )

σx in-plane tension = Max ( σxin-plane, 0.0 )

σy in-plane tension = Max ( σyin-plane, 0.0 )

σx in-plane compression = Min ( σxin-plane, 0.0 )

σy in-plane compression = Min ( σyin-plane, 0.0 )

For envelopes, the maximum tension and compression values are determined by applying the above equations to the enveloped values. Envelopes yield two values for each of the 4 entries in the dropdown.

Calculation of maximum tension and compression stress for envelopes

For envelopes, the maximum tension and compression values are determined by applying the above equations for loadcases and combinations to the enveloped values.

Envelopes yield two values for each of the 4 entries in the droplist.

For tension stresses (x or y - only x shown for brevity) the values are returned are:

σx max tension = m1 / m2 , where:

m1 = Min ( σxtop max across all cases & combs , σxbottom max across all cases & combs , 0.0 )

m2 = Max ( σxtop max across all cases & combs , σxbottom max across all cases & combs , 0.0 )

For compression stresses (x or y - only x shown for brevity) the values returned are:

σx max compression = m1 / m2 , where:

m1 = Min ( σxtop min across all cases & combs , σxbottom min across all cases & combs, 0.0 )

m2 = Max ( xtop min across all cases & combs , σxbottom min across all cases & combs , 0.0 )

In summary the values visible in the tooltip are:

σx max tension
 = 

Min (σxtopmax across all cases & combs, σxbottommax across all cases & combs, 0.0) /

Max (σxtopmax across all cases & combs, σxbottommax across all cases & combs, 0.0)

     
σy max tension
 = 

Min (σytopmax across all cases & combs, σybottommax across all cases & combs, 0.0 ) /

Max (σytopmax across all cases & combs, σybottommax across all cases & combs, 0.0)

     
σx max compression
 = 

Min (σxtopmin across all cases & combs, σxbottommin across all cases & combs, 0.0) /

Max (σxtopmin across all cases & combs, σxbottommin across all cases & combs, 0.0)

     
σy max compression
 = 

Min (σytopmin across all cases & combs, σybottommin across all cases & combs, 0.0 ) /

Max (σytopmin across all cases & combs, σybottommin across all cases & combs, 0.0)

Key points when using stress values

  1. In Walls X direction is horizontal in plane of wall and Y is vertical
  2. “Top”/”Bottom” is dependent on shell local axis system, but if you are only concerned about max values you don’t need to worry about this - use the “max” options which consider both faces.
  3. For engineers wanting to consider tensile stresses in walls the “σy in-plane tension” option will be of greatest interest.
    • This is based purely on the membrane tension stress (i.e. ignoring out of plane bending effects).
    • This can be viewed for enveloped results
    • It is very easy to see walls/panels in which no tension stress is developing.
    • In a full 3D view it may be difficult to assess whether a particular cracking stress level is exceeded. Viewing results in 2D views or sub structures may be helpful here.
    • It should be clear that this is based on the concrete section only - reinforcement content is not considered.
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