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Stochastic structural dynamics: Research vs. practice
Structural Safety, 6 (1989) 129-134 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
129
STOCHASTIC STRUCTURAL DYNAMICS: RESEARCH VS. PRACTICE * T.T. Soong Department of Civil Engineering, State University of New York at Buffalo, Buffalo, NY 14260 (U.S.A.)
Key words: structural dynamics; secondary systems; seismic design.
ABSTRACT An attempt is made to examine the extent to which research results generated in the area oj stochastic structural dynamics have been incorporated into practice in terms of codes and regulations, formulation of design guidelines and performance evaluation. This issue is examined in this paper in the areas of seismic response and design of secondary systems. Current practice in terms of codes, regulations, and design guidelines is compared with the state-of-the-art in research. The gap between research and practice, it appears, is widening, not only from the viewpoint of knowledge base, but also from that of thinking processes involved Comments are made regarding the role of researchers in making an effort to reverse this trend
1. INTRODUCTION While research in stochastic analysis of mechanical and structural systems has been progressing at a steady pace over the last 25 years, its rate of growth as evidenced by technical publications appears to be near its peak at the present. With research output at such a high energy level, it is well to pause and ask how much of it is being adopted and utilized by the practicing sector of this profession in terms of formulation of design guidelines, evaluation methodologies, damage surveys, and vulnerability studies. To give some focus, this question is examined by considering seismic response and design of secondary systems which are anchored or attached to primary structural systems. Examples of secondary systems include mechanical and electrical equipment, architectural dements, and building contents. They can be broadly classified into the following categories: * Paper presented at an International Symposium on Methods of Stochastic Mechanics and Applications, Urbana, IL, U.S.A., October 31-November 1, 1988. 0167-4730/89/$03.50
© 1989 Elsevier Science Publishers B.V.
130 TABLE 1 Estimates loss in major future earthquakes (taken from Ref. [3]) Fault
Northern San Andreas Hayward Newport-Inglewood Southern San Andreas
Loss to buildings ($ in billions) 25 29 45 11
Loss of contents ($ in billions) 13 15 24 6
Total loss ($ in billions) 38 44 69 17
Estimates uncertain by a possible factor of two to three.
(a) Non-structural secondary systems. Computer systems, control systems, machinery, panels, storage tanks and heavy equipment are examples in this category. Performance integrity of these systems under seismic loads, transmitted through the primary structural system, is important since they serve a vital function and their failure may have far reaching ramifications. (b) Structural secondary systems. Examples of these systems include stairways, structural partitions, suspended ceilings, piping systems and ducts. For these systems, not only is their seismic behavior of practical concern, but their interaction with the primary structural system is also important since their presence is capable of modifying structural behavior of the primary system to which they are attached. The importance of secondary system issues in seismic design and performance evaluation is now well recognized by researchers as well as practicing engineers. The subject received special attention after the San Fernando earthquake of 1971 when it became clear that damage to secondary systems not only can result in major economic loss, but also can pose real threat to life safety. For example, an evaluation of various VA hospitals following the San Fernando and other previous earthquakes revealed that many facilities still structurally intact were no longer functional because of loss of essential equipment and supplies [1]. Economic loss due to seismic damage to secondary systems can also be considerable. A case in point is the seismic damage sustained by a seven-story hotel during the 1971 San Fernando earthquake. Of $143,000 in total damage in 1971-value dollars, only $2,000 was structural damage while the remaining 98.6% was non-structural [2]. Recent federal estimates of earthquake property damage after selected future major earthquakes in California are given in Table 1 [3].
2. STATE-OF-RESEARCH Research activities in the area of seismic response of secondary systems have been quite extensive in recent years. A recent survey cites 150 references [4]. The problem is of interest not only because of its importance, but also because it is challenging due to inherent complexities involved in the stochastic analysis of a primary-secondary structural system. These include: (a) Large number of degrees of freedom. Both primary and secondary systems are multi-degree-of-freedom systems and the number of degrees of freedom of the combined system is in general prohibitively large. Moreover, the large differences in the stiffness, damping and mass terms between the primary and secondary systems pose serious numerical problems.
