Seismic Response of Equipment Supported on Structures

SEISMIC RESPONSE OF EQUIPMENT SUPPORTED ON STRUCTURES

Yadira M. Perez, P.E.1, Eddie M. Guerra, P.E.2, and Enrique Bazan-Zurita, Ph.D.3

1_{Project Engineer, Rizzo Associates, USA} 2_{Senior Project Engineer, Rizzo Associates, USA} 3_{Principal, Rizzo Associates, USA}

ABSTRACT

Nuclear power plants in Central Eastern Unites States (CEUS) are currently undergoing Seismic Probabilistic Risk Assessments (SPRAs) in response to regulatory requirements. A frequently identified challenge in these SPRAs involves high In-Structure Response Spectra (ISRS) relative to the plant design basis. These high demands could lead to conservatively biased seismic fragilities for structure-mounted equipment and therefore potential costly plant modifications. A commonly used practice for the seismic analysis of secondary components is the in-cascade approach which consists of modelling only the primary structure and lumping the masses of supported secondary components at the support locations. Accelerations at such locations are used to develop ISRS which, in turn, are used to calculate the response of the secondary systems. It is recognized that, within the framework of elastic behaviour, a more accurate procedure involves a coupled modelling of the components along with the supporting primary structure. Numerous studies have examined the accuracy of the in-cascade approach for relatively simple models, and have developed procedures to achieve more accurate results. This paper presents a confirmatory assessment of the added accuracy than can be gained with the couple modelling over the in-cascade approach, using realistic three-dimensional structural models. Results show the acceleration response of the secondary components, when using a coupled analysis, are significantly affected by its weight and stiffness, proving that modelling of secondary systems could improve the fragility assessment and SPRA results, helping to avoid unnecessary costs to the nuclear industry.

INTRODUCTION

In response to the accident at the Fukushima Dai-ichi Nuclear Power Plant caused by the 2011 Great Tohoku Earthquake, the Unites States Nuclear Regulatory Commission requires reactor licensees to re-evaluate the seismic hazards. To satisfy this requirement, nuclear power plants in CEUS sites are currently undergoing SPRAs. An important task of an SPRA is the calculation of the response of structures and components that could contribute to the frequency of core damage using as input a representative earthquake ground motion. As the first group of nuclear plants complete their risk assessments, high ISRS relative to the plant design basis constitute a commonly identified challenge. These high seismic demands are attributed to an increase in high frequency content in the ground motion, characteristic of CEUS sites, coupled with analytical limitations in industry-accepted methodologies. Unrealistic high demand levels could lead to conservatively biased seismic fragilities for structure-mounted equipment and therefore potential costly plant modifications. An alternative for calculating a more realistic, perhaps lower, seismic demand, within the linear elastic analytical framework, is to use coupled modelling of the secondary components along with the supporting primary structure.

and acceleration histories at the locations where relevant secondary systems are placed. The time-histories are used to develop ISRS which then serve as input for response-spectrum or static-equivalent analyses of the secondary components.

