Numerical Analysis in a Three-Dimensional Virtual World

Seismic analysis is now being required on many existing buildings and sophisticated modelling methods are being increasingly used.  Although a complex technical subject, it is relevant to the wider community and particularly to building owners. 

When might three-dimensional modelling be of benefit?   What are the advantages and is it cost effective?

It is generally understood that structural engineers spend much of their time sizing beams and columns.  Everybody is familiar with the gravity and structural elements such as walls and frames.  These elements  have the added advantage of providing horizontal resistance to forces as well as just supporting  vertical gravity loads.  This characteristic makes them a useful element in resisting earthquake loads.  So there we have it; the evolution from gravity support to seismic design.

Consider a  rectangular building  a few storeys high.  The earthquake forces may be resisted by walls in each direction, frames in each direction, or perhaps a combination of walls one way and frames the other.   If everything is regular and has similar stiffness it is easy to imagine the forces being divided evenly among the elements which makes it  relatively easy for an engineer to calculate the stresses and deflections.

This is how many engineers would prefer architects to design all buildings.  Fortunately for engineers,  architects make life ‘interesting’.  This they achieve seemingly without effort, creating seemingly insurmountable challenges for the problem-solving engineer.  The architect may mix up the use of frames and walls, split storey heights, require big swimming pools at the top and large cavernous spaces at the bottom.  Up to a point the engineer can make judgements about how the earthquake forces make their way through the complex structure, but their predictions would not be that accurate and the design would be conservative to compensate for the inherent uncertainty.

The magic is provided by  finite element analysis.  It breaks the building up into a whole lot of small discrete elements and enables the engineer to create an accurate virtual three dimensional model of the structure.  The walls, frames and floors can by modelled according to their relative stiffness and mass.  When the earthquake forces are applied the model responds accordingly and the areas of increased stress are easily identified by colour.  The critical design elements may then be analysed and designed.

The interface is very user friendly, but incredibly the underlying functions of the program have not changed since the 1980’s.  The big difference in those days was the program(ETABS)   we use  ran on main frame computers, with punch-cards for data entry and screeds of dot matrix print-outs.  A highlighter was essential to identify the critical stresses among a vast array of numbers.

For complex multi-storey structures, finite element analysis is ideal in providing accurate results based on the actual building elements and their characteristics.  One of the main advantages is  in carrying out Detailed Engineer Evaluation (DEE) assessments is to target any strengthening work required.  Critical structural weaknesses may be identified by an Initial Evaluation Procedure (IEP) or Detailed Engineering Evaluation, but remedial design may be overly conservative and expensive without the benefit of an accurate modelling process.

The cost of  analysis can be be paid many times over by the cost saving in strengthening.

Another method of evaluating the earthquake resisting capacity of an early century, often historic,  reinforced concrete or structural steel multi-storey structure is push-over analysis.  This requires accurate modelling of existing elements and connections.  The structure is then loaded laterally until failure occurs.  This provides a measure of the actual building capacity as opposed to evaluating the building behaviour when a design code earthquake is applied to it.

I have occasionally pondered the virtual world engineers often inhabit.  There seems to be a mathematical model for almost everything around us; structures, floods, the even sports such as yacht racing.  Even though the ETABS model is part of this virtual world, it is important to realise that its value depends upon the judgement and experience of the engineer.   In the right hands it is an invaluable tool that helps provide clever, economic and dependable solutions.  As one of my colleagues comments:

Utilising the power of comprehensive finite element software assists in the development of  a sophisticated and realistic  model .  The  analysis results provides the designer with  answers for the  real behaviour  of a structural system which enables the  preparation of  the most realistic assessment . The client receive the most accurate results and the designer has the opportunity to provide excellent  service ….Elena

Cathy Thomas

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