131 (b) Tuning. Resonance effects must be considered since any number of frequencies of the secondary system may be arbitrarily close to or coincide with the frequencies of the primary system. The presence of other secondary systems may cause additional tuning problems. (c) Attachment configuration. Attachment configurations between the secondary and the primary systems vary and can be quite complex, causing difficulties in modeling of the combined system. (d) Non-classical damping and gyroscopic effects. Non-classical damping occurs when different damping ratios exist in the primary and secondary systems and its effect is particularly significant at tuning. Moreover, when the secondary system has dynamics of its own, such as a rotating machinery, it gives rise to gyroscopic effects. (e) Nonlinearity. Structures are generally designed to dissipate some of the input energy during severe earthquake ground motion by means of inelastic deformation. Hence, seismic analysis of the combined primary-secondary system needs to be extended to the inelastic range. Recent advances have addressed the following [4]: Floor response spectrum. Recent attempts at improving the floor response spectrum approach include finding more efficient procedures for generating the desired spectrum while including in the spectrum some of the primary-secondary (P-S) system interaction effects. In the development of more direct methods of generating the floor response spectrum, modal analysis approaches and random vibration analysis fiave been used. Interaction and non-classical damping. Floor response spectra including the primary-secondary system interaction effect can in principle be extracted from analyses involving a combined P-S system. Recent advances in performing combined system analysis, e.g., using perturbation techniques or simplified modal synthesis have facilitated this effort. Cross-correlation. Currently, a major approach to accounting for the effect of cross-correlation between multiple-support excitations is to generate cross-correlation spectra through random vibration analysis. As a result, a new cross-correlation floor spectrum is introduced and the calculated secondary system response takes into account the effect of cross correlation between multiple-support excitations. Inelastic response spectrum. The determination of inelastic response spectrum has been made using equivalent linearization and time history integration techniques. For example, inelastic floor response spectra have been generated following a time history analysis where the types of hysteresis curves included origin-oriented type, degrading trilinear type and slip type. Other investigations in this area include the development of simplified procedures for determining the dynamic response of nonlinear primary systems, from which corresponding inelastic floor response spectra can be generated. Response sensitivity to uncertainties. The sensitivity of secondary system response to uncertainties in structural modeling and in parameter values of the primary system has also received some attention. Included in this consideration are uncertainties in mass, stiffness and damping magnitudes and distributions, discretization, structural modeling, geometric and material nonlinearities, decoupling and boundary conditions, design errors, and structural degrading effects. 3. STATE-OF-PRACTICE
In contrast, what one finds in practice is that structural and secondary (or nonstructural) systems are traditionally treated independently in the seismic design and evaluation of building
132
structures. Secondary systems are thus considered as being subjected to forces applied by the structures to which they are attached. Today, major building codes and seismic design guidelines exist which address the seismic force input to various secondary systems. Nationally, the Uniform Building Code (UBC) [5] is widely used for seismic design standards for structures and secondary systems, from which local jurisdictions and some federal agencies have developed similar seismic design requirements. The UBC formulates the design force for secondary systems as an equivalent static lateral force applied to the approximate center of gravity of the system being analyzed. It is given by
Fp = ZICpW
(1)
where Fp is the lateral design force and Z is the seismic zone factor, taking values of 0, 3/16, 3/8, 3/4 and 1 for seismic zones 0, 1, 2, 3 and 4, respectively. I is the importance factor which takes the value of 1 for most structures, 1.25 for buildings with room occupancy loads of 300 or more, and 1.5 for essential buildings such as fire stations and hospitals. W is the weight of the secondary system and Cp is the lateral force coefficient. A portion of the Cp-table stipulated in Title 24 of the California Administrative Code is reproduced in Table 2 [6].
TABLE 2 Horizontal force factor Cp Category 1. Mechanical and electrical components: a. All mechanical and electrical equipment or machinery which is a part of the building service systems. b. Tanks (plus contents) and support systems. c. Emergency power supply systems in public school buildings. Essential communication equipment and emergency power equipment in hospitals, such as engine generators, battery racks and fuel tanks necessary for operation of such equipment. d. Hospital piping, electrical conduit, cable trays and air handling ducts. 2. Hospital equipment when permanently attached to building utility services such as: surgical, morgue and recovery room fixtures, radiology equipment, medical gas containers, food service fixtures, essential laboratory equipment, TV supports, etc. 3. a. Storage racks with the upper storage level more than 5 feet in height (plus contents). b. Floor supported cabinets and bookstacks more than 5 feet in height (plus contents). 4. Wall hung cabinets and storage shelving (plus contents). 5. Suspended ceiling framing systems 6. a. Suspended light fixtures. b. Surface mounted light fixtures. Taken from Ref. [6], Table No. 2-23J, Part B.
