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EUROSTEEL 2017, September 13–15, 2017, Copenhagen, Denmark © Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017) Numerical Investigation of Short Seismic Links in Shear Mladen Bulic* ,a , Mehmed Causevic a a University of Rijeka, Faculty of Civil Engineering, Rijeka, Croatia [email protected], [email protected] ABSTRACT It is well known that seismic links are usually designed to remain in elastic region during ordinary loading but withstand nonlinear deformation during seismic event having capability to dissipate seismic energy. The use of short seismic links is recommended because they are capable of dissipating seismic energy in larger quantity by shear, while the webs in these links are expected to yield in shear during large seismic events, i.e. dissipation of seismic energy by bending in links is negligible. Shear deformations are basically plane deformations of the cross section web of the link, without any significant tendency towards lateral torsional buckling. To achieve the required plastic rotation, local instabilities such as flange or web buckling should be delayed. The flange local buckling is delayed by specifying width to thickness ratio, while the web local buckling will be prevented by adding number of transverse stiffeners along the web of the link. The main purpose of the stiffeners is to preserve buckling of the seismic link web, i.e. to achieve plastification of the cross section by shear. Dissipation of energy in the stiffened link will occur sooner through inelastic shear deformations than through inelastic web buckling. The seismic links were chosen having the same cross section and the same length, but with different number of stiffeners, i.e. with three couples of stiffeners, two, one and without any stiffener respectively. A finite element modelling approach in investigating the structural behaviour of short links is presented. Both the material and geometric nonlinearities are considered in the FE modelling using the software ABAQUS and the Shear force – Displacement relationships was obtained. The FEA results are validated against the test results and the comparisons indicated that the FE analysis procedures agree well with the test results. Keywords: short seismic links, seismic energy, steel frames, finite element method 1 INTRODUCTION Seismic design of structures must satisfy two basic criteria. A structure must have sufficient stiffness to keep deflections below the limit of non-structural damage during minor seismic events, and possess sufficient ductility to prevent collapse in the event of a rare overload which might occur during the major earthquake. Eccentrically Braced Frames (EBFs) have been used as a seismic load resisting system, primarily in buildings. The economy of the eccentrically braced framing scheme is realized by allowing large local inelastic deformations to occur in the eccentric elements when the frame is subject to lateral loading. The inelastic deformations are forced to occur in short beam segments (seismic links) which separate the axial force transmitting members (i.e. braces or columns). Large amounts of energy can be dissipated through inelastic shearing of these seismic links, thereby facilitating energy dissipation and endowing the system with ductility. This system which relies on the yielding of a short beam between eccentric braces, has been shown to provide ductility and energy dissipation under seismic loading, and its behaviour in various configurations has been investigated. The viability of the eccentric bracing concept was demonstrated by Roeder and Popov [1] with a series of tests on three-story models. Subsequent research on eccentrically braced frames by Hjelmstad and Popov [2] was concerned mainly with web buckling of eccentric elements with complete lateral restraint. Kasai and Popov [3, 4] extended the web buckling studies to the case of unequal end moments in the presence of axial force. The design of eccentrically braced frames is

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Page 1: Numerical Investigation of in · Numerical Investigation of Short Seismic Links in Shear Mladen Bulic*,a, Mehmed Causevica aUniversity of Rijeka, Faculty of Civil Engineering, Rijeka,

EUROSTEEL 2017, September 13–15, 2017, Copenhagen, Denmark

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)

NumericalInvestigationofShortSeismicLinksinShear

Mladen Bulic*,a, Mehmed Causevica aUniversity of Rijeka, Faculty of Civil Engineering, Rijeka, Croatia

[email protected], [email protected]

ABSTRACT

It is well known that seismic links are usually designed to remain in elastic region during ordinary loading but withstand nonlinear deformation during seismic event having capability to dissipate seismic energy. The use of short seismic links is recommended because they are capable of dissipating seismic energy in larger quantity by shear, while the webs in these links are expected to yield in shear during large seismic events, i.e. dissipation of seismic energy by bending in links is negligible. Shear deformations are basically plane deformations of the cross section web of the link, without any significant tendency towards lateral torsional buckling. To achieve the required plastic rotation, local instabilities such as flange or web buckling should be delayed. The flange local buckling is delayed by specifying width to thickness ratio, while the web local buckling will be prevented by adding number of transverse stiffeners along the web of the link. The main purpose of the stiffeners is to preserve buckling of the seismic link web, i.e. to achieve plastification of the cross section by shear. Dissipation of energy in the stiffened link will occur sooner through inelastic shear deformations than through inelastic web buckling. The seismic links were chosen having the same cross section and the same length, but with different number of stiffeners, i.e. with three couples of stiffeners, two, one and without any stiffener respectively. A finite element modelling approach in investigating the structural behaviour of short links is presented. Both the material and geometric nonlinearities are considered in the FE modelling using the software ABAQUS and the Shear force – Displacement relationships was obtained. The FEA results are validated against the test results and the comparisons indicated that the FE analysis procedures agree well with the test results. Keywords: short seismic links, seismic energy, steel frames, finite element method

