All structural analysis software has at least two options when analysing the forces and displacement in a structure: Linear Analysis and Non-Linear Analysis. This choice falls under what is broadly referred to as linear or non-linear analysis.
Why is there a choice? If a structure needs non-linear, why provide linear? Does a structure really need non-linear analysis? Computers are fast – who uses linear analysis anyway?
To answer these questions, it’s worth knowing the difference between linear or non-linear analysis. Once we understand that, we can make an informed decision about which to use, and when.
Linear or Non-Linear? – That is the Question Linear Analysis
When we analyse a structure, we get to know how it behaves when loads are placed on it.
Consider a plank across a creek. When a person stands on it, the plank bends. A linear analysis will tell us the deflection of the plank for a given load. We can do this by hand or use a software program such as Microstran or Staad.Pro. Both overkill for a simply supported beam, but who does hand calcs these days?!
What about a more complex structure? There are various loads – gravity loads from equipment, building materials and people; sidewards loads from equipment, wind or earthquake. The loads act in various directions and combinations. We will definitely use Microstran or Staad.Pro for such a structure, and the linear or non-linear analysis will tell us the same thing – the forces and the displacements under load, depending on which method is appropriate for the structure’s behaviour.
Non-Linear Analysis
The linear analysis results in a structure where the columns are now not dead-straight; the beams have bent and rotated, braces have “shortened” etc and this begs the question – in its new state, can the structure still resist the applied loads?
Prior to 1998, we were happy to say ‘yes’. Linear Analysis was the method and we’d design the members and connections based on the output.
Non-linear analysis is merely an extension of linear analysis – the structure is re-analysed with the loads applied, but now the geometry has changed (geometric non-linearity), the material behaviour has changed (material non-linearity), or both. This distinction highlights the need to understand linear or non-linear analysis to uncover how structures truly behave.
I remember some structures that were deemed compliant when analysed in 2D using linear analysis but no good when modelled in 3D and analysed using non-linear analysis.
Flexible structures and poorly conceived structural systems were put to the test — as were their designers! Such structures (and designers?) are still around today. But overall, non-linear analysis, supported by improved design rules, has enabled us to create more economical and realistic structures.
So Which One?
Our software and our computers are getting more powerful. It’s easy just to press the NLA button and wait for the result. But so too are our structural models getting massive. A 2D representation of a truss is now a 3D portion in a model that also includes the trestles, footings, take-up towers and drive station! Putting all that in the software, guessing the sizes and structural systems and expecting a quick and successful analysis is asking for problems.
Design time can significantly increase, and worse, the final resulting structure “works” but would have John Connell turning in his grave if he saw it!
To get the best outcomes, we should break down complex models, assess structural systems in parts, and use linear or non-linear analysis appropriately. Start with linear analysis to evaluate deflections and estimate member sizes. Then, near the end of the design process, combine everything into a full model and run a final non-linear analysis for more accurate and predictable results.
Two Case Studies
Case 1 – Braced Frame
This is a typical braced frame. It did not respond any differently to linear or non-linear analysis. The structure’s movement was minimal, so the non-linear geometry change was insignificant.
Case 2 – SWAY FRAME (Conveyor Trestle)
Lateral forces from wind or seismic action will cause structures to displace significantly. In this example, performing a linear or non-linear analysis makes a clear difference, relying on linear analysis alone would have resulted in a deficient design. The “P-Delta” effects captured through non-linear analysis reduce the capacity of the columns.
Structural analysis software is merely a tool – use all the features by all means, but not as a replacement for good ‘ol understanding of structural systems and behaviour.
