by R. Rao and R. White
This article presents research resulting from NCEER's Building Project, to evaluate the earthquake performance of gravity load designed structures and to determine retrofit schemes for these structures. It is dedicated to the memory of Professor Peter Gergely, a long-time leader in NCEER and Chairman of Dr. Rao's Ph.D. committee, up to July 1995. More information about this study is available in a forthcoming NCEER technical report by the authors entitled Retrofit of Non-Ductile Reinforced Concrete Frames Using Friction Dampers, NCEER-95-0020. Comments and questions should be directed to Richard White, Cornell University, at (607) 255-6497; fax: (607) 255-4828; email: firstname.lastname@example.org.
Many retrofit schemes have been developed for upgrading the seismic performance of reinforced concrete (RC) frame buildings originally designed for gravity loads (referred to hereafter as GLD frames). Among the newer approaches are the use of supplemental damping devices such as friction, viscous, or viscoelastic dampers. Many of these devices have been evaluated by Professor Andrei Reinhorn and his colleagues at the University at Buffalo.
Friction dampers show substantial promise for improving the seismic resistance of these rather flexible structures, but there is a need for a simplified design approach. A study at Cornell University is developing such a design methodology and aspects of this work are described in this article including:
The details of this NCEER-sponsored research study are given in Rao (1996) and Rao et al., (1995), with an extended summary in Rao et al., (1996).
The friction damper system used in this study consists of the friction unit (cold steel plates rubbing against clutch-lining pad material), clamped together by one or more bolts, and a structural system for integrating the friction unit with the structure. The structural system can be either steel braces bolted to corner regions of the open bay space in the frame, or an infill wall with gaps around the edges to prevent stiffness interaction of the wall with the frame members.
The installation strategy adopted here was to use a masonry infill wall with gaps around the sides and top of the wall, with the friction unit installed between the top of the wall and a beam spanning between columns at the top of the open bay of the frame, as shown in figure 1. This system has the advantage of needing only simple compression-type connections between the damper and the frame, with little or no drilling required (and hence no noise or dust problems) for anchorage of tension/shear connections required for normal steel bracing systems.
Effects of Friction Dampers on Structural Response
The incorporation of a friction damper system into a structural frame increases the stiffness of the structure until a certain shear level is reached, at which point the dampers can be set to slip, hence limiting the base shear demand on the foundations. Also, the appropriate slip level can be selected to give the optimum response for the given design earthquake loading. The energy dissipated by a friction damper reduces the energy demand on the structure and damps the structural response. A friction damper system changes the displacement characteristics and the shear demands on the structure with a strong dependency on the frequency content of the ground motion.
The primary advantage of the friction damper approach is that much of the hysteretic energy is dissipated by friction rather than by damage within the members of the frame.
Design Parameters and Performance Criteria
Critical design parameters include the design ground motions, the number of friction devices, their placement within the structure, the method of attachment of the dampers to the frame, and the load at which each damper slips.
The seismic loading and desired performance criteria are based on substantial damage control (peak interstory drift of 1% or less) for a 500 year return period earthquake, and collapse prevention (peak interstory drift of 4% or less) for a 2500 year earthquake. It is suggested that the dampers be designed for the 500 year earthquake and then checked for the 2500 year earthquake.
Inelastic Demand Spectrum Method
Several multi-degree of freedom nonlinear time history analyses, each for a different slip load setting of the dampers, would be required to obtain the design value of the damper slip load. A simplified approach is described here; the interested reader is referred to Rao (1996) and Rao et al., (1995, 1996) for more details. In summary, the method begins with a pushover analysis of the frame to obtain the capacity curve. The force distribution used for the pushover analysis must incorporate the various modes of vibration (first mode is sufficient for low-rise structures). At each stage of the analysis, the floor displacements and column shears are converted to spectral displacements (Sd) and spectral accelerations (Sa). The structure is pushed to incipient collapse, with frame stiffness properties being continuously modified with plastic hinges inserted into the frame as they occur. The resulting plot of Sa vs. Sd provides the capacity curve. This capacity curve can be viewed as the envelope of secant responses of an equivalent single-degree-of-freedom (SDOF) system. For typical RC frames, it can be approximated with a bilinear plot.
The demand on the system can be calculated by performing a time history analysis on an equivalent bilinear SDOF system, approximated from the capacity curve. In order to obtain the response of the retrofitted structure for different damper slip load settings, time history analyses can be performed on a series of bilinear SDOF systems with different yield levels and initial stiffness corresponding to pre-slip stiffness of the retrofitted frame. When the maximum responses are plotted on the Sa-Sd plane and connected, the inelastic demand spectrum curve is obtained. Use of the inelastic demand spectrum curve to obtain the design slip load is illustrated in the next section.
Case Study: Retrofit of a 3-Story GLD RC Frame
The design case study utilizes a three-story, three-bay GLD reinforced concrete frame
located on a stiff soil in Zone 3. The Kern County 1952 (Taft) earthquake recorded ground
motion time history was scaled such that the response spectrum matches the appropriate
design spectrum in the period of interest, resulting in peak ground acceleration (PGA)
values of 0.262g and 0.485g, respectively, for the ground
motions corresponding to 500 year and 2500 year return period. Nonlinear time-history analysis using IDARC showed that the as-built structure was not able to meet the performance criteria for the two design loading levels when the structure was subjected to 500 and 2500 year scaled Taft ground motions.
The demand spectrum curve was constructed by carrying out time history analyses of a series of bilinear SDOF systems with different yield levels and initial stiffness corresponding to the pre-slip stiffness of the retrofitted frame. From the demand spectrum, the bilinear capacity curve which gives the optimum response and also satisfied the drift limits and maximum base shear limits was obtained (figure 2).
The design slip load setting in the dampers can be calculated from the optimum capacity curve (See Rao (1996) for details).
The part of the base shear resisted by the dampers is calculated by subtracting the base shear in the frame from the total base shear; this is the shear level in the first story wall at which the dampers slip. The distribution of slip forces in each story is then set proportional to the shears developed in each story from a lateral loading with triangular distribution. This procedure results in slip forces of 15.0 kips, 12.6 kips, and 7.6 kips in stories 1, 2, and 3, respectively.
The adequacy of the design slip values was checked by doing several time history
analyses on the three-story frame using different slip load levels. Figure 3 shows that the design slip load distribution given above
is indeed an
optimum distribution, and leads to acceptable drift and shear levels for the 500 and 2500 year Taft earthquake loadings. Results in figure 4 show that for both levels of loading, the retrofitted structure met the target performance criteria.
This article presents a design methodology for a retrofit scheme utilizing friction dampers in frame structures. The design approach utilizes the inelastic demand spectrum method for obtaining the design values of damper slip loads, thus avoiding the need to do multiple inelastic time history analyses. The approach can be extended to account for multiple ground motions.
Rao et al., (1995, 1996) also contains a design example for the retrofit of a ten-story nonductile reinforced concrete frame.
Rao, R.S., (1996), Retrofit of Non-Ductile Reinforced Concrete Frames Using Friction Dampers, Ph.D. thesis, Cornell University.
Rao, R.S., Gergely, P., and White, R.N., (1995), Retrofit of Non-Ductile Reinforced Concrete Frames Using Friction Dampers, Technical Report NCEER-95-0020, National Center for Earthquake Engineering Research, State University of New York at Buffalo (in press).
Rao, R., Gergely, P., and White, R.N., (1996), "A Simplified Design Method for Retrofit of Gravity Load Design RC Frames with Friction Dampers," Proceedings, 11WCEE, Acapulco, Mexico, June 1996.
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