SAC Phase 1 Analytical Studies of Building Performance


Project Title:
Influence of Vertical Ground Motion on Special Moment-Resisting Frames
Gary C. Hart, Ph.D., C.E., University of California, Los Angeles/Hart Consultant Group
Sampson Huang, Ph.D., S.E., Hart Consultant Group
Roy Lobo, Ph.D., Hart Consultant Group
Matthew J. Skokan, University of California, Los Angeles
Project Summary:
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.


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