Numerical characteristics of peer-to-peer (P2P) internet online hybrid test system and its...

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2008; 37:265–282Published online 19 September 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.755

Numerical characteristics of peer-to-peer (P2P) internet onlinehybrid test system and its application to seismic simulation

of SRC structure

Tao Wang1,∗,†,‡, Nobuya Yoshitake2,§ , Peng Pan3,¶ , Tae-Hyung Lee4,¶

and Masayoshi Nakashima5,‖

1Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan2Graduate School of Engineering, Disaster Prevention Research Institute, Kyoto University, Gokasho,

Uji, Kyoto 611-0011, Japan3Department of Civil Engineering, Tsinghua University, Beijing, 100084, China4Department of Civil Engineering, Konkuk University, Seoul 143-701, Korea

5Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan

SUMMARY

The peer-to-peer (P2P) Internet online hybrid test system has been developed for the seismic simulation of astructure. In this study, the stability and accuracy of the system are investigated analytically by studying thespectral radius of the recursive matrix of the test scheme featuring a two-round quasi-Newton test scheme.The applicability of the system is further examined by exploring the seismic responses of a complexstructure, a steel-encased reinforced concrete (SRC) structure with a steel tower on the top. The structureis divided into two numerical substructures and one tested part for hybrid test. The numerical substructuresare simulated by sophisticated finite element method (FEM) models with material nonlinearities to capturelocal plastifications. Two types of FEM programs, namely OpenSEES and ABAQUS, which are suitable forthe SRC part and the steel tower, respectively, are employed. The results demonstrate that the P2P systemis able to simulate complex structures with significant nonlinearities. As compared with the previous studyin which two elastic numerical substructures were considered, increase in the number of iterations in thisstudy is not significant, because the associated nonlinearities are limited due to the small time intervaladopted in the test. Copyright q 2007 John Wiley & Sons, Ltd.

Received 8 April 2007; Revised 14 July 2007; Accepted 24 July 2007

KEY WORDS: P2P Internet online hybrid test; stability; finite element method; steel-encased reinforcedconcrete (SRC); quasi-static loading

∗Correspondence to: T. Wang, Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji, Kyoto611-0011, Japan.

†E-mail: [email protected]‡JSPS Postdoctoral Fellow.§Graduate Student.¶Assistant professor.‖Professor.

Copyright q 2007 John Wiley & Sons, Ltd.

266 T. WANG ET AL.

1. INTRODUCTION

The online hybrid test [1–4] (also called the pseudo-dynamic test) is one of the most effective waysto explore the seismic behavior of a structure. It solves the equations of motion in a computer byusing the restoring forces obtained from an associated quasi-static test. When the substructuringtechnique is adopted, the online hybrid test, commonly referred to as the substructural online hybridtest [5–13], is capable of handling large-scale structures. The substructures can be distributedto geographically different locations connected via Internet [11–13], which greatly expands thecapacity of the online hybrid test.

The recently developed peer-to-peer (P2P) Internet online hybrid test system [14] is one of themost appealing substructural online hybrid test systems. The unique feature of the P2P system isthat the equations of motion are not formulated for the entire structure, but for each substructureindependently. The ‘Coordinator’ program equipped with a two-round quasi-Newton test scheme isdevised to maintain the equilibrium and compatibility at the boundaries between the substructures.Pan et al. [14] provided the theoretical basis of the P2P system, in which the test scheme wasproved effective when applied to a base-isolated structure.

This paper is a continuation of the previous paper [14], further exploring the effectiveness ofthe proposed P2P system. Two topics are presented in this paper. One is the stability and accuracycharacteristics of the P2P system, particularly those associated with the linear stiffness assumptionadopted for the tested substructure to avoid iteration. Although the application was successful inthe previous paper, these characteristics were not fully examined. To this end, the two-round quasi-Newton test scheme is recast into a recursive matrix form for an equivalent linear single degreeof freedom (SDOF) undamped model, and the stability and accuracy conditions are obtained byexamining the spectral radius of the matrix.

The second topic is an application of the P2P system for the simulation of a complex structuresystem. In the previous paper, the numerical substructures had a small number of degree offreedoms (DOFs), and were assumed to behave linearly. Examined in this paper is a steel-encasedreinforced concrete (SRC) structure with a steel tower on the top. The weakest story of the toweris taken as the tested portion, while the remaining parts, i.e. the SRC frame and the upper part oftower, are discretized with many DOFs and numerically analyzed by two different FEM models.

2. STABILITY AND ACCURACY OF P2P INTERNET ONLINE HYBRID TEST SYSTEM

2.1. Outline of P2P system

The theoretical basis and detailed implementation of the P2P system can be found in Reference[14]. Described here is the outline of the system design and the test scheme.

