an investigation on the accuracy of pushover analysis for...

International Conference on Civil Engineering Architecture & Urban Sustainable Development

27&28 November 2013, Tabriz , Iran

An Investigation on the Accuracy of Pushover

Analysis for Estimating the Seismic Perfarmance of Steel

Plate Shear Walls Subjected to the “TOHOKU Eearthquake”

Babak Behforooz *1* , Parham Memarzadeh1†, Farhad BehnamFar2‡

1. Department of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran 2. Department of Civil Engineering, Isfahan University of Technology, Isfahan, Iran

Abstract AISC-341 provides requirements for designing of SPSWs by means of a capacity-design method in which boundary elements are designed for forces corresponding to the fully yield strength of the web plate. This paper investigates the potentialities of the pushover analysis to estimate the seismic deformation demands of steel plate shear wall (SPSW). Reliability of the pushover analysis has been verified by conducting nonlinear dynamic analysis on 9,6 & 3 story frames subjected to “STRONG MOTION RECORDS FROM THE 2011 OFF THE PACIFIC COAST OF TOHOKU EARTHQUAKE”. The analysis utilizes a finite element method involving both material and geometric nonlinearities. It is shown that pushover analysis with predetermined lateral load pattern provides questionable estimates of interstory drift, lateral displacement and base shear.

Key words: SPSW, TOHOKU EARTHQUAKE, pushover analysis, capacity-design method.

1. INTRODUCTION During the past two decades, major changes are being made in the field of earthquake engineering. Based on conventional elastic methods of seismic design a pseudo-capacity is provided to resist the prescribed lateral force. It is been postulated that the structure is capable to resist the imposed load of earthquake by the means of yielding into the inelastic range, energy absorption and ductile behavior. The significant destructions and massive human and economic losses of engineered buildings during major seismic events such as Northridge, California (1994), Kobe, Japan, (1995) have verified the deficiency of such methods. Since

* M.Sc

† Assistant Professor

‡ Assistant Professor



these approaches did not provide insight of how the structure would actually perform under severe earthquake conditions. Distinguishing the actual performance of the structure through the performance-oriented procedures and guidelines termed as “Performance-Based Design Engineering”, (PBDE) is frequently highlighted in this realm. This new analytic procedure has two major differences with the conventional perspectives on earthquake engineering: first, the direct connection between designs to structural performance; second, a multiple performance. The performance targets may be a level of stress not to be exceeded, a load, a displacement, a limit state or a target damage state. A mathematical tool, which works under tight time constraints, is able to handle all analyses and often exceeds the capabilities of a design office. Investigating for a reliable, less time-consuming method, results in Nonlinear Static Pushover method. The objective of this paper is to evaluate of the accuracy of the conventional push over procedures based on FEMA-356 load patterns for estimating seismic performance of typical SPSW subjected to “STRONG MOTION RECORDS FROM THE 2011 OFF THE PACIFIC COAST OF TOHOKU EARTHQUAKE”. The study subjects of the investigation are three typical 3, 6 and 9 storey SPSW frames designed according to AISC requirements [6].

2. WHY WAS Tohoku Earthquake?

The 2011 earthquake off the Pacific coast of Tohoku often referred to in Japan as also known as the 2011 Tohoku earthquake, the Great East Japan Earthquake, and the 3.11 Earthquake, was a magnitude 9.0 (Mw) undersea mega thrust earthquake off the coast of Japan that occurred at 14:46 JST (05:46 UTC) on 11 March 2011, with the epicenter approximately 70 kilometers (43 mi) east of the Oshika Peninsula of Tohoku and the hypocenter at an underwater depth of approximately 30 km (19 mi). It was the most powerful known earthquake ever to have hit Japan, and the fifth most powerful earthquake in the world since modern record-keeping began in 1900. The earthquake triggered powerful tsunami waves that reached heights of up to 40.5 meters (133 ft) in Miyako in Tohoku's Iwate Prefecture, and which, in the Sendai area, travelled up to 10 km (6 mi) inland. The earthquake moved Honshu (the main island of Japan) 2.4 m (8 ft) east and shifted the Earth on its axis by estimates of between 10 cm (4 in) and 25 cm (10 in). On 12 September 2012, a Japanese National Police Agency report confirmed 15,883 deaths, 6,144 injured, and 2,676 people missing across twenty prefectures, as well as 129,225 buildings totally collapsed, with a further 254,204 buildings 'half collapsed', and another 691,766 buildings partially damaged. The earthquake and tsunami also caused extensive and severe structural damage in north-eastern Japan, including heavy damage to roads and railways as well as fires in many areas, and a dam collapse. Japanese Prime Minister Naoto Kan said, "In the 65 years after the end of World War II, this is the toughest and the most difficult crisis for Japan." Around 4.4 million households in northeastern Japan were left without electricity and 1.5 million without water.



