INTRODUCTION
Many kinds of piping, made of various materials and having different dimensions are vastly used in petrochemical facilities for transferring fuel oil or high pressure gases from some equipment or a specific production site to another one. Most of the containing materials in such pipes are actually hazardous materials that if released they would have insite and offsite destructive consequences. Regarding the fact that few industrial sites have been affected by the past earthquakes, reports about sustained damages and seismic behavior of industrial equipments and structures are limited. Also, in the walkthrough investigations of industrial plants, damaged due to the past earthquakes, because of damages imposed to heavy and major structures, fires and falling of the adjacent structures on piping, adequate attention has not been paid to such facilities disruptions. As a result, there are just few codes, guidelines or recommendations for seismic design and/or evaluation of nonbuilding structures located in industrial plants. Therefore, in many cases of seismic assessment of combined structures such as on pipeway piping, which have an important role in maintaining the operation, dynamic interactions between connected structures and/or equipments are neglected. Neglecting the interactions can lead to some variations in estimated response of either pipes or pipeway and resulting stresses, which can finally lead to under or overestimation of design requirements. This in turn can result in unreliable or uneconomical seismic design. Obviously, the unreliable design can lead to major damages, as shown in Fig. 1a and b, which would interrupt operation of the whole industrial complex for long time to carry out the repair works. Regarding these facts, developing simplified methods and their inclusion in codes and guidelines are of great importance in civil and mechanical engineering communities for practical applications.
From the research viewpoint, some studies have been conducted for seismic analysis
of the combined primarysecondary systems as a single unit and several methods
have been developed for simplified analysis of such systems. In simplified methods,
analysis of seismic behavior of combined systems are broadly classified into
two groups: (1) coupled analysis and (2) decoupled analysis. In the coupled
analysis cases, the combined Eigen properties of the primarysecondary system
are determined by considering the two subsystems as a single and independent
dynamic unit and modal analysis is carried out for investigating their seismic
behavior (Igusa and Der Kiureghian, 1985; Veletsos
and Ventura, 1985). Since, the masses and stiffnesses of the secondary system
are usually small compared to those of the primary system, there may be illconditioning
of matrices in the proposed simplified methods (Ray and
Gupta, 2002).