In the P2P system, the simulated structure is divided into multiple substructures, with theequations of motion formulated for each substructure, but not for the entire structure. There-fore, the dynamics of substructures are treated independently. A ‘Coordinator’ program is de-vised to enforce the substructures to behave unitarily. It is essentially a trial-and-error procedureto find the compatible displacements that minimize the imbalanced forces at the boundaries.The quasi-Newton method is adopted to find the compatible displacement systematically. A testscheme featuring a two-round quasi-Newton procedure is devised to avoid iteration for the testedsubstructures.

Copyright q 2007 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2008; 37:265–282DOI: 10.1002/eqe

NUMERICAL CHARACTERISTICS OF P2P INTERNET ONLINE HYBRID TEST SYSTEM 267

~ ~dn+1 dn+1 dn+1

Fn

Fn+1

F

K0(k0,m,c)

KI(kI,m,c)

d*dn(dn,dn) *

3. Correction

Error

Imbalanced forceKI

1. Prediction

2. Loading.

Figure 1. Error introduced by the test scheme featuring two-round quasi-Newton procedure [14].

The test scheme is a predicting–correcting method, each corresponding to one round of thequasi-Newton procedure. During the predicting and correcting procedures, the restoring force ofthe tested substructure is always obtained numerically. Physical loading is conducted only oncebetween the predicting and correcting procedures. For the numerical substructures, the actualstiffness can be used, but for the tested substructures use of the actual stiffness is not practical,because of the limited resolutions in the measurement. Therefore, an assumed stiffness, kI, isadopted instead. The initial stiffness is commonly adopted as the assumed stiffness. This treatmentintroduces a force error. This will be explained for a linear tested substructure having a stiffnessof k0. The dynamics of the tested substructure is recast into an effective static form [15] andis illustrated as in Figure 1. Definitions of all variables are listed in Nomenclature. Supposethat all previous n steps are exactly simulated. In the beginning of the (n + 1)th step, kI isused to calculate the predicting displacement dn+1. This predicting path is plotted as the thicksolid arrow in Figure 1. The tested substructure is then loaded from dn to dn+1 with respect tothe actual effective stiffness k0 (the dashed arrow as shown in Figure 1). At the displacementof dn+1, a force imbalance is present. To compensate for the imbalanced force, the correctingprocedure, indicated by the dotted arrow, is implemented. Note that the corrected displacement,dn+1, may not be the same as the exact displacement, d∗

n+1. The error is introduced due to thedifference between kI and k0. This infers that the assumed stiffness, kI, had better not be too muchdifferent from the actual stiffness, k0. Quantification of this error is explored in the followingsections.

2.2. Recursive matrix of two-round quasi-Newton test scheme

Stability and accuracy characteristics of the proposed P2P test scheme are examined in termsof the error introduced by the linear assumption adopted for the tested substructures. All othererrors, such as the controlling and measuring errors and other noises, are ignored. To focuson this error, the model with a single tested substructure is adopted. The tested substructurecontains only one DOF and this DOF is treated as the boundary, with the absence of the adja-cent numerical substructures. Viscous damping is not considered. With this treatment, the errorcharacteristics associated with the linear assumption can be singled out. In the following deriva-tion, the ratio of the initial stiffness kI to the actual stiffness k0 is denoted as �, i.e. � = kI/k0.Note that �>1 corresponds to the case when the structure exhibits hysteresis of a softeningtype.


268 T. WANG ET AL.

F

Ln

Ln+1UnbFn+1

~ ~

Path experienced in P2P system

Cn

Loading path of tested substructure

dn+1

Pn+1 Cn+1

ddn dndn+1

Fn+1

Fn

K0(k0,m,c)

KI(kI,m,c)

Figure 2. Restoring force vs displacement in two-round quasi-Newton test scheme.

Suppose that the equilibrium at the end of the nth step has already been achieved at pointCn , as shown in Figure 2. In the (n + 1)th step, the predicted displacement dn+1 is calculatedby solving the equation of motion using the initial stiffness kI, and the balanced point is de-noted as Pn+1. The predicting procedure adopts the averaged acceleration algorithm [15] and isexpressed as

man+1 + rn + kI(dn+1 − dn) = fn+1 (1)

dn+1 = dn + �tvn + 14 (an + an+1)�t

2 (2)

vn+1 = vn + 12 (an + an+1)�t (3)

rn = k0dn + kI(dn − dn) (4)

where the displacement dn represents the predicted displacement in the nth step.Then, the system is loaded from the previous predicted displacement dn to the current predicted

displacement dn+1, correspondingly from point Ln to point Ln+1, shown in Figure 2, which resultsin an imbalanced force of UnbFn+1, represented by the vertical arrow from point Pn+1 to pointLn+1. Then, the correcting procedure is implemented using the initial stiffness kI once again, andthe balanced point Cn+1 is achieved. The equation of motion is solved again using the averagedacceleration algorithm, as expressed as

man+1 + rn+1 = fn+1 (5)

dn+1 = dn + �tvn + 14 (an + an+1)�t

2 (6)

vn+1 = vn + 12 (an + an+1)�t (7)

rn+1 = k0dn+1 + kI(dn+1 − dn+1) (8)