Direction of horizontal force
Value of Cp
Any direction
0.33 0.33
Any direction
0.50
Any direction
0.50
Any direction
0.33
Any direction
0.30
Any direction Any direction Any direction
0.30 0.30 0.30
Any direction
1.00
133 Some variations and refinements of the basic formula (1) are found in other codes depending on whether they consider earthquake response characteristic of the ground, attachment details, and vibrational characteristics of the primary-secondary systems. The Applied Technology Council (ATC), for example, has developed more elaborate guidelines. For seismic design of electrical and mechanical equipment, the formula is [7]
Fp=ACpMWpPm
(2)
where A is the effective peak ground acceleration, Cp is the lateral force coefficient, M is the equipment amplification factor, Wp is the equipment weight, P is the performance level coefficient, and m is the attachment amplification factor. The exception, it appears, is the nuclear power industry where much more stringent and rigorous standards are recommended. For, example, in seismic qualification of class 1E equipment for nuclear power generation stations, the recommended qualification methods consist of [8]: (a) Predicting the equipment's performance by analysis, including dynamic analysis of the combined structure-equipment system and nonlinear equipment response. (b) Testing the equipment under simulated seismic conditions. (c) Qualifying the equipment by a combination of test and analysis. (d) Qualifying the equipment through the use of experience data. The discussion given above generally reflects the current practice in seismic design and evaluation of secondary systems. By and large, it involves the calculation of an equivalent static design force against which a secondary system is to be designed.
4. RESEARCH VS. PRACTICE AND CONCLUDING REMARKS.
As observed in Section 2, significant research progress has been made over the last few years, leading to a better understanding of the dynamic behavior of secondary systems. The major research thrust has been the development of more accurate and rigorous methodologies which can account for more realistically the dynamic environment in which secondary systems operate. On the other hand, as summarized in Section 3, seismic response calculation procedures and design guidelines for secondary systems as practiced today revolve around simple static force formulas. Any improvements to these formulas more likely will come in the form of refinements of these simple equations in a minor way. It thus appears that the gap between research and practice is wide and is widening as research takes on added mathematical sophistication. The question of research needs in this area was posed at a recent workshop on nonstructural (secondary) issues of seismic design and construction [9]. The responses were varied, ranging from the viewpoint that only simple guidance, rather than research, was required to improve design significantly, to the opinion that while research was needed, new knowledge in itself without it being tailored to the design practice was not very effective in improving the state of design and construction. There is no room for dispute that the ultimate impact of new methodologies and approaches rests with their applicability in practice. It then appears that the key for researchers to forge a converging path between research and practice is to be involved in the process of translating new research results into a form which can be readily used to improve simple design procedures in practice. While one can argue that the practicing sector must at least share the responsibility for this technology transfer process, the reality is that practicing engineers have neither the time, nor
134 the resource, n o r the expertise to a c c o m p l i s h it. This responsibility m u s t be s h o u l d e r e d to a large degree b y the researcher.
ACKNOWLEDGEMENT This research was s u p p o r t e d in p a r t b y the N a t i o n a l C e n t e r for E a r t h q u a k e Engineering Research u n d e r G r a n t No. N C E E R - 8 7 - 2 0 0 8 .
REFERENCES 1 Veterans Administration, Study to Establish Seismic Protection Provisions for Furniture, Equipment and Supplies for VA Hospitals, Washington, DC, 1976. 2 L. Murphy (Ed.), San Fernando, California Earthquake of February 9, 1971, Vol. 1A, NOAA, Washington, DC, 1973. 3 FEMA, An Assessment of the Consequences and Preparations for a Catastrophic California Earthquake, Washington, DC, 1981. 4 Y. Chert and T.T. Soong, Seismic response of secondary systems, Eng. Struct., 10(3) (1988) 218-228. 5 International Conference of Building Officials, Uniform Building Code, Whittier, CA, 1988. 6 State of California, California Administrative Code, Title 24 Building Standards, Sacramento, CA, 1986. 7 Applied Technology Council, Tentative Provisions for the Development of Seismic Regulations for Buildings, NBS Spec. Pub. 510, Washington, DC, 1978. 8 IEEE, Recommended Practice for Seismic Qualification of Class 1E Equipment for Nuclear Power Generating Stations, IEEE, New York, NY, 1987. 9 EERI, Nonstructural Issues of Seismic Design and Construction, Publication No. 84-04, Berkeley, CA, 1984.
