Optimum X-Plate Dampers for Seismic Response Control of Piping System

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International Journal of Pressure Vessels and Piping 83 (2006) 672685

Optimum X-plate dampers for seismic response control

of piping systems

S.V. Bakrea, R.S. Jangida,, G.R. Reddyb

aDepartment of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, IndiabReactor Safety Division, Bhabha Atomic Research Center, Anushaktinagar, Mumbai 400 058, India

Received 20 April 2005; received in revised form 2 May 2006; accepted 20 May 2006

Abstract

In a vibrating system, the most effective mechanism to dissipate energy is the inelastic strain of supplemental metallic elements with

plastic deforming characteristics. An X-plate damper (XPD) is one device that is capable of sustaining many cycles of stable yielding

deformation resulting in a high level of energy dissipation or damping. The present paper focuses on a numerical study to investigate the

seismic effectiveness of an XPD for piping systems in industrial units (e.g. chemical and petrochemical industries) and utilities such as

thermal and nuclear power plants. The seismic performance of piping systems is investigated under important parametric variations of

the damper properties (i.e. height, width and thickness of the XPD) under arbitrary ground motions. Investigations are reported for an

industrial piping system equipped with an XPD and the response quantities of interest are the relative displacements, absolute

accelerations and support reactions of the piping system. The response quantities of the controlled (with XPD) piping system are

compared with the corresponding uncontrolled (without XPD) piping systems, to establish the seismic effectiveness of the XPD. Seismic

energy dissipation in the piping system, which is represented by the hysteretic energy of the XPD, is also evaluated and compared. It is

observed that the XPDs are very effective in reducing the seismic response of piping systems. Moreover, for a given piping system and

ground motion, it is difficult to arrive at the optimum properties of an XPD from the parametric variation of the properties of the XPD

and by monitoring the responses of the piping system. Therefore, use of hysteretic energy dissipation by an XPD is proposed to obtain

the optimum properties of the XPD. Furthermore, the effects of the properties of an XPD on the free vibration characteristics of the

piping system are also presented, which is crucial for the design of piping systems with XPDs.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Piping system; X-plate damper; Hysteretic; Seismic; Energy; Parametric; Optimum parameters

1. Introduction

Structural control using energy dissipating devices is an

appealing alternative to the traditional earthquake-resis-

tant design approaches. In this approach, a substantialportion of the vibration energy is absorbed or consumed at

selected locations within a structure through protective

devices especially designed for this purpose. In particular,

passive control devices offer various advantages over

functionally complex active and semi-active control de-

vices. Devices in this class have the ability to dissipate the

earthquake input energy by virtue of their nonlinear

behavior. Since these protective devices are separated from

the main structure, they act as structural fuses that can be

replaced, if damaged, after the occurrence of a severe

seismic event. For piping systems, these devices should

satisfy the basic requirement of thermal expansion withoutgeneration of undesired stresses. During strong earth-

quakes, it should be ensured that these devices dissipate

most of the earthquake input energy and thereby reduce

the forces transferred to the piping system. At present,

snubbers are used in nuclear power plants to reduce the

seismic forces in the piping system. However, snubbers are

very expensive and are associated with problems of oil

leakage (in the case of hydraulic snubbers) and locking (in

the case of mechanical snubbers) and as a result, require

frequent inspection. Hence, Olson and Tang [1] and Cloud

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Corresponding author. Tel.: +91 22 25722545; fax: +91 22 25723480.

E-mail address: [email protected] (R.S. Jangid).
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et al. [2] proposed the reduced use of snubbers and

proposed seismic stops instead. It is very difficult to

frequently inspect snubbers in the high-radiation condi-

tions that exist in nuclear power plants and there are huge

costs required for yearly maintenance of snubbers. More-

over, malfunctioning of snubbers develops undesired loads

[3] on the piping systems thus questioning their safe

functioning.