Equations (1)–(8) can be recast into the following recursive matrix form:

Xn+1 = AXn + Ln+1 (9)



A =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

4(4 + (2� − 1)�2)

(4 + ��2)2

4�t (4 + (2� − 1)�2)

(4 + ��2)2

�t2(4 + (2� − 1)�2)

(4 + ��2)2

(� − 1)2�4

(4 + ��2)2

−2�2(4 + �2�2)

�t (4 + ��2)21 − 2�2(4 + �2�2)

(4 + ��2)2

�t

2− �t�2(4 + �2�2)

2(4 + ��2)2

2(� − 1)2�4

�t (4 + ��2)2

−4�2(4 + �2�2)

�t2(4 + ��2)2−4�2(4 + �2�2)

�t (4 + ��2)2−�2(4 + �2�2)

(4 + ��2)2

4(� − 1)2�4

�t2(4 + ��2)2

4

4 + ��2

4�t

4 + ��2

4�t2

4 + ��2

(� − 1)�2

4 + ��2

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(10)

Xn =

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

dn

vn

an

dn

⎫⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎭

, Ln+1 =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4 + (2�−1)�2)�t2

(4 + ��2)2

2(4 + (2�−1)�2)�t

(4 + ��2)2

4(4 + (2�−1)�2)�t

(4 + ��2)2

�t2

4 + ��2

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

fn+1

m, �= ��t, �=

√k0m

(11)

where � and � are the sampling and circular frequencies of the SDOF system, respectively.

2.3. Stability characteristics

The stability of a time integration algorithm is characterized by whether or not the error intro-duced by the previous steps remains uniformly bounded during the following steps, which canbe represented by the spectral radius �(A) of the amplification matrix A. This is also called thespectral stability criterion [15], described such that ‘the error is bounded for n → ∞ if and only if�(A)�1’. In this study, A has four eigenvalues and is determined by the following characteristicequation, with � as an eigenvalue:

�{(��2 + 4)�3 + [�(1 + �)�4 − 20(� − 1)�2 − 32]�2 + [�(2 − �)�4 + 8(2� − 1)�2 + 16]�

+[�(1 − �)�2 − 4(� − 1)]}= 0 (12)

Figure 3 shows the spectral radii obtained from the above equation. In Figure 3(a), the stiffnessratio � ranges from 1 to 100, and the spectral radius does not exceed unity, suggesting that thestability of the test scheme is ensured when ��1, that is, the test scheme is unconditionally stablefor structures having a force–displacement relationship of a softening type. When � ranges from 0

to 1, it may exceed unity if � is larger than 1.42e12.714�4.486

, as shown in Figure 3(b). This impliesa conditional stability in this range.


270 T. WANG ET AL.

2040

6080

100

02

46

8 100,10 0,10

0.97

0.98

0.99

1

A

2040

60801,1001

24

00.25

0.50.75

10,1

02

46

8 10

0

50

100

150

A

24

(a) (b)

Figure 3. Spectral radii of two-round quasi-Newton test scheme: (a) spectral radius for ��1 and(b) spectral radius for 0��<1.

2.4. Accuracy characteristics

According to Reference [15], the displacement in one step can be written as a linear combinationof the eigenvalues of the amplification matrix A. Among the four eigenvalues of Equation (9), twoare real values, with one of them equal to zero, and the other two are a pair of complex conjugates.Then, dn can be expressed as

dn = exp(−��tn)(c1 cos�tn + c2 sin�tn) + c3�n3 (13)

where

�1,2 = A±Bi= exp[�(−�±i)]�3 is a real value, and �4 = 0

� = �/�t

� = − ln(A2 + B2)/(2�)

� = arctan(B/A)

� = T − T

T= � − �

�= � − �

�

� is defined as the numerical dissipation, � is the period distortion, � is the numerical circularfrequency, and � is the numerical sampling frequency.

Three numerical cases, Cases 1–3 with � = 1, 16, and 100, respectively, are taken as examples.Unconditional stability is ensured for all cases. The numerical characteristics of Case 1 with � = 1are actually identical to those of the averaged acceleration algorithm. To show the acceptableaccuracy of the proposed P2P system, the period distortions of the three cases are compared andplotted in Figure 4. It is observed from Figure 4 that the P2P system is accurate at small samplingfrequencies (when �

√� = 0.6, the period distortion � = 3%, −0.3%, and 2% for � = 1, 16, and

100, respectively) and still commensurate in accuracy with the averaged acceleration algorithm for



-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10

=100

=16

=1

Per

iod

dist

ortio

n

=1

Figure 4. Comparison of period distortion for three cases.

larger sampling frequencies (for example, when �√

� = 4, the period distortion � = 80%, −50%,and −80% for � = 1, 16, and 100, respectively).