The tsunami caused nuclear accidents, primarily the level 7 meltdowns at three reactors in the Fukushima Daiichi Nuclear Power Plant complex, and the associated evacuation zones affecting hundreds of thousands of residents. Many electrical generators were taken down, and at least three nuclear reactors suffered explosions due to hydrogen gas that had built up within their outer containment buildings after cooling system failure. Residents within a 20 km (12 mi) radius of the Fukushima Daiichi Nuclear Power Plant and a 10 km (6.2 mi) radius of the Fukushima Daini Nuclear Power Plant were evacuated. In addition, the U.S. recommended that its citizens evacuate up to 80 km (50 mi) of the plant. Early estimates placed insured losses from the earthquake alone at US$14.5 to $34.6 billion. The Bank of Japan offered ¥15 trillion (US$183 billion) to the banking system on 14 March in an effort to normalize market conditions. The World Bank's estimated economic cost was US$235 billion, making it the costliest natural disaster in world history[4].

Only a small part of this destructive earthquake is expressed above. Because of this reasons the authors of this paper decided to estimate the effects of this earthquake on the seismic performances of Steel Plate Shear Walls (SPSWs) as a ductile system with a well known lateral stiffness under different analysis, such as Time History Analysis (THA) and Pushover Analysis (PA). For this propose one of the top 5 records (MYG004-NS) of this earthquake selected for THA and PA. These top 5 records were obtained from stations marked in Figure 1. The acceleration of selected record is shown in Figure 2.

Figure 1 – PGA of the 2011 Tohoku M9.0 Earthquake [4]



Figure 2 – Acceleration record at Tsukidate (MYG004-NS) in Kurihara City (Used for THA in this paper) [4]

3. NONLINEAR STATIC PROCEDURES FOR SEISMIC DEMAND ESTIMATION

There are several procedures that could be adopted for conducting a nonlinear static analysis. While the fundamental procedure for the step-by-step analysis is essentially the same, the procedures vary mostly in the form of lateral force distribution applied to the structural model in each step of the analysis [3],[7]. FEMA-356 and similar references recommend the following procedures:

Inverted Triangular Pattern A lateral load pattern represented by the following FEMA-356 equation:

Vhw

hwF

n

xxx

xxX

1

(1)

where, XF is the lateral load at floor level x, xW is the weight at floor level x, xh is the height

from base to floor level x and V is the total lateral load (base shear) to be applied. This load pattern results in an inverted triangular distribution at the height of the building and is normally valid when more than 75% of the mass participates in the fundamental mode of vibration.

Uniform Load Pattern

A uniform load pattern based on the lateral forces that are proportional to the total mass at each floor level is obtained as follows:

‐3

‐2

‐1

0

1

2

3

0 50 100 150 200 250 300

ACCELER

ATION (g)

TIME (SECOND)



Vw

wF

n

nii

xx

(2)

This pattern is expected to simulate the story shears.

4. NONLINEAR STATIC PROCEDURES FOR SEISMIC DEMAND ESTIMATION

The geometry and section properties of the SPSW structures are considered in this study are presented in Fig. 3. These structures are designed according to AISC 341 for the lateral earthquake forces specified by ASCE 7 where equivalent lateral force procedures are applied [10],[2]. The SPSW structures are 3,6 and 9-storey 3-bay frames with infill plates in the second bay's panels. The reduced beam section at both ends of HBE is assumed to have two-thirds of the plastic section modulus of the corresponding HBE. The mechanical properties of the structures are presented in the Table.1 [1],[2].

Table 1: Mechanical properties of typical bi-linear kinematic hardening model

1E 2E ypF ybF

200(GPa) 200(MPa) 0.3 7.8 )/( 3mton 248(MPa) 345(MPa)

Here, E, υ and ρ are the Young's modulus, Poison's ratio and density of steel material, and ypF

and ybF are the plate and boundary member yield stresses, respectively. All beam and column

material properties are the same as the boundary member properties. The beam, column and plate cross sections are presented in Fig.3.

Figure 3. Dimensions and properties of SPSW building [8]



In order to evaluate the validity of the model in ABAQUS program [5], the finite element model of the SPSW structure is subjected to a sinusoidal force at the roof level with a frequency of the first vibration mode for a time interval of 5 seconds. Afterwards SPSW was allowed to vibrate freely. Finding here correspond to that of the (Memarzadeh et al.2011). Some analyses were performed to check the efficiency of the degree of the meshing; where the results confirmed that for the various energy quantities, the shear forces as well as the displacements and accelerations are verified.[8],[9]

5. COMPUTATION OF TARGET DISPLACEMENT IN (PA) METHOD For computing target displacement in PA method, peak deformation Dn of the nth-“mode” of inelastic SDF system defined by the bilinear force-deformation relation of Figure 4 and damping ratio

05.0n ,was computed by nonlinear time history analysis with MYG004-NS record. Bilinear and

real performance curve of 9 storeys SPSW is shown in the figure 4. The fundamental concepts of 6&3 storey PA curves are like 9 storey SPSW.

Figure 4. Bilinear curve of PA for 9 storey SPSW, (a) Inverted Triangular Pattern, (b) Uniform Load Pattern

6. EVALUATION OF CONVENTIONAL PUSHOVER PROCEDURES

The conventional pushover procedures are evaluated by comparing the computed roof drift ratio (maximum roof displacement normalized by building height), inter-story drift ratio (relative drift between two consecutive stories normalized by story height) and story shear values to nonlinear time-history results. The time-history results are based on a MYG004-NS record and both the mean THA and tow estimated load patterns are presented in the plots (Fig5 to 7).

0

500

1000

1500

2000

0 10 20 30

BASE SHEA

R(Kips)

(a) DISPLACEMENT(IN)

0

500

1000

1500

2000

2500

0 10 20 30

BASE SHEA

R(Kips)

(b) DISPLACEMENT(IN)



Figure 5. Evaluation of different seismic parameter in 9 storey SPSW



0

1

2

3

4

5

6

7

8

9

0 10 20 30 40

STOREY

DISPLACEMENT(in)

0

1

2

3

4

5

6

7

8

9

0 1000 2000 3000

STOREY

STOREY SHEAR (Kips)

0

1

2

3

4

5

6

7

8

9

0 2 4 6

STOREY

DIRIFT(%)

THA

UNIFORM LOAD PATERNINVERTED TRIANGULAR

0

1

2

3

4

5

6

0 10 20 30

STOREY

DISPLACEMENT(in)

0

1

2

3

4

5

6

0 2 4 6 8 10

STOREY

Drift(%)

0

1

2

3

4

5

6

0 1000 2000 3000 4000

STOREY

Storey Shear (Kips)

THA

UNIFORM

TRIANGULAR

0

1

2

3

0 10 20 30

STOREY

DISPLACEMENT(in)

0

1

2

3

0 1 2 3 4

storey

Dirift(%)

0

1

2

3

0 500 1000 1500 2000

storey

Storey Shear (kips)

THA

UNIFORM

TRIANGULAR



7. CONCLUSIONS

The following conclusions are obtained from the accuracy assessment of conventional nonlinear static procedures in estimating the seismic demands of SPSW buildings using TOHOKU intense ground motion (MYG004-NS). These conclusions are based on a comparison of PA estimates of seismic demands and the corresponding values determined by THA for 3, 6, and 9-story SPSW buildings, designed to meet seismic code criteria:

(1) The equivalent bilinear SDF systems for 9-story SPSW, determined from nonlinear static procedures can estimate the peak roof displacement quite accurately in comparison with the peak roof displacement from THA method, while this is not applicable for 3 and 6-story SPSW models in intense earthquakes.

(2) The degree of precision of all procedures suggested in estimating the maximum story drift and roof displacement in mid-rise models across all stories is generally low; however, the degree of precision of these procedures in estimating peak story drift at an individual story can be applicable for certain cases. All of the adopted procedures provide similar results in practice; while, the Uniform Load Pattern is slightly simpler and more practical than other load patterns

(4) It is found that, the degree of precision in estimating floor displacements, story drift ratios and story shear of SPSWs estimated with conventional nonlinear static pushover analysis for high-rise model is great.

REFERENCES

[1] American Institute of Steel Construction (AISC) .Seismic provisions for structural steel buildings, Chicago, IL, 2005.

[2] American Society for Civil Engineers (ASCE). Minimum design loads for buildings and other structures (including Supplement No. 1), Reston, VA., 2005.

[3] FEMA 356. Prestandard and Commentary for the Seismic Rehabilitation of Buildings, Federal Emergency Management Agency, Washington, D.C., 2000.

[4] Furumura, T. et al. (2011). “Strong Ground Motions from the 2011 Off the Pacific Coast of Tohoku,Japan (Mw=9.0) Earthquake Obtained from a Dense Nation-wide Seismic Network.” Landslides,Vol. 8, No.3, pp.333-338.

[5] Hibbitt, Karlsson, Sorensen, Inc (HKS). ABAQUS Analysis user's manual (v 6.7), Hibbitt, Karlsson, Sorensen, Inc of Pawtucket, Rhode Island., 2007.

[6] International Conference of Building Officials (ICBO)., California Building Code, Whittier, CA., 2007.

[7] Krawinkler, H., and Seneviratna (1998), G. Pros and cons of a pushover analysis of seismic performance evaluation, Engineering structures, 20 pp 452-464.

[8] Memarzadeh, P., Mirlohi, J., Behnamfar, F (2011),., Seismic response of steel plate shear walls considering soil structure interaction", second European conference of civil engineering (ECCIE'11), Puerto De La Cruz, Tenerife, Spain, pp.107-112.

[9] Memarzadeh, P., Saadatpour, M. M., Azhari, M(2010). Nonlinear Dynamic Response and Ductility Requirements of a Typical Steel Plate Shear Wall Subjected to El Centro Earthquake, Iranian Journal of Science & Technology, Transaction B: Engineering, B4 pp 371-384.

[10] Sabelli, R. & Bruneau, M. Steel plate shear wall, AISC Steel Design Guide 20, USA, 2007.

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