A variety of passive devices have been proposed for the

structural control of piping systems including the visco-

elastic damper, the compact dynamic absorber, friction

damper and X-plate damper (XPD) [4,5]. The XPD

consists of an assembly that holds either single or multiple

components of thin metallic or layered plates of X or V

shape. It utilizes the plastic deformation characteristics of

the steel components to damp the input seismic energy. TheXPD can sustain many cycles of stable yielding deforma-

tion without fatigue thus dissipating the input seismic

energy in the form of hysteretic deformation. Kelly et al. [6]

were the first to propose the use of XPDs for seismic energy

dissipation in structures, and this work was extended by

Skinner et al. [7] and Tyler [8]. Proposals for the use of

XPDs in piping systems was first presented, again by Kelly

et al. [9]. Schneider et al. [10] performed a series of

experimental tests on a complex spatial piping system

equipped with XPDs. Kobayashi [4] reported studies on

composite laminated plates for a triangular plate damper.

Later, several experimental and analytical studies were

reported on a piping system equipped with metallic energy

absorbers [1117]. More recently, Parulekar et al. [18] and

Bakre and Jangid [19] performed several component tests

on X-plate metallic damper and on piping systems with an

XPD. In all the aforementioned studies, XPDs were found

to be very effective in seismic control of structures.

However, comparatively detailed studies are not yet

available on parametric variations of the properties of

XPD, which play an important role in the seismic analysis

and design of piping systems equipped with XPD. More-

over, the stiffness being added to the piping structure in the

form of an XPD significantly alters the vibration char-

acteristics of the system. Hence, it is important to study the

effect of the damper properties on the free vibration

characteristics of the piping system.

The present preliminary research focuses on a numerical

study to investigate the seismic effectiveness of an XPD as

a seismic protective system for industrial piping systems.

The seismic performance of a piping system is studied

under important parametric variation of the damper

properties for an industrial piping system under real

earthquake ground motions. The damper parameters

considered are height, width and thickness. It is observed

that the optimal XPD properties are very difficult to obtain

by simply monitoring the piping responses. Hence, use of

hysteretic energy dissipation by the XPD is proposed to

obtain the optimal properties of an XPD for a given piping

system and ground motion. Lastly, the effect of the

properties of an XPD on the free vibration characteristicsof the piping system is also studied.

2. Mechanism of XPD

XPDs are made of thin metallic plates that dissipate

energy through their flexural yielding deformation. They

can sustain many cycles of stable yielding deformation

[16,17], resulting in high levels of energy dissipation or

damping. The X shape of the damper is adopted so as to

have a constant strain variation over its height, thus

ensuring that yielding occurs simultaneously and uniformly

over the full height of the damper. A typical XPD with the

holding device used in the present work and its application

to a piping system is shown in Fig. 1(a). A series of

experimental tests was conducted at Bhabha Atomic

Research Centre (BARC) [18] and IIT Bombay [19] to

study the behavior of these dampers. The following

observations are noted from the forcedeformation char-

acteristics of the XPD shown in Fig. 1(b): (i) it exhibits

smoothly nonlinear hysteretic loops under plastic deforma-

tion, (ii) it can sustain a large number of yielding reversals,

(iii) there is no significant stiffness or strength degradation

and (iv) it can be accurately modeled by Wens hysteretic

model [20] or as a bilinear elasto-plastic material. A

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Nomenclature

a post-to-pre-yield stiffness ratio

b Wens model parameter

g Wens model parameter

t Wens model parametersy yield stress of an XPD

a half the height of an XPD

b width of an XPD

n Wens model parameter

t thickness of an XPD

A Wens model parameter

E modulus of elasticity

Ed percentage energy dissipated by an XPD

Eh hysteretic energy in an XPD

EI input energy to the piping system

F force in an XPD

Fy yield force of an XPDH rate of hardening

Kd initial stiffness of an XPD

q yield displacement of an XPD

xp displacement of piping systemxp absolute acceleration of piping system_xp relative velocity of piping system

S.V. Bakre et al. / International Journal of Pressure Vessels and Piping 83 (2006) 672685 673


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comparison of experimental and Wens representation of

the hysteresis loop is also shown in Fig. 1(b).

Using beam theory, the elastic properties of the XPD are

expressed as

Kd Ebt3

12a3, (1)

Fy sybt

2

6a, (2)

q 2sya

2

Et, (3)

where Kd is the initial stiffness, Fy is the yield load and q is

the yield displacement of the XPD; E and sy are elastic

modulus and yield stress of the damper material, respec-

tively; a, b and t are the height, width and thickness of the

XPD as shown in Fig. 1(a).