129
STOCHASTIC STRUCTURAL DYNAMICS: RESEARCH VS. PRACTICE * T.T. Soong Department of Civil Engineering, State University of New York at Buffalo, Buffalo, NY 14260 (U.S.A.)
Key words: structural dynamics; secondary systems; seismic design.
ABSTRACT An attempt is made to examine the extent to which research results generated in the area oj stochastic structural dynamics have been incorporated into practice in terms of codes and regulations, formulation of design guidelines and performance evaluation. This issue is examined in this paper in the areas of seismic response and design of secondary systems. Current practice in terms of codes, regulations, and design guidelines is compared with the state-of-the-art in research. The gap between research and practice, it appears, is widening, not only from the viewpoint of knowledge base, but also from that of thinking processes involved Comments are made regarding the role of researchers in making an effort to reverse this trend
1. INTRODUCTION While research in stochastic analysis of mechanical and structural systems has been progressing at a steady pace over the last 25 years, its rate of growth as evidenced by technical publications appears to be near its peak at the present. With research output at such a high energy level, it is well to pause and ask how much of it is being adopted and utilized by the practicing sector of this profession in terms of formulation of design guidelines, evaluation methodologies, damage surveys, and vulnerability studies. To give some focus, this question is examined by considering seismic response and design of secondary systems which are anchored or attached to primary structural systems. Examples of secondary systems include mechanical and electrical equipment, architectural dements, and building contents. They can be broadly classified into the following categories: * Paper presented at an International Symposium on Methods of Stochastic Mechanics and Applications, Urbana, IL, U.S.A., October 31-November 1, 1988. 0167-4730/89/$03.50
© 1989 Elsevier Science Publishers B.V.
130 TABLE 1 Estimates loss in major future earthquakes (taken from Ref. [3]) Fault
Northern San Andreas Hayward Newport-Inglewood Southern San Andreas
Loss to buildings ($ in billions) 25 29 45 11
Loss of contents ($ in billions) 13 15 24 6
Total loss ($ in billions) 38 44 69 17
Estimates uncertain by a possible factor of two to three.
(a) Non-structural secondary systems. Computer systems, control systems, machinery, panels, storage tanks and heavy equipment are examples in this category. Performance integrity of these systems under seismic loads, transmitted through the primary structural system, is important since they serve a vital function and their failure may have far reaching ramifications. (b) Structural secondary systems. Examples of these systems include stairways, structural partitions, suspended ceilings, piping systems and ducts. For these systems, not only is their seismic behavior of practical concern, but their interaction with the primary structural system is also important since their presence is capable of modifying structural behavior of the primary system to which they are attached. The importance of secondary system issues in seismic design and performance evaluation is now well recognized by researchers as well as practicing engineers. The subject received special attention after the San Fernando earthquake of 1971 when it became clear that damage to secondary systems not only can result in major economic loss, but also can pose real threat to life safety. For example, an evaluation of various VA hospitals following the San Fernando and other previous earthquakes revealed that many facilities still structurally intact were no longer functional because of loss of essential equipment and supplies [1]. Economic loss due to seismic damage to secondary systems can also be considerable. A case in point is the seismic damage sustained by a seven-story hotel during the 1971 San Fernando earthquake. Of $143,000 in total damage in 1971-value dollars, only $2,000 was structural damage while the remaining 98.6% was non-structural [2]. Recent federal estimates of earthquake property damage after selected future major earthquakes in California are given in Table 1 [3].
2. STATE-OF-RESEARCH Research activities in the area of seismic response of secondary systems have been quite extensive in recent years. A recent survey cites 150 references [4]. The problem is of interest not only because of its importance, but also because it is challenging due to inherent complexities involved in the stochastic analysis of a primary-secondary structural system. These include: (a) Large number of degrees of freedom. Both primary and secondary systems are multi-degree-of-freedom systems and the number of degrees of freedom of the combined system is in general prohibitively large. Moreover, the large differences in the stiffness, damping and mass terms between the primary and secondary systems pose serious numerical problems.