3. SEISMIC SIMULATION OF AN SRC STRUCTURE USING THE P2P INTERNETONLINE HYBRID TEST SYSTEM

The P2P system is applied to investigate the earthquake response of an SRC structure with a steeltower built on the top. Under a severe earthquake, both the SRC part and the steel tower maysustain great plastification. To simulate such a situation, nonlinearities are included in the numericalsubstructure models. Sophisticated FEM models, having hundreds of DOFs, are developed tocapture local plastification. Two FEM programs, OpenSEES [16] and ABAQUS [17], are adoptedfor the SRC part and the steel tower, respectively. Incorporations of these programs are realizedby the repeated use of the restart option equipped in both programs [18].

3.1. Description of the selected structure and its division into substructures

The selected structure, shown as Figure 5, consists of an SRC structure and a braced steel tower.The SRC structure is a seven-story frame with a penthouse. The columns and beams are madeof SRC, and two bays of concrete shear walls provide large horizontal stiffness. This structure isvirtual, but it resembles in dimension a structure actually built in Japan. A typical concrete slabis placed in each story. The SRC frame is relatively stiff with a natural period of about 0.6 s. Thetower is an 11-story steel braced frame. All columns and braces have a circular cross section,and the braces exist only in the first nine stories. All beams are made of H-shaped steel. A thickconcrete slab of 150mm exists only on the second floor to accommodate special facilities. Whenthe base is fixed, the period of the steel tower is 0.7 s.

The weight of this structure is mostly concentrated on the SRC frame, 220MN in this case.The steel tower is relatively light, 5MN in weight. Most of the weights of the tower (3MN) isconcentrated on the first story where special facilities are placed. The stiffness of this story is


272 T. WANG ET AL.

Large Column

Small Column

Brace

Concrete Shear WallSRC Column

SRC Beam

Tower Beam

337.

75m

42.0

5m

24.3m 40.5m

72.9m

8.1m

79.8

m

Figure 5. SRC building with a steel tower.

nearly identical to those of the upper stories. This would naturally cause large deformations inthe first story. Given this condition, it is reasonable to take out the first story of the tower for thephysical test. The remaining two parts, i.e. the SRC frame and the upper part of tower, are analyzedseparately. Two horizontal displacements, one between the upper part and the first story of thetower and the other between the first story of the tower and the SRC frame, are controlled by the‘Coordinator’ program. The boundaries between the substructures were idealized to accommodatethe limitation of the loading facilities.

3.2. Finite element modeling of numerical substructures

Two FEM programs, namely OpenSEES and ABAQUS, are incorporated to simulate the SRCframe and the upper part of the tower, respectively. The use of two separate FEM programs isdeemed unique, intending to make the good use of the strengths of individual programs. Note thatOpenSEES has excellent fiber beam–column elements [19], which are suitable to model the SRCmembers, while ABAQUS is adept at handling geometrical nonlinearities, so that the nonlinearbehavior of the steel tower should be simulated accurately.

Each SRC member, a beam or a column, is modeled by one fiber beam–column element.Five integration points are monitored along the element. It is assumed that the bases of thecolumns are fixed on the ground. The shear wall is simulated by a beam–column element withconcentrated plasticity. A plastic hinge, which is to represent a nonlinear shear force–story driftangle relationship, is inserted at each end of one element. The beam–column element representingthe shear wall’s flexural behavior is placed at the middle point of one span and is connected withthe surrounding frame by rigid beams, as shown in Figure 6(a) [20]. This FEM model has 177elements and 178 DOFs in total.

The upper part of the tower is modeled using ABAQUS, as shown in Figure 6(b). The Euler–Bernoulli beam element is used to represent columns, beams, and braces. Both material andgeometric nonlinearities are considered. An initial imperfection (1/750) is imposed at the midlength of each brace to reproduce buckling. This model has 334 elements and 867 DOFs in total.



Rigid Base Beam

Element for Column

Element for Beam

Rigid Connect BeamElement for Shear Wall

Plastic Hinge

Element for Column

Element for Brace

Imperfection

Element for Beam

(a) (b)

Figure 6. FEM models for numerical substructures: (a) FEM model for an SRC frame and (b) FEM modelfor the upper part of the tower.

For both numerical substructures, the story mass is distributed to each node at the same floorlevel. The averaged acceleration algorithm is adopted with the time interval of 0.01 s for timeintegration.