The properties of the plastically deformed XPD are

expressed as

Psyb

12Ea4y20 3t

2H E Ht3

y0

, (4)

where P is the plastic force in the XPD due to given

displacement d; H is rate of strain hardening and y0 is the

elastic depth given by

y0 sya

2

Ed. (5)

It is to be noted here that using the above equations, the

properties of the XPD, i.e. Kd, Fy, q and a, could be

obtained for a particular combination of a, b and t of an

XPD. These properties are required in Wens hysteretic

model.

3. Modeling of piping system with XPD

The piping system considered for the present study is

made of carbon steel having Youngs modulus (E) of

192.2 GN/m2 and Poissons ratio 0.214, and is supported

on guides with its ends anchored. Fig. 2 shows a schematic

and FE model of the industrial piping system with XPD.

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-20 -15 -10 -5 0 5 10 15 20

-600

0

600

Experimental Wen's (15 mm peak)

Wen's (10 mm peak) Wen's (5 mm peak)

DamperForce(N)

Displacement (mm)

Connecting Lugs

a

b

x

zy

x

F

t

X-plate

(a)

(b)

Fig. 1. (a) X-plate damper and (b) forcedeformation behavior of X-plate

damper.Rx

69 kg

69 kg

69 kg

69 kg

FKd

X

Z

Y

Anchorage

Restraint

Pipe diameter=165 mmPipe thickness=5.5 mmElbow radius=225 mm

3.12m4.1

m

3.05m

1.2

4m

0.8

3m 1

.55m

2.42m

2.74m

2.54m

XPD

(a)

(b)

Fig. 2. Schematic and FE model of a piping system with an XPD.

S.V. Bakre et al. / International Journal of Pressure Vessels and Piping 83 (2006) 672685674


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All the bends in the piping system are 901 with bend radius

of 225 mm. Fig. 2 also shows the location of the lumped

masses and the XPD in the piping system.

The following assumptions are made for seismic analysis

of a piping system with XPDs:

(1) The straight members in the piping system are modeledas 3D Beam elements and the bends are modeled as 3D

Elbows having six degrees-of-freedom at each node.

(2) The mass of each member is assumed to be distributed

between its two nodes as a point mass. In addition to

the mass of the piping system, the externally lumped

masses are assumed to be effective in the three

translational degrees-of-freedom.

(3) Only the XPD behaves nonlinearly whereas the piping

system remains linear.

(4) The forcedeformation behavior of the XPD is

considered as hysteretic, based on the nonlinear model

proposed by Wen [20].

4. Hysteretic modeling of XPD

XPDs, when subjected to cyclic loading, show stable

hysteresis loops dissipating significant amounts of energy.

As noted from Fig. 1(b), the transition of this hysteresis

loop from its initial value, called the initial stiffness ( Kd), to

its limiting value, called the post-yield stiffness, is very

smooth. For such smoothly varying hysteretic behavior,

Wen has proposed a mathematical model that can be used

to represent the force in the XPD. Based on the versatility

of Wens smooth hysteretic model to achieve various

forcedeflection characteristics, it is adopted to represent

the hysteretic force in the damper.

The restoring force (fd) in the XPD is given by

fd aKdxp 1 aKdqZ, (6)

where Z is expressed as

dZ

dt A _xp bj _xpjjZj

n1 g _xpjZjn, (7)

in which A, b, g and n are dimensionless Wens model

parameters; and a is the post- to pre-yield stiffness ratio for

the XPD, Z is a function (whose value varies from 1 to

+1) governed by Eq. (7), xp and _xp are, respectively, the

displacement and velocity of the piping system at the XPD

location. For the present study, Wens model parameters

are obtained by a trial and error method to fit the

experimental hysteresis loops shown in Fig. 1(b). The

parameters obtained are A 0.545, b 0.22, g 0.22 and

n 1. The shape of the hysteresis loop is controlled by

adjusting Wens model parameters.

