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# Linear Time history Analysis against Response spectrum Aalysis

• To: seaint(--nospam--at)seaint.org
• Subject: Linear Time history Analysis against Response spectrum Aalysis
• From: "A.M.Zaki" <amzaki(--nospam--at)soficom.com.eg>
• Date: Sun, 01 Nov 1998 08:51:22 +0200

```here is a discussion under the titel 'LONG SPAN GIRDER'. Now I think our
subject is the comparison between the results and capabilities of the
Linear Time History Analysis and Response Spectrum Analysis.
I want to put this in a new discussion so more engineers can share us.

on Sat, 24 Oct 1998 osama ree wrote,

"Hi Every body

I'm trying to design  20meter span frame, which will carry a tower above
it consist of 12 floor, the depth of the girder to be 3.5 meter, column
dim. are 1.5X1.5 meter.
1. What should i take care of rather than the usual design criteria?
2. is some one knows about good references dealing with this subject?
thanks"

On Tue, 27 Oct 1998, my reply was,

"I think you should take care of earthquake load, because your structure is
not regular so you should analyse it against earthquakes using time history
analysis (equivilant static load and response spectrum analysis can not be
used)
You need a design earthquake to excite the structure. An expert can
simulate such earthquake according to the seismicity of the place, where
the structure will be built, and the dynamic characteristics of the structure.
This will cost too much.
In general you should be careful of seismic loads and hence the ductility
of the structure."

On Wed, 28 Oct 1998 Mark Gilligan, reply to me,

"Mr. Zaki

I would be interested in the rational why only a time history analysis is
appropriate for an irregular structure.

Is the time history analysis linear or non-linear?

If the analysis is linear what information is reflected in the results that
is not reflected in a response spectrum analysis?  The answer is none since
a linear time history analysis can be defined in terms of the mode shapes
just as a response spectrum analysis.  In both cases the usefullness is
dependent on the validity of the input motion and both types of input have
their limitations.

If you are doing a non-linear analysis what non-linear aspects are you
considering and which are you ignoring?

>From my point of view 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.  Given that the transfer structure won't
fail the next point to consider is whether the structure is torsionally
balanced.  The point being that with a little common sence you can safely
design an irregular structure with rather simple analysis tools.

It amazes me that people design a URM upgrade, which can asume very
non-linear behavior, using manual calculations,  while a base isolated
structure which is typically a very regular structure requires  time
history analyses. "

On Fri, 30 Oct 1998, my reply to Mr. Mark was,

"Mr. Mark

There is a difference between the results of the linear response spectrum
analysis and time history analysis.

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.

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

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.

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

A.M.Zaki
Structural Engineer
Cairo-Egypt

```