ms04-03 - council on tall buildings and urban habitat · 2015-05-18 · in the romanian seismic...

Title: Seismic Response Analysis of Tall Buildings Under Uncertain Conditions

Authors: Mihail Iancovici, Department of Structural Mechanics, Technical University ofCivil Engineering of BucharestOvidiu Bogdan, Department of Strength of Materials, Technical University ofCivil Engineering of BucharestBogdan Stefanescu, Department of Steel Structures, Technical University ofCivil Engineering of Bucharest

Subject: Structural Engineering

Keywords: SeismicStructure

Publication Date: 2011

Original Publication: CTBUH 2011 Seoul Conference

Paper Type: 1. Book chapter/Part chapter2. Journal paper3. Conference proceeding4. Unpublished conference paper5. Magazine article6. Unpublished

© Council on Tall Buildings and Urban Habitat / Mihail Iancovici; Ovidiu Bogdan; Bogdan Stefanescu

ctbuh.org/papers

http://ctbuh.org/papers

MS04-03

Seismic Response Analysis of Tall Buildings under Uncertain Conditions

Mihail Iancovici1, Ovidiu Bogdan2, Bogdan Stefanescu3

1 Department of Structural Mechanics, Technical University of Civil Engineering of Bucharest, Romania,

[email protected] 2 Department of Strength of Materials, Technical University of Civil Engineering of Bucharest, Romania,

[email protected] 3 Department of Steel Structures, Technical University of Civil Engineering of Bucharest, Romania,

[email protected]

Mihail Iancovici Biography Mihail Iancovici is Civil Engineer, PhD, lecturer for the Structural Analysis, Structural Dynamics and Earthquake Engineering courses at Technical University of Civil Engineering of Bucharest (UTCB). He is team-member in research projects on tall buildings analysis and design for earthquake and wind.

Abstract In the last years, a large number of tall buildings were erected in dense urban and historical areas in Bucharest and the development of actual building stock is undergoing. This drew the attention on the seismic analysis framework applicable to these particular and complex structures and on the potential seismic risk both, intrinsic and incident- to the existent civil infrastructure. Some important medium-rise buildings collapsed 10 November 1940 (Mw=7.6) and 4 March 1977 (Mw=7.4) earthquakes in Bucharest. There is any evidence how highly flexible and complex structures will perform on medium-soft soil conditions in the Bucharest-city under Vrancea earthquakes. Current Romanian seismic design code (EC 8 format) provides two performance levels (Serviceability-IMR=30yr. and Life Safety-IMR=100yr.) and is little to no applicable to tall buildings. While analysis and design procedures in the time-domain are not yet available in a standardized format, current design procedure may lead to highly risk-exposed and cost non-effective structures. It is widely recognized that time-domain approach has the capability to account for (i) uncertainties in the ground motion characterization (peak values, amplitude, frequency content, phase, directivity, duration etc.), (ii) uncertainties in the structural properties (mass, damping, restoring force characteristics, P-Δ effects, the soil-structure interaction and incorporated energy dissipation devices effects etc.) and it is appropriate for a performance-based design framework. The objective of paper is to analyze the distribution of seismic loads and typical response parameters (i.e. drift ratios, shears, bending moments) when the random nature of ground motion and structural properties are considered. Using appropriate time-series of ground acceleration, a large number of sensitivity analyses and parametric studies on tall building models are performed in order to study the applicability of a comprehensive probabilistic approach to tall buildings performance evaluation, thanks to large hardware and software capabilities. We also discuss the applicability of time-domain approach analysis in the practical seismic performance evaluation and design framework. Keywords: tall building, artificial accelerogram, design spectrum, seismic performance

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CTBUH 2011 World Conference October 10-12, 2011, COEX, Seoul, KOREA_____________________________________________________________________________________________________________________________________________________________

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Introduction

A large variety of innovative shapes and complex structural layouts are proposed nowadays. Structural designers have to think technical and cost-effective solutions in order to fulfill the complex architectural needs, the owner demands and provide appropriate structural robustness to multi-hazard sources: wind, earthquake, impact, explosions etc. Standard seismic analysis procedure - based on equivalent static loads, using the response spectrum method approach and inelastic response reduction factors, is little to no applicable to tall buildings design. This may lead to inappropriate performance and highly cost non-effective structures. The limit state seismic design gained much consistency by extending it to the seismic performance concept. Firstly introduced by SEAOC (1995), the concept of seismic performance requires basically (i) a more accurate characterization of local seismic hazard, structural properties and performance states associated to Serviceability, Reparability and Life Safety levels, based on large amount of data and uncertainties modeling, (ii) use of full nonlinear capability analysis methods, and (iii) use of seismic vulnerability and risk analyses tools. While various initiatives (Vision 2000, FEMA series) and later (PEER, LATBSDC), made important conceptual steps forward in implementing a performance-based design format in the current practice, still remains much work to make this generous concept applicable to practice. The performance-based analysis and design is a fertile format ready to incorporate a reliability-based framework, accounting thus for a broad range of uncertainties.

