Advances in Civil and Environmental Engineering

ACEE – Volume 02(1), 01-19

ISSN 2345-2722

Advances in Civil and Environmental Engineering www.jacee.us – copyright © 2013-2014 Jacee.us official website.

SEISMIC BEHAVIOUR OF X-BRACED FRAMES WITH SHAPE MEMORY ALLOYS M. Mahmoudi *, A. Havaran Department of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran. *

Corresponding author, Tel: +98 (212) 2970021, Fax: +98 (212) 2970021 E-mail: [email protected]

Abstract Shape memory alloys (SMA) are novel materials that have high elastic strain, so they can be used as materials to improve the seismic performance of structures. The purpose of this paper is to compare seismic behavior of ordinary X-braced frames (XO), with SMA X-braced one, called (XS). As the current paper takes into account the effect of SMA on the ordinary X-braced frames response modification factor, several frames with similar dimensions but various heights are designed based on the Iranian code of practice. For this purpose, initially, SMA material has been used at the end of the X-braces and subsequently the seismic behavior of two kind of bracing are evaluated and their response modification factor are compared based on non-linear incremental dynamic analysis (IDA). The response modification factor for (XO) and (XS) frames have been obtained 10 and 11.7, respectively. The results reveal that the use of SMA as a part of X-braced frames can reduce frames' residual displacement significantly. Keywords: X-braced frame, Shape Memory Alloy (SMA), SMA X-braced, Increment Dynamic Analysis (IDA), Response modification factor (R).

1. Introduction The earthquake is a phenomenon that releases high amount of energy in a short time through the earth. In the early of twentieth century, structural engineers became conscious of potential hazard induced by strong earthquakes. Structures designed to resist moderate and frequently occurring earthquakes must have sufficient stiffness and strength to control deflection and prevent any possible collapse (Maheri and Akbari, 2003), With regard to the lateral load resistance in steel frames, the

M. Mahmoudi et al. Journal of Advances in Civil and Environmental Engineering, Volume 02(1), 01-19

moment resisting frame (MRF) and the concentrically braced frame (CBF) were the two common frames applied. Although MRF possesses fine ductility owing to flexural yielding beam elements yet it suffers from limited stiffness, due to buckling of the diagonal brace (Mofid and Lotfollahi, 2006). On the other hand, CBF benefits from acceptable stiffness yet it suffers from inadequate ductility due to buckling of the diagonal brace (Asgarian and Moradi, 2011). Since the inelastic behavior of X-braced frames subjected to lateral loads is forcefully dependent on the behavior of bracing members, to eliminate this deficiency, concept of SMA can apply to the connection of braces to beam-column to improve their behavior. The current paper is an attempt to apply energy adsorbent SMA materials into the ordinary X-braced frames in order to increasing their seismic behavior such as response modification factors, ductility factors, decreasing permanent displacement and inter-story drift of the structure compared to ordinary braced frames (Asgarian and Moradi, 2011). To this purpose twenty frames, designed according to Iranian code of practice for seismic resistant design of building and AISC89 (AISC, 1989), with and without SMA materials. Subsequently, their seismic performances have been evaluated through non-linear Incremental Dynamic Analysis (IDA) and linear dynamic analysis. Small parts of the structure like active links, it does not affect the total cost of the structures to a great extent.

2. Shape Memory Alloys concept Buehler and Wiley developed a series of nickel-titanium alloys in the 1960s with a composition of 53 to 57% nickel by weight that showed an unusual effect: severely deformed specimens of the alloys, with residual strain of 8-15%, regained their original shape after a thermal cycle. This effect became known as the shape-memory effect and the alloys exhibiting it were named shape-memory alloys (SMAs). It was later found that at sufficiently high temperatures such materials also possess the property of super elasticity, that is, the ability of recovering large deformations during mechanical loading-unloading cycles performed at constant temperature (Fugazza, 2003). SMAs have no lifetime limits such as problem of maintenance or substitution, even after several strong earthquakes. Recentering capability, high fatigue resistance, and the recovery of strains are among the characteristics that have made SMAs an effective material for seismic applications (Dolce et al., 2003; Dolce and Cardone, 2001; Des Roches et al., 2004). SMAs have two crystal structures. The predominant crystal structure or phase in a polycrystalline metal depends on both temperature and external stress. The high temperature phase is called austenite, whiles the low temperature phase is called martensite (Song et 2