1 INTRODUCTION

Seismic design of structures must satisfy two basic criteria. A structure must have sufficient stiffness to keep deflections below the limit of non-structural damage during minor seismic events, and possess sufficient ductility to prevent collapse in the event of a rare overload which might occur during the major earthquake. Eccentrically Braced Frames (EBFs) have been used as a seismic load resisting system, primarily in buildings. The economy of the eccentrically braced framing scheme is realized by allowing large local inelastic deformations to occur in the eccentric elements when the frame is subject to lateral loading. The inelastic deformations are forced to occur in short beam segments (seismic links) which separate the axial force transmitting members (i.e. braces or columns). Large amounts of energy can be dissipated through inelastic shearing of these seismic links, thereby facilitating energy dissipation and endowing the system with ductility. This system which relies on the yielding of a short beam between eccentric braces, has been shown to provide ductility and energy dissipation under seismic loading, and its behaviour in various configurations has been investigated. The viability of the eccentric bracing concept was demonstrated by Roeder and Popov [1] with a series of tests on three-story models. Subsequent research on eccentrically braced frames by Hjelmstad and Popov [2] was concerned mainly with web buckling of eccentric elements with complete lateral restraint. Kasai and Popov [3, 4] extended the web buckling studies to the case of unequal end moments in the presence of axial force. The design of eccentrically braced frames is

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© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)

philosophically different from traditional design practice. Excursions into the inelastic range are accepted for extreme overloads, and hence must be anticipated in the design process. The eccentric elements may repeatedly reach or exceed their limit capacity under reversing loads. Hence, the cyclic post-buckling behavior of these elements is of primary concern under conditions of repeated overloading [5]. The seismic links should be designed in a way that it may bear great inelastic deformations without losing resistance, i.e. that most of the seismic energy is possible to dissipate within it. To achieve the required plastic rotation local instabilities (such as flange or web buckling) should be delayed. The web local buckling will be prevented by adding number of transverse stiffeners along the web of the link. Dissipation of energy in the stiffened link will occur sooner through inelastic shear deformations than through inelastic web buckling [6-8]. Seismic links are classified into three categories according to the type of plastic mechanism development: short, long and intermediate links. The short length of the eccentric elements is important both to promote a high elastic lateral stiffness and to insure that shear yielding occurs rather than flexural yielding, since shear yielding is considerably more efficient. The use of short seismic links in EBFs is generally preferred to long ones, mainly due to their high rotation capacity and energy dissipation under cyclic loadings. However, long links have the advantage of providing openings in the braced spans of EBFs [9]. In this paper, a three dimensional finite-element model using software package ABAQUS [10] is developed for the inelastic nonlinear analysis of short links to investigate their rotation capacity. It was found that using intermediate stiffeners, a large rotation capacity can be achieved. The research in this work was restricted to the short seismic links because they are capable of dissipating seismic energy in larger quantity by shear, while the webs in these links are expected to yield in shear during large seismic events, i.e. dissipation of seismic energy by bending in links is negligible. Shear deformations are basically plane deformations of the cross section web of the link, without any significant tendency towards lateral torsional buckling. The short link is subject to high shear force along its entire length but low axial force and bending moments, Fig. 1 [11-13].

N

V

M M

V

N

Fig. 1. Cross-section forces in the beam and in the link under lateral load in both directions

2 DESIGN OF SEISMIC LINKS

The seismic links are designed to act as a fuse by yielding and dissipating energy while preventing buckling of the brace members. The inelastic response of a link is strongly influenced by the link length and the linkplinkp VM ,, / ratio of the link cross-section which is correlated to the capability to

dissipate seismic energy and the collapse mechanism of the system. In such a system the danger of brace buckling may be prevented since the seismic link acts as a fuse which limits the axial force in the bracing. The seismic link should be designed so that it may bear great inelastic deformations without losing resistance and so that most of the seismic energy is dissipated within it [13, 14].

