EUROSTEEL 2011, August 31 - September 2, 2011, Budapest, Hungary

E-SIMULATOR VIRTUAL SHAKING-TABLE TEST
Comparative Study on Elastoplastic Dynamic Responses of Super-Highrise Steel Frame
Between Virtual Shaking-Table Test Using E-Simulator and Beam Element Analysis
Masayuki Kohiyama a, Tomoshi Miyamura b, g, Daigoro Isobe c, Makoto Ohsaki d, Kunizo Onda e,
Muneo Hori f, Hiroshi Akiba e, Koichi Kajiwara g and Tatsuhiko Ine ga

Keio University, Dept. of System Design Engineering, Japan
Nihon University, Dept. of Computer Science, College of Engineering, Japanc
University of Tsukuba, Dept. of Engineering Mechanics and Energy, JapandHiroshima University, Dept. of Architecture, Graduate School of Engineering, JapaneAllied Engineering Corporation, Japanf
The University of Tokyo, Earthquake Research Institute, JapangNational Research Institute for Earth Science and Disaster Prevention, Hyogo Earthquake Engineering Research Center, JapanbINTRODUCTION
The project of the E-Simulator [1] is under way at the Hyogo Earthquake Engineering ResearchCenter of the National Research Institute for Earth Science and Disaster Prevention (E-Defense
NIED), Japan, which facilitates the world’s largest shaking table. The E-Simulator is a parallel
finite element (FE) analysis software package that uses ADVENTURECluster [2] as a platform, andconstitutive laws and laws of fracture of materials have been implemented to analyze civil andbuilding structures.
A virtual shaking-table test of a 31-story high-rise office building is carried out using the ESimulator in order to demonstrate its capability to analyze dynamic response of a large-scale
structural model. The preliminary study using a model with a simplified mesh has been reported by
Ohsaki et al. [3]. In this study, a more detailed model is constructed and we report the comparison
results between the FE-analysis using the E-Simulator and the beam element analysis.
1A VIRTUAL SHAKING-TABLE TEST OF A 31-STORY STEEL BUILDING FRAME

1.1 Analysis model
A virtual shaking-table test of a 31-story high-rise office building is conducted, which has been
designed for this study. The story heights are 5.4 m for the 1st and 2nd stories and 4.1 m for theothers. The total height is 129.7 m, and the size of the plan is 50.4 m × 36.0 m as shown in Fig. 1.
The structural system of the building is a steel moment-resisting frame with a center core, which issurrounded by buckling-restrained braces of hysteretic passive dampers. The slab is allocatedexcept an elevator shaft in the center core.
All the members and floor slabs except the braces are modeled by 8-node hexahedral solidelements; the braces are modeled by truss elements connecting gusset plates. All the plate members,
such as webs and flanges, are discretized into two-layer elements. Regarding a direction
perpendicular to the thickness direction of the plate, the size of elements is about 70 mm near thebeam-to-column connections. Studs connecting a flange and a slab are neglected in the model andelement nodes are shared by the upper face of the flange and the lower face of the slab. The bottomof each column of the 1st story is connected to the elastic base beams, which have the same shape
as beams under the 2nd floor but have the modulus of elasticity 5.5 times as large as those.
The model has 15,592,786 hexahedral solids, 78,686 rigid beams, 372 truss elements, 1,503,130
slave points on stick contact surfaces, 24,765,275 nodes and 74.29 million degrees of freedom. The
steel material of the model has the mass density of 7.86 × 103 kg/m3, the modulus of elasticity of
205 GPa, the Poisson ratio of 0.3, the yield stress of 330 MPa and the hardening ratio of 1/1000 forthe bilinear model with kinematic hardening. For the reinforced concrete slabs, the material is
assumed to be an elastic body with the modulus of elasticity of 22.7 GPa and the Poisson ratio of

0.3. The dead loads due to non-structural components and live loads are considered by increasing
the mass density of the slabs.