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al., 2006; Janke et al., 2006). The specific macroscopic behavior of SMA is closely linked to transformations between the two phases. The shape memory effect (SME) and superelastic effect (SE) are known as two unique properties of SMAs. At relatively high temperatures a SMA is in its austenitic state. It undergoes a transformation to its martensitic state when cooled. The austenite phase is characterized by a cubic crystal structure, while the martensite phase has a monoclinic (orthorombic) crystal structure (Fugazza, 2003). The former property is the capacity to regain the original shape by heating and the latter is related to the ability of recovering large deformations after remove the external load (Fugazza, 2005). In the stress-free state, SMA is defined in four transformation temperatures: Ms and Mf during cooling and As and Af during heating. The former two (with Ms > Mf) indicate the temperatures at which the transformation from the austenite (also named as parent phase) into martensite respectively starts and finishes, while the latter two (with As < Af) are the temperatures at which the inverse transformation (also named as reverse phase) starts and finishes (Fugazza, 2003). When a unidirectional stress is applied to an austenitic specimen (Figure. 1), at a temperature less than Mf, austenite transforms into martensite, upon unloading, a large residual strain remains. However, by heating above Af, martensite transforms into austenite and the specimen recovers its initial undeformed shape (Fugazza, 2003). When the material re-transforms into twinned martensite. This phenomenon is generally named as shape-memory effect.

Figure. 1 Shape-memory effect (AISC, 1989).

When a unidirectional stress is applied to an austenitic specimen Figure. 2, at a temperature greater than Af, there is a critical value whereupon a transformation from austenite to martensite occurs.

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Figure. 2 Superelastic effect (AISC, 1989).

As deformation proceeds in isothermal conditions, the stress remains almost constant until the material is fully transformed (Fugazza, 2003). Further straining causes the elastic loading of the martensite. Upon unloading, since martensite is unstable without stress at temperature greater than Af, a reverse transformation takes place, but at a lower stress level than during loading so that a hysteretic effect is produced. If the material temperature is greater than Af, the strain attained during loading is completely and spontaneously recovered at the end of unloading. This remarkable process gives rise to an energy absorption capacity with zero residual strain, which is termed super elasticity (or pseudo elasticity). If the material temperature is less than Af, only a part of stress-induced martensite retransforms into austenite. A residual strain is then found at the end of unloading, which can be recovered by heating above Af. This phenomenon is generally referred to as partial super elasticity (Fugazza, 2003). Up to now many applications have been proved for SMA materials due to their unique properties and many experimental and numerical studies have been done for their seismic performances. A number of the past studies have presented a review of the SMA properties and the applications of SMA technology in civil engineering (Song et al., 2006, Fugazza, 2005). However, more experimental and numerical studies are needed to find out a suitable performance of SMA devices and to develop seismic design criterion for these new materials. 3. Models of frames Figure. 3, presents the Geometry of the Ordinary X-bracing 3-story frame. In the present study, the framing system has been taken equal to 5m length and 3m height. The number of frame stories are chosen at five levels i.e. 3-story, 5-story, 7- story, 10- story and 12-story level. In this article two types 4

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of X-braced frames have been exploited: The ordinary X-braced frames called "XO" and X- braced frames with SMA bracing systems called "XS". In cases XS, The braces are replaced with superelastic SMA segments connected to the frame. Figure. 4, shows the detail of the XS-frame.

Figure. 3 Geometry of the 3-story frame. (a) Plan of the structures. (b) Brace configurations

Figure. 4 Configuration of XS-frame cases.