Fig. 1(a, b): 
Deformation and damages of piping and pipeways
(Suzuki, 2008) 
The real Eigen properties of the classically damped subsystems
have also been used in the evaluation of the combined systems properties (Igusa et al., 1983; Suarez and Singh, 1987). Some studies have been also carried out for decoupling combined systems to
subsystems and formulating the exact transfer functions directly in terms of
the fixedbase modes of the individual subsystems (Dey
and Gupta, 1998, 1999; Gupta,
1997; Rao, 1998). Also, several attempts have been
made for developing methods for decoupling analysis of the two subsystems,
such as floor response spectrum, frequencybased, responsebased and modeacceleration
(Asfura and Der Kiureghian, 1986; Burdisso
and Singh, 1987; Reddy et al., 1998; Surya
et al., 2002) and some criteria have been proposed and compared for
this purpose (Chen and Wu, 1999). Some studies have
been carried out as well on influences of primary and secondary systems, assumed
as rigid blocks, on each other’s dynamic behavior for which various connection
conditions have been considered (Der Kiureghian, 1999;
Sharif et al., 2009).
In all of the aforementioned studies the primarysecondary system is assumed to be composed of two subsystems: (1) supporting subsystem, which is mostly the heavier subsystem, as the Primary and (2) supported subsystem, which is mostly the lighter subsystem as the multiplysupported secondary. It should be mentioned that the multiplysupported secondary subsystem has been considered as just a single dynamic system, while in the case of on pipeway piping systems, especially in industrial complexes, usually there are varieties of pipe combinations with different diameters, connecting links and end conditions, which create several secondary subsystems instead of just one. Therefore, assumption of a single secondary system for decoupling the equations of motion could lead to gross errors in response predictions of such primarymultiple secondary systems.
One of the guidelines, widely accepted by engineering communities for aseismic
design of the petrochemical structures, is the ASCE Guidelines for Seismic Evaluation
and Design of Petrochemical Facilities (ASCE, 1997). Other
codes and reports also exist for designing and retrofitting of piping systems
such as ASME Code for Pressure Piping, B31.3 (ASME, 1999)
and its (a) and (b) addenda as well as ALA Report on Seismic Design and Retrofit
of Piping Systems (ALA, 2002).
In section 4.4.3 of ASCE document it is stated that if the weight of the nonstructural element is less than about 25% of the weight of the structure, or if the nonstructural element is rigid, interaction effect need not be considered. This study focuses on validation of this ASCE proposed design and evaluation provision and discusses how the interaction between multiple piping and pipeway with respect to the limitations presented in the ASCE guidelines can affect the seismic behavior of the whole system. By performing several Time History Analysis (THA) it has been investigated that how the piping combination, connecting Ubolt rings and endconditions could affect the seismic responses of the whole system in comparison with the pipes and pipeway systems as separate structures. The pipeway structures have been assumed to support multiple pipes so that the weight of the piping can be either about 25% of the pipeway structure, or in some cases more and some cases less than that amount to evaluate how this ASCE recommendation for analyzing the piping and pipeway separately or as a whole system is valid.
For the considered THA four different acceleration time histories at three
different PGA levels have been used and the finite element method with beam
elements has been employed to assess the earthquake induced forces on the systems.
Two different piping combinations have been assumed supported on the pipeway
structures to find out the effects of the pipes dimensions on the system responses.
The on pipeway piping has been assumed to be laterally and vertically restrained
with Ubolt supports on frame structures’ main beams, which are usually
used in industrial plants, while it’s longitudinal and rotational movements
have been assumed to happen freely.
DESCRIPTION AND MODELING OF THE STUDIED STRUCTURES
For selecting a real case of on pipeway piping system for this study, some petrochemical facilities were visited in Imam Port Petrochemical Complex, located in South of Iran at the Persian Gulf shore. In the visited facilities there were many types of piping and supporting structures having various lengths, heights, supporting levels and piping dimensions, end conditions and so on. The overall view of one of the actual systems considered for this study and the close up view of the used Ubolt supports of the pipes on main beam of the frame supports are shown in Fig. 2a and b.
Obviously, any combination of the mentioned features could result in some special
behavior and analytical conditions. The selected structures for this study are
located in Low Density Poly Ethylene (LDPE) producing part of the petrochemical
site, which support many types of high pressure piping containing actually toxic
and hazardous materials. Details of profile sections of the supporting structures’
frames were obtained from the technical drawings of the selected structure,
designed and built in late 70s Imam Port Petrochemical Complex
(1977). The spacing between the main lateral frames of the pipeway structures
in longitudinal direction is usually 8.0 m and the structures usually have a
midspan gravity deformation controlling beam between each two adjacent frames.
The piping in many cases was attached to the pipeway structures using Ubolt
supports at upper wing of the main frame beams as the bolts diameter were equal
for all different dimensions piping. Some of these bolts were disconnected at
maintenance or repair works from the piping and were not assembled at their
location again which could induce much deflection of piping under extreme loads
such as earthquakes. In this study, it has been assumed that all Ubolt rings
are assembled and their absence has not been modeled in the seismic analysis,
since the randomness in this absence is very high and it is very timeconsuming
to consider all possible cases. In many cases the frames of the pipeway structure
supports piping at two different levels for carrying more pipes. This feature
was also considered in the support structures in this study.
The structure for which the results of analysis are presented in this study
includes six main lateral frames at 8.0 m spacing, giving a total length of
48.0 m for the whole pipeway structure.

Fig. 2: 
The overall and closeup views of the sample structure of
the study, (a) overall view of the sample selected combination structure
and (b) the closeup view of the Ubolt supports of main beams 
The actual selected frame structure supports a set of pipes weighing more
than 50% of its weight at two levels with 4.4 and 5.6 m heights. Bracing of
the pipeway in actual system is in longitudinal direction and horizontal levels
at every other 5 spans and there is no bracing in transverse direction to facilitate
the access for repair and maintenance works. These features were considered
in the structural models of the sample systems.
To achieve the goals of the study, the combination structures of piping and pipeway were modeled with different weight ratios of piping to supporting structure of 15, 25 and 35%. The pipes crosssectional dimensions were considered as 70.0x2.6, 159.0x4.0 and 419.0x6.3 mm. As it was observed in visited sites, just one or two branch line(s) of large diameter pipes were supported on upper level of frame structures. Hence, in this study it was decided to develop the structural models in two main piping combinations, as shown in Table 1.