3.3. Test specimen

The first story of the tower is treated as the tested part. The dynamics of the tested part issimulated numerically as an SDOF model, while the corresponding restoring force is obtainedfrom the associated test. The time interval is set to be 0.01 s to maintain the same pace as thenumerical substructures. The first story of the tower is scaled to one-quarter of the prototype,as shown in Figure 7(a). Although small differences do exist in the configuration between theprototype and specimen, similitude is maintained by proper selection of the force scale ratio.

Shown in Figure 7(b) is the test setup, which includes the reaction frame, two jacks, andthe test specimen. The specimen is securely fastened by high-tension bolts to the base beam at thebottom and to the jacks at the top. The out-of-plane movement of the specimen is restricted at thetop of the specimen where two jacks are attached. The quasi-static loading system, developed bythe writers, is adopted for the test. The details of this system can be found elsewhere [4].

3.4. Load control scheme

The specimen is loaded by adopting an external load control scheme (Figure 8). This is aniterative procedure, using the displacement measured directly from the specimen to allow for extradeformation provided by the flexibility of the reaction frame. In each iteration, the horizontaljack tries to compensate for the difference between the target displacement and the specimendisplacement. If the measured displacement is close to the target displacement within a giventolerance range, loading stops, and the restoring force is sent back to the coordinator. A preliminarytest shows that it takes about five iterations in one step of loading on the average, and the control


274 T. WANG ET AL.

Vertical Jack

Specimen

Horizontal Jack

Reaction Frame

(a)

(b)

Figure 7. Specimen design and installation: (a) scaled specimen (mm) and (b) test setup.

tolerance is nearly 0.05mm, slightly larger than the inherent control tolerance of the jack, i.e.0.04mm.

Because of the control tolerance, the steps having a displacement increment not greater than thecontrol tolerance are jumped over, and the restoring force of these steps is estimated in reference tothe prescribed initial stiffness. This scheme is called ‘virtual loading scheme’. The virtual loadingtolerance is set to be identical to the control tolerance, 0.05mm. Tests described in the next sectionshowed that this virtual loading scheme was not harmful, because the control tolerance was atmost 0.1% of the maximum displacement imposed on the specimen.

3.5. Distributed online hybrid test environment

In this online hybrid test, the substructures, the SRC frame, the first story of the tower, and the upperpart of the tower, are distributed geographically to three locations, namely an office at Katsuracampus of Kyoto University, the structural laboratory at Uji campus of Kyoto University, and anoffice at Uji campus of Kyoto University. The constitution of the distributed system is shown inFigure 9. The experimental substructure is located in the laboratory at Uji campus. The PC forcomputation is used to solve the dynamics of the first story of the tower. The numerical simulation



Get target displacement from Coordinator: DT

Get Jack displacement of current state: DJ

Measure specimen displacement of current state: DS

Measure specimen displacement of loaded state: DS

Calculate loading displacement: DL=DJ+(DT-DS)

Loading

| DT-DS |<Tol.

DS > DT (Overshoot))

No

No

Yes

Yes

Figure 8. External load control scheme.

Base Story of Tower

Hydraulic Pump

Controller

PC for Control

Jack

Jack

Switch Box

Uji LaboratorySubNet: Kuins III

SubNet: Kuins IIIData Logger

Firewall

PC for Proxy

Firewall

PC forCoordinator Simulation of

Super-TowerFirewall

Katsura CampusSubNet: Kuins III

Uji Office

Uji OfficeSubNet: Kuins II

Simulation ofSRC buildingFirewall

Uji OfficeSubNet: Kuins III

PC forComputation

Figure 9. Distributed online hybrid test system.

of the SRC frame is carried out by a computer at the office of Uji campus. The upper part of thetower is simulated numerically at the office of Katsura campus. The ‘Coordinator’ program runson a computer at the office of Uji campus. All computers belong to a network called ‘Kuins III’,but on different subnets that are protected by strict firewalls from each other. A computer, locatedat the office of Uji campus but belonging to another network called ‘Kuins II’, is set outside allfirewalls, and a proxy program, developed to exchange data through strict firewalls, runs on this


276 T. WANG ET AL.

computer. All communications between the substructures and the ‘Coordinator’ are transferred bythe proxy program.