4. Loading and design The gravity loads include dead and live loads of 600kg/m2 and 200kg/m2 respectively. Eq. 1 calculates the equivalent static lateral seismic loads assuming that the response modification factor R for the knee-bracing system is 7. V  CW  C 

ABI R

(1)

Where V represents the base shear, A is the design base acceleration ratio (for very high seismic zone=0.35g), B is response factor of building (depending on the fundamental period T), and I the importance factor of building (depending on its performance, taken equal to 1.0 in this paper), And A × B called the design spectral acceleration (Figure. 5) (BHRC, 2005; Naeemi and Bozorg, 2009). All of the frames are designed according to the AISC89 allowable stress design (AISC, 1989). Table 1 summarizes the size of members in frames. As observed, the buildings contain H-shaped columns, Ishaped beams, and box braces. The columns, beams and braces were made of st37. The beam–column joints were assumed to be pinned at both ends, in this way, the earthquake lateral forces are carried 5

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only by the vertical braces system; however the gravity loads are sustained mainly by the beams and columns (Asgarian and Shokrgozar, 2009).

Figure. 5 Variation of spectral acceleration with period of structure.

5. Modeling and design of superelastic SMA braces In this article, for presenting the superelastic behavior of the SMA braces a constitutive model proposed by Fugazza (Fugazza, 2003) was chosen. Figure. 6 shows the necessary parameters to construct the model. These parameters include the austenite to martensite starting stress (  sAS ), the austenite to martensite finishing stress (  fAS ), the martensite to austenite starting stress (  sSA ), the austenite finishing stress (  fSA ), modulus of elasticity for austenite and martensite phases ( E SMA ) and the superelastic plateau strain length (  L ). The necessary material parameters obtained from typical uniaxial cyclic tests on wires carried out by (Des Roches et al., 2004). Table 2 provides the mechanical properties of the superelastic SMA braces.

Figure. 6 Superelastic stress-strain relationship of SMA member needed for the model (Fugazza, D., 2003)

More details of the model’s formulation and the integration technique can be found in the work by (Fugazza 2003). In present study for designing cross section and length of the SMA braces, they should be determined in such a way that two frame cases XO and XS be comparable. For this reason, 6

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superelastic SMA braces were designed to provide the same allowable strength, (Fy in AISC89) and the same axial stiffness (K) as XO-braces. So, the XO- frames and XS-frames will have the same natural period (note that, the mass of the corresponding XO-frames and XS-frames were assumed equal), the following relations were achieved according to these considerations. For verifying the numerical simulation of SMA with experimental data Figure. 7 shows the comparison of the responses of the Numerical superelastic model with experimental data under cyclic axial load pattern (Figure. 8) (Ikeda et al., 2004; Mishra, 2006) respectively. A SMA 

LSMA 

Fysteel

 sAS



f yAlowable  A steel

 sAS

E SMA  A SMA E SMA  A SMA   Lsteel K steel 2e 6  A steel

(2) (3)

SMA Cross section area, A and element length of superelastic SMA braces can be calculated through

these equations. It was also assumed that the SMA elements are made of a number of large diameter superelastic bars able to undergo compressive loads without buckling.

Figure. 7 Stress-strain hysteresis loops for experimental (Mishra SK., 2006) and Numerical data subjected to the axial load pattern shown in Figure. 8.

Figure. 8 Axial load pattern applied the Numerical superelastic model and experimental data (Mishra SK., 2006).

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6. Definition of response modification factor Elastic analysis of structures under earthquake could create base shear force and stress which are noticeably larger than real structural response. The structure is capable of absorbing a lot of earthquake energy and resisting when it enters the inelastic range of deformation (Naeemi and Bozorg, 2009). In forced-based seismic design procedures, the response modification factor (FEMA, 1997) is utilized to reduce the linear elastic response spectra from the inelastic response spectra. In other words, response modification factor is the ratio of the strength required to maintain elastic to inelastic design strength of the structure. The behavior factor, R (shown in Eq. 4), accounts for the inherent ductility and overstrength of a structure as well as the difference in the level of stresses considered in its design (UBC, 1997). As shown in Fig. 9, the real nonlinear behavior is usually idealized by a bilinear elastoperfectly plastic relation (Uang, 1991).

Figure. 9 General structure response (Uang, 1991).

Yield force and yield displacement of the structure are represented by Vy and Δy, respectively. In this figure Ve (Vmax) correspond to the elastic response strength of the structure. The maximum base shear in an elasto-perfectly behavior is Vy. It is generally expressed in the following form taking into account the above three components (Miri et al., 2009). R  R  .R s .Y

(4)

where R represents ductility-dependent component also known as ductility reduction factor, Rs the overstrength factor, and Y the allowable stress factor (Miri et al., 2009). The ratio of maximum base shear considering elastic behavior Ve to maximum base shear in elasto perfectly behavior Vy demonstrated in Eq. 5 is called ductility reduction factor. R 

8

Ve Vy

(5)

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The overstrength factor shown in Eq. 6 is defined as the ratio of maximum base shear in actual behavior Vy to first significant yield strength in structure Vd. Rs 

Vy

(6)

Vs

The overstrength factor demonstrated in Eq. 6 is based on the use of nominal material and other factors. Representing this overstrength factor by Rso, the actual overstrength factor Rs which can be utilized to formulate R should take into account the beneficial contribution of some other effects: R s  R S0 F1F2 ...Fn .

(7)

In this equation, F1 accounts for the difference between actual static yield strength and nominal static yield strength. For structural steel, a statistical study shows that the value of F1 may be taken as 1.05 (Uang, 1991). Parameter F2 might be applied to consider the augmentation in the yield stress as a result of strain rate effect during an earthquake excitation. A value of 1.1, a 10% increase to account for the strain rate effect, could be used. In this article the steel type st37 was used for all structural members. Parameters F1 and F2 equal to 1.05 and 1.1 were considered taking into 1.155 as material overstrength factor. Other parameters can also be included when reliable data is available. These are included to the parameters such as nonstructural component contributions, variation of lateral force profile. To design for allowable stress method, the design codes decrease design loads from Vs to Vw. This decrease is done in Eq. 8.

Y

Vs Vw

(8)

This paper utilizes the design base shear Vw, instead of Vs. So the allowable stress factor Y becomes unity and the overstrength factor is defined as: Rs 

Vy

(9)

Vw

7. Modeling the structure in OpenSees software The computational model of the structures was developed using the modeling capabilities of the software framework of OpenSees (Mazzoni et al., 2007). This software is finite element software which has been specifically designed in performance systems of soil and structure under earthquake. For modeling of the members in nonlinear range of deformation, following assumptions were made. For the dynamic analysis, story masses were placed in the story levels considering rigid diaphragms action. For the modeling of braces, nonlinear beam and columns element with the materials behavior of Steel01 were exploited. Figure. 10 demonstrates the idealized elasto-plastic behavior of steel material. 9

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Compressive and tensional yield stresses were taken equal to steel yield. The used section for each member is the uniaxial section. The strain hardening of 2% was assumed for the member behavior in inelastic range of deformation (Figure. 10). For linear and non-linear dynamic analysis a damping coefficient of 5% was assumed. For prediction of linear and nonlinear buckling of columns, both element usual stiffness matrix and element geometric stiffness matrix were considered. An initial mid span imperfection of 1/1000 for all braces was considered to predict linear buckling. An Uniaxial section and nonlinear Beam Column element was considered for plastification of element over the cross section and member length for linear and nonlinear buckling prediction. For considering geometric nonlinearities, the simplified P-∆ stiffness matrix is considered.

Figure. 10 Steel 01 Material for nonlinear elements (FEMA, 2000).