Fig. 3: 
The overall view of the whole structural model of the sample
system 
Table 1: 
Number of pipes of various dimensions in considered pipe combinations
for various weight ratios 

W^{P}: Pipe weight, W^{S}: Structure weight 
As it is seen in Table 1 in the first combination for all weight ratios just pipes with diameters of 70.0 and 159.0 mm were used, but in the second combination pipes with diameters of 70.0 and 419.0 mm were used for 15% weight ratio, while pipes with diameters of all three considered values were used to reach the desired weight ratios of 25 and 35%. Also to find out the effects of the stiffness of Ubolt links on the responses of the whole systems, the rods of 4.0, 6.0 and 8.0 mm diameters were used in structural models.
For more detailed investigation of the responses in various conditions, it was assumed that the end conditions of all pipes supported on frame structures would be one of the following cases:
• 
Both ends are fixed, indicated hereinafter as FF 
• 
One end is fixed and the other one has a spring type support,
indicated hereinafter as FS 
• 
Both ends have spring type supports, indicated hereinafter
as SS 
These spring type supports were applied at all six components of the pipes
end nodes to take into account the effect of remaining parts which can not be
included in the structural model.

Fig. 4: 
The closeup view of a part of the structural detailed model 
The stiffness values of these springs were derived using the assumption that
the continuing parts of the pipes have a vertical bend attached to a heavy structure
at ground level. The total length of the piping supported by the 48.0 m pipeway
was assumed to be 50.0 m, letting the pipe to pass 1.0 m over with respect to
each of the end frames of the pipeway structure. Figure 3
and 4 show respectively the overall view of the structural
model created by the computer program for the 48.0 m long pipeway structure,
supporting pipes of various diameters in two different levels and a close up
view of it which shows more detail of the structural model of the system and
its connections.
STIFFNESS OF THE UBOLT CONNECTING RINGS
As it was shown in Fig. 2b, the Ubolt rings encircle the
pipes, so that they constrain transversal and vertical movements of pipes, but
let them move freely in longitudinal direction to avoid thermal stresses due
to expansion or contraction, or similar deformations in piping. For taking into
account the lateral stiffness of the Ubolt rings in finite element models of
the combined structures, some twonode compressiontension spring elements were
assumed to connect the pipes’ lower nodes to the main beam upper nodes
just beneath them. For obtaining the springs’ stiffness values, finite
element modeling of the Ubolt rings in presence of the pipes were carried out,
to get the realistic behavior of rings in contact with pipes. To find out the
effect of rings’ stiffness on the responses of combined structures, diameter
of bolts were assumed to be 4.0, 6.0 and 8.0 mm in the analyzed models. Regarding
that three different diameters were assumed for pipes and also three different
diameters for the rings’ rods, nine sets of finite element contact analysis
were needed for obtaining the rings’ stiffness.

Fig. 5: 
Final deformed shape of the 70×2.6 mm pipe and 8.0 mm ring
rod combination subjected to a lateral unit displacement 
Table 2: 
Calculated lateral stiffness values of Ubolt rings (kN m^{1}) 