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© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)

To achieve the required plastic rotation, local instabilities such as flange or web buckling are delayed. The flange local buckling is delayed by specifying width to thickness ratio, while the web local buckling will be prevented by adding number of transverse stiffeners along the web of the link [15]. The seismic links are designed for the design seismic action effect in shear EdV or in bending EdM

of the link [16], so that:

linkpEd VV , ; linkpEd MM , (1)

where linkpV , and linkpM , is, respectively, the plastic shear and bending resistance of the link which,

for I sections, have the following values:

3

,y

wflinkp

fttdV ; linkpM , yff ftdtb (2)

if RdplEd NN ,/ in the link is less or equal to 0.15, where yf the nominal yield strength of steel, d

the cross section height, b the cross section width, wt the web thickness and ft the flange

thickness. Seismic links are classified into three categories according to the type of plastic mechanism development: - short links at which the energy is dissipated by forming plastic hinges due to shear

linkplinkps VMee ,, /6,1 (3)

- long links at which the energy is dissipated by forming plastic hinges due to bending

linkplinkpL VMee ,, /0,3 (4)

- intermediate links at which the plastic mechanism occurs due to bending and shear

Ls eee (5)

The link rotation angle p between the link and the element outside of the link (Fig. 2) should be

consistent with global deformations. It should not exceed the following values:

radpRp 08,0 (short links) (6)

radpRp 02,0 (long links) (7)

e

p

Fig. 2. Rotation of seismic link

Web stiffening of the short seismic link improves the capability of dissipating seismic energy in the link by delaying the inelastic web shear buckling and it slows down the decrease of the load bearing capability of the seismic link by controlling the displacement amplitude outside the web plane. The seismic link must be free of any supports. Such supports can prevent occurrence of inelastic deformations in the link, which can lead to deformation of other system elements [6].

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© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)

3 FINITE ELEMENT MODELLING

The nonlinear finite element modelling were performed using the finite element program ABAQUS [10]. Some preliminary analyses were conducted to study the effect of mesh refinement, and to determine whether reduced integration elements could be used to improve computational time without loss of significant accuracy. ABAQUS has the ability to consider both geometric and material nonlinearities in a given model. Large displacement effects were accounted for by utilizing the nonlinear geometry option in ABAQUS. The nonlinear kinematic hardening plasticity material model available in ABAQUS was used in the finite element model. The applied Solid 3D (8-nodal brick) elements, although much more complicated to model than plane elements, give more accurate results and are recommended for scientific numerical simulations of steel systems. The nonlinearity of actual materials was introduced into the numerical model. Finite element analysis of the seismic links was done on base of experimentally obtained stress–strain curves, Fig. 3 [11].

0

100

200

300

400

500

0 10 20 30 40

Fig. 3. Experimentally obtained stress–strain curves for material

In this study, four models of short seismic links were done, each having the same cross section (HEA100) and the same length (300 mm) but with different number of web stiffeners, i.e. without any stiffener on the seismic link length, with one, two and three couples of web stiffeners (Fig. 4).

Fig. 4. Four models of short seismic links

The link length for all models was chosen in a way to fulfil the requirement for short seismic links with two and three couples of web stiffeners [16]. The nominal geometrical characteristics of the cross-section HEA 100 (height mmd 96 , width mmb 100 , web thickness mmtw 5 and

flange thickness mmt f 8 ) were adopted for all models. At the seismic link ends 15 mm thick

endplates were placed. Web stiffeners were 10 mm thick plates placed on both side of the web. Fillet welds connecting a web stiffeners to the link web should have a design strength adequate to resist a force styov Af , where stA is the area of the stiffener and ov is material overstrength factor

[17]. The design strength of fillet welds fastening the stiffener to the flanges should be adequate to resist a force of 4/styov Af [16]. The 5 mm thickness of fillet welds fulfils these requirements.

Str

ess

(N/m

m2 )

Strain (%)

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© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)

On the connection of the endplate to the seismic links and on the connection of the stiffeners to the profile, it was necessary to find a network of finite elements that would correspond to the network of finite elements of the profile. A model without stiffeners is composed of 24072 elements, a model with one couple of stiffeners has 25496 elements, a model with two couples of stiffeners has 26920 elements and finally a model with three couples of stiffeners is made up of 28344 elements (Fig. 5).