Uncertainties in the seismic design of tall buildings

Due to the random nature of ground motion and structural properties, a performance-based analysis framework should include advanced tools able to accurately grasp a broad range of uncertainties (both, aleatory and epistemic) and finally provide relevant information in probabilistic sense (e.g. reliability index, probability of exceedance of different limit states, failure probability etc.). Design codes assume that the seismic hazard (expressed in terms of PGA associated to a MRI) is constant over a given zone. This would not necessarily produce risk-consistent and cost-effective structures.

From thousands of records obtained after the 1977 earthquake, only a very few number are significant

from structural point-of-view. It is therefore a primary importance to assess on-site the seismic hazard and to

finally provide realistic input motions associated to different performance levels.

As for the structural properties and associated limit states, experimental results on damping for instance, revealed the dependency by vibration frequency and top story drift (Jeary, 1986; Lagomarsino, 1993). Available hysteretic test data (Berry et al., 2004), obtained on 244 reinforced concrete rectangular section columns, having different reinforcement and axial force ratios, revealed (Iancovici, 2005) that the nonlinearity degree controls the distribution of performance points (yield and ultimate displacements, corresponding shear and bending moments and hysteretic energy- generally of Weibull distribution type). Thus, a structural effect in a certain section (deflection, velocity, acceleration, bending moment, shear, axial force, torque etc.) might be expressed as a convolution between seismic hazard and structural properties as

)|,,()( tsmEE e α= (1) where, e is the structural element, m represents the input motion coming from α directivity, s- structural properties- all random variables and t is time variable. Obviously, for all possible situations, the design objective consists of minimizing the effect and quantifies the associated reliability level.

The input ground motion in the response analysis of tall buildings: response spectra vs.

acceleration time-series

In the Romanian seismic design code P100-1/2006 (EC 8 format), a single level of structural

performance is explicitly stated. This addresses the ultimate limit state (Life Safety) and the prescribed peak

ground acceleration is associated to 100 yr. Mean Return Interval (MRI). A draft document under current

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PGA = 0.24 g | Tc = 0.7 s PGA = 0.24g | Tc = 1.0 s PGA = 0.24g | Tc = 1.6 s

PGA = 0.36g | Tc = 0.7 s PGA = 0.36g | Tc = 1.0 s PGA = 0.36g | Tc = 1.6 s

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Frequency,Hz

PSD,

m2 /

s3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Frequency,Hz

PSD,

m2 /s

3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency,Hz

PSD,

m2/s3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Frequency,Hz

PSD,

m2/s

3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

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Frequency,Hz

PSD,

m2/s

3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

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0.8

1

1.2

1.4

1.6

1.8

Frequency,Hz

PSD,

m2/s

3

professional debate proposes local seismic hazard evaluation in conjunction with increase of hazard level,

when tall buildings are to be designed (0.32g for Bucharest, MRI = 475 yr.).

The alternate approach to standard response spectrum method is to use site-dependant acceleration

time-series. Although difficult to implement it straightforward, the evaluation of probabilistic local seismic

hazard becomes more important in the design of complex tall buildings, based on large amount of recorded

data.

Site-dependant time-series can be obtained by various existing techniques: (i) recorded accelerograms,

(ii) simulated accelerograms at various ground levels, (iii) methods based on source properties and

simulation of fault process or using the attenuation relationships of ground motion parameters, (iv) simulated

ground acceleration at free field, compatible with a prescribed time-history envelope, Fourier amplitude

spectrum/power spectrum and (v) artificial accelerograms compatible with an acceleration response

spectrum/design spectrum (Gasparini et. al, 1976). The use of one or another technique may raise obviously

various comments. We choose for our paper objectives, two simulation approaches: (1)-design code spectra-

compatible accelerograms and (2)- scaled accelerograms at subterranean level.

(i) Code spectra-compatible acceleration time-series

Compatible accelerograms with similar frequency content and duration characteristics as the possible real ones, corresponding to various soil conditions and two hazard levels (MRI=100yr. and MRI=475yr.) were obtained, using the procedure proposed by Gasparini et al. (1976).

