What are the "2nd Order" Analysis options listed on the Analyze Ribbon in TSD? Are they the same as "P-Delta" analysis?

Tekla Structural Designer
Not version-specific
Tekla Structural Designer
p-delta
2nd order
second order
Environment
Not environment-specific

Answer

For an explanation of 2nd Order analysis and effects in general, please see the attached article A brief overview of 2nd Order (or P-Delta) Analysis.

(A version of this article was published in the Jan 2003 edition of the New Steel Construction magazine).

TSD has both Linear and Non-linear 2nd Order analysis options.  Both types will give both P-"BIG" delta (P-Δ) and P-"little" delta (P-δ) effects (for both 1D and 2D elements), as described in the attached article and illustrated in the diagrams below.  As such they may also be termed "P-Delta" analysis.  However, as the attached article discusses, this term can mean different things depending on how it is implemented in a particular solution/ application.

So the answer to the above question is a qualified Yes :-

  • Yes the 2nd Order Analysis in TSD gives what are commonly termed "P-Delta effects" (both of them).
  • However it may not be the same as that implemented in other solutions using the term "P-Delta" analysis.

The TSD 2nd Order Linear analysis implements the Two-Cycle Iterative Method (Chen and Lui (1991)) using the Geometric (stress) Stiffness Matrix as discussed in the attached article.  As such it has no significant limitations on its use or applicability* (providing the model is linear). 

The TSD 2nd Order Non-linear analysis implements an iterative solution using the Geometric (stress) Stiffness Matrix (initially with a single load step then, only where solution of this fails, with multiple steps).  2nd Order Non-linear analysis is required when the model contains non-linear elements, such as tension-only bracing or non-linear spring supports.

  • *Note that neither form of 2nd Order analysis is suitable for structures/ situations involving large displacements**.  Examples of situations where large displacement analysis is critical include the catenary behaviour of flexible cables, chains or rods or fabric membranes, in which relatively large displacements (in relation to the overall structure size) are required to develop the equilibrium position and associated axial stresses.  This requires Large-displacement Non-linear analysis which is not currently available in TSD.
    • **In terms of structural analysis solutions, a definition of "large displacements" is when they are sufficiently large - in the context of the overall structure dimensions - that the small-angle approximation (which is assumed in the current static analyses) no longer gives reasonable accuracy.  For more on this see for example Wikipedia - Small-angle approximation.

P-"BIG" delta (P-Δ)

Image
Big P-Delta.png

P-"little" delta (P-δ)

Image
Little P-Delta.png

 

 

 

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