The in-cascade approach has been used for almost four decades in the seismic analysis of nuclear facilities to avoid cumbersome, time-consuming and error prone operations required when numerous secondary systems are modelled. Recognizing that the uncoupled analyses can lead to appreciably conservative results, several researchers studied the interaction effects of combined systems. Igusa and Der Kiureghian (1985) used modal synthesis perturbation techniques to estimate modal shapes and frequencies of a coupled structure-equipment systems in terms of the separate dynamic properties of the structure and the secondary system. Villaverde (1997, 2004, 2009) presented reviews of the developments related to the seismic design of mechanical and electrical equipment, architectural components, as well as other secondary structures components attached to the floors, roof, and walls of buildings, including the methods adopted in various building codes. Some of these methods have been incorporated into building codes, and the seismic provisions for the design of non-structural components have been examined by Singh et al. (2006a, 2006b) who also presented improved formulas to enhance the provisions, particularly, to eliminate excessive conservatism while still avoiding more involved analyses. Suarez and Singh (1987) demonstrated the effects of secondary systems by a mode synthesis-based direct approach to incorporate the dynamic interaction between the primary structure and the equipment using the modal properties of the combined structure-equipment system. Chaudhuri and Gupta (2002) proposed a decoupling criterion to identify cases where these errors in approximate procedures are likely to be larger than an acceptable level. Additionally, Ma et al. (2003) used a finite element models implementing a new pseudo-substructure method without increasing the size of the model of the primary structure. In this work, vertical ISRS were generated including higher modes to evaluate the effect of secondary component with different mass ratios on acceleration transfer functions of the primary structures and secondary components. Clayton and Medina (2012) have proposed a probabilistic method to quantify peak component acceleration demands for components attached to elastic and inelastic structures. They conclude that the variability in the component responses highlights the need for a robust probabilistic seismic demand estimation methodology for non-structural components. Furthermore, based on studies by Villaverde (2009) and Taghavi and Miranda (2008), it has been found that the assumption that the secondary system has a small impact on the response of primary system may be inaccurate and the interaction between both systems could affect the response of each other, particularly when the secondary system is relatively heavy. In general, the in-cascade approach results in overestimating the response of the secondary system when tuning occurs. Within the framework of linear analyses, the development of coupled models for the primary and secondary systems remains the most reliable means to estimate the response of the secondary system.

This paper presents several analytical examples representative of mechanical and electrical equipment in US nuclear plants to demonstrate the potential effects of the aforementioned studies for addressing current industry challenges. Three specific examples are provided aiming to show the effect of flexibility and mass from real equipment on floor response spectra. The horizontal and vertical acceleration responses are calculated for each case and compared with values obtained by ignoring the effects of secondary systems on ISRS. Results from these examples provide fragility analysts and PRA managers with analytical options for generating more accurate estimates of seismic demand by considering coupled primary/secondary analyses.

SEISMIC ANALYSIS

properties of the primary and secondary systems have been assigned to model realistic values in actual nuclear power plants.

The main structure (primary system) consists of a three-dimensional six-storey symmetric building with 7% material damping for concrete and 4% damping for steel, corresponding to concrete structures undergoing appreciable cracking. Without affecting the intent of our study, the seismic analyses considered fixed based boundary conditions.

For the equipment (secondary system), three specific components have been selected to assess the effects of different flexibilities and masses of real equipment on the seismic response. Specific equipment properties are listed in Table 1. The components were modelled as a Single Degree of Freedom (SDOF) system and are located at the middle portion of the slab of the sixth floor of the primary model, limited by four columns, as shown in Figure 1. This location was selected because it is expected that the effects of interaction between primary and secondary systems will be more evident at high elevations. The components have the geometric and dynamic properties typical of a 4-legged water storage vertical tank, a Motor Control Center (MCC) and a Switchgear assembly. This equipment sample allows comparative evaluation of the seismic forces on anchorage and in-cabinet amplification demand. The latter is of special interest in view of the current conservatively biased amplification factors used for relay evaluations.

Figure 1. Equipment modelled as a SDOF system.

Table 1. Equipment Properties.

Equipment Weight

[lbs]

Center of Gravity Height above the Floor [ft]

Damping [%]

MCC 800 4 5

Switchgear 5000 4 5

Vertical Tank 30000 5 5

Figure 2. Horizontal Time History.

Figure 3. Vertical Time History.

The seismic forces on each equipment were calculated with two approaches. First, the in-cascade method was used lumping the secondary mass on the supporting floor. The ISRS at that location was calculated which provides the pseudo-acceleration on the equipment from the uncoupled method. Then, coupled models were developed where the mass, stiffness and damping of the secondary systems were specifically represented and attached to the structural model of the primary building. Maintaining the primary structure unchanged, the stiffness of the secondary system was varied to yield the range of frequencies displayed in the ISRS. For consistent comparison with the ISRS, the force acting on the secondary system was divided by the secondary mass to calculate the corresponding pseudo-acceleration.