Figure 1. PSD of simulated ground motion accelerograms A sufficiently large number of time-series were obtained (40 series for each case) of 1% damping ratio design spectrum. The control power spectral density functions are shown in the fig. 1. One can observe that the synthetic signal’s frequency content (ε is the Cartwrigth & Longuet-Higgins, bandwidth indicator) is sensitive both to PGA and Tc.

Table 1. Statistics of synthetic time-series parameters (soft soil conditions only)

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PGA= 0.24g, Tc = 1.6 s

PGA ,m/s/s PGV, m/s PGD,m Tp, s ε

Mean 2.354 0.573 1.070 1.633 0.976

σ 0.000 0.146 0.978 0.190 0.002

CoV 0.000 0.255 0.915 0.116 0.002

PGA= 0.36g, Tc = 1.6 s

PGA ,m/s/s PGV, m/s PGD,m Tp, s ε

Mean 3.532 0.830 1.948 1.139 0.958

σ 0.000 0.136 1.038 0.293 0.002

CoV 0.000 0.164 0.533 0.258 0.002 The stability of ground motion parameters is good, except PGD (table 1). (ii) Scaled accelerograms at subterranean level

Two sets of free-field available records, recorded on the soft-soil conditions were considered:

(i) 5 small-moderate intensity earthquakes (4.8<Mw <6.0 ) occurred at 9/27/2004, 10/27/2004, 5/14/2005, 6/18/2006 and 12/13/2005 (Aldea et. al, 2006), recorded by the National Center for Seismic Risk Reduction (NCSRR) seismic network (10 records), and

(ii) 3 large intensity earthquakes (Mw>7.0) occurred at 3/4/1977, 8/30/1986 and 5/30/1990 recorded by the National Building Research Institute (INCERC) seismic network (6 records).

The initial accelerograms were scaled to MRI’s of 100 yr (0.24g) and 475 yr (0.32g). Both sets were then de-convoluted (Bardet et al., 2000), to the subterranean level (21m). While for the case of large intensity earthquakes, the power content in the small frequency range is considerable, the destructive potential of small intensity scale motions at subterranean level almost vanishes for the interest frequency range (fig.2; Bogdan, 2007).

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PGA = 0.24g (-21m)

PGA = 0.32g (-21m)

Figure 2. Power spectra of accelerograms at subterranean level The power content is significantly larger for 0.32g. For the serviceability range, scaled small intensity motions might be used.

Figure 3. Envelopes of scaled motion power spectra (ground level and subterranean level) Smoothed power spectra can be hence obtained and a sufficiently large number of artificial compatible acceleration time-series can be generated at various subterranean (foundation) level (Vanmarcke et al., 1997).

0

200

400

600

800

1000

1200

1400

1600

0 2 4 6 8

envGL 0.24g SIenvGL 0.32g SIenvGL 0.24g MIenvGL 0.32g MI

Frequency,Hz

Pow

erSp

ectru

m,c

m^2

/s^3

0

200

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600

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1200

0 2 4 6 8

env21m 0.24g SIenv21m 0.32g SIenv21m 0.24g MIenv21m 0.32g MI

Frequency,Hz

Pow

erSp

ectru

m,c

m^2

/s^3

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Time-domain vs. standard approach in the response analysis of tall buildings While the response spectrum method is the basic approach used by practitioners due to simplicity of use and fairly good accuracy for a large class of common structures, the time-history analysis fully accounts for the ground motion features and structural properties, allowing higher accuracy results and use of comprehensive probabilistic analysis tools. We use then largely the “exact” time-domain approach in order to evaluate the applicability of response spectrum method to tall buildings in the linear behavior range (Serviceability range) and to study the sensitivity of time-history response to input ground motion, soil conditions and structural properties variability, at the structural and individual element level. Numerical example 1:

A generic 60 story model consisting of a central core and outer gravity frames is used in the analyses (fig.4). The plan dimensions are Lx=36m, Ly=36m and the total height of 210 m. For the sake of clarity in the analyses, the model is assumed to behave linearly-elastic.

Figure 4. 60 story model and typical floor plan

Due to plan-symmetry, the set of accelerograms of 0.24g and soft soil conditions (Tc = 1.6 s) was applied in the x-direction only. The mean seismic loads distribution from time-history, is underestimated up to 60%-for the lower stories and overestimated up to 33%- for the middle stories (fig.5).

Figure 5. Time-history vs. standard approach: story seismic loads and story drift ratios,

x-direction

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000

Story

Load, kN

SRSS1‐10

mean th

mean+1stdv

0

10

20

30

40

50

60

0 0.5 1 1.5 2 2.5

Story

Drift ratio, %

SRSS16

mean th

mean+1std

CENTRAL CORE

FRAMING SYSTEM

x CSk

CMk

y

z

Lx

Ly

ex,k

ey,k

CENTRAL CORE

FRAMING SYSTEM

STORY k

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The mean drift ratios are severely overestimated as well as mean story shears and bending moments- up to 65% in the lower stories (fig.6).

Figure 6. Story shears and bending moments, x-direction

The statistics of time-history results is presented in table 2.

Table 2. Statistic of peak response parameters from time-history analyses One can observe that the story seismic loads are most stable to input motion but the internal forces are the most variable.

The soil condition has considerable influence on the story seismic loads distribution as well as on the displacement demand (fig.7).

0

10

20

30

40

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60

0 2000 4000 6000 8000

Story

Load, kN

mean 0.7s

mean 1.6s

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Story

Drift ratio, %

mean 0.7s

mean 1.6s

0

10

20

30

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60

0 20000 40000 60000 80000 100000

Story

Shear force, kN

SRSS15

mean th

mean th+1stdv

0

10

20

30

40

50

60

0 2000000 4000000 6000000 8000000

Story

Bending moment,kNm

mean th

SRSS1‐5

mean th+1stdv

Parameter CoVmax Story Story seismic load 0.357 54

Drift ratio 0.556 21 Story shear force 0.766 60

Story bending moment 0.703 60

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Figure 7. Mean of peak story seismic loads, drift ratios and internal forces, x-direction

(40 acc., stiff and soft soil conditions) The story internal forces (shears and bending moments) are little influenced by the ground condition. Numerical example 2: A normal distribution of the Young’s modulus is considered, with small (0.1) variability around the mean of 210 MPa (100 random samples). The model is subjected by a synthetic input motion of 0.24 g in the x-direction (0- mean and 1- standard deviation). The first natural period coefficient of variation is 0.42. The same tendency can be observed in the load and drift ratio also (fig.9).

Figure 9. Peak story seismic loads and drift ratios, x-direction

Numerical example 3:

We refined the analyses focusing on the structural element, using a full FEM model with deterministic properties (fig.10). The structure was pre-designed for 0.36g and soft soil conditions. It consists of braces- macro X on 8 stories, placed on the exterior frames on both main directions, to resist lateral forces and inner frames-to resist gravity loads.

Figure 10. 60 story FEM model

0

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0 10000 20000 30000 40000 50000 60000

Story

Shear force, kN

mean 0.7s

mean 1.6s

0

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60

0 1000000 2000000 3000000 4000000 5000000 6000000

Story

Bending moment,kNm

mean 0.7s

mean 1.6s

2000 3000 4000 5000 6000 7000 80000

10

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40

50

60

Load x-dir,kN

Sto

ry

-1 0 1 2 3 4 50

10

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30

40

50

60

Drift ratio x-dir,%

Sto

ry

analyzed columns

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15 synthetic accelerograms compatible with the corresponding design elastic response spectrum (fig.11) were applied in the x-direction.

Figure 11. Design and mean response acceleration and displacements spectra (15 accelerograms) The mean time-history to response spectrum ratio of bending moments at the columns base on the same vertical, are shown in the fig.12.

Figure 12. Mean time-history to spectrum ratios, base bending moments (x-direction)

The results are showing a significant underestimate by response spectrum approach and a large variability of ratios as well. While the variability in the input is small, the response variability is higher (CoVmax=0.24, CoVmin=0.12), the mean ratio of base bending moments in the columns is 1.20.

Structural performance in the time-domain approach

Time-domain approach gives the full range of advantages and is the most appropriate tool in the performance-based analysis and design format, making use of stochastic tools for reliability-based design. From practical point-of-view if internal forces are the interest response parameters, the demand to capacity ratio would control de structural design through interaction formulae for steel structures given in Eurocode 3 and LRFD. If the control response parameters would be for instance the drift ratios (threshold limit states are given e.g. Eurocode 8, section 4.4.3.2; PEER Guidelines), then the design framework can accommodate a “peaks over threshold” approach.

We consider the generic model, having 20% stiffness eccentricity ratios in both direction and uncertain ground motion directivity. A bi-directional set of synthetic spectrum compatible input of PGA=0.24g (Serviceability Level input) under 10o incremental directivity is considered and the mean crossing rates over 0.5% (Serviceability Limit) threshold drift limit are computed. Thus, for normally distributed parameters, the mean rates of crossings with positive slope over a threshold limit u, given by Rice (1969):

0

10

20

30

40

50

60

0.00 0.50 1.00 1.50 2.00

Bending moments ratio th/spec

Story

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8

SA

,m/s

/s

T,s

mean th

code

CoV max SA=0.13

0 1 2 3 4 5 6 7 80

0.5

1

1.5

2

2.5

3

T, s

SD,m

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0.04 0.06 0.08 0.1 0.12 0.14 0.160

10

20

30

40

50

60

Drift Ratio Mean Crossings Rate

Sto

ry

x-diry-dir

0 0.2 0.4 0.6 0.8 1 1.2 1.40

10

20

30

40

50

60

Drift ratio,%

Sto

ry

x-dir

y-dir

(2)

where, and are the 0th and the 2nd order moments about the mean (Vanmarcke, 2010). For the input motion set from 60o, story drift ratios and corresponding mean crossing rates are shown in the fig.13.

Figure 13. Drift ratios and the corresponding mean crossings rate of limit threshold (60o input directivity) For all possible input directions and any structural response parameter, a reliability approach can be incorporated in the analysis and design. This format would conceptually serve for rational decision on the structural performance and related cost-effectiveness criteria.

Conclusions

The performance-based design framework must be a reliability-based design one. The time-domain approach gives the full range of advantages and is the most appropriate tool for a comprehensive reliability approach. This can be incorporated in the analysis and design, by making use of advanced models, thanks to large databases of ground motion accelerograms and structural properties. Due to its limitations the response spectrum method approach is little applicable to tall buildings analysis and design, even for the linear analysis level. The results are showing that the current approach gives non-uniform demand values of the seismic loads and induced effects (internal forces and drift ratios) when compared to the time-history analysis “exact” approach. Further efforts must be oriented toward accurate ground motion simulation, full nonlinear structural and ground modeling, accuracy control of nonlinear numerical procedures and reliability-based analysis.

Akcnowledgement

The authors are grateful to the Romanian National Research Council (CNCS) for funding this research under the Grant IDEI 814.

References Aldea, A., Okawa, I., Koyama, S.,Poiata, N., (2006), Dense urban seismic instrumentation for site-effects assessment in Bucharest, Romania, First European Conference on Earthquake Engineering and Seismology, Geneva 2006 Bardet, J.P., K., Ichii, and C.H., Lin (2000), EERA -- A computer program for equivalent-linear earthquake site response analyses of layered soil deposits, University of Southern California, Department of Civil Engineering Bogdan, O.,(2007), Site effects estimation in Bucharest using medium intensity earthquake motions, Master Thesis, Building Research Institute/ National Graduate Institute for Policy Studies, Tokyo, Japan Gasparini, D.A., Vanmarcke, E.H. (1976). Simulated Earthquake Motions Compatible With Prescribed Response Spectra, Department of Civil Engineering, Research Report R76-4, Massachusetts Institute of Technology, Cambridge, Massachusetts. Iancovici, M., (2005), The assessment of structural performance of RC buildings, Ph. D. thesis, Technical

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University of Civil Engineering Bucharest, 234 pag., 624.042.7/I-24 DOC Iancovici, M., Stefanescu, B., Bogdan, O., Vezeanu, G., (2010), Tall Buildings under Long Predominant Period Ground Motions: Analysis vs. Code Provisions, 14th European Conference on Earthquake Engineering ECEE 2010, August 30-September 3, Ohrid, Macedonia (on CD) Kashima, T.,(2007), ViewWave ver. 1.53, Building Research Institute, Tsukuba, Japan Vanmarcke, E., (2010), Random Fields. Analysis and Synthesis. World Scientific Publishing Co. Pte. Ltd

EN1998-1:2004 Eurocode 8: Design of structures for earthquake resistance: Part 1 General Rules, Seismic Actions and Rules for Buildings, European Committee for Standardization Los Angeles Tall Buildings Structural Design Council (LATBSDC, 2008). An alternative procedure for seismic analysis and design of tall buildings located in the Los Angeles region, Council on Tall Buildings and Urban Habitat (CTBUH), Consensus Document, Los Angeles, CA, 2008 Manual of steel construction, 2001: Load and Resistance Factor Design. 3rd Edition, American Institute of Steel Construction (AISC), Chicago, IL, 2001. P100-1 (2006). Code for seismic design of buildings, The Ministry of Construction, Romania Pacific Earthquake Engineering Research Center (PEER), Report no.2010/05-TBI, Guidelines for Performance-Based Seismic Design of Tall Buildings http://peer.berkeley.edu/tbi/index.html. Mathworks-Matlab&Simulink for Technical Computing, http://www.mathworks.com

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