SEISMIC BEHAVIOUR OF X-BRACED FRAMES WITH ...jacee.us/archive/file/ACEE2014v02i01n01.pdfKeywords: X-braced frame, Shape Memory Alloy (SMA), SMA X-braced, Increment Dynamic Analysis

ACEE – Volume 02(1), 01-19

Advances in Civil and Environmental Engineering

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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

ISSN 2345-2722

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

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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


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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 re-

transforms 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


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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.

ABIV CW C

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, I-

shaped 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


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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 ( AS

s ), the

austenite to martensite finishing stress ( AS

f ), the martensite to austenite starting stress ( SA

s ), the

austenite finishing stress ( SA

f ), modulus of elasticity for austenite and martensite phases ( SMAE ) 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,


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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.

y

steel Alowable steel

ySMA

AS AS

s s

F f AA

(2)

2 6

SMA SMA SMA SMASMA steel

steel steel

E A E AL L

K e A

(3)

Cross section area, SMAA 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 elasto-

perfectly 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).

sR R .R .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.

e

y

VR

V

(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.

y

s

s

VR

V (6)

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:

s S0 1 2 nR R FF ...F . (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.

s

w

VY

V (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:

y

s

w

VR

V (9)

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.


01

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).


00

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.


02

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.


04

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


05

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

Beam Mid Column Side Column Diagonal elements

Similar Story Dimensions Similar

Story

Dimensions Similar

Story

Dimensions Similar Story Dimensions

3 1,2,3 IPE270 1 IPB180 1,2,3 IPB100 1 Box100x100x14.2

- - 2,3 IPB160 - - 2 Box90x90x12.5 - - - - - - 3 Box80x80x10

5

1,2,3,4,5 IPE270 1 IPB240 1,2 IPB120 1 Box120x120x12.5 - - 2 IPB220 3,4,5 IPB100 2,3,4 Box100x100x14.2 - - 3 IPB200 - - 5 Box80x80x10 - - 4,5 IPB140 - - - -

7

All stories IPE270 1 IPB320 1,2,3,4 IPB140 1,2,3,4 Box120x120x12.5 - - 2,3 IPB260 5,6,7 IPB100 5 Box100x100x14.2 - - 4,5,6,7 IPB200 - - 6 Box90x90x12.5

- - - - - - 7 Box80x80x10

10

All stories IPE270 1 IPB500 1,2 IPB160 1 Box120x120x17.5 - - 2 IPB450 3,4,5,6 IPB140 2 Box120x120x14.2 - - 3 IPB360 7,8,9,10 IPB120 3,4,5,6 Box120x120x12.5 - - 4,5 IPB300 - - 7,8 Box100x100x14.2 - - 6,7,8 IPB240 - - 9 Box90x90x12.5 - - 9,10 IPB200 - - 10 Box80x80x10

12

All stories IPE270 1 IPB650 1 IPB180 1 Box120x120x17.5 - - 2 IPB550 2,3,4 IPB160 2,3 Box120x120x14.2 - - 3,4,5,6 IPB450 5,6,7 IPB140 4,5,6,7,8 Box120x120x12.5 - - 7,8 IPB280 8,9,10,11,12 IPB120 9,10 Box100x100x14.2 - - 9,10 IPB220 - - 11 Box90x90x12.5 - - 11,12 IPB200 - - 12 Box80x80x10

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

Value Quantity

27579 (MPa)

SMAE

414 (MPa)

AS

s 550

(MPa)

AS

f 390

(MPa)

SA

s 200

(MPa)

SA

f 3.5

)%(L


07

Table. 3 Ground motion data.

Record Date Station Data

Source Site conditions Distance (Km) Magnitude PGA (g)

Duration

(Sec)

Chi-Chi, Taiwan 20/09/1999 TCU095 CWB USGS (B) 43.44 M ( 7.6 ) 0.378 90

Northridge 17/1/1994 Santa Monica City Hall CDMG USGS (B) 27.6 M ( 6.7 ) 0.37 40

Tabas 16/09/1978 Dayhook - CWB (B) 17.0 M ( 7.4 ) 0.328 40

Table. 4 Nonlinear maximum Base Shear and PGA for XO and XS under Tabas, Northridge and Chichi ground motion.

No. Story

XO XS

Tabas 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.

No. Story

XO XS

Tabas Northridge chichi AVG Tabas Northridge chichi AVG

PGA (g)

Ve (KN)

PGA (g)

Ve (KN)

PGA (g)

Ve (KN)

Ve

(KN)

PGA (g)

Ve (KN)

PGA (g)

Ve (KN)

PGA (g)

Ve (KN)

Ve

(KN)

3 0.93 2330 0.78 1654 1.25 1545 5529 0.75 2248 0.73 1528 1.25 1670 5446

5 0.85 1942 0.73 1886 0.65 2224 6052 1 2241 0.98 1243 0.63 2119 5603

7 0.78 1714 0.78 2045 0.89 1946 5705 0.8 1769 0.93 2427 0.9 2039 6235

10 0.83 1342 0.85 2391 0.75 1663 5396 0.65 1558 0.98 1616 0.78 1725 4899

12 0.98 1893 0.83 2708 0.95 2244 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 Rs Rµ R

XO XS XO XS XO XS

3 7.6 5.4 1.5 2.7 13.4 16.8 5 10.2 8.5 1.2 1.6 13.9 15.6 7 7.2 6.7 1.1 1.3 9.0 10.1

10 4.7 5.1 1.1 1.4 6.1 8.0 12 5.1 4.3 1.3 1.6 7.6 8.0

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Documents

SEISMIC BEHAVIOUR OF X-BRACED FRAMES WITH ...jacee.us/archive/file/ACEE2014v02i01n01.pdfKeywords: X-braced frame, Shape Memory Alloy (SMA), SMA X-braced, Increment Dynamic Analysis