(a) Vertical section(b) Floor plan

Fig. 1. Typical vertical section and floor plan
1.2 Result of a virtual shaking-table test
The eigenvalue analysis has been conducted. The natural frequencies up to the 6th mode are 0.3074,0.3484, 0.3822, 0.9688, 1.0518 and 1.1763 Hz. The damping is modeled to be proportional to theinitial stiffness with the damping factor of 2% for the fundamental frequency, i.e. the coefficient to
the initial stiffness matrix is 0.02071. The massively parallel computer T2K in the University ofTokyo, of which CPU is AMD Quad Core Opteron 2.3 GHz, is utilized and 192 cores (24 node × 8core/node) are used in total for the computation.
A 10-second segment of the JR Takatori record of the 1995 Hyogo-ken Nanbu Earthquake that
includes principal strong motion is used as input ground motion (Fig. 2). After the static analysis ofself-weight loading, the EW- and NS-components are applied to the longitudinal (X-axis) and thelateral (Y-axis) directions, respectively, and the UD-component to the vertical (Z-axis) direction.
Considering elastoplastic large deformation, a time-history analysis is carried out to examine
seismic response up to the 10 s. The average elapsed time for one step is 12,312 s when 192 coresof T2K are used. Fig. 3 shows the deformation of (a) the whole building and (b) the stories withlarge stress around the 22nd floor at a time of 4.99 s; the deformation is scaled by a factor of 20 andthe color contour of the equivalent stress is overlaid.
Fig. 4 shows the deformation of (a) the whole building and (b) the stories near the 1st floor at atime of 6.21 s, at which the displacement of the top of the corner column of the 31st story is amaximum. In Fig. 4, the deformation is scaled by a factor of 10 and the colors indicate equivalent
plastic strain. It is observed that the lower parts of the first-story columns are yielding.
Fig. 5 shows the time history of the Z-component of the nodal stress in the center of (a) thenorthward surface and (b) the westward surface at the bottom of the X1-Y6 (the north-west corner,i.e. the upper-left corner in Fig. 1) column on the first story. The average value of the Z-component
stress is positive because of the own weight of the building, but negative values are also observed.
This is possibly due to bending deformation of the column along with the story deformation anddue to the tensile sectional force in the column caused by the overturning motion of the wholebuilding. The time history of the relative displacement responses is shown in the next section.

2Acceleration [cm/s ]1000
EWmax: 657.0500
0-500-1000
012

345Time [s]678910(a) EW-component
1000
2Acceleration [cm/s ]NSmax: 605.5

5000-500-1000
012345Time [s]678910(b) NS-component
2Acceleration [cm/s ]400UDmax: 279.3
2000-200-400012345Time [s]678910(c) UD-component
Fig. 2. Input ground motion(a) The whole building(b) The stories with large stress around the 22nd floor

Fig. 3. Deformation (scaled by a factor of 20) and distribution of equivalent stress at a time of 4.99s

(a) The whole building(b) Stories near the 1st floor

6060

4040
Nodal stress [MPa]Nodal stress [MPa]Fig. 4. Deformation (scaled by a factor of 10) and distribution of equivalent plastic strain at a timeof 6.21 s

200-20-40-60

200-20-40-600246Time [s](a) Northward surface

8100246810Time [s](b) Westward surface

Fig. 5. Time history of the Z-component of the nodal stress in the center of (a) the northwardsurface and (b) the westward surface at the bottom of the north-west-corner column on thefirst story
2BEAM ELEMENT ANALISYS

2.1 ASI-Gauss technique
To compare with the result of the FE-analysis with solid elements using the E-Simulator, the beam
element model is next analyzed. The ASI-Gauss technique [4], which can reduce calculation cost byadaptively shifting numerical integration points based on material property, is employed for aelastoplastic seismic response analysis. The beam element model has 90,648 degrees of freedom.
The elapsed time is 15,358 s for the computation of the 10-second input wave when two cores of a
CPU of Intel Core2 1.86 GHz are used. The material properties of the model are the same asdescribed in Section 1.1. However, undamped vibration is assumed for simplicity.

2.2 Result of an analysis based on ASI-Gauss techniqueFig. 6 depicts the deformation (not scaled) at a time of 5.2 s and the colors show the values of theyield function; the red color indicates yielding. The lower parts of the columns of the core in the 1ststory and braces of truss elements exhibit yielding as observed in the E-Simulator model.
the time history of the relative displacement of the bottom of the corner column (the centroid of thesection) at X1-Y1 (the lower-left corner in Fig. 1) on the 23rd and the 32nd (roof) floors are shownin Fig. 7 and Fig. 8, respectively. The relative displacement of the beam element model is slightly
larger than that of the E-Simulator model. This is likely due to the assumption of undamped
vibration in the beam element analysis. Other possible reasons are model difference in slabs and anerror due to modeling of a plastic region with a plastic hinge.

Fig. 6. Deformation (not scaled) and distribution of the plastic region analyzed by ASI-Gausstechnique
23F(NS)

23F(EW)500
0-500

23F(UD)500

Displacement [mm]Displacement [mm]Displacement [mm]50100010000-500-1000E-Simulator
ASI-Gauss technique-1000
0246Time [s](a) EW-component

8100246Time [s](b) NS-component

8-50-100E-Simulator
ASI-Gauss technique-1500

010E-Simulator
ASI-Gauss technique
0246Time [s](c) UD-component

Fig. 7. Comparison of the time history of relative displacements on the 23rd floor

81032F(NS)

32F(EW)

5000-50032F(UD)500

Displacement [mm]Displacement [mm]Displacement [mm]50100010000-500-1000-1000
02E-Simulator
ASI-Gauss technique
468Time [s]10(a) EW-component

0246Time [s](b) NS-component

8-50-100E-Simulator
ASI-Gauss technique-1500

010E-Simulator
ASI-Gauss technique
0246Time [s]810(c) UD-component

Fig. 8. Comparison of the time history of relative displacements on the 32nd (roof) floor
3CONCLUSIONS

A virtual shaking-table test of a 31-story high-rise office building has been carried out using the ESimulator. The model consists of solid elements and the result of the E-Simulator analysis wascompared with that of the beam element analysis based on the ASI-Gauss technique. Consequently,
the response difference between the E-Simulator models and the beam element possibly arose frommodel differences in damping, slabs and modeling error of plastic hinge of the beam element model.
In the future, it is expected to evaluate the accuracy of a plastic hinge in a macro model based on avirtual experiment using the E-Simulator.
4ACKNOWLEDGMENTS

This study is part of the E-Defense Seismic Experimental Study and Simulation SystemConstruction Project conducted by the E-Simulator Production Committee (Leader: Prof. Muneo
Hori, The University of Tokyo). The authors acknowledge valuable contributions from thecommittee members, and financial support from NIED. The contributions of Mr. Kiyoshi Yuyama
from Allied Engineering Corporation with regard to computation and mesh generation and of Mr.
Yuta Arakaki from the University of Tsukuba with regard to analysis based on the ASI-Gauss
technique are also gratefully acknowledged.
REFERENCES[1] Hori, M, Noguchi, H, Ine, T, “Project report of development of numerical shaking table coping with EDefense”, Journal of Earthquake Engineering (JSCE), Vol. 29, pp. 1420–1425 (in Japanese), 2007.
[2] Allied Engineering Corporation, http://www.alde.co.jp/english/advc/index.html, as of 2011/2/13.
[3] Ohsaki, M, Miyamura, T, Kohiyama, M, Hori, M, Noguchi, H, Akiba, H, Kajiwara, K, Ine, T, “Highprecision finite element analysis of elastoplastic dynamic responses of super-highrise steel frames”,
Earthquake Engineering and Structural Dynamics, Vol. 38, No. 5, pp. 635-654, 2009.
[4] Lynn, KM, Isobe, D, “Finite Element Code for Impact Collapse Problems of Framed Structures”,
International Journal for Numerical Methods in Engineering, Vol. 69, No. 12, pp. 2538-2563, 2007.