Fig. 5. Finite element mesh

Since, in this study, the behaviour of isolated seismic links is investigated, boundary conditions are the same as proposed by Richards and Uang [18]. These boundary conditions allow axial deformation of the link while preventing rotation at both ends. As can be seen in Fig.6, nodes on the left end were restrained against all degrees of freedom except horizontal translation. Nodes on the right end were restrained against all degrees of freedom except vertical translation. Loading in this manner resulted in constant shear along the length of the link with equal end moments and no axial forces [18]. Loading was applied through the application of vertical displacement at the link end. In terms of horizontal and vertical nodal displacements, ux and uy respectively, and rotations, rz, the boundary conditions used can be expressed as:

uy(0) = rz(0) = ux (L) = rz(L) = 0 (8)

Fig. 6. FEM model boundary conditions applied to the links

The models were developed to predict the performance for four types of short seismic links tested at the University of Zagreb, Faculty of Civil Engineering [11]. Models were based on the dimensions of the experimental specimens. Boundary conditions, loading protocol, material properties and other details of modelling were the same as experimental conditions.

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© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)

4 RESULTS AND DISCUSSION

The plasticity model used in the analyses was based on a von Mises yield surface and an associated flow rule. The plastic hardening was defined using a nonlinear kinematic hardening law. By adding incremental displacements on one end of the link, that is, by increasing the shear force, the plastification of seismic link web occurs. Fig. 7 - 10 shows the von Mises stress contours for four types of seismic links, i.e. without any stiffener, with one, two and three couples of web stiffeners.

Fig. 7. Von Misses stress contour (link without stiffeners) (N/m2)

Fig. 8. Von Misses stress contour (link with one couple of stiffeners) (N/m2)

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© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)

Fig. 9. Von Misses stress contour (link with two couples of stiffeners) (N/m2)

Fig. 10. Von Misses stress contour (link with three couples of stiffeners) (N/m2)

On the base of finite element analysis of the seismic links with different number of stiffeners Shear-Rotation relationships was obtained. The comparison of results obtained by nonlinear numerical analysis by finite elements method and experimental results [11] for all four types of seismic links is presented in Fig. 11. It can be seen that good agreement was obtained between the numerical and experimental results in terms of both their behaviour and overall deformation patterns. The stresses and strains at key locations in the finite element model were also near their expected values.

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© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)

0

20

40

60

80

100

120

140

160

180

200

0 0,02 0,04 0,06 0,08 0,1

3 couples-experimentally3 couples-numerically2 couples-experimentally2 couples-numerically1 couple-experimentally1 couple-numericallywithout-experimentallywithout-numerically

Fig. 11. Comparison of numerical and experimental results

Behaviour of different seismic links in elastic region is identical. When adding stiffeners, shear force at which the seismic link yields, increases. According to the design resistance model the value of plastic shear force is 82 kN. This value is approximately identical to the shear force values obtained numerically and experimentally at which a nonlinear inelastic deformation of seismic link specimen without web stiffeners occurs. By adding web stiffeners this force increases, so that at the specimen of seismic link with one couple of web stiffeners the shear force is 94 kN (15% increase), at the specimen with two couples of stiffeners the shear force is 110 kN (35% increase) while at the specimen with three couples of stiffeners it is 114 kN (40% increase). The rotation angle p between the seismic link and the beam outside the link must be in accordance

to global deformations and must not exceed 0,08 rad in short seismic links, Eq. (6). If the seismic link rotation angle is larger than 0,08 rad the elastic deformation of other frame elements occurred at the frame model, which caused the reduction of shear force in the seismic link. The seismic links without stiffeners reach the link rotation of 0,08 rad at shear force 113 kN, while the seismic links with three couples of stiffeners reach the link rotation of 0,08 rad at shear force 160 kN, which is an increase of 42%. By increasing the number of web stiffeners a linear increase of shear force at the link rotation angle of 0,08 rad occurs. It was found that its moment-shear (M-V) interaction can be neglected, as both the plastic shear and plastic moment capacity of the cross-section, calculated using actual material properties, were exceeded due to strain hardening. Furthermore, the maximum link shear exceeded the plastic shear strength calculated using the ultimate stress of the web material, indicating that some shear was likely being carried by the flange as well. Berman and Bruneau [19], in their finite element parametric study, obtained similar behaviour and comparing the link shear force versus rotation hysteresis curves in Fig. 12 shows reasonable agreement with the experimental results. This study parallