Published at : 18 Sep 2024
Volume : IJtech
Vol 15, No 5 (2024)
DOI : https://doi.org/10.14716/ijtech.v15i5.7084
Madhavi Latha Annamdasu  Department of Civil Engineering, Koneru Lakshmaiah Education Foundation (Deemed to be University), Vaddeswaram, Guntur (Dt.), Andhra Pradesh, 522302, India 
N. Lingeshwaran  Department of Civil Engineering, Koneru Lakshmaiah Education Foundation (Deemed to be University), Vaddeswaram, Guntur (Dt.), Andhra Pradesh, 522302, India 
Surya Prakash Challagulla  Thornton Tomasetti, M Agile, Baner Pune, Maharashtra411045, India 
Omar Shabbir Ahmed  Engineering Management Department, College of Engineering, Prince Sultan University, 11586 Riyadh Saudi Arabia 
Musa Adamu  Engineering Management Department, College of Engineering, Prince Sultan University, 11586 Riyadh Saudi Arabia 
Analyzing secondary structures (SSs) during earthquakes is vital due to their vulnerability and potential impact on building functionality and occupant safety. Understanding the seismic performance of SSs requires analyzing the Floor Response Spectra (FRS). This research investigates how the dynamic interaction between the primary structure (PS) and SSs affects the FRS under nearfield (NF) and farfield (FF) earthquake conditions. Both the elastic PS and SS are modeled as singledegreeoffreedom (SDOF) systems. The governing equations of motion of the PS and SS are derived and numerically solved using the RK4 method. The study examines the influence of the PS vibration period (T_{p}), tuning ratio (T_{r}), mass ratio , and SS damping ratio on FRS. Twenty horizontal ground motion excitations were selected for the study. Timehistory analysis results indicate that the dynamic interaction is negligible at a lower mass ratio . For values of 0.01, 0.1, and 0.5, the peak acceleration response of the SS under nearfield (NF) excitation decreased by 15.7%, 68.3%, and 79.1%, respectively, and by 15.2%, 68.9%, and 78.8% under farfield (FF) excitation, compared to the uncoupled case. The spectral acceleration response of the SS is significantly influenced by dynamic interaction within dynamic interaction has no effect on FRS across all considered values. Parametric analysis showed that NF earthquakes induce larger FRS peaks compared to FF events. In conclusion, a comparison between simulated FRS and those predicted by Eurocode 8 shows discrepancies, with the codebased formulation often either underestimating or overestimating the FRS magnitude.
Dynamic interaction; Farfield earthquakes; Floor response spectra; Nearfield earthquakes; Nonstructural component
Certain
building components are unable to bear loads and are classified as secondary
structures (SSs). The ground motion of an earthquake can be intensified by a
structure, resulting in floor accelerations exceeding those of the ground. If
secondary structures (SSs) postearthquake is crucial for maintaining emergency
services and public safety and
Extensive
research has been conducted over the years to understand the behavior of
secondary structures (SSs) during earthquakes, aiming to protect public safety
and mitigate financial losses from resulting damage. The floor response
spectrum (FRS) method is a widely used technique for assessing earthquake
forces on secondary structures. It is common practice to utilise the FRS technique
to determine the input force of a SS (Bhavani
and Challagulla,
2023; Challagulla et al., 2023a; 2023b; Pesaralanka et al., 2023;
Vyshnavi et al., 2023; Landge and Ingle, 2021; Pramono et al.,
2020; Berto et al., 2020; Surana, Singh and Lang, 2018a). Engineers frequently employ
this technique in the design of secondary structures. A key assumption of this
method is that the secondary structure does not interact with the primary
structure, meaning its presence has no influence on the dynamic response of the
primary system, and vice versa.
In cases
where the secondary structure (SS) carries significant weight, the assumption
of independent behavior between the primary structure (PS) and SS may not hold.
This interdependence necessitates a comprehensive consideration of the entire
structural system to accurately assess seismic performance. As highlighted by (Annamdasu
et al., 2024; Salman, Tran and Kim, 2020; Lim and Chouw, 2018; Kelly and
Sackman, 1978), the dynamic interaction between
the PS and SS can substantially influence the overall response of the structure
during seismic events. Neglecting this interaction typically leads to an
overestimation of SS demands, resulting in overly conservative designs that may
not be costeffective or efficient. SmithPardo
et al. (2015) emphasize that this
overestimation can lead to unnecessary material use and increased construction
costs without a corresponding increase in safety or performance. Consequently,
understanding and incorporating the dynamic interaction between PS and SS is
crucial for accurate seismic performance evaluation and optimized structural
design. Research into the seismic performance of secondary structures should,
therefore, take into account their interaction with the primary structure. This
approach ensures a more realistic and holistic assessment of structural
behavior under seismic loads, leading to safe and economical designs. By
integrating this dynamic interaction into the analysis, engineers can better
predict the actual demands on both primary and secondary structures, leading to
more effective mitigation strategies and improved overall structural resilience
during earthquakes. The authors have performed numerical analysis
to investigate the behavior of the Floor Response Spectrum (FRS). The primary
aim of this research is to thoroughly investigate and understand the seismic
performance of secondary structures considering their dynamic interaction with
primary structures.