It is to be noted that Wens model parameters will only

affect the shape of the hysteresis loop whereas the seismic

performance of the piping systems will be controlled by the

geometrical properties of the XPD (i.e. a, b and t). It will be

interesting to investigate the effects of these (geometric)

properties on the seismic performance of a piping system.

Moreover, the seismic energy in the piping system is

absorbed by the hysteretic forcedeformation behavior of

the XPD. The control of the seismic energy being

transmitted to the piping system is predominantly gov-

erned by the hysteretic characteristics of the XPD, whichdepend on the properties of the XPD. The response of the

piping system is thus significantly influenced by the

hysteretic loss of input energy. The rate of the hysteretic

energy dissipated in any XPD in the piping system at time

T is given by

dEh

dT 1 aKdZ_xp (8)

and the total hysteretic energy dissipated by an XPD at

time T is given by

Eh 1 aKd ZT

0

Z_xp dT. (9)

The input energy to the piping system is given by

EI

ZT0

f _ugTMfrg ug dT, (10)

where [M] is the mass matrix of the controlled piping

system, {r} is the influence coefficient vector and ug is the

earthquake ground acceleration. The percentage energy

dissipated in the piping system is expressed as

Ed 100Eh

EI. (11)

It will also be interesting to study the effect of theproperties of XPD on the percentage seismic energy being

dissipated.

5. Governing equations of motion

The equations of motion of a piping system equipped

with an XPD, under a uni-directional component of

ground motion, are expressed in the following matrix form:

Mf ug Cf _ug Kfug UfFg Mfrg ug, (12)

fug fx1;y1; z1; x2;y2; z2; x3;y3; z3; . . . . . . ; xN;yN; zNgT,

(13)

where [C] and [K] represents the damping and stiffness

matrix, respectively, of the piping system of order 6N 6N,

where N is the number of nodes; f ug; f _ug and {u} representacceleration, velocity and displacement vectors, respec-

tively; [U] is the location matrix for the restoring force of

the XPD; {F} is the vector containing the restoring force of

the XPD; and xi, y

iand z

iare the displacements of the ith

node in the piping system in X-, Y- and Z-directions,

respectively. The mass matrix has a diagonal form. The

stiffness matrix of the piping system with friction support is

constructed separately and then static condensation is

carried out to eliminate the rotational degrees-of-freedom.

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With the first two natural frequencies of the piping system

known, and the damping ratio obtained from the test

model, the damping matrix is obtained using Rayleighs

method.

6. Incremental solution technique

Because of the hysteretic behavior of the XPD, the

governing equations of motion are solved in the incre-

mental form using Newmarks time-stepping method

assuming linear variation of acceleration over a small time

interval, Dt. The equations of motion in incremental form

are expressed as

MfD ug CfD _ug KfDug UfDFug MfrgD ug,

(14)

where {DFu} is the incremental restoring force vector of the

XPD.

Following the assumption of linear variation of accel-

eration over the small time interval, DT, fD ug and fD _ugare

given as

fD ug a0fDug a1f _uTg a2f u

Tg, (15)

fD _ug b0fDug b1f _uTg b2f u

Tg, (16)

where a0 6=DT2, a1 6=DT, a2 3, b0 3=DT,

b1 3 and b2 DT=2, and the superscript denotesthe time.

Substituting Eqs. (15) and (16) in Eq. (14), we get

^

KfD

ug fD ^

Pg UfD

Fug, (17)where

K a0M b0C K U Kf, (18)

DP MrfD ugg Ma1f _uTg a2f u

Tg

Cb1f _uTg b2f u

Tg. 19

After solving for incremental displacement vector from

Eq. (17), the incremental acceleration and velocity vectors

are obtained from Eqs. (15) and (16), respectively. Finally,

the displacement and velocity vectors are obtained using

Eqs. (20) and (21), respectively, as given below:

fuTDTg fuTg fDug, (20)

f _uTDTg f _uTg fD _ug. (21)

Eq. (14) can be solved by an iterative technique. The

iterations in each time step, DT, are required due to

dependence of the incremental damper force, fd, on the

response of the system (see Eqs. (6) and (7)). The solution

of the first-order nonlinear differential Eq. (7) for evalua-

tion of incremental damper force is carried out using the

RungeKutta method. The DT is expressed by

DT dT

Nd, (22)

where dT is the time interval at which the ground motions

are recorded and Nd are the number of divisions adopted

for convergence of the structural responses due to the

nonlinearity of frictional forces, which is based on the

ground motion considered and lies in the range of 140160

for the present study.

