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# Dynamic seismic design

• To: "INTERNET:seaint(--nospam--at)seaint.org" <seaint(--nospam--at)seaint.org>
• Subject: Dynamic seismic design
• From: Mark K Gilligan <MarkKGilligan(--nospam--at)compuserve.com>
• Date: Fri, 19 Feb 1999 01:02:34 -0500

```Stan

Reading through the CBC 1998 and UBC 1994 prompted me to query the
following (and comment) :

>1.     What factor is used to multiply the custom spectrum ordinates in
UBC figure 16.3,  to get the model spectral
>accelerations ?  I find that accelerations (and units) seem to become
obscure in earthquake formulas.

The response spectrum shape in UBC figure 16.3 is not as good as a site
specific spectrum but can be used when better information is not available.
These curves can be thought of as response spectrum curves scaled to a 1g
ground acceleration.  These curves can be multiplied by Z*I*S/Rw to give
you something that approximates a site specific spectum.  The resulting
units of the values are  gravities.  When the results are scaled to match
the elastic base shear the spectrum curves provided need not be scaled.

>2.    I understand that the dynamic base shear reactions are to be
compared with the statically calculated
>reactions and brought in line. All member forces are then similarly
factored up or down.

The scaling of the base shear was adopted because of difficulty in
obtaining agreement on how dynamic analysis should be handled in the 1988
Blue Book.  Prior to that time the code was based purely on the equivalent
static approach.  Scaling was seen as a check on the practice of
underestimating the building stiffness and thus reducing the base shear.
The code does not require that you scale the results down, rather the code
sets a minimun not a maximum.

>This suggest that all we are achieving with a dynamic analysis is
distributing the effects of the earthquake
>realistically over the structure and using the static calculated shear
force as a base value for design forces. The
>period used in the static method must therefore be very important. For
combination of forces further reductions >(1.4) are allowed.

The effect of the building periods is addressed by the equivalent static
base shear and the shape of the response spectrum. The shape of the
response spectrum curve makes sure that the relative contribution of the
different modes is appropriate.  The equivalent static base shear formula
is a function of the period of the structure thus reducing the base shear
as the period gets longer.  This methodology may not be theoretically
correct but it does a reasonably good job in producing "safe" buildings.

>The ductility of the steelwork is being heavily relied upon ? Are these
adjustments implying that the theory isnot
>reliable ?

The concern about the ductility demand on the steelwork should be seperated
from the discussion of dynamic analysis as addressed in the code.  The code
specified response spectrum analysis is just another way to obtain elastic
forces which are used to design the individual members.

Ouruse of elastic analyses to design a system that will perform
inelasticaly is based on the assumption that the building drift calculated
using the code forces with Rw=1 is essentially the same as the building
drift calculated using a non-linear analysis and the real ground
accelerations.  For reasons that nobody seems to know this relationship
appears to be reasonable.

The elastic forces calculated in the code make sure that the building is
not  too flexible and will not suffer excessive damage in a small
earthquake.  The Rw term is an attempt to control the ductility demand.

An approach that I sometimes use is to develop preliminary  member sizes
using the code forces.  Then I postulate the hinge locations and a collapse
mechanism for the lateral system.  At this point you can throw away the
elastic analysis.  The forces in the hinges are then applied to the
structure which allows you to calculate the forces in the members of the
lateral system.  The structure is then designed for these  forces with
sufficient factor of safety to assure that the hinges will occur only where
assumed.  This is essentially what the code attempts to do in a much more
inderect manner.

Mark Gilligan

```