For modeling flexibletoflexible contact between ring and pipe solid elements,
the Penalty Function method with minimum penetration were used. This method
was utilized by Hallquist et al. (1985) and Nakajima
and Padovan (1987) for contactimpact problems. A comprehensive review of
the method with particular emphasis on computational aspects has been presented
as well (Aliabadi and Brebbia, 1993).
To get a realistic solution of the equations related to described analytical models of pipe and ring the outer elements of pipe wall as well as ring body should be defined as both contact and target elements. Contact condition was set to sticking state, where no gap exists between the two bodies and no sliding takes place. Also for convergence of the calculations friction forces between elements were neglected. Figure 5 shows the final deformed shape of one of analyzed models, composed of pipe with 70.0x2.6 mm dimensions and ring with rod diameter of 8.0 mm subjected to a lateral unit displacement applied at the indicated node of the pipe inner surface.
The deformation of the pipe crosssection and the gap between the outer surface of the pipe and the Ubolt ring can be seen clearly in Fig. 5. The calculated lateral stiffness values of Ubolt rings for various pipering combinations are shown in Table 2.
Values shown in Table 2 have been used for lateral spring connections of pipes’ beam elements, employed for seismic analysis of on pipeway piping.
EARTHQUAKE RECORDS FOR THE THA
The acceleration records of four earthquakes, given in Table 3, scaled to three different PGA levels of 0.3, 0.5 and 0.7 g were used for THA in this study.
Figure 6, which is related to the KJM000 component of Kobe earthquake as a sample of the used records, shows the acceleration time history and its Fourier amplitude spectrum of the record which indicates its frequency content.
As it can be seen in Fig. 6, the frequencies higher than 1.0 Hz with large Fourier Amplitudes of Kobe acceleration record used in this study, starts from 1.19 Hz with other peaks at 1.45, 1.91, 2.09, 2.29, 2.58 and 2.88 Hz. These values are discussed later in the paper with regard to the dominant frequencies of the on pipeway piping systems.
DISCUSSION ON NUMERICAL RESULTS OF THE THA
Regarding that various parameters can affect the seismic response of the on
pipeway piping systems and considering the main goal of this study some sets
of parameters, including the piping weight ratio, pipes combination in the setting
and pipe dimensions, pipes endconditions and the diameter of the Ubolt rods
were considered in THA. The considered results contain displacement response
time histories of the system in its various points, including the frame corner,
the midspan of the pipes as well as the Fourier amplitude spectra and dominant
frequencies of those response time histories.

Fig. 6: 
Acceleration time history of KJM000 component of Kobe earthquake
and its Fourier amplitude spectrum 

Fig. 7: 
Time history and Fourier amplitude spectrum of displacement
response of the corner point of pipeway frame, analyzed individually subjected
to KJM000 component of Kobe earthquake 
Table 3: 
Specifications of the earthquake records used in the study 

Just some samples of results, related to on pipeway piping system with 48.0
m length of pipeway and pipes being 50.0 m long and having different weight
ratios of 15, 25 and 35% are presented here in Fig. 718
and Table 410. More result cannot be presented
here because of lack of space and can be found in the main report of the study
(Azizpour, 2009).
The first set of results relates to the pipeway frame and the pipes, modeled and analyzed individually subjected to KJM000 component of Kobe earthquake, scaled to 0.3 g. Figure 7 shows the displacement response time history of pipeway frame corner point and its Fourier amplitude spectrum.
As shown in Fig. 7, the extreme values of displacement response
of pipeway frame, modeled as an individual structure subjected to scaled KJM000
component of Kobe earthquake and the corresponding dominant frequencies are,
respectively 6.98E3 m and 2.88 Hz. This value is same as the highest dominant
frequencies of the used earthquake accelerogram. It is worth mentioning that
the fundamental modal frequency of the pipeway structure is 3.51 Hz, which
is higher than 2.88 Hz and therefore the structure’s frequency has not
been able to dominate the seismic response.
Figure 810a and b
show the same results for midspan points of the considered pipes of various
diameters in two cases of Ubolt rod diameters of 4.0 and 8.0 mm only for FS
end conditions because of lack of space. Results of other cases can be found
in the main report of the study (Azizpour, 2009).
Based on Fig. 810 the extreme values
of displacement responses of pipes with various diameters, connection and end
conditions, modeled as individual structures subjected to KJM000 component of
Kobe earthquake, scaled to 0.3 g and the corresponding dominant frequencies
are as shown in Table 4.
Comparing the extreme values of displacement responses and their corresponding
dominant frequencies of the pipeway frame and pipes of various diameters, modeled
individually, shows that these responses are quite different in both amplitude
and dominant frequency.