7. Numerical study

The seismic response of the piping system with an XPD

is investigated under uni-directional excitation of four

components of real earthquake ground motions. The

specific components of these ground motions are indicated

in Table 1. The response quantities of interest for the

piping system under consideration are the relative dis-

placements (xp), absolute accelerations xp of the piping

system at the XPD location and the support reaction (Rx)

as indicated in Fig. 2(b). In addition, the percentage energy

dissipated (Ed) by the XPD (as expressed by Eq. (11)) isalso noted. The relative displacements and the absolute

accelerations of the piping system are crucial from a design

point of view of the XPD and the piping system and the

reactions at the support are directly proportional to the

forces exerted on the piping system. In contrast, the

percentage energy dissipated reflects the effectiveness of the

XPD for seismic control of the piping system.

In Table 2, the peak response quantities of the piping

system with and without an XPD are compared under all

ground motions. The results are tabulated for an XPD of

size a and b 60 mm and for four different thicknesses of

the XPD (i.e. 25 mm). The percentage energy dissipated in

the piping system is also compared for the XPD of various

thicknesses. Reduction in the peak responses of the piping

system is noted under all ground motions for higher

thicknesses of the XPD. However, only in the case of the

Northridge earthquake is the response of the piping system

with a 2 mm thick XPD marginally increased. This is

because of the typical frequency contents of the Northridge

earthquake motion.

The time variation of the relative displacement, absolute

acceleration at the XPD location and the support reaction

at the end support of the controlled piping system under

the Northridge earthquake are shown in Fig. 3 for

t 2 mm and 4 mm along with the corresponding

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Table 1

Peak ground acceleration of various ground motions

Earthquake Recording station Component Peak ground

acceleration (g)

Imperial Valley, 1940 El-Centro N00E 0.348

Northridge, 1994 Sylmar Converter

Station

N00E 0.843

Loma Prieta, 1989 Loas Gatos

Presentation Center

N00E 0.57

Kobe, 1995 JMA N90E 0.629



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responses of the uncontrolled piping system. It is evident

from Fig. 3 that there is a significant reduction in the

displacements, accelerations and reactions for the piping

system with an XPD. This implies that XPDs are effective

in reducing the seismic response of the piping system.

Moreover, the forcedeformation hysteresis and the time

variation of the hysteretic energy of the XPD are shown in

Figs. 4 and 5, respectively, under various earthquakes. It is

noted from Figs. 4 and 5 that XPDs are very effective in

dissipating large amounts of the input seismic energy being

transferred to the piping systems under all ground motions.

The hysteretic energy decreases with increase in thickness

of the XPD. Thus, the hysteretic energy decreases as the

piping system becomes rigid.

To study the effect of the properties of the XPD (i.e. a, b

and t) on the seismic response of the piping system, the

controlled piping system is analyzed by varying the

properties of the XPD, in the practical range of its sizes

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Fig. 3. Time variation of displacement, acceleration and support reaction of the piping system under the 1994 Northridge earthquake (for a 30mm and

b 80mm).

Table 2

Peak response quantities for piping system without and with X-plate damper under various ground motions (for a 60mm and b 60mm)

Piping system Imperial Valley, 1940 Northridge, 1994 Loma Prieta, 1989 Kobe, 1995

xp (mm) Rx (kN) Ed (%) xp (mm) Rx (kN) Ed (%) xp (mm) Rx (kN) Ed (%) xp (mm) Rx (kN) Ed (%)

Without damper 11.397 1.561 13.813 2.255 15.663 2.246 24.47 3.509

With X-plate damper, t 2 mm 10.019 1.362 42.76 13.983 2.274 43.48 14.9 2.167 40.6 21.517 3.16 39.78With X-plate damper, t 3 mm 9.189 1.275 70.59 11.744 1.91 71.19 13.327 1.96 67.02 16.321 2.562 71.51

With X-plate damper, t 4 mm 6.306 0.918 77.39 11.046 1.754 82.93 12.746 1.915 77.39 13.16 2.191 84.52

With X-plate damper, t 5 mm 3.912 0.631 86.52 7.913 1.193 87.28 12.17 1.853 79.69 7.596 1.417 89.67



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Fig. 4. Hysteresis loops of the XPD for the piping system under various real-earthquake ground motions.