3.6. Results

A fault-normal ground motion recorded by the Japan Meteorological Agency (JMA), Kobe,1995, was adopted and enlarged two times to examine responses involving very large non-linearity. The responses of the first story and the top story of the SRC frame and the towerare shown in Figure 10. These results are compared with those obtained by an FEM analy-sis applied to the overall structure. OpenSEES is adopted to analyze the overall FEM model,because is good at handling composite members. In the overall FEM model, the braces are sim-ulated by ‘truss’ elements with no buckling assumed. This assumption was adopted to avoida numerical difficulty experienced in OpenSEES when both material and geometric nonlineari-ties are significant. On the other hand, buckling behavior of the braces was simulated numeri-cally by ABAQUS or physically by the test in the P2P system. This leads to the difference inthe responses of the tower obtained from the overall FEM model and the P2P test, as shown

-100

-50

0

50

100

0 2 4 6 8 10Time (s)

0 2 4 6 8 10Time (s)

0 2 4 6 8 10

Time (s)

0 2 4 6 8 10

Time (s)

Dis

plac

emen

t (m

m)

-600

-400

-200

0

200

400

600

Dis

plac

emen

t (m

m)

-800

-600

-400

-200

0

200

400

600

Dis

plac

emen

t (m

m)

-1600

-1200

-800

-400

0

400

800

1200

Dis

plac

emen

t (m

m)

Story 1 - Experiment

Story 1 - Numerical prototype

Story 8- Experiment

Story 8 - Numerical prototype

T1 - Experiment

T1 - Numerical prototype

T11 - Experiment

T11 - Numerical prototype

(a) (b)

(c) (d)

Figure 10. Response comparison between test and numerical analysis: (a) first story of SRC frame;(b) top story of SRC frame; (c) first story of tower; and (d) top story of tower.



-6000

-4000

-2000

0

2000

4000

6000

-300 -200 -100 0 100 200

Res

torin

g F

orce

(kN

)

-6000

-4000

-2000

0

2000

4000

6000

Res

torin

g F

orce

(kN

)

Displacement (mm)-300 -200 -100 0 100 200

Displacement (mm)

ExperimentOpen SEES Model Experiment

ABAQUS Model

(a) (b)

Figure 11. Comparisons of hysteretic behavior: (a) hysteretic behavior from test and openSEES overallmodel and (b) hysteretic behavior from test and ABAQUS model.

in Figure 10(c) and (d). The response of the SRC frame in the overall FEM model and the P2P testis very close to each other, as shown in Figure 10(a) and (b). For example, the difference betweenthe peak values for the first and eighth stories is not greater than 0.5%. The results obtained areclose because the SRC frame models are identical between the overall model and the P2P test, andthe tower weighs so little compared with the SRC frame that the difference in the tower modelhas a minimal effect on the response of the SRC frame.

Comparison of the hysteretic behavior of the first story of the tower between the overall FEMmodel and the P2P test indicates that buckling and post-buckling strength reductions are not presentin the overall FEM model, while significant unstable behavior is notable in the P2P test, as shownin the rectangle of Figure 11(a). An FEM model is also constructed for the first story of the towerusing ABAQUS, and the loading history obtained from the P2P test is applied statically to thismodel. The hysteretic curve obtained from the ABAQUS model is compared with the P2P testin Figure 11(b). Although the initial stiffness and the buckling strength are well simulated byABAQUS, this is not necessarily true for the post-buckling behavior. As shown in Figure 11(b),the result obtained from ABAQUS simulation seems much stiffer and more dissipative in thepost-buckling range, as compared with the test result. This justifies the adoption of the physicaltest for the first story of the tower. On the contrary, the upper part of the tower has significantlysmaller deformations than the first story as shown in Figure 12, where the maximum story driftangle of each story is plotted. It is reasonable to treat this part using ABAQUS. Note that slightbuckling is observed in the ABAQUS graphical output as shown in Figure 13 where the deformedshape is shown. The numbers listed beside the drawing represent the buckling sequence of thebraces. The top two pairs of braces did not buckle.

To evaluate the effectiveness of the predicting–correcting procedure and the external loadingcontrol, the predicted, loaded, and corrected displacements are compared in Figure 14(a). Themaximum difference between the predicted and corrected displacements is as small as 0.2% ofthe maximum displacement of 70mm. The maximum displacement error is 4.62mm (shown bya circle) and takes place only at the instant of brace buckling. At this instant, the displacementis very difficult to control because of a sharp stiffness change. In other steps, the loading error islimited to a range of 0.05mm. Two relationships, i.e. the jack force vs the specimen displacement


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0 0.02 0.04 0.06 0.08

Story 1Story 2Story 3Story 4Story 5Story 6Story 7Story 8

T1T2T3T4T5T6T7T8T9

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Figure 12. Maximum story drift angle.

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Figure 13. Maximum response of the upper part of the tower and sequence of buckling.

and the corrected force vs the corrected displacement, are compared in Figure 14(b). The steeppeak on the curve of the corrected force (shown by a circle) represents one round of virtual loadingin which the initial stiffness is used for calculation. The difference highlighted by a rectangle inFigure 14(b) corresponds to the control error when buckling occurs, indicating that the externalcontrol was destined to lose precision at that moment.

