SAC Phase 1 Analytical Studies of Building Performance
Influence of Vertical Ground Motion on Special Moment-Resisting Frames
Gary C. Hart, Ph.D., C.E., University of California, Los Angeles/Hart Consultant
Sampson Huang, Ph.D., S.E., Hart Consultant Group
Roy Lobo, Ph.D., Hart Consultant Group
Matthew J. Skokan, University of California, Los Angeles
The response of special steel moment-resisting frames subjected to both
horizontal and vertical components of earthquake ground motions is presented.
A building that sustained damage, in the form of weld fractures, during
the Northridge earthquake of January 17th, 1994 is selected for study.
The top two-stories of a North-South frame of this building are isolated
and used as a two-story plane frame model in a sensitivity analysis. The
sensitivity analysis parameters varied include the lateral and vertical
mass tributary to the frame, as well as the earthquake time history. A
response spectum approach is employed, with the response spectra being
obtained from synthetic time histories developed for the building site.
In addition, a time history analysis is performed using the synthetic time
histories. Column axial forces and beam bending moments due to horizontal
ground motion, vertical ground motion, and combined horizontal and vertical
ground motion are studied. The arrival time of peak member force responses
is investigated using a time history analysis, for the two-story model
and a single-degree-of-freedom system.
The findings from the sensitivity study show that the effect of vertical
ground motion on the response of a two-story moment-resisting frame can
be significant. This response is however sensitive to the applied earthquake
time history. The results show that element internal forces for exterior
columns and all beams in general, vary over a wide range depending on the
earthquake time history selected. The interior columns of the frame are
found to be relatively earthquake independant. Vertical ground motion was
found to have a significant impact on the member force response of interior
columns and interior bay beams. Furthermore, the arrival of the peak element
force responses for horizontal and vertical ground motion is of major consequence.
Overall, it was found that it is important to use time histories, specific
to the building site, in the analysis of frame response.
The conclusions drawn from this study are:
1) It is important to use measured or generated time histories, specific
to the building site, in the analysis of frame response.
2) The variation of horizontal and vertical mass, as well as the variation
of ground motion, has a significant impact on the response of the moment-resisting
frame element forces.
3) The arrival time of the peak element force responses for horizontal
and vertical ground motion is of importance.
The vertical ground motion tended to be of higher frequency compared to
the North-South motion for all nine element grid locations. In addition,
it was shown that the magnitudes of peak ground acceleration for the vertical
motion were in general 60-70% of the peak ground acceleration for horizontal
motion. Higher ratios of peak vertical acceleration to peak horizontal
acceraltion have been calculated for actual measured earthquake records,
several records indicating ratios in excess of unity. It can be concluded
that the UBC's recommendation of vertical ground motion, taken to be the
horizontal ground motion scaled by two thirds, would result in a false
representation of the vertical motion. The scaling of the horizontal ground
accelerations would result in the loss of the frequency content and possibly
the magnitude of vertical seismic accelerations.
The variation of mass and earthquake time history resulted in a significant
scattering of element force results. Column axial forces were seen to be
increased by the application of vertical ground acceleration to the frame.
These increases are significant in that, in some instances, the impact
of vertical ground motion causes the column members to experience an increase
in axial force which equals the dead load force. However, in comparison
to the effect of the horizontal acceleration on the column axial force,
the effect of vertical ground motion on the axial force in exterior columns
appears to be minimal due to the use of the SRSS method. The interior columns,
on the other hand, show little axial force induced by horizontal ground
motion, therefore, the axial force response of interior columns to vertical
ground motion becomes of importance. Beam moments were also shown to be
increased by vertical seismic accelerations, with the interior bay beams,
in particular the upper level beam, exhibiting the largest increases in
bending moment. In some instances, the beam bending moments in the interior
bay beams were shown to be nearly equal in magnitude to the bending moments
induced by horizontal ground motion.
The response spectrum approach to combining frame element responses to
vertical and horizontal ground motion involves the use of the SRSS technique.
For frame members with element forces, caused by horizontal acceleration,
that are significantly larger than those forces caused by vertical acceleration,
the SRSS technique of combining response tends to minimize the impact of
the vertical ground motion. From the time history study, the results show
that the use of the SRSS technique in a response spectrum analysis tends
to be substantiated, if an adequate time history analysis is not feasible.
It was observed that the peak horizontal and peak vertical axial force
responses occurred at different instances in time. However, the time difference
between these peak responses was of utmost significance. In fact, the study
of the time of response showed that response values which are high percentages
of both horizontal and vertical ground motion exist within a very narrow
time interval. Understanding that earthquake ground motion is highly variable
and that structural response to such motion depends on site conditions
which are seldom known, the significance of this result indicates that
a high probability exists for the peak responses to exist at the same instant
in time. In this case, the use of the SRSS method for combining horizontal
and vertical frame ensure the safe design of a moment-resisting frame,
the element forces due to horizontal and vertical ground accelerations
be combined using and absolute sum method.
An important aspect of the seismic design of buildings is the uncertainty
that exists in the characteristics of ground motion leading to the randomness
in the behavior of the structure. This study has shown that within a "family"
of synthetic earthquake time histories, the uncertainty in the ground motion
has caused a wide scattering of response quantities. Therefore, it is essential
that an in-depth geologic and seismologic study be performed and a "family"
of site-dependent ground motions be obtained. Evaluating the building response
for each of the generated ground motions, results in reducing the uncertainty
of the building response.