Several
studies have explored the dynamic properties and interaction effects of
integrated systems with a combined oscillatorstructure model (Singh
and Suarez, 1987; Suarez and Singh, 1987; Igusa and Der Kiureghian, 1985;
Sackman and Kelly, 1979; Kelly and Sackman, 1978). However, prior studies have
neglected to consider the effect of dynamic characteristics of both primary and
secondary structures on the seismic response of secondary structures. While
earlier research has explored the seismic response of primary and secondary
structures under typical ground motions, there is a gap in understanding the
seismic performance of secondary structures under near and far field earthquake
excitations. Nearfield and farfield ground motions significantly impact
structural responses differently than typical ground motions. Nearfield ground
motions often induce higher acceleration peaks and demand on structures due to
their proximity to the fault, causing rapid energy release. In contrast,
farfield motions, originating further from the fault, generally produce
lowerfrequency content and extended shaking duration, leading to different
dynamic responses in structures (Mehta
and Bhandari, 2023; Lin, 2022; Salimbahrami and Gholhaki, 2022; Zamanian,
Kheyroddin and Mortezaei, 2022; Akbari, Rozbahani and Isari, 2021). Therefore, further
investigation is warranted in this regard. This study aims to evaluate how near
and far field earthquake events affect floor spectral accelerations. This study
uses the dynamic interaction between an elastic PS and SS to examine how the SS
performs seismically. To evaluate how secondary structures respond to seismic
activity, the floor response spectra (FRS) incorporating dynamic interaction
between the primary structure (PS) and secondary structure (SS) are analyzed.
The study analyses the effects of various factors on the FRS, including the
mass ratio, the time period of the PS, and the secondary structure’s damping
ratio. Finally, comparisons are drawn between the floor response spectra
obtained from this study and those derived from existing codebased
formulations.
The
structure of the paper is as follows: Section 2 provides a brief summary of the
modeling of coupled and uncoupled systems. Section 3 addresses the selection of
ground motions, along with other relevant details for this study. Section 4
discusses the study results, with a focus on floor response spectra. Finally,
Section 5 offers brief concluding remarks.
Modelling and Analysis
This study uses a
singledegreeoffreedom (SDOF) system for elastic PS and SS. Coupled analysis
accounts for the dynamic interaction between the PS and SS, whereas uncoupled
analysis neglects this relationship. Figure 1 illustrates the PS connected to
an accelerationsensitive SS. It is assumed in this study that the primary
structure’s damping ratio is 5%.
Figure 1
Secondary structure attached to a Primary structure
2.1. Uncoupled
Analysis
This
analysis method ignores the PS and SS dynamic interaction (see Figure 1).
Equation 1 may be used to determine how the PS will respond dynamically to a
given earthquake loading.
where m_{p, }c_{p, }and k_{p }are the mass, damping, and stiffness of the primary structure: is the given primary structure’s frequency; are the relative displacement, velocity, and acceleration of the primary structure with reference to the ground; is the acceleration of the ground motion; is the primary structure’s absolute acceleration response. Equation 2 may be used to compute the SS response, which is then used to assess the SS.
where k_{s}, c_{s} and m_{s}, are the stiffness, damping, and mass of the secondary structure: are the damping ratio and frequency of the SS; are the relative displacement, velocity, and acceleration of the SS, respectively. Figure 2 shows how to generate the floor response spectrum.
2.2. Coupled
Analysis
This method
studies the dynamic relationship between the structures. The PS and SS’s
response to a certain dynamic loading can be calculated using Equations 3 and
4, respectively.
The matrix version of Equations 3 & 4 is as follows:
Figure 2 The process of creating floor response spectrum using uncoupled analysis
2.3. FourthOrder
RungeKutta Method for Solving Differential Equations
In order to solve ordinary differential equations (ODEs) and especially address the dynamic behavior described by the secondorder differential equations given in Equations 1– 4, we utilize the FourthOrder RungeKutta (RK4) technique as a numerical tool in this work. The RK4 approach makes it easier to derive dynamic solutions that are necessary to understand how the system reacts to external influences (Challagulla et al., 2023b; Challagulla, Parimi and Thiruvikraman, 2020; Reyes et al., 2020; 2016; SmithPardo et al., 2015). This numerical method approximates solutions to ODEs by utilizing known initial conditions. By breaking the problem into smaller segments, the method calculates slopes at various points within each step. The approximation is progressively refined until the desired endpoint is reached by updating the solution at the end of each step. Smaller step sizes lead to greater accuracy, and the precision can be adjusted by modifying the step size (Yaakub and Evans, 1999). The RK4 approach is utilized extensively in several scientific and engineering fields to solve ODEs in situations when precise analytical solutions are not available. This paper presents the steps involved in solving the secondorder differential equation given in Equation 1. This is how a firstorder system that is equal to the ordinary differential equation in Equation 1 might be redefined Equation 6:
The
system of autonomous firstorder ordinary differential equations (Equations 7
and 7) that follows is produced by combining Equations 8 and 9 with the initial
condition .
The numerical solution of Equation 10 was
achieved by the development of a MATLAB code that employs the explicit RK4 technique.
Other ODEs, such as Equations 2 – 4, can be solved using the same method
described above.
3. Selection
and Scaling of Ground Motions
In the context of seismic
response assessment, realistic responses are generated by utilizing actual
groundmotion records, readily accessible from the Pacific Earthquake
Engineering Research Centre (PEER) NGAWest2 Database. Therefore, for the
current research, we have incorporated 20 horizontal ground motion excitations,
as specified by ASCE 716 (ASCE,
2016) tailored for hard soil conditions
with a shear wave velocity (V_{s30}) greater than 350 m/sec. Additionally, for
this study, we have chosen to employ a set of groundmotion records recommended
in FEMA P695 (FEMA,
2009). These records will be used to
carry out both linear and nonlinear dynamic analyses on the building structures
under consideration, as detailed in Table 1. According to the classification in
FEMA P695, the farfield record set comprises ground motions originating from sites
situated at a distance equal to or greater than 10 km from the fault rupture.
In contrast, the nearfield record set includes ground motions recorded at
sites located within a distance of less than 10 km from the fault rupture, as
determined by the JoynerBoore distance (R_{jb}). The groundmotion records under
consideration were obtained from sites with rock soil conditions, specifically
falling within NEHRP site classes B and C. These records are associated with
moment magnitudes (M_{w}) ranging from 6.69 to 7.62, with an average
magnitude of 7.05. Among the selected records, the closest distances to the
fault rupture, calculated as the average JoynerBoore distance, span from 0 to
26 km, with an average distance of 8.11 km. The epicentral distances (R_{epi}) for this chosen set of ground motions vary
between 4.5 and 86 km, with an average distance of 33.4 km. The peak ground
acceleration (PGA) values of these selected records range from
0.22 to 1.49 g, and their average PGA is 0.494 g. For more comprehensive information
regarding these ground motions, further details can be found in FEMA P695. To
achieve compatibility with the target response spectrum, which is the Zone V
elastic design spectrum of IS 1893 (Part 1): 2016
(Indian Standard, 2016), the chosen ground motion
records were subjected to scaling. The process employed for this purpose
involved the utilization of a timedomain spectral matching approach to
generate earthquake excitations that align with the desired spectrum. The
target spectrum, according to IS 1893:2016 (Indian Standard, 2016), is shown in Figure 3, which is
linked to 5% damping, along with the mean spectra of ground excitations. In
accordance with ASCE 716 standards, the mean spectra must not fall below 90%
of the target spectrum across the entire period range. It is evident from the
figure that the mean spectra comfortably exceed this 90% threshold.
Table 1 Details of nearfield and farfield records




Near field
records 




S. No 
RSN 
Earthquake Name 
Year 
Station Name 

(km) 
(g) 
(km) 
1 
802 
Loma Prieta 
1989 
Saratoga  Aloha

6.93 
7.58 
0.514 
27.2 
2 
821 
Erzican_ Turkey 
1992 
Erzincan 
6.69 
0 
0.386 
9 
3 
828 
Cape Mendocino 
1992 
Petrolia 
7.01 
0 
0.597 
4.5 
4 
1086 
Northridge01 
1994 
Sylmar  Olive 
6.69 
1.74 
0.604 
16.8 
5 
1165 
Kocaeli_ Turkey 
1999 
Izmit 
7.51 
3.62 
0.165 
5.3 
6 
825 
Cape Mendocino 
1992 
Cape Mendocino 
7.01 
0 
1.49 
3398 
7 
1004 
Northridge01 
1994 
LA  Sepulveda 
6.69 
0 
0.752 
44.49 
Farfield
records  
1 
953 
Northridge 
1994 
Beverly
HillsMulhol 
6.7 
9.4 
0.52 
13.3 
2 
1787 
Hector Mine 
1999 
Hector 
7.1 
10.4 
0.34 
26.5 
3 
1111 
Kobe, Japan 
1995 
NishiAkashi 
6.9 
7.1 
0.51 
8.7 
4 
1148 
Kocaeli, Turkey 
1999 
Arcelik 
7.5 
10.6 
0.22 
53.7 
5 
900 
Landers 
1992 
Yermo Fire
Station 
7.3 
23.6 
0.24 
86 
6 
1633 
Manjil, Iran 
1990 
Abbar 
7.4 
12.6 
0.51 
40.4 
7 
125 
Friuli, Italy 
1976 
Tolmezzo 
6.5 
15 
0.35 
20.2 
Figure 3 Scaled ground motions mean
spectra and the target spectrum (a) nearfield data, (b) farfield data
The subsequent sections delve into an examination of secondary structures'
behavior. The acceleration timehistory response of the secondary structure is
studied in a few cases. The key response parameter used to characterize the
performance of the secondary structure includes the Floor Response Spectrum
(FRS).
4.1. Time
History Response
The secondary structure's acceleration response is displayed in this section, as seen in Figure 4. The system depicted in Figure 1 is exposed to ground motions in order to study the impact of the dynamic interaction on the dynamic behavior of the SS. For this particular analysis, two ground motions (one nearfield: RSN 802 and one farfield: RSN 1111) were selected from Table 1. These ground motions were chosen to have identical PGA and duration. The impact of the mass ratio and the SS damping ratio on the SS's acceleration response is examined. The ratio of the mass of the secondary structure to the mass of the primary structure is known as the mass ratio For the coupled analysis, the values of are 0.001, 0.01, 0.1, and 0.5 are considered. For the purpose of this analysis, the PS (T_{p}) and SS (T_{s}) vibration periods are assumed to be 0.5 seconds. The SS damping ratios are assumed to be 1% and 5%. As expected, the acceleration response's amplitude increases as the SS's damping ratio decreases. The seismic response of the secondary structure (SS) is not significantly affected by the dynamic interaction between the PS and SS when the mass ratio is as low as 0.001 (0.1%). This is evident as the acceleration response at ? = 0.001 closely resembles that of the uncoupled system. Therefore, at this mass ratio, the seismic demands on the secondary structure can be computed using the uncoupled analysis. The dynamic interaction between the PS and SS has a significant effect on the SS's acceleration response as the A similar conclusion was observed in the study by (Kaiyuan et al., 2023).
The peak acceleration response of the SS is shown in Table 2 for = 5%, as peak values of any seismic response quantity provide important information about the bbehaviorof the structure. In comparison to the uncoupled evaluation conducted under NF and FF ground motions, Table 2 clearly demonstrates that for 0.01, 0.1, and 0.5, the peak acceleration response of the SS has decreased significantly. Under nearfield (NF) excitation, the peak acceleration of the secondary structure (SS) experiences reductions of 15.7%, 68.3%, and 79.1% compared to the uncoupled case. Additionally, when compared to the uncoupled case, the peak acceleration of the secondary structure (SS) under farfield (FF) excitation decreases by 15.2%, 68.9%, and 78.8%. Overall, in both near and farfield excitations, the secondary structure coupled with the primary structure shows notable reductions in peak accelerations compared to the uncoupled scenario. Furthermore, it is worth mentioning that nearfield (NF) excitation tends to impose higher seismic demands on the secondary structure (SS), as evidenced by the data presented in Figure 4 and Table 2. In the specific scenario outlined in Table 2, it is observed that the response of the secondary structure (SS) exhibits an average increase of 10% under NF excitations compared to FF excitations. This finding underscores the notion that NF excitation imposes greater seismic loads on the SS (BravoHaro, Virreira and Elghazouli, 2021; Zhai et al., 2016) in contrast to FF excitation. This trend highlights the importance of considering the specific characteristics of ground motion in assessing seismic performance. A similar pattern was seen for the = 1% also.
Table 2 Peak acceleration of the SS () for = 5%
Ground motion 
Uncoupled Analysis 
Coupled Analysis  
=0.001 
=0.01 
=0.1 
=0.5  
NF 
4.58 
4.61 
3.86 
1.45 
0.96 
FF 
4.16 
4.17 
3.51 
1.29 
0.88 
Figure 4 Timehistory response (a)
nearfield data, (b) farfield data
4.2. Floor
Response Spectrum
The maximum design forces for the design of the SS can be obtained from the floor response spectrum (FRS) approach (Haymes, Sullivan and Chandramohan, 2020). The FRS method disregards the PS and SS's dynamic interaction (Surana, Singh and Lang, 2018b; Adam, Furtmüller and Moschen, 2013). As a result, the current study tried to examine the FRS by considering the coupling effect. The floor response spectrum represents the SS’s peak responses to input ground motion. The effects of the vibration period (Tp) of the PS, the mass ratio , and the damping ratio on the floor response spectrum are studied. For this purpose, scaled near and farfield ground motions are input data for time history analyses. Absolute acceleration responses are individually obtained and subsequently utilized to calculate the corresponding FRS. These FRS are derived using a 5% damping ratio of the PS, and the mean results are then plotted and analyzed. The graphs depicted in Figures 5 and 6 illustrate the correlation between the average spectral acceleration of an SS and the tuning ratio is the vibration period of the SS. Analysis of Figures 5 and 6 reveals that dynamic interaction significantly influences the FRS within the range of the impact of dynamic interaction appears negligible across all considered values of the damping ratio () and mass ratio (). Thus, it may be said that the coupling effect is noteworthy only when the closely aligns with that of the PS, and a similar conclusion is observed in the study by (Zheng, Shi, and Sui, 2023). Regardless of the and type of ground motions, the reduces with an increase in the primary structure's vibration period for a given damping ratio of the SS.
When the SS
has lower damping ratios, there is a noticeable coupling impact on the FRS.
These findings indicate that as the damping in the SS decreases, the dynamic
interaction has a more significant impact on the FRS. Put differently, as the decreases in the SS,
the significance of the interaction in shaping the FRS becomes more pronounced.
This observation underscores the importance of considering damping ratios,
particularly in the SS, when analyzing the dynamic response of structures subjected
to seismic forces. Peaks (in the vicinity of ) in the Floor Response Spectrum (FRS) show how the SS
responds to earthquakes. When we look at these peaks at different mass ratios,
we see that earthquakes nearby (nearfield) make bigger peaks than those far
away (farfield) at some combination of damping ratios and mass ratios.
As an
illustration, consider the FRS value associated with the to see
the effect of nearfield (NF) and farfield (FF) records on the seismic
response of the SS. The analysis was conducted for different periods of vibration
(), including 0.1 sec, 0.5 sec, 1 sec, and 2
sec. For each , the impact of NF and FF records on FRS was
investigated across various and . At = 0.1
sec, it was observed that NF records consistently resulted in a decrease in compared
to FF records across all damping and mass ratios. The magnitude of these
decreases varied, with higher damping ratios generally leading to larger
percentage decreases.
At = 0.5
sec, the influence of NF records on exhibited variability depending on the damping
and mass ratios. For = 0.01
and = 0.5,
NF records consistently yielded higher values, indicating a significant effect.