Fig. 5. Time variation of the hysteretic energy for various thicknesses of the XPDs for the piping system under various real-earthquake ground motions.



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Fig. 6. Effect of a, for various thicknesses of the XPDs, on the seismic responses of the piping system under various real-earthquake ground motions.

Fig. 7. Effect of b, for various thicknesses of the XPDs, on the seismic responses of the piping system under various real-earthquake ground motions.



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for different thicknesses (t) of the XPD (ranging from 2 to

5 mm). For each of the above combinations, the controlled

piping system is analyzed under all ground motions and the

peak response quantities are plotted against the properties

of the XPD, a and b, respectively in Figs. 6 and 7. It is

noted that the seismic response of the piping system is

significantly affected by changes in the properties of the

XPD. The responses of the piping system are reducing for a

particular range of lower values of a and remains

unaffected for further increase in the values of a. Similarly,

the responses of the piping system are reducing for a

particular range of b and remains unaffected for further

increase in the value of b. Moreover, the responses are

reducing with increase in the thickness of the XPD. This is

expected because increasing the thickness of the XPD

makes the piping system more rigid thereby reducing the

response values.

Fig. 8 shows variation of the displacement response of

the piping system against both a and b under various

earthquakes. The displacement responses are more sensi-

tive to a than b with reduction in the responses observed at

lower values of a and higher values of b. Moreover, the

responses are unaffected with no further reduction in the

response values for higher values of a and lower values of

b. Thus, it can be predicted that further reduction in a leads

to impractical values and increase in b is of no use as the

responses are very little sensitive to b. Moreover, it can also

be predicted that further variation in the XPD properties

will not lead to any optimal combination of the XPD

properties that will result in the minimum responses of the

controlled piping system implying that this criterion of the

response reduction of the piping system is not valid to

numerically obtain the optimum properties of XPDs that

yield the minimum response quantities.

Hysteretic energy dissipated by any nonlinear system can

be effectively used as a criterion to obtain the optimal

properties of the nonlinear system. In the present problem,

the optimality criterion can be based upon the hysteretic

energy dissipated by the XPD. For each combination of the

XPD properties, the input energy and the corresponding

hysteretic energy is obtained and the total energy dissipated

by the XPD (Ed, as expressed by Eq. (11)) is plotted in

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Fig. 8. Variation of the displacements of the piping system against properties of the XPD (a and b) for t 2 mm for the piping system under various real-

earthquake ground motions.



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Figs. 9 and 10 against a and b, respectively. The dissipated

energy is plotted for four thicknesses of the XPD. It is

noted that the hysteretic energy is significantly affected by

changes in the damper properties, a and b. Unlike the

variation of the responses of the piping system, the plot of

energy dissipated shows a particular combination of the

properties of the XPD for which the percentage energy

dissipated is a maximum. It is observed that for each of the

thicknesses of the XPD, the plot of percentage energy

dissipation against a (Fig. 9) shows a particular value of a

for which the maximum percentage energy dissipation in

the controlled piping system is obtained. Similarly, the plot

of percentage energy dissipation against b (Fig. 10) shows a

particular value of b for which the maximum percentage

energy dissipation is observed. The present piping system

has a static stiffness of 388198kN/m at the damper

location. For this piping system under the Imperial Valley

earthquake, Fig. 9 shows maximum energy dissipation of

84.05% for an XPD of size a 30 mm and b 60 mm (i.e.

having properties Kd 2488 kN/m, Fy 1.173 kN and

a 0.0258). This implies that there exists a combination of

the properties of XPD, which results in maximum energy

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Fig. 9. Effect of a on the hysteretic energy for various thicknesses of the XPDs for the piping system under various real-earthquake ground motions.



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dissipation in the controlled piping system. Moreover, it is

observed that the energy dissipation in the piping system is

more sensitive to the variation in a than b.

Fig. 11 shows the plot of percentage energy dissipated in

the controlled piping system against the properties of the

XPD. It is confirmed from Fig. 11 that there exists a certain

combination of the properties of the XPD for which the

maximum energy dissipation is obtained. However, it is to

be noted here that the optimal combination of the

properties of XPD obtained is not the global optimal

solution and varies with respect to the given piping layout.

Thus, there exist different solutions dependent on the type,

layout and the earthquake excitation used for analyzing the

piping system.

Application of XPDs in a piping system increases the

stiffness of the entire system depending on the number of

XPDs used. Though the stiffness of an individual XPD

may be small compared to the stiffness of the piping

system, it affects the free vibration characteristics of the

piping system. Moreover, using a large number of XPDs in

a piping system will significantly affect the free vibration

characteristics of the piping system. Therefore, to study the

effect of the properties of the XPD on the free vibration

characteristics of the piping system, the fundamental

ARTICLE IN PRESS

Fig. 10. Effect of b on the hysteretic energy for various thicknesses of the XPDs for the piping system under various real-earthquake ground motions.



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frequency of the piping system is plotted in Fig. 12 against

the damper properties, a and b. The frequencies are plotted

for two sizes of XPD and for four thicknesses. It is observed

that the frequency of the piping system is notably affected

by change in b and is very sensitive to a, where significant

reduction in the frequency is noted with increase in a. This is

expected as increasing a makes the piping system more

flexible and reduces the natural frequency whereas increase

in the thickness of the XPD makes the piping system rigid

thereby increasing the natural frequency. The effect ofa and

b on the natural frequency of the piping system is crucial as

it may bring the system into the zone of high acceleration

amplitudes of the input ground motions, consequently

attracting more earthquake forces.

8. Conclusions

A numerical study is presented in this paper that

investigates the seismic effectiveness of the X-plate damper

(XPD) for piping systems in industrial installations. The

seismic responses of a spatial piping system are then

studied under important parametric variation of the

damper properties under real earthquake ground motions

to obtain the optimum properties of the XPD. The damper

properties considered are height, width and thickness of the

XPD. The effect of damper parameters on the response

quantities of the piping system is studied for damper width

and height in the practical range of 20100 mm for four

different thicknesses of the XPD in the range of 25 mm.

However, it is observed that the criterion to obtain minimal

response quantities with variation in the damper properties

does not yield any optimal solution. Therefore, the role of

the hysteretic energy dissipated by the XPD is also studied

by using the percentage energy dissipation in the piping

system as a criterion to decide the optimal combination of

the properties of the XPD. The effect of the damper

properties on the natural frequency of the piping system is

also investigated. Based on the trends of the results, the

following conclusions are drawn.

(1) XPDs are very effective in reducing the seismic

response of piping systems.

(2) The effectiveness of the XPD increases as the percen-

tage energy dissipated by the XPD increases, implying

ARTICLE IN PRESS

Fig. 11. Variation of the hysteretic energy in the XPD against properties of the XPD (a and b) for the piping system under various real-earthquake ground

motions.



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that the dissipated energy controls the effectiveness of

the XPD in the controlled piping system.

(3) There exist optimal combinations of the properties ofan XPD for which maximum energy is dissipated by the

XPD in the controlled piping system. The energy

dissipated in the piping system is dependent on the

thickness of the XPD and the input ground motion.

(4) The percentage energy dissipated by the XPD in the

controlled piping system is higher for XPDs having

lower values of a (half the height of the XPD), and

higher values of b (width of the XPD).

(5) The natural frequency of the system based on the initial

stiffness of the XPD is significantly affected by changes

in a and b. Moreover, it is observed to be very sensitive

to a. The frequency of the piping system significantlyreduces with increase in a, as the piping system becomes

more flexible and increases with increase in the

thickness of the XPD.