RESULTS

Figures 4 through 6 present the horizontal and vertical acceleration response of the three models. The green (solid) line displays the response of the building at the equipment location calculated with the in-cascade approach, i.e. the conventional ISRS, while the blue (dotted) line are the accelerations obtained with the coupled models. These accelerations can be taken as the “exact results”.

Figure 4(a) shows that the horizontal acceleration response of the MCC from the coupled primary/ secondary model increases with respect to that yielded by the ISRS calculated from the primary building response (with just the lump mass at the equipment location). The demand increases from 0.82g to 1.05g at around 3Hz. From Figure 5(a), the coupled analysis produces a horizontal acceleration on the switchgear nearly the same as that from the ISRS approach, 0.81g and 0.82g at around 3Hz. On the other hand, Figure 6(a) shows the coupled horizontal acceleration response of the vertical tank is reduced with respect to the un-coupled response. The decrease is from 0.82g to 0.63g at around 3Hz.

Figures 4(b) through 6(b) show the coupled analyses result in lower vertical accelerations for all equipment cases studied. The peak MCC’s response decreases from 1.55g to 1.20g at 5 Hz, the

switchgear’s response is reduced from 1.58g to 1.14g at 5Hz and the tank’s response presents a reduction

Figure 4. (a) Horizontal (left) and (b) vertical (right) acceleration response – MCC (800lbs).

Figure 5. (a) Horizontal (left) and (b) vertical (right) acceleration response – Switchgear (5000lbs).

DISCUSSION

The results depicted in Figures 4 through 6 illustrate that the coupling of secondary and primary systems can play a significant role on the extend of dynamic amplification of the seismic response. Our results indicate an amplification of approximately 28% on the horizontal acceleration response for light equipment such as a MCC, and a reduction of around 30% on the horizontal response of heavy equipment such as a vertical tank. Additionally, a reduction on the vertical acceleration response is achieved in all the studied equipment cases. This reduction becomes more significant as the weight of the equipment increases. It is important to note that these changes occur when the frequency of the secondary system is tuned with the frequency of the primary system.

Our results indicate that the relative weight of the equipment can affect the dynamic response of the secondary system, and confirm the conclusion of previous studies which found that estimating the coupled primary/secondary response could bring significant changes in the demand for flexible equipment (cabinets, tanks, etc) with relatively small masses. For massive/rigid equipment (horizontal pumps, motor generators, etc) the beneficial effects are smaller because the amplification or reduction takes place in the low frequency region rather than the high frequency range (i.e. above 20Hz).

The Electric Power Research Institute (EPRI) proposes a series of amplification factors for relays located in electrical cabinets being subjected to fragility evaluation. These amplification factors vary from 3.6 to 7.2, depending on the type of cabinet and the direction considered. Also, these factors are applicable for both low and high frequency ranges EPRI (2015). Although this paper does not address the effects of anchorage flexibility in the upwards direction of the secondary system, the results presented herein provide an insight on the expected degree of conservativeness in these amplification factors relative to the effects of coupled primary/secondary systems. Therefore, appreciable benefits could be obtained by including secondary systems into the main structure model. Even if the results are not favourable, they will be more realistic.

CONCLUSIONS

The inclusion of secondary systems in models of the primary structure may have a significant effect on the seismic demand of the secondary components. In this paper, three different types of equipment (MCC, Switchgear and Vertical Tank) were modelled in a three-dimensional structural model to illustrate the effect of flexibility and mass from real equipment on floor response spectra. The frequency of the equipment was varied to obtain a maximum the maximum acceleration response curve for the secondary component. Results show that the horizontal acceleration response of light equipment, such as an MCC, can be amplified in a coupled analysis in comparison with the in-cascade response without consideration of the stiffness of the equipment. However, for heavy equipment, consideration of coupling leads to a reduced horizontal response. The results also show a reduction on the vertical acceleration response of all equipment cases studied herein. The reduction becomes more significant as the weight of the equipment increases.

coupled primary/secondary structural models. As a rule, these methods can be used within the limitations imposed by the developers. However, previous results, as well as the numerical findings presented in this paper, show that it is rather difficult to infer generally applicable conclusions, and the use of approximate methodologies can be challenged, particularly when they lead to favorable estimates. Thus, approximate methods, including the in-cascade approach, are only acceptable when the approximate estimates suffice for the intended use of the results.

Nonetheless, for analyses that require more accuracy in the results, performing a coupled analysis will yield to a more reliable and realistic estimate of the seismic response of secondary systems, especially when the equipment being considered is of flexible nature. Our results show the acceleration curve of the secondary system could be either amplified or reduced, therefore it is highly recommended to include the equipment/secondary system in the structural model in order to obtain specific results for the desired case. It is important to also notice the reduction in acceleration response will be greater when the equipment frequency is tuned with the natural frequency of the primary structure, therefore equipment with other frequencies will not be similarly affected. Results from these examples indicate when the use of generic amplification factors seems to be overly conservative, appreciable benefits could be obtained by considering the coupling models secondary systems into the main structure model. This can be achieved by direct development of coupled models or with the improved approximate procedures developed by several researchers (see for instance, Heredia et al. (2006); Clayton and Medina (2012); and Matta and De Stefano (2015)).

It is the intent of this paper to bring to the attention of fragility analysts and PRA managers that limited added analytical work could improve the accuracy of the in-cascade approach. This information can assist the SPRA project team to allocate project resources more effectively given the potential increase in equipment fragility values.

REFERENCES

Chaudhuri, S. R., and Gupta, V. K. (2002).

“

Clayton, J. S. and Medina, R. A. (2012). “Proposed Method for Probabilistic Estimation of Peak Component Acceleration Demands,” Earthquake Spectra: February 2012, Vol. 28, No. 1, 55-75.

Computers and Structures, Inc. (2014). “SAP2000 Integrated Solution for Structural Analysis and Design,” CSI Analysis Reference Manual, Version 17.

Heredia-Zavoni, E., Pérez-Pérez, A. and Barranco-Cicilia, F. (2006), “A Method for the Transfer

Function Matrix of Combined Primary–Secondary Systems Using Classical Modal

Decomposition,” Earthquake Engineering & Structural Dynamics, Volume 35, Issue 2, 251–266. Igusa, T. and Der Kiureghian, A. (1985). “Generation of Floor Response Spectra Including

Oscillator-Structure Interaction,” Earthquake Engineering and Structural Dynamics, Vol. 13, 661-676.

EPRI (2015). “High Frequency Program: Application Guidance for Functional Confirmation and Fragility Evaluation,” Electric Power Research Institute, Palo Alto, CA.

Ma, T., Hossain, Q. and Ostadan, F. (2003). “Generation of In-Structure Response Spectra Considering Secondary System Mass Interaction,” ASME Pressure Vessels and Piping Conference, Ohio, USA. Matta, E. and De Stefano, A. (2015). “Model Calibration in the Presence of Resonant Non-structural

Elements,” Journal of Civil Structural Health MonitoringVolume 5, Issue 1, 37-55.

Singh, M., Moreschi, L., Suarez, L. and Matheu, E. (2006a). “Seismic Design Forces I. Rigid Nonstructural Components,” J. Struct Eng, 132(10), 1524-1532.

Singh, M., Moreschi, L., Suarez, L. and Metheu, E. (2006b). “Seismic Design Forces II. Flexible

Suarez, L. E. and Singh, M. P. (1987). “Floor Response Spectra with Structure-Equipment Interaction Effects by a Mode Synthesis Approach,” Earthquake Engineering and Structural Dynamics, Vol. 15, 141-158.

Taghavi, S. and Miranda, E. (2008). “Effect of Interaction between Primary and Secondary Systems on Floor Response Spectra,” World Conference on Earthquake Engineering, Beijing, China.

Villaverde, R. (1997). “Seismic Design of Secondary Structures: State of the Art,” J. Struct Eng, 123(8), 1011-1019.

Villaverde, R. (2004). “Seismic Analysis and Design of Nonstructural Elements,” Earthquake Engineering: From Engineering Seismology to Performance-Based Engineering, Chapter 19, CRC Press LLC.