However, for = 0.1,
NF records showed a slight decrease in Sa compared to FF records, suggesting a
less pronounced impact. At = 1
sec, similar variability in the influence of NF records on was
observed. For = 0.01
and = 0.1,
NF records consistently led to lower values, indicating a significant effect.
Conversely, for = 0.5,
NF records showed a slight increase in compared to FF records. Finally, at = 2
sec, the pattern of influence of NF records on varied
based on the damping and mass ratios. NF records consistently resulted in
higher values
for = 0.01
and = 0.5,
indicating a significant effect. However, for = 0.1,
NF records showed a slight decrease in compared to FF records, suggesting a less
pronounced impact. These findings underscore the complex interplay between
ground motion characteristics, , and the in
influencing secondary structural response to seismic events.
Figure
5 FRS Vs.
tuning ratio under nearfield records for (a) = 0.1
sec, (b) = 0.5
sec, (c) = 1
sec, (d) = 2
sec
The vibration period of the primary structure is a critical factor in determining its response to ground motion. Structures with shorter periods are more susceptible to the highfrequency motions characteristic of nearfield (NF) records, whereas longerperiod structures are predominantly influenced by the lowerfrequency content typical of farfield (FF) records. It is essential to emphasize the significance of considering both NF and FF records in seismic hazard assessment and structural design. From Sections 4.1 and 4.2, the important points or analysis results can be summarized as follows:
Figure
6 FRS Vs.
tuning ratio under farfield records for (a) = 0.1
sec, (b) = 0.5
sec, (c) = 1
sec, (d) = 2 sec
The findings underscore the need for
sitespecific analyses that account for the complex interplay between ground
motion characteristics and structural response. This conclusion underscores the
importance of considering the sourcetosite distance and the ground motion
characteristics when assessing the seismic response of PS and SS to withstand
earthquakes.
4.3. Comparing
the FRS with Eurocode 8 (EC8) Formula
A comparative examination between the FRS
generated in this study using nearfield (NF) and farfield (FF) records and
the approach outlined in Eurocode 8 (NSAI, 2005) is conducted in the present section. Eurocode
8 provides a formulation for computing the spectral acceleration () applied to a SS, as depicted in Equation
11:
where represents the ratio of ground
acceleration to gravity , while denotes a soil amplification
factor. The term indicates the relative height of
the structure where the component is located, stands for the period of the
secondary structure and represents the primary structure’s
vibration period.
Two fundamental factors affect
the design of FRS: the tuning ratio () and the relative height of the SS. The formula provided by Eurocode
provides a series of curves that show the highest spectral acceleration values
for each floor when equals . Plots of the elastic generated and the Eurocode 8 (EC8) spectra are shown
for the PS under consideration in Figure 7 and 8.
When the mass of SS is negligible ( = 0.01), the EC8 approach tends to
underestimate the maximum demand for SSs at under both nearfield (NF) and
farfield (FF) seismic records, assuming a primary structure with = 0.5 sec and varying . For = 1 sec, under NF and FF records,
the EC8 formulation underestimates the maximum demand for SSs with damping
ratios of = 0.1% and 0.5%. Conversely, for
damping ratios of = 2% and 10%, the EC8 tends to
overestimate the maximum demand for SSs. In contrast, for SSs with mass ratios,
= 0.1 & 0.5, in both
nearfield (NF) and farfield (FF) records, the EC8 formulation tends to predict
higher floor acceleration demands across various of the SS within the same range. If falls below 0.5, the EC8
consistently predicts higher demands on SSs without regard to mass ratios,
damping ratios, primary structure type, or record type. Conversely, when surpasses 2.5, the EC8
consistently underestimates demands on SSs, regardless of mass ratios and
damping ratios for a flexible primary structure ( = 1 sec). The dynamic interaction
between the primary and secondary structures is thus not considered by the EC8
formulation. Figure 7 and 8 show a notable discrepancy in which the floor
spectral acceleration is either greatly overestimated or underestimated by the
criteria given in EC8. This inconsistency emphasizes the requirement of
updating the codebased approach. To enhance the accuracy of the formulation, it is crucial to incorporate
the effects of dynamic interaction between the PS and SS. This adjustment is
vital for improving the seismic evaluation of secondary structures, as it
aligns codebased predictions more closely with observed spectrum
accelerations.
Figure 7 Comparing the predicted FRS of a PS (Tp = 0.5
sec) with codebased FRS for (a) nearfield records and (b) farfield records
4.4. Engineering Application
The above analysis results can be effectively utilized in practical engineering applications, such as the seismic design of hospital equipment. Hospitals house numerous critical secondary structures (SS), such as medical equipment, electrical panels, and storage units, which are essential for patient care and hospital operations. Ensuring the functionality of these structures during and after an earthquake is crucial. The dynamic interaction between the hospital building (PS) and these secondary structures can significantly impact their seismic response. The present research findings can be applied in the practical field as follows:
· Hospital equipment can be modeled as singledegreeoffreedom (SDOF) systems, characterized by parameters such as mass ratio (), damping ratio (), and vibration period (). This modeling allows for a detailed understanding of the equipment’s behavior during seismic events.
· Ground motion records, including both nearfield (NF) and farfield (FF) events, can be used to simulate the seismic response of the hospital building and its equipment. Numerical tools like MATLAB can facilitate these simulations, providing realistic scenarios of seismic activity.
· The research shows how the peak acceleration response of secondary structures varies with different mass and damping ratios. These insights help in predicting the seismic demands on the equipment.
· Understanding that dynamic interaction is minimal at very low mass ratios (? = 0.001) and significant at higher mass ratios allows engineers to optimize the design of equipment supports and anchors. Robust anchoring systems can be designed for equipment with higher mass ratios to ensure they can withstand seismic forces effectively.
· The study’s findings on the Floor Response Spectrum (FRS) can be applied to derive maximum design forces for hospital equipment. By considering the coupling effects, the FRS method provides a more accurate estimate of seismic demands, preventing over or underdesign.
Figure
8 Comparing
the predicted FRS of a PS (Tp= 1 sec)
with codebased FRS for (a) nearfield records and (b) farfield records
The purpose of this article is to examine how dynamic interaction affects secondary structures' seismic needs. This paper delves into a parametric investigation of the dynamic interaction between primary and secondary structures. The dynamic interaction exhibits a notable impact on the acceleration demands of the SS with increasing mass ratio. NearField excitations impose greater seismic loads on the SS in contrast to FarField excitations. At a very low mass ratio , the dynamic interaction is negligible. For values of 0.01, 0.1, and 0.5, the peak acceleration response of the SS under nearfield (NF) excitation decreased by 15.7%, 68.3%, and 79.1%, respectively, and by 15.2%, 68.9%, and 78.8% under farfield (FF) excitation, compared to the uncoupled case. Only in the cases when the secondary structure closely matches the main structure's vibration period—that is, in the region of coupled analysis required. Conversely, for the influence of interaction on the FRS appears insignificant across all examined values of
Lower damping ratios in the SS increase the significance of dynamic interaction on the FRS. Peaks in the FRS within the range of show higher responses to NF excitations compared to FF excitations. The finding that lower damping ratios in SS enhance the impact of dynamic interaction on FRS was unexpected. This underscores the need for detailed consideration of damping properties in seismic analysis and design, as it significantly affects the seismic response of SS. The Floor Response Spectrum (FRS) provides essential insights into the seismic response of secondary structures (SSs), particularly within the range of where peaks are most prominent. Nearfield (NF) earthquakes tend to generate larger peaks in FRS compared to farfield (FF) events, especially at specific combinations of damping and mass ratios. Our analysis across various vibration periods (Tp) highlights the nuanced impact of NF and FF records on spectral accelerations (Sa). Notably, NF records consistently lead to higher Sa values for shorter periods (Tp= 0.1 sec), while the influence varies at longer periods.
The design of FRS is influenced by the relationship between the period of secondary structure (SS) and the primary structural system. However, the current Eurocode 8 (EC8) formulation doesn't fully account for this dynamic interaction. Our analysis found that for lightweight SS EC8 underestimates maximum floor acceleration demands in certain scenarios, while for heavier SS , it tends to overestimate them. Additionally, EC8 consistently overestimates acceleration demands when and underestimates them when . This discrepancy highlights the need to revise EC8 to consider the effects of dynamic interaction. Incorporating these effects will improve the accuracy of predictions and ensure better seismic performance of secondary structures.
The authors would like to acknowledge the support of Prince Sultan University
in paying the Article Processing Charges (APC) for this publication.
Adam, C.,
Furtmüller, T., Moschen, L., 2013. Floor Response Spectra For Moderately Heavy
Nonstructural Elements Attached To Ductile Frame Structures. In: Computational
Methods in Earthquake Engineering. Volume 2, pp. 69–89
Akbari,
J., Rozbahani, S., Isari, M., 2021. Effect of Moving Resonance
on The Seismic Responses Under FarField and NearField Earthquakes. Asian
Journal of Civil Engineering, Volume 22, pp. 159–173
American
Society of Civil Engineers (ASCE), 2016. Minimum Design Loads and Associated
Criteria for Buildings and Other Structures. American Society of Civil
Engineers, pp. 7–16
Annamdasu,
M.L., Challagulla, S.P., Kontoni, D.P.N., Rex, J., Jameel, M., Vicencio, F.,
2024. Artificial Neural NetworkBased Prediction Model of Elastic Floor
Response Spectra Incorporating Dynamic PrimarySecondary Structure Interaction.
Soil Dynamics and Earthquake Engineering, Volume 177, p. 108427
Berto,
L., Bovo, M., Rocca, I., Saetta, A., Savoia, M., 2020. Seismic Safety of
Valuable NonStructural Elements in RC Buildings: Floor Response Spectrum
Approaches. Engineering Structures, Volume 205, p. 110081
Bhavani,
B.D., Challagulla, S.P., Noroozinejad Farsangi, E., Hossain, I. and Manne, M.,
2023. Enhancing Seismic Design of Nonstructural Components Implementing
Artificial Intelligence Approach: Predicting Component Dynamic Amplification
Factors. International Journal of Engineering, Volume 36(7), pp.