Fig. 8: 
Time history and Fourier amplitude spectrum of displacement
response of midspan point of the 70*2.6 mm diameter pipe, analyzed individually
subjected to KJM000 component of Kobe earthquake. In the case of Ubolt
rod with (a) 4.0 mm and (b) 8.0 mm diameter 

Fig. 9: 
Time history and Fourier amplitude spectrum of displacement
response of midspan point of the 159*4.0 mm diameter pipe, analyzed individually
subjected to KJM000 component of Kobe earthquake. In the case of Ubolt
rod with (a) 4.0 mm and (b) 8.0 mm diameter 

Fig. 10: 
Time history and Fourier amplitude spectrum of displacement
response of midspan point of the 419×6.3 mm diameter pipe, analyzed individually
subjected to KJM000 component of Kobe earthquake. In the case of Ubolt
rod with (a) 4.0 mm and (b) 8.0 mm diameter 

Fig. 11: 
The fundamental mode shapes of the three considered pipes
of the study, modeled as individual structures, for FS end conditions and
Ubolt rod diameter of 4.0 mm. In the case of the (a) 70×2.6, (b) 159×4.0
and (c) 419×6.3 mm pipe 
It can be observed that for the 70x2.6 mm pipe the extreme displacement responses have all the same value of about 0.22 cm for all end conditions and both Ubolt rod diameters of 4.0 and 8.0 mm, while for the 159x4.0 mm pipe the extreme displacement responses are almost independent of the pipe end conditions, but are dependent on the Ubolt rod diameter, resulting in a value of around 0.14 cm for 4.0 mm rod and around 0.06 cm for 8.0 mm rod. In the case of 419x6.3 mm pipe both end conditions and Ubolt rod diameter are effective on the extreme response values, which are varying from 1.7 cm for FS end condition and Ubolt rod diameter of 8.0 mm to 9.8 cm for SS end conditions and Ubolt rod diameter of 4.0 mm. The reason behind these differences is the relative stiffness of the pipe and its ring restrains as described hereinafter in more details.
Concerning the dominant frequencies, it can be seen in Table
4 that the value of this parameter is 1.465 Hz for both 70x2.6 and 159x4.0
mm pipes irrespective of their end conditions and the Ubolt rod diameter, while
for 419x6.3 mm pipes has values varying from 1.416 Hz for FS and SS end conditions
and 4.0 mm Ubolt rod diameter, to 2.832 Hz for FF end conditions and 8.0 mm
Ubolt rod diameter. To find out if the dominant frequency in each case is related
to the input or the structure itself, the fundamental modal frequencies of the
three pipes in the case of FS end conditions, modeled as individual structures
are shown in Table 5.

Fig. 12: 
Time history and Fourier amplitude spectrum of displacement
response of on pipeway piping at its various points in the case of first
combination for 15% weight ratio, subjected to KJM000 component of Kobe
earthquake, (a) At frame corner in the case of 8.0 mm rod and FF end conditions,
(b) At midspan of the 70x2.6 mm pipe with 8.0 mm rod and FF end conditions,
(c) At midspan of the 159x4.0 mm pipe with 8.0 mm rod and FF end conditions,
(d) At frame corner in the case of 4.0 mm rod and SS end conditions, (e)
At midspan of the 70x2.6 mm pipe with 4.0 mm rod and SS end conditions
and (f) At midspan of the 159x4.0 mm pipe with 4.0 mm rod and SS end conditions 

Fig. 13: 
Time history and Fourier amplitude spectrum of displacement
response of on pipeway piping at its various points in the case of second
combination for 15% weight ratio, subjected to KJM000 component of Kobe
earthquake, (a) At frame corner in the case of 8.0 mm rod and FF end conditions,
(b) At midspan of the 70x2.6 mm pipe with 8.0 mm rod and FF end conditions,
(c) At midspan of the 419x6.3 mm pipe with 8.0 mm rod and FF end conditions,
(d) At frame corner in the case of 4.0 mm rod and SS end conditions, (e)
At midspan of the 70x2.6 mm pipe with 4.0 mm rod and SS end conditions
and (f) At midspan of the 419x6.3 mm pipe with 4.0 mm rod and SS end conditions 

Fig. 14: 
Time history and Fourier amplitude spectrum of displacement
response of on pipeway piping at its various points in the case of first
combination for 25% weight ratio, subjected to KJM000 component of Kobe
earthquake, (a) At frame corner in the case of 8.0 mm rod and FF end conditions,
(b) At midspan of the 70x2.6 mm pipe with 8.0 mm rod and FF end conditions,
(c) At midspan of the 159x4.0 mm pipe with 8.0 mm rod and FF end conditions,
(d) At frame corner in the case of 4.0 mm rod and SS end conditions, (e)
At midspan of the 70x2.6 mm pipe with 4.0 mm rod and SS end conditions
and (f) At midspan of the 159x4.0 mm pipe with 4.0 mm rod and SS end conditions 

Fig. 15: 
Time history and Fourier amplitude spectrum of displacement
response of on pipeway piping at its various points in the case of second
combination for 25% weight ratio, subjected to KJM000 component of Kobe
earthquake, (a) At frame corner in the case of 8.0 mm rod and FF end conditions,
(b) At midspan of the 70x2.6 mm pipe with 8.0 mm rod and FF end conditions,
(c) At midspan of the 159x4.0 mm pipe with 8.0 mm rod and FF end conditions,
(d)At midspan of the 419x6.3 mm pipe with 8.0 mm rod and FF end conditions,
(e) At frame corner in the case of 4.0 mm rod and SS end conditions, (f)
At midspan of the 70x2.6 mm pipe with 4.0 mm rod and SS end conditions,
(g) At midspan of the 159x4.0 mm pipe with 4.0 mm rod and SS end conditions
and (h) At midspan of the 419x6.3 mm pipe with 4.0 mm rod and SS end conditions 
Table 4: 
Extreme values of displacement responses and the corresponding
dominant frequencies of pipes with different conditions, modeled as individual
structures subjected to KJM000 component of Kobe earthquake 

Table 5: 
The fundamental modal frequencies of the three pipes (in Hz)
in the case of FS end conditions, modeled as individual structures 

It is seen in Table 5 that the fundamental modal frequencies
of the 70x2.6 mm pipe in both cases of Ubolt rod diameter have almost the same
value of 3.13 Hz, while for the 159x4.0 and the 419x6.3 mm pipes they are different
values for different Ubolt rod diameters. The lower fundamental frequencies
of the 419x6.3 mm pipe comparing to other two pipes relate to the structural
conditions and the relative stiffness of the pipe and the Ubolt rings, which
results in different dynamic behavior in this case. In fact, the low stiffness
of the 70x2.6 and the 159x4.0 mm pipes relative to the Ubolt rings makes the
behavior of the system similar to a multispan beam, while the high relative
stiffness of the 419x6.3 mm pipe relative to the Ubolt rings makes the dynamic
behavior of the pipe similar to a very longspan beam with some lateral weak
restrains. These different behaviors can be observed in Fig.
11, which shows the fundamental mode shapes of the three considered pipes,
modeled as individual structures for FS end conditions and Ubolt rod diameter
of 4.0 mm.
Figure 1217af show
the displacement response time histories of the system, subjected to KJM000
component of Kobe earthquake scaled to 0.3 g, in its various points, including
the frame corner, the midspan of the pipes as well as the Fourier amplitude
spectra of those response time histories for different combination structures,
creating various weight ratios of 15, 25 and 35%.
It can be seen in Fig. 12 and 13 that
although the extreme values of displacement responses of the combination structure
at its different points are different, the general forms of all time histories
are almost the same, except for the case of 4.0 mm Ubolt rod diameter in the
second combination, which is due to the high relative stiffness of the 419x6.3
mm pipe to the Ubolt rings, leading to the dominancy of the 419x6.3 mm pipe
dynamic characteristics (Fig. 11) in the whole combination
system response.

Fig. 16: 
Time history and Fourier amplitude spectrum of displacement
response of on pipeway piping at its various points in the case of first
combination for 35% weight ratio, subjected to KJM000 component of Kobe
earthquake, (a) at frame corner in the case of 8.0 mm rod and FF end conditions,
(b) at midspan of the 70x2.6 mm pipe with 8.0 mm rod and FF end conditions,
(c) at midspan of the 159x4.0 mm pipe with 8.0 mm rod and FF end conditions,
(d) at frame corner in the case of 4.0 mm rod and SS end conditions, (e)
at midspan of the 70x2.6 mm pipe with 4.0 mm rod and SS end conditions
and (f) at midspan of the 159x4.0 mm pipe with 4.0 mm rod and SS end conditions 

Fig. 17: 
Time history and Fourier amplitude spectrum of displacement
response of on pipeway piping at its various points in the case of second
combination for 35% weight ratio, subjected to KJM000 component of Kobe
earthquake, (a) at frame corner in the case of 8.0 mm rod and FF end conditions,
(b) at midspan of the 70x2.6 mm pipe with 8.0 mm rod and FF end conditions,
(c) at midspan of the 159x4.0 mm pipe with 8.0 mm rod and FF end conditions,
(d) at midspan of the 419x6.3 mm pipe with 8.0 mm rod and FF end conditions,
(e) at frame corner in the case of 4.0 mm rod and SS end conditions, (f)
at midspan of the 70x2.6 mm pipe with 4.0 mm rod and SS end conditions,
(g) at midspan of the 159x4.0 mm pipe with 4.0 mm rod and SS end conditions
and (h) at midspan of the 419x6.3 mm pipe with 4.0 mm rod and SS end conditions 
Table 6: 
Extreme values of displacement responses and corresponding
dominant frequencies in various points of the considered combination structures 

This statement is supported by paying attention to the Fourier spectra graphs
as well.
The facts pointed out for the case of 15% weight ratio, shown in Fig.
12 and 13, can be shown also in Fig. 14
and 15, which are related to 25% weight ratio as well as
Figure 16 and 17, which are related to
35% weight ratio. The extreme values of displacement responses in various points
of the combination structure and the corresponding dominant frequencies, shown
in Fig. 1217 are presented in Table
6.
It can be seen in Table 6 that the extreme values of displacement
responses are different at various points of the combination structures, as
expected. It is observed that as the softer end conditions (SS) and Ubolt
rings (with 4.0 mm diameter) are used the absolute extreme response values decrease
for the cases of pipeway frame and the 70x2.6 mm pipe in both combinations
and also for the case of 159x4.0 mm pipe in the second combination, while they
increase for the cases of the 419x6.3 mm pipe and the 159x4.0 mm pipe in the
first combination.

Fig. 18: 
Displacement response histories and corresponding Fourier
spectra of the three considered pipes with FS end conditions and Ubolt
rod diameter of 4.0 and 8.0 mm, subjected to displacement time history of
the pipeway frame’s top level, (a) at midspan of the 70x2.6 mm pipe
with 4.0 mm rod and FS end conditions, (b) at midspan of the 70x2.6 mm
pipe with 8.0 mm rod and FS end conditions, (c) at midspan of the 159x4.0
mm pipe with 4.0 mm rod and FS end conditions, (d) at midspan of the 159x4.0
mm pipe with 8.0 mm rod and FS end conditions, (e) at midspan of the 419x6.3
mm pipe with 4.0 mm rod and FS end conditions and (f) at midspan of the
419x6.3 mm pipe with 8.0 mm rod and FS end conditions 
Table 7: 
The extreme values of the total displacement responses of
the three considered pipes with FS end conditions and Ubolt rod diameter
of 4.0 and 8.0 mm, subjected to displacement time history of the pipeway
frame’s top level and their corresponding dominant Frequencies 

Table 8: 
Modal frequencies of the combination structures for 15% weight
ratio 

Bold values are modal frequencies which are close to the dominant
frequencies 
Table 9: 
Modal frequencies of the combination structures for 25% weight
ratio 

Bold values are modal frequencies which are close to the dominant
frequencies 
Table 10: 
Modal frequencies of the combination structures for 35% weight
ratio 

Bold values are modal frequencies which are close to the dominant
frequencies 
It is also noticeable that as the weight ratio increases
from 15% to 35% the absolute extreme displacement values increase as well at
all response points, however, this increase is less remarkable for the 419x6.3
mm comparing with other pipes. These variations can be due to the ratio of the input dominant frequency to
the fundamental frequencies of the combination structures; however, in the case
of the 419x6.3 mm pipe the extreme response values are dependent mostly on the
relative stiffness of the pipe to the Ubolt ring, regardless of the weight
ratios.
Furthermore, comparing the extreme response values with their corresponding values of pipeway and pipes, modeled as individual structures, shown in Table 4, it can be seen that there are remarkable differences between the corresponding responses and their dominant frequencies, even in the case of 15% weight ratio, however, these differences can reach up to almost 10 times in the case of the 70x2.6 mm pipe, up to almost 13 times for the 159x4.0 mm pipe and up to almost 2 times in the case of the 419x6.3 mm pipe.
To better understand the reason behind these differences and their amount for different pipes the displacement response histories and corresponding Fourier spectra of the three considered pipes with FS end conditions and Ubolt rod diameter of 4.0 and 8.0 mm, subjected to displacement time history of the pipeway frame’s top level as the seismic input have been calculated, which are shown in Fig. 18 and the extreme values of the total displacement responses (summation of frame response and pipe response relative to frame) along with the corresponding dominant frequencies in Table 7.
It is shown in Fig. 18af
that the general form of all response histories as well as their Fourier spectra
are very similar, except for the cases of the 419x6.3 mm pipe in which the case
with Ubolt rod diameter of 4.0 mm it is quite different with other cases, but
for the case with Ubolt rod diameter of 8.0 mm it is less different. This is
because of the higher stiffness of the latter which makes the system more similar
to other combinations with the 70x2.6 mm and the 159x4.0 mm pipes. It should
be pointed out that in the results shown in Fig. 1217
and also Table 6 the interaction (stiffness and mass related
effects) between pipes and pipeway structure has been taken into account, while
in the results shown in Fig. 18 this interaction has not
been taken into consideration. In fact, by comparing the results of the cases
with consideration of interaction and without it, it can be said that the interactive
effect of relative stiffness of pipes and connecting links of pipes to the pipeway
frame, is much more on the response values than the interactive effect of masses.
This statement is confirmed by comparing the results shown in Table
7 with those shown in Table 6.
For better illustration of the stiffness interactive effects and its relation
with modal properties of the combination structures the first two modal frequencies
of those combination structures whose responses are shown in Table
6 are shown in Table 810.
It is seen in Table 810 that in some
cases, indicated by bold characters, the modal frequencies are close to the
dominant frequencies of the applied used earthquake and obviously in these cases
the response values are higher. By considering on the results shown in Table
810, as it was expected, by incrementing weight ratio
the fundamental frequency decrease and due to reduction in stiffness of the
system via end conditions, connecting links and pipes dimensions, fundamental
frequency of the system decrease except for the first modal frequency of the
systems in second combination, SS end condition and 4.0 mm ring type. The reason
behind equality of first modal frequency of those systems is presence of the
419x6.3 mm pipe with connecting links of lower stiffness in the system, which
prevents participation of the pipeway frame and other pipes in modal characteristics
of the whole system. The first modal frequency of this system almost corresponds
to the 419x6.3 mm pipe, considered as an Individual structure. While in the
case of second modal frequency of the stated system, characteristics of all
elements participated in the modal properties. It could be found out that presence
of a pipe with relatively high stiffness relative to the connecting links could
affect and change the whole systems dynamic properties.
Finally, from all previously presented results and discussions, it could be claimed that decoupling combination structures as to analyze individually or without consideration of interaction between primary and secondary systems could produce gross errors in evaluation and estimation of dynamic behavior of such systems. It seems that in dynamic assessment of such systems in addition to the weight ratio of secondary to primary structure, to achieve the economical and reliable retrofitting or designing of such systems, attention should be paid to the end conditions of secondary systems, relative stiffness of primary to secondary systems and also relative stiffness of secondary systems to connecting links.
CONCLUSION
Based on the numerical results it can be concluded that not only the weight percentage of piping but also the pipes’ end conditions and particularly the type of connection between pipes and the pipeway structure are also important factors affecting the whole system’s behavior and may cause the system’s conditions to be different from the code assumptions. In fact, it can be said that the stiffness interactive effect of pipes and connecting links of pipes to the pipeway frame, is much more on the response values than the mass interactive effect. Therefore, it is recommended to modify the code provisions for seismic evaluation, design and retrofit of combination structures in petrochemical plants to take into account the pipe’s relative stiffness to the connecting links (if there is any), end conditions and also pipe combination in the response values. Finally, it can be said that in the cases of combination structures consisted of a primary structure and single multiplysupported secondary structure the weight ratio may be an appropriate factor for making decision on inclusion or exclusion of weight interaction effects, however, in cases with multiple extended secondary structures weight ratio alone is not enough and more research is needed in this regard.