References

[1] Olson DE, Tang YK. Decreasing snubber inservice inspection costs

through snubber reduction and improved test limits. Nucl Eng Des

1988;107(12):18399.

[2] Cloud RL, Anderson PH, Leung JS. Seismic stops vs. snubbers, a

reliable alternative. Nucl Eng Des 1988;130(3):41133.

[3] Jonczyk J, Gruner P. Loads of piping systems due to malfunctions of

snubbers. Nucl Eng Des 1991;107(1-2):20513.

[4] Kunieda M, Chiba T, Kobayashi H. Positive use of damping devices

for piping systemssome experiences and new proposals. Nucl Eng

Des 1987;104(2):10720.[5] Shimuzu N, Suzuki K, Watanabe T, Ogawa N, Kobayashi H. Large

scale shaking table test on modal responses of 3D piping system with

friction support. Seismic Eng ASME PVP 1996;340:26975.

[6] Kelly JM, Skinner RI, Heine AJ. Mechanisms of energy absorption

in special devices for use in earthquake resistant structures. Bull NZ

Soc Earthquake Eng 1972;5(3):6388.

[7] Skinner RJ, Kelly JM, Heine AJ. Hysteresis dampers for earthquake-

resistant structures. Earthquake Eng Struct Dyn 1975;5(3):28796.

[8] Tyler RG. Tapered steel energy dissipators for earthquake resistant

structures. Bull NZ Nat Soc Earthquake Eng 1978;11(4):28294.

[9] Kelly JM. The design of steel energy-absorbing restrainers and their

incorporation into nuclear power plants for enhanced safety, vol. 2;

development and testing of restrainers for nuclear piping systems.

Report no. UCB/EERC 80/21, Earthquake Engineering Research

Center, University of California, Berkeley, California, 1980.[10] Schneider SS, Lee HM, Godden WG. Piping seismic test with energy

absorbing devices. EPRI NP-2902, Electric Power Research Institute,

1983.

[11] Bergman DM, Goel SC. Evaluation of cyclic testing of steel-plate

devices for added damping and stiffness. Report no. UMCE 87-10,

University of Michigan, Ann Harbor, MI, 1987.

[12] Chiba T, Kobayashi H, Aida S. Application of elasto-plastic dampers

to piping systems. Seismic Eng ASME PVP 1988;133:1016.

[13] Namita Y, Yoshinga T, Shibata H, Kunieda M, Hara F, Suzuki K, et

al. Development of the energy absorber and its application to piping

systems in nuclear power plant. Seismic Eng ASME PVP 1991;211 p. 51.

[14] Shibata H, Kunieda M, Hara F, Suzuki K, Ichihashi I, Fukuda T, et

al. Development of the elasto-plastic damper as a seismic support for

piping systems in nuclear power plants. Seismic Eng. ASME PVP

1991;211 p. 63.

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Fig. 12. Effect of the properties of the XPD (a, b and t) on the natural frequency of the piping system.



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[15] Whittaker AS, Bertero VV, Thompson CL, Alonso LJ. Seismic

testing of steel plate energy dissipation devices. Earthquake Spectra

1991;7(4):563604.

[16] Aiken AD, Nims DK, Whittakar AS, Kelly JM. Testing of passive

energy dissipation systems. Earthquake Spectra 1993;9(3):33570.

[17] Namita Y, Yoshinga T, Shibata H, Kunieda M, Hara F, Suzuki K, et

al. Development of energy absorber and its application to piping

system in nuclear power plants. J Press Vessel Piping Div ASME1997;211:517.

[18] Parulekar YM, Reddy GR, Vaze KK, Kushwaha HS. Elasto-plastic

damper for passive control of seismic response of piping systems.

BARC Internal Report no. BARC/2003/E/028, Reactor Safety

Division, BARC, Mumbai, 2003.

[19] Bakre SV, Jangid RS. Simplified seismic analysis of piping systems

with energy dissipating devices. Project no. 2002/36/7-BRNS/469,

Indian Institute of Technology, Bombay, 2004.

[20] Wen YK. Methods of random vibration for inelastic structures. ApplMech Rev ASME 1989;42(2):3952.

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Optimum X-Plate Dampers for Seismic Response Control of Piping System