1211–1218
BravoHaro,
M.A., Virreira, J.R., Elghazouli, A.Y., 2021. Inelastic Displacement Ratios for
NonStructural Components In Steel Framed Structures Under ForwardDirectivity
NearFault StrongGround Motion. Bulletin of Earthquake Engineering,
Volume 19, pp. 2185–2211
Challagulla,
S.P., Bhavani, B.D., Suluguru, A.K., Jameel, M., Vicencio, F., 2023a. Influence
of Ground Motion Scaling on Floor Response Spectra. Current Science,
Volume 124(8), p. 928
Challagulla,
S.P., Kontoni, D.P.N., Suluguru, A.K., Hossain, I., Ramakrishna, U., Jameel,
M., 2023b. Assessing the Seismic Demands on NonStructural Components Attached
to Reinforced Concrete Frames. Applied Sciences, Volume 13(3), p. 1817
Challagulla,
S.P., Parimi, C., Anmala, J., 2020. Prediction of Spectral
Acceleration of A Light Structure with a Flexible Secondary System Using
Artificial Neural Networks. International Journal of Structural Engineering,
Volume 10(4), pp. 353–379
Challagulla,
S.P., Parimi, C., Noroozinejad Farsangi, E., 2022. Effect of Flexibly Attached
Secondary Systems on Dynamic Behavior of Light Structures. Practice
Periodical on Structural Design and Construction, Volume 27(1), p. 4021057
Challagulla,
S.P., Parimi, C., Thiruvikraman, P.K., 2020. Effect of
the Sliding of Stacked Live Loads on the Seismic Response of Structures. Engineering
Journal, Volume 24(4), pp. 97–110
Faisal,
A., Anshari, A., Nazri, F.M., Kassem, M.M., 2023. NearCollapse Probability of
RC Frames in Indonesia Under Repeated Earthquakes Containing FlingStep Effect.
International Journal of Technology, Volume 14(2), pp. 339–350
Federal
Emergency Managemnt Agency (FEMA), 2009. Quantification of Building Seismic
Performance Factors. US Department of Homeland Security, Federal Emergency
Managemnt Agency (FEMA)
Filiatrault,
A., Perrone, D., Merino, R.J., Calvi,
G.M., 2018. PerformanceBased Seismic Design of Nonstructural Building
Elements. Journal of Earthquake Engineering, Volume 25(2), pp. 237–269
Haymes, K.,
Sullivan, T.J., Chandramohan, R., 2020. A PracticeOriented Method for Estimating
Elastic Floor Response Spectra. Bulletin of the New Zealand Society for
Earthquake Engineering, Volume 53(3), pp. 116–136
Igusa,
T., DerKiureghian, A., 1985. Dynamic Characterization of TwoDegreeofFreedom
EquipmentStructure Systems. Journal of Engineering Mechanics, Volume
111(1), pp. 1–19
Indian
Standard, 2016. Industrial Structures Including StackLike Structures. In:
Criteria For Earthquake Resistant Design of Structures. IS 1893, 2016
Kaiyuan,
Z., Xudong, Z., Feng, F., Peng, D., Jun, G., 2023. Experimental And Numerical
Studies of The Dynamic Coupling Effect In The PrimarySecondary System. Structures,
Volume 54, pp. 732–745
Kamble,
V., Bharti, S.D., Shrimali, M.K., 2021. Seismic Response of the Secondary
Piping System under BiDirectional Earthquake. Asian Journal of Civil
Engineering, Volume 22(6), pp. 1221–1234
Kamble,
V., Dayal Bharti, S., Kumar Shrimali, M., Kanti Datta, T., 2022. Control of
Secondary Systems Response in a BaseIsolated Building under Tridirectional
Ground Motion. Practice Periodical on Structural Design and Construction,
Volume 27(1), p. 04021060
Kelly,
J.M., Sackman, J.L., 1978. Response Spectra Design Methods For Tuned
EquipmentStructure Systems. Journal of Sound and Vibration, Volume
59(2), pp. 171–179
Landge,
M.V., Ingle, R.K., 2021. Comparative Study of Floor Response Spectra for
Regular and Irregular Buildings Subjected to Earthquake. Asian Journal of
Civil Engineering, Volume 22(1), pp. 49–58
Lim, E.,
Chouw, N., 2018. Prediction of the Response of Secondary Structures Under
Dynamic Loading Considering Primary–Secondary Structure Interaction. Advances
in Structural Engineering, Volume 21(14), pp. 2143–2153
Lin, J.,
2022. Vibration Reduction Performance of Structures with Viscous Dampers under
Near?Field Earthquakes. Advances in Civil Engineering, Volume 2022(1),
p. 1315213
Mehta,
R., Bhandari, M., 2023. Evaluation of Seismic Response of Composite Buildings
under NearField Earthquakes. In: IOP Conference Series: Earth and
Environmental Science. IOP Publishing. p. 12016
Murty,
C.V.R., Goswami, R., Vijayanarayanan, A.R., Kumar, R.P., Mehta, V.V., 2012.
Earthquake Protection of NonStructural Elements in Buildings. Gujarat State
Disaster Management Authority, Volume 2012, pp. 1–145
National
Standards Authority of Ireland (NSAI), 2005.
Eurocode 8: Design of Structures for Earthquake ResistancePart 1: General
Rules, Seismic Actions and Rules For Buildings. I.S. EN 19981:2005. European
Committee for Standardization, Brussels
Partono,
W., Irsyam, M., Nazir, R., Asrurifak, M., Sari, U.C., 2022. Site Coefficient
and Design Spectral Acceleration Evaluation of New Indonesian 2019 Website
Response Spectra. International Journal of Technology, Volume 13(1), pp.
