Castalia S.r.l.
tel. +39.2.26681083
fax. +39.2.26681876
Spectrum Error: a simple freeware program

In the book "Reasoned Modal Analysis" it has been shown that it is completely illusive to believe in a 3 or more digits precision when computing structural seismic response by using Response Spectrum method. This is true not only for Modal Analysis and Response Spectrum Analysis, but also for complex nonlinear time-history analyses, due to the many uncertainties in the seismic risk evaluation (nobody knows PGA but with serious "errors").

So Paolo Rugarli developed a simple freeware software program, named SPE, SPectrum Error (but also "with hope" in ancient Latin), which is able to compute the expected "error factors" on Response data like Displacement and Force, by using as input values the expected error factors on Mass, Stiffness and Behavior Factor. Error factor is basically a number in the range around 1.0 and is quite similar to well known "load and resistance factors" like gM or gF.

Suppose you wish to evaluate the response of a simple oscillator having T=0,83sec natural period, using an Eurocode 8 spectrum type 1, Soil C. Let your site PGA be 0.35 and your behavior factor be 2.5. If you expect a 10% error on your mass data, a 10% error on your behavior factor estimate, and only a 5% error on your stiffness data (quite good values), then which is the possible range of the error expected on the response data? SPE computes this for you. In this example you would get:

Displacement expected value: 0.84 Dnominal < D"true" < 1.2 Dnominal

Force expected value: 0.88Snominal < S"true" < 1.14 Snominal

The "force" expected value clearly applies to all internal stresses.

So, it is completely meaningless to design using 3-4 digits PGA precision input, and also 3-4 digits precision on output data , as you may easily have a 20% error on displacements, and a similar error on stresses. It depends on the initial errors and on the Response Spectrum Curve point you will land to.

Please discuss it with Italian Professors who wrote the Seismic Standard!