131 (b) Tuning. Resonance effects must be considered since any number of frequencies of the secondary system may be arbitrarily close to or coincide with the frequencies of the primary system. The presence of other secondary systems may cause additional tuning problems. (c) Attachment configuration. Attachment configurations between the secondary and the primary systems vary and can be quite complex, causing difficulties in modeling of the combined system. (d) Non-classical damping and gyroscopic effects. Non-classical damping occurs when different damping ratios exist in the primary and secondary systems and its effect is particularly significant at tuning. Moreover, when the secondary system has dynamics of its own, such as a rotating machinery, it gives rise to gyroscopic effects. (e) Nonlinearity. Structures are generally designed to dissipate some of the input energy during severe earthquake ground motion by means of inelastic deformation. Hence, seismic analysis of the combined primary-secondary system needs to be extended to the inelastic range. Recent advances have addressed the following [4]: Floor response spectrum. Recent attempts at improving the floor response spectrum approach include finding more efficient procedures for generating the desired spectrum while including in the spectrum some of the primary-secondary (P-S) system interaction effects. In the development of more direct methods of generating the floor response spectrum, modal analysis approaches and random vibration analysis fiave been used. Interaction and non-classical damping. Floor response spectra including the primary-secondary system interaction effect can in principle be extracted from analyses involving a combined P-S system. Recent advances in performing combined system analysis, e.g., using perturbation techniques or simplified modal synthesis have facilitated this effort. Cross-correlation. Currently, a major approach to accounting for the effect of cross-correlation between multiple-support excitations is to generate cross-correlation spectra through random vibration analysis. As a result, a new cross-correlation floor spectrum is introduced and the calculated secondary system response takes into account the effect of cross correlation between multiple-support excitations. Inelastic response spectrum. The determination of inelastic response spectrum has been made using equivalent linearization and time history integration techniques. For example, inelastic floor response spectra have been generated following a time history analysis where the types of hysteresis curves included origin-oriented type, degrading trilinear type and slip type. Other investigations in this area include the development of simplified procedures for determining the dynamic response of nonlinear primary systems, from which corresponding inelastic floor response spectra can be generated. Response sensitivity to uncertainties. The sensitivity of secondary system response to uncertainties in structural modeling and in parameter values of the primary system has also received some attention. Included in this consideration are uncertainties in mass, stiffness and damping magnitudes and distributions, discretization, structural modeling, geometric and material nonlinearities, decoupling and boundary conditions, design errors, and structural degrading effects. 3. STATE-OF-PRACTICE
In contrast, what one finds in practice is that structural and secondary (or nonstructural) systems are traditionally treated independently in the seismic design and evaluation of building
132
structures. Secondary systems are thus considered as being subjected to forces applied by the structures to which they are attached. Today, major building codes and seismic design guidelines exist which address the seismic force input to various secondary systems. Nationally, the Uniform Building Code (UBC) [5] is widely used for seismic design standards for structures and secondary systems, from which local jurisdictions and some federal agencies have developed similar seismic design requirements. The UBC formulates the design force for secondary systems as an equivalent static lateral force applied to the approximate center of gravity of the system being analyzed. It is given by
Fp = ZICpW
(1)
where Fp is the lateral design force and Z is the seismic zone factor, taking values of 0, 3/16, 3/8, 3/4 and 1 for seismic zones 0, 1, 2, 3 and 4, respectively. I is the importance factor which takes the value of 1 for most structures, 1.25 for buildings with room occupancy loads of 300 or more, and 1.5 for essential buildings such as fire stations and hospitals. W is the weight of the secondary system and Cp is the lateral force coefficient. A portion of the Cp-table stipulated in Title 24 of the California Administrative Code is reproduced in Table 2 [6].
TABLE 2 Horizontal force factor Cp Category 1. Mechanical and electrical components: a. All mechanical and electrical equipment or machinery which is a part of the building service systems. b. Tanks (plus contents) and support systems. c. Emergency power supply systems in public school buildings. Essential communication equipment and emergency power equipment in hospitals, such as engine generators, battery racks and fuel tanks necessary for operation of such equipment. d. Hospital piping, electrical conduit, cable trays and air handling ducts. 2. Hospital equipment when permanently attached to building utility services such as: surgical, morgue and recovery room fixtures, radiology equipment, medical gas containers, food service fixtures, essential laboratory equipment, TV supports, etc. 3. a. Storage racks with the upper storage level more than 5 feet in height (plus contents). b. Floor supported cabinets and bookstacks more than 5 feet in height (plus contents). 4. Wall hung cabinets and storage shelving (plus contents). 5. Suspended ceiling framing systems 6. a. Suspended light fixtures. b. Surface mounted light fixtures. Taken from Ref. [6], Table No. 2-23J, Part B.