115–124
Pesaralanka,
V., Challagulla, S.P., Vicencio, F., Chandra Babu, P.S., Hossain, I., Jameel,
M., Ramakrishna, U., 2023. Influence of a Soft Story on the Seismic Response of
NonStructural Components. Sustainability, Volume 15(4), p. 2860
Pramono,
S., Prakoso, W.A., Rohadi, S., Karnawati, D., Permana, D., Prayitno, B.S.,
Rudyanto, A., Sadly, M., Sakti, A.P., Octantyo, A.P., 2020. Investigation of
Ground Motion and Local Site Characteristics of the 2018 Lombok Earthquake
Sequence. International Journal of Technology, Volume 11(4), pp. 743–753
Reyes,
J.C., ArdilaBothia, L., SmithPardo, J.P., VillamizarGonzalez, J.N.,
ArdilaGiraldo, O.A., 2016. Evaluation of The Effect of Containers on The
Seismic Response of PileSupported Storage Structures. Engineering Structures,
Volume 122, pp. 267–278
Reyes,
J.C., Herrera, M.T., Smithpardo, J.P., Córdoba, L.S., 2020. Effective Live
Load Mass for Storage Buildings on FrictionPendulum Isolators. Engineering
Structures, Volume 218, p. 110843
Sackman,
J.L., Kelly, J.M., 1979. Seismic Analysis of Internal
Equipment and Components in Structures. Engineering Structures, Volume
1(4), pp. 179–190
Salimbahrami,
S.R., Gholhaki, M., 2022. Response of Concrete Buildings with Steel Shear Walls
to Nearand FarField Earthquakes. In: Proceedings of the Institution of
Civil EngineersStructures and Buildings, Volume 175(1), pp. 17–33
Salman,
K., Tran, T.T., Kim, D., 2019. Grouping Effect on The Seismic
Response of Cabinet Facility Considering PrimarySecondary Structure
Interaction. Nuclear Engineering and Technology, Volume 52(6), pp.
1318–1326
Singh,
M.P., Suarez, L.E., 1987. Seismic Response Analysis of Structure–Equipment
Systems with Non?Classical Damping Effects. Earthquake Engineering & Structural
Dynamics, Volume 15(7), pp. 871–888
SmithPardo,
J.P., Reyes, J.C., ArdilaBothia, L., VillamizarGonzalez, J.N.,
ArdilaGiraldo, O.A., 2015. Effect of Live Load on The Seismic Design of SingleStory
Storage Structures Under Unidirectional Horizontal Ground Motions. Engineering
Structures, Volume 93, pp. 50–60
Suarez,
L.E., Singh, M.P., 1987. Floor Response Spectra with Structure–Equipment
Interaction Effects by a Mode Synthesis Approach. Earthquake Engineering
& Structural Dynamics, Volume 15(2), pp. 141–158
Sullivan,
T.J., 2020. PostEarthquake Reparability of Buildings: The Role of
NonStructural Elements. Structural Engineering International, Volume
30(2), pp. 217–223
Surana,
M., Singh, Y., Lang, D.H., 2018a. Effect of Irregular Structural Configuration
On Floor Acceleration Demand In HillSide Buildings. Earthquake Engineering
and Structural Dynamics, Volume 47(10), pp. 2032–2054
Surana,
M., Singh, Y., Lang, D.H., 2018b. Floor Spectra of Inelastic RC Frame Buildings
Considering Ground Motion Characteristics. Journal of Earthquake Engineering,
Volume 22(3), pp. 488–519
Taghavi,
S., Miranda, E., 2004. Estimation of Seismic Acceleration Demands in Building
Components. In: 13^{th} World Conference on Earthquake
Engineering Vancouver, p. 3199
Villaverde,
R., 2009. Fundamental Concepts of Earthquake Engineering. CRC Press
Vyshnavi,
P., Challagulla, S.P., Adamu, M., Vicencio, F., Jameel, M., Ibrahim, Y.E.,
Ahmed, O.S., 2023. Utilizing Artificial Neural Networks and Random Forests to
Forecast the Dynamic Amplification Factors of NonStructural Components. Applied
Sciences, Volume 13(20), p. 11329
Wang, T.,
Shang, Q., Li, J., 2021. Seismic Force Demands on AccelerationSensitive Nonstructural
Components: a StateOfTheArt Review. Earthquake Engineering and
Engineering Vibration, Volume 20(1), pp. 39–62
Yaakub,
A.R., Evans, D.J., 1999. A fourth order Runge–Kutta RK(4,4) Method With Error
Control. International Journal of Computer Mathematics, Volume 71(3), pp.
383–411
Zamanian,
M., Kheyroddin, A., Mortezaei, A., 2022. Study on Passive and Semiactive
Control Systems in Structures under Near?and Far?Field Earthquakes. Shock
and Vibration, Volume 2022(1), p. 1103434
Zhai,
C.H., Zheng, Z., Li, S., Pan, X., Xie, L.L., 2016. Seismic Response Of
Nonstructural Components Considering The NearFault PulseLike Ground Motions. Earthquake
and Structures, Volume 10(5), pp. 1213–1232
Zheng, Z., Shi, C., Sui, X., 2023. Sensitivity
Study of Coupling Effect of Upper Substructure on Main Structure in Floor
Response Spectrum Analysis of Nuclear Power Plant Building. In:
International Conference on Advanced Civil Engineering and Smart Structures.
pp. 58–67