To verify the results, some numerical analyses were carried out by another software (SAP2000 software) and subsequently the results obtained from the two modeling were compared. Roof displacements of the frames were utilized to compare the results. The results give weight to the accuracy of the modeling. It implies that the roof displacements obtained are approximately the same in both modeling. For example, Figure. 11 shows the time history of chichi ground motion for the top floor displacement of XO and XS 3-story frames.

Figure. 11 Time history of top floor displacement of KO and KE frames (3-story frames subjected to chichi ground motion).

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8. Determination of response modification factor In this article, two factors Rs and Rμ have been calculated as follows: 8.1. Overstrength factor (Rs) To calculate Vy, the Incremental Nonlinear Dynamic Analysis of the models subjected to strong ground motions was carried out. In these analysis the records of Tabas, Northridge and Chichi earthquake (Table 3) were used. These records were selected based on the Iranian Standard Code No. 2800s criteria. The response spectra and the design spectrum are shown in Fig 5. Nonlinear dynamic response of frames is evaluated for a set of predefined ground motions that are systematically scaled to increasing intensities until one of following failure criteria is established. The maximum nonlinear base shear of this time history is the inelastic base shear of structure (Mwafy, 2002). Finally the material overstrength factor of 1.155 was considered for actual overstrength factor. The failure criteria are defined by following two levels: (i) The relative floor displacement: The maximum limitation of the relative story displacement was selected based on the Iranian Standard Code No. 2800: (a) For frames with the fundamental period less than 0.7 sec:

 M < 0.025H

(10)

(b) For frames with the fundamental period more than 0.7 sec:

 M < 0.02H.

(11)

In which ‘H’ is the story height. (ii) Reaching the life safety structural performance: Generally, the component behavior induced by nonlinear load-deformation relations is defined by a series of straight line segments suggested by FEMA-273, Figure. 12. The nonlinear dynamic analysis was stopped and the last scaled earthquake base shear will be selected as the one reaching to life safety structural performance level as well as the nonlinear behavior of elements as suggested by FEMA-356.

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Figure. 12 Generalized force-deformation relation for steel elements (FEMA 1997).

8.2. Rμ Calculation To calculate Rμ, linear and nonlinear dynamic analyses were carried out. The nonlinear base shear Vy was calculated utilizing incremental nonlinear dynamic analysis as well as trials on PGA of earthquake time histories as aforementioned. Subsequently, the maximum linear base shear Ve was computed through linear dynamic analysis of the structure under the same time history; and ultimately the ductility reduction factor was evaluated.

9. Results The time history of Northridge ground motion for the top floor displacement of XO and XS 3-story frames is showed in Figure. 13. The ground acceleration (PGA) is scaled to 0.35g, based on Standard No. 2800. The peak roof displacements for the XO and XS braced frame are approximately 33 mm and 35 mm, respectively, But by the comparison of the values of residual roof displacement in Figure. 13, the use of SMA braces results in approximately no residual roof displacement, while the XO braced frame have 3.9 mm of residual displacement.

Figure. 13 Time history of top floor displacement of ordinary and SMA 3-story frames subjected to Northridge ground motion

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Besides, Figures. 14-16 show the values of residual roof displacement for the considered frames and the three aforementioned ground motion records. The Permanent roof displacement for the XS frames is less than that for XO frames. This result specifies the advantage of use of SMA braces in reducing the residual displacement of the top floor. As well as the residual roof displacement, the maximum inter-story drift, can be considered to study the seismic performance of structures subjecting to dynamic loads Figure. 17 and 18 show the comparison of nonlinear dynamic analysis for 3, 5, 7, 10 and 12 story of XO with XE frames in term of the maximum inter-story drift subjected to scaled ground acceleration (PGA). The result indicated that the average value of maximum inter-story drift is smaller for the buildings taller up to 16%. In the Table 4 the ultimate base shear Vy and maximum acceleration from nonlinear dynamic analysis under Tabas, Northridge and Chichi events for XO and XS frames are shown.

Figure. 14 Permanent roof displacement for the XO and XS frames subjected to Tabas ground motion.

Figure. 15 Permanent roof displacement for the XO and XS frames subjected to Northridge ground motion.

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Figure. 16 Permanent roof displacement for the XO and XS frames subjected to Chichi ground motion.

Figure. 17 Maximum inter-story drift for the XO and XS braced frames subjected to scaled ground motions ((a) Tabas, (b) Northridge, and (c) Chichi).

Table 5, provides maximum elastic base shear, Ve, resulted from linear dynamic analysis under above-mentioned time histories. In the Table 6, overstrength factor, ductility factor and response modification factor of XO and XS Specimens are shown. It can be observed that the overstrength factors, ductility factors and response modification factors in XS frames are greater than XO frames. In the other hand these parameters increase as the height of building decrease. Response modification factor for different Specimens was calculated statistically as follow: 1. For XO bracing system R=10, Rµ =1.24 2. For XS bracing system R=11.7, Rµ =1.72

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Figure. 18 Average of the maximum inter-story drift for the XO and XS braced frames subjected to scaled ground motions.

Figure. 19 Number of story- overstrength factor.

Figure. 20 Number of story- ductility factor.

Figure. 21 Number of story- response modification factor.

The Comparison of overstrength, ductility factor and response modification factors for difference type of bracing are shown in Figures. 19-21. It can be seen that ductility factor of XS specimens is greater than ductility factor of XO specimens in all frames and this parameter decreases as the number of story increases. Although overstrength factor of frames don’t change significantly in 7, 10 and 12 story frames but this parameter decreases in 3 and 5 story frames up to 41%. Ductility factor and overstrength factor gradually stables in the high story. For all type of bracing the response modification factor decreases as the height of building increases (Figure. 21).

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10. Conclusion In this article, Shape Memory Alloy material (SMA) was used as a part of X-braced frames. The result of the study is best summarized as follows: 1. Use of SMA as a part of X-braced frames, can decrease the residual displacement significantly. 2. With comparison of results, the response modification factors increase 17% in XS specimens. 3. The obtained overstrength factor for XO and XS specimens are, 6.96 and 6 respectively. 4. Response modification factor for XO and XS specimens are suggested as, 10 and 11.7 respectively. Table. 1 The member sizes for specimens. Number of Story 3

5

7

10

12

Beam

Mid Column

Similar Story

Dimensions

1,2,3 1,2,3,4,5 All stories All stories All stories -

IPE270 IPE270 IPE270 IPE270 IPE270 -

Similar Story 1 2,3 1 2 3 4,5 1 2,3 4,5,6,7 1 2 3 4,5 6,7,8 9,10 1 2 3,4,5,6 7,8 9,10 11,12

Dimensions IPB180 IPB160 IPB240 IPB220 IPB200 IPB140 IPB320 IPB260 IPB200 IPB500 IPB450 IPB360 IPB300 IPB240 IPB200 IPB650 IPB550 IPB450 IPB280 IPB220 IPB200

Side Column Similar Story 1,2,3 1,2 3,4,5 1,2,3,4 5,6,7 1,2 3,4,5,6 7,8,9,10 1 2,3,4 5,6,7 8,9,10,11,12 -

Diagonal elements

Dimensions IPB100 IPB120 IPB100 IPB140 IPB100 IPB160 IPB140 IPB120 IPB180 IPB160 IPB140 IPB120 -

Table. 2 Mechanical properties of SMA (Fugazza, D., 2003). Quantity

Value

E SMA  s AS  f AS  s SA  f SA L

27579

)%(

06

(MPa)

(MPa)

(MPa)

414 550

(MPa)

390

(MPa)

200 3.5

Similar Story 1 2 3 1 2,3,4 5 1,2,3,4 5 6 7 1 2 3,4,5,6 7,8 9 10 1 2,3 4,5,6,7,8 9,10 11 12

Dimensions Box100x100x14.2 Box90x90x12.5 Box80x80x10 Box120x120x12.5 Box100x100x14.2 Box80x80x10 Box120x120x12.5 Box100x100x14.2 Box90x90x12.5 Box80x80x10 Box120x120x17.5 Box120x120x14.2 Box120x120x12.5 Box100x100x14.2 Box90x90x12.5 Box80x80x10 Box120x120x17.5 Box120x120x14.2 Box120x120x12.5 Box100x100x14.2 Box90x90x12.5 Box80x80x10

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Table. 3 Ground motion data. Data Source

Site conditions

Distance (Km)

Magnitude

TCU095

CWB

USGS (B)

43.44

M ( 7.6 )

0.378

90

Santa Monica City Hall

CDMG

USGS (B)

27.6

M ( 6.7 )

0.37

40

-

CWB (B)

17.0

M ( 7.4 )

0.328

40

Record

Date

Station

Chi-Chi, Taiwan

20/09/1999

Northridge

17/1/1994

Tabas

16/09/1978

Dayhook

Duration (Sec)

PGA (g)

Table. 4 Nonlinear maximum Base Shear and PGA for XO and XS under Tabas, Northridge and Chichi ground motion. XO No. Story

Tabas

XS

Northridge

chichi

AVG

Tabas

Northridge

chichi

AVG

PGA (g)

Vy (KN)

PGA (g)

Vy (KN)

PGA (g)

Vy (KN)

Vy (KN)

PGA (g)

Vy (KN)

PGA (g)

Vy (KN)

PGA (g)

Vy (KN)

Vy (KN)

3

0.93

1531

0.78

1454

1.25

1544

4529

0.75

1012

0.73

1152

1.25

1090

3254

5

0.85

1678

0.73

1824

0.65

1661

5163

1

1496

0.98

1351

0.63

1427

4274

7

0.78

1603

0.78

1707

0.89

1811

5121

0.8

1074

0.93

2126

0.9

1617

4817

10

0.83

1100

0.85

1735

0.75

1345

4180

0.65

1058

0.98

2013

0.78

1405

4476

12

0.98

1832

0.83

1915

0.95

2276

6023

0.8

1450

0.78

1535

1

1240

4225

Table. 5 linear maximum Base Shear and PGA for XO and XS under Tabas, Northridge and Chichi ground motion. XO No. Story

Tabas PGA (g)

Ve (KN)

3

0.93

5

0.85

2330 1942

0.78 0.73

1654 1886

7

0.78

1714

0.78

0.83

1342

0.85

0.98

1893

0.83

10 12

XS

Northridge PGA (g)

Ve (KN)

chichi PGA (g)

AVG

Ve (KN)

Ve (KN)

1.25 0.65

1545 2224

5529 6052

2045

0.89

1946

2391

0.75

1663

2708

0.95

2244

Tabas PGA (g)

Northridge

Ve (KN)

PGA (g)

chichi

Ve (KN)

PGA (g)

AVG

Ve (KN)

Ve (KN)

1.25 0.63

1670 2119

5446 5603

0.75 1

2248 2241

0.73 0.98

1528 1243

5705

0.8

1769

0.93

2427

0.9

2039

6235

5396

0.65

1558

0.98

1616

0.78

1725

4899

6845

0.8

1565

0.78

2582

1

1241

5388

Table. 6 Minimum Overstrength factors, Ductility factors and Response modification factors of XO and XS. No. Story 3 5 7 10 12

Rs

Rµ

R

XO

XS

XO

XS

XO

XS

7.6 10.2 7.2 4.7 5.1

5.4 8.5 6.7 5.1 4.3

1.5 1.2 1.1 1.1 1.3

2.7 1.6 1.3 1.4 1.6

13.4 13.9 9.0 6.1 7.6

16.8 15.6 10.1 8.0 8.0

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