Direction of horizontal force
Value of Cp
Any direction
0.33 0.33
Any direction
0.50
Any direction
0.50
Any direction
0.33
Any direction
0.30
Any direction Any direction Any direction
0.30 0.30 0.30
Any direction
1.00
133 Some variations and refinements of the basic formula (1) are found in other codes depending on whether they consider earthquake response characteristic of the ground, attachment details, and vibrational characteristics of the primary-secondary systems. The Applied Technology Council (ATC), for example, has developed more elaborate guidelines. For seismic design of electrical and mechanical equipment, the formula is [7]
Fp=ACpMWpPm
(2)
where A is the effective peak ground acceleration, Cp is the lateral force coefficient, M is the equipment amplification factor, Wp is the equipment weight, P is the performance level coefficient, and m is the attachment amplification factor. The exception, it appears, is the nuclear power industry where much more stringent and rigorous standards are recommended. For, example, in seismic qualification of class 1E equipment for nuclear power generation stations, the recommended qualification methods consist of [8]: (a) Predicting the equipment's performance by analysis, including dynamic analysis of the combined structure-equipment system and nonlinear equipment response. (b) Testing the equipment under simulated seismic conditions. (c) Qualifying the equipment by a combination of test and analysis. (d) Qualifying the equipment through the use of experience data. The discussion given above generally reflects the current practice in seismic design and evaluation of secondary systems. By and large, it involves the calculation of an equivalent static design force against which a secondary system is to be designed.
4. RESEARCH VS. PRACTICE AND CONCLUDING REMARKS.
As observed in Section 2, significant research progress has been made over the last few years, leading to a better understanding of the dynamic behavior of secondary systems. The major research thrust has been the development of more accurate and rigorous methodologies which can account for more realistically the dynamic environment in which secondary systems operate. On the other hand, as summarized in Section 3, seismic response calculation procedures and design guidelines for secondary systems as practiced today revolve around simple static force formulas. Any improvements to these formulas more likely will come in the form of refinements of these simple equations in a minor way. It thus appears that the gap between research and practice is wide and is widening as research takes on added mathematical sophistication. The question of research needs in this area was posed at a recent workshop on nonstructural (secondary) issues of seismic design and construction [9]. The responses were varied, ranging from the viewpoint that only simple guidance, rather than research, was required to improve design significantly, to the opinion that while research was needed, new knowledge in itself without it being tailored to the design practice was not very effective in improving the state of design and construction. There is no room for dispute that the ultimate impact of new methodologies and approaches rests with their applicability in practice. It then appears that the key for researchers to forge a converging path between research and practice is to be involved in the process of translating new research results into a form which can be readily used to improve simple design procedures in practice. While one can argue that the practicing sector must at least share the responsibility for this technology transfer process, the reality is that practicing engineers have neither the time, nor
134 the resource, n o r the expertise to a c c o m p l i s h it. This responsibility m u s t be s h o u l d e r e d to a large degree b y the researcher.
ACKNOWLEDGEMENT This research was s u p p o r t e d in p a r t b y the N a t i o n a l C e n t e r for E a r t h q u a k e Engineering Research u n d e r G r a n t No. N C E E R - 8 7 - 2 0 0 8 .
REFERENCES 1 Veterans Administration, Study to Establish Seismic Protection Provisions for Furniture, Equipment and Supplies for VA Hospitals, Washington, DC, 1976. 2 L. Murphy (Ed.), San Fernando, California Earthquake of February 9, 1971, Vol. 1A, NOAA, Washington, DC, 1973. 3 FEMA, An Assessment of the Consequences and Preparations for a Catastrophic California Earthquake, Washington, DC, 1981. 4 Y. Chert and T.T. Soong, Seismic response of secondary systems, Eng. Struct., 10(3) (1988) 218-228. 5 International Conference of Building Officials, Uniform Building Code, Whittier, CA, 1988. 6 State of California, California Administrative Code, Title 24 Building Standards, Sacramento, CA, 1986. 7 Applied Technology Council, Tentative Provisions for the Development of Seismic Regulations for Buildings, NBS Spec. Pub. 510, Washington, DC, 1978. 8 IEEE, Recommended Practice for Seismic Qualification of Class 1E Equipment for Nuclear Power Generating Stations, IEEE, New York, NY, 1987. 9 EERI, Nonstructural Issues of Seismic Design and Construction, Publication No. 84-04, Berkeley, CA, 1984.