The entire simulation took 12.4 h. OpenSEES took 7 h (25.2 s/step), ABAQUS took 5.3 h(19.1 s/step), and the physical loading took 4.7 h (16.9 s/step). A long time consumed by both



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Figure 14. Effectiveness of two-round quasi-Newton procedure and external load control: (a) com-parison among predictor, corrector, and loading displacements and (b) comparison between force

from jack and corrected force.

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Figure 15. Efficiency of P2P Internet online hybrid test system: (a) number of iterations of coordinatorin each step and (b) number of load increment in each step.

FEM programs is due to the repeated use of their restart option [18]. In this simulation, theOpenSEES and ABAQUS simulations are processed in parallel, while they have to wait duringthe physical loading. Time efficiency is improved somewhat by this parallel mechanism, andthe simulation time is reduced by 27% [ = (7 + 5.3 + 4.7 − 12.4)/17]. The number of itera-tions of each step is shown in Figure 15(a). On average, one step required about 4.5 iterations:2.6 iterations for the predicting procedure and 1.9 iterations for the correcting procedure. Com-paring this with the previous study [14], where 3.0 iterations in one step were needed on theaverage, the increase in the number of iterations is not significant. It is for this reason that thetime interval is so small that the degree of nonlinearity of each substructure in one step is notsignificant.


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The external control took several load increments in one step to achieve the target displacement.The number of load increments is shown in Figure 15(b). In the beginning, it took 6–10 timesbecause of the limited precision of the measuring devices when controlling small displacements.On average, one step of loading consisted of 3.5 load increments. Observed from this figure, 211steps of actual loading were skipped due to the adoption of the virtual loading scheme.

4. CONCLUSIONS

In this study, the stability and accuracy of the proposed P2P Internet online hybrid test system areinvestigated analytically by studying the spectral radius of the recursive matrix of the test scheme.The applicability of the system is further demonstrated by exploring the seismic responses of anSRC structure with a steel tower on the top. Sophisticated FEM models considering nonlinearitiesare adopted to capture local plastification. Two types of FEM programs, namely OpenSEES andABAQUS, are employed for the SRC frame and the upper part of the tower, respectively. Thissystem was operated reasonably with acceptable time efficiency. The following conclusions canbe drawn from this study:

(1) The convergence of the two-round quasi-Newton test scheme is guaranteed if the referencedstiffness (normally the initial stiffness) is not smaller than the actual stiffness.

(2) The error is introduced by the linear assumption adopted in the test scheme. However, theP2P system is accurate when the integration time interval is small and commensurate inaccuracy with the averaged acceleration algorithm for larger sampling frequencies.

(3) The P2P system is demonstrated to be able to handle numerical substructures having sig-nificant nonlinearities, and also able to accommodate multiple FEM programs, each chosenaccording to the characteristics of the concerned substructure. The use of sophisticated FEMmodels and the selection of FEM program most suitable for a given substructure are able toimprove the simulation accuracy greatly. Nonlinearities of the numerical substructures donot necessarily increase the number of iterations significantly.

(4) The P2P test took 12.5 h because of the iterative procedure employed in this online hybrid testsystem, and the rather time-consuming nature of the restart option of the FEM programs.Partial parallelism of numerical substructures can improve the efficiency of the system(shortened by 27% in this study).

One limitation of the test presented in this study is the boundary simplification. Because of theshortage of loading facilities, the effect of varying axial forces applied to the two columns at thefirst story of the tower was ignored. In this study, only one experimental substructure is included.The applicability of the P2P system to a test involving multiple experimental substructures hasnot been verified. Because the test scheme adopts the linear assumption for the iteration of thetested substructures, handling more experimental substructures may result in larger errors in thestructural response. The applicability of the system to multiple tested substructures is a subject ofthe ongoing research.

NOMENCLATURE

kI assumed stiffness for tested substructures, also called the initial stiffness in the contextk0 actual stiffness of a linear elastic substructure



� stiffness ratio of assumed stiffness to actual stiffness, i.e. � = kI/k0( )n value of the nth simulation step�t time interval used in direct integration algorithmm mass associated with the tested substructurec damping associated with the tested substructurefn+1 excitation forceKI effective stiffness which is a function of mass, damping, and assumed

stiffnessK0 effective stiffness which is a function of mass, damping, and actual stiffnessFn, Fn+1 effective forces which is a function of excitation force and previous state

variablesrn, rn+1 restoring forces of tested substructuresan, an+1 predicted acceleration after the first round quasi-Newton procedurevn, vn+1 predicted velocity after the first round quasi-Newton proceduredn, dn+1 predicted displacements after the first round quasi-Newton procedurean, an+1 corrected acceleration after the second round quasi-Newton procedurevn, vn+1 corrected velocity after the second round quasi-Newton proceduredn, dn+1 corrected displacements after the second round quasi-Newton procedured∗n , d∗

n+1 exact displacement if the actual stiffness is kept following exactlyUnbFn+1 imbalanced force after loading to the predicted displacementPn+1 balanced point by first round quasi-Newton procedureCn,Cn+1 balanced points by the second round quasi-Newton procedureLn+1 imbalanced point representing physical loadingXn,Xn+1 state vector with displacement, velocity, acceleration, and predicted

displacementA amplification matrixLn+1 load operatorT,�, and � natural period, circular frequency, and sampling frequency�i eigenvalues� spectral radiusT , �, and � numerical values for period, circular frequency, and sampling frequency� numerical damping� period distortion

REFERENCES

1. Takanashi K, Udagawa K, Tanaka H. Earthquake response analysis of steel frames by computer-actuator on-linesystem. Proceedings of the 5th Japan Earthquake Engineering Symposium, Tokyo, Japan, November 1978;1321–1328.

2. Mahin SA, Shing PB. Pseudodynamic method for seismic testing. Journal of Structural Engineering (ASCE)1985; 111(7):1482–1501.

3. Shing PB, Nakashima M, Bursi OS. Application of pseudodynamic test method to structural research. EarthquakeSpectra 1996; 12(1):29–56.

4. Nakashima M, Akazawa T, Igarashi H. Pseudo-dynamic testing using conventional testing devices. Journal ofEarthquake Engineering and Structural Dynamics 1995; 24:1409–1422.


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5. Wallace M, Sieber J, Neild S, Wagg D, Krauskopf B. Stability analysis of real-time dynamic substructuringusing delay differential equation models. Journal of Earthquake Engineering and Structural Dynamics 2005;34:1817–1832.

6. Wu B, Xu G, Wang Q, Williams M. Operator-splitting method for real-time substructure testing. Journal ofEarthquake Engineering and Structural Dynamics 2006; 35:293–314.

7. Ghaboussi J, Yun G, Hashash Y. A novel predictor-corrector algorithm for sub-structure pseudo-dynamic testing.Journal of Earthquake Engineering and Structural Dynamics 2006; 35:453–476.

8. Jung RY, Shing PB. Performance evaluation of a real-time pseudodynamic test system. Journal of EarthquakeEngineering and Structural Dynamics 2006; 35:789–810.

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10. Wu B, Wang QY, Shing PB, Ou JP. Equivalent force control method for generalized real-time substructure testingwith implicit integration. Journal of Earthquake Engineering and Structural Dynamics 2007; 36:1127–1149.

11. Yang Y, Wang S, Wang K, Lin M, Weng Y, Cheng W, Chang Y, Tsai K, Lau D, Hsieh S, Lin F, Lin S. Networksystem for a transnational collaborative pseudo-dynamic experiment on a DSCFT-pier bridge system. Proceedingsof 8th U.S. National Conference on Earthquake Engineering, San Francisco, CA, 2006 (DVD-ROM).

12. Pan P, Tada M, Nakashima M. Online hybrid test by Internet linkage of distributed test-analysis domains. Journalof Earthquake Engineering and Structural Dynamics 2005; 34:1407–1425.

13. Takahashi Y, Fenves GL. Software framework for distributed experimental–computational simulation of structuralsystems. Journal of Earthquake Engineering and Structural Dynamics 2006; 35:267–291.

14. Pan P, Tomofuji H, Wang T, Nakashima M, Ohsaki M, Mosalam KM. Development of peer-to-peer (P2P) Internetonline hybrid test system. Journal of Earthquake Engineering and Structural Dynamics 2006; 35:867–890.

15. Belytschko T, Hughes TJR. Computational methods for transient analysis. Computational Methods in Mechanics,vol. 1. Elsevier Science B.V.: Amsterdam, Netherlands, 2001.

16. OpenSees version 1.7 User Manual, Pacific Earthquake Engineering Research Center, University of California,Berkeley, 2006, http://opensees.berkeley.edu.

17. ABAQUS version 6.4 Documentation, ABAQUS, Inc, U.S.A., 2003, http://www.abaqus.com.18. Wang T, Pan P, Nakashima M. On-line hybrid test combining with general-purpose finite element software.

Journal of Earthquake Engineering and Structural Dynamics 2006; 35:1471–1488.19. Taucer FF, Spacone E, Filippou CF. A fiber beam–column element for seismic response analysis of reinforced

concrete structures. Report No. UCB/EERC-91/17. Earthquake Engineering Research Center, University ofCalifornia, Berkeley, 1991.

20. Lee TH, Mosalam KM. Seismic demand sensitivity of reinforced concrete shear-wall building using FOSMmethod. Journal of Earthquake Engineering and Structural Dynamics 2005; 34(14):1719–1736.


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