Need a book? Engineering books recommendations...

Return to index: [Subject] [Thread] [Date] [Author]

Linear Time history Analysis against Response spectrum Aalysis

[Subject Prev][Subject Next][Thread Prev][Thread Next]
In my original posting I made the point that "...the most critical issue
with transfer 
structures and earthquakes is that the transfer structure not fail during
the big one.  
To deal with this you should consider the maximum forces from the supported
structure in a major earthquake".  What I did not clearly say was that to
achieve 
this goal you need to focus your efforts on understanding the inelastic
mechanisms 
of the structure and not the accuracy of an linear elastic analysis. This
means that 
you want to design the mechanism so that the yielding does not occur in the
transfer 
structure.   In most cases the necessary evaluation of the collapse
mechanism can be 
done by hand.  

Most structures are designed so that in the major earthquake the structure
will respond 
inelastically thus raising questions about the applicability of an elastic
analysis. 

When considering the type of elastic analysis there is a tendency to assume
that a time 
history analysis is superior to a response spectrum analysis.  This is not
necessarily 
the case.

In response to comments by  A.M.Zaki:

>1- Finally in a response spectrum analysis you solve a static problem with
>a lateral story shear forces that correspond to the instant where the base
>shear is maximum. Some elements may have maximum response at different
>instant, so its response may be under-estimated.
 
The reason some parameters achieve their maximum value at different times
is
because different modes of  vibration are excited.  The response spectrum
method 
deals with this by the way it combines the modal effects.  For most
situations 
the CQC methodology is considered adequate.  If you are really concerned
you 
can use the absolute sum method or another methodology of your choice.  

>2- In a response spectrum analysis, the response is restricted to the
>number of modes specified by the engineer.

In a Time History (TH) analysis the choice of integration time step will
determine 
what modes of the structure are excited by the input.  

It is possible to put an upper bound on the error resulting from limiting
the 
number of modes considered.  This is helpful in deciding on the number of
modes 
you should consider. 
You can correct for the effect of modes not considered but these techniques

seem not to be used much outside of the nuclear industry.

Note that some programs perform a TH analysis by analyzing several modes
for the 
TH loading and then combining the results.  

The choice of time histories can bias the results since each TH will
reflect certain 
frequency content.  The response spectrum method deals with this by
enveloping the 
likely different frequencies.  In addition the process of developing time
histories 
introduces a number of assumptions that may not be appropriate.   To
compensate for 
this you should analyze the structure for several time histories to
compensate for the 
fact that certain frequencies may be under represented in a given TH.

For most situations the errors introduced from each of these sources make
the TH 
analysis not necessarily any better, than the response spectrum analysis. 
When you 
consider in the fact that in the major earthquake the structure is
considered to act 
inelastically, you have to question what benefit you get from the
considerably greater 
effort of a TH analysis.

>3- In a response spectrum analysis you can not take the effect of soil
>structure interaction, which may cause significant change to the structure
>response.

For most structures a soil structure analysis is not required nor is it
considered.  Where 
this issue is a real concern I would think that you would want to undertake
an analysis
with special elements to model the nonreflecting boundary conditions that
result from 
the need to simulate the infinite extent of the soil. 

>4- Some Codes do not allow the use of the response spectrum analysis for
>irregular structures (e.g. The 1995 Egyptian Code). "

While as a minimum we must comply with the building codes, they are subject
to the 
biases and agenda of the authors.  This is definitely true in the US and it
seems that it 
is equally true in other countries.

In the United States the codes allow the use of the response spectrum
methodology. 
When the dynamic analysis provisions, that exist in the Uniform Building
Code, were being 
developed permission to use TH analysis was added in response to requests
by some 
individuals.  To this day there appears to have been little use made of
linear elastic TH 
analyses in seismic analysis.

To recap my points:
1) You have to move beyond an elastic analysis when dealing with a transfer
structure 
subject to seismic loading.
2) An elastic time history analysis is not necessarily any better than a
response spectrum
analysis.


Mark Gilligan
Markkgilligan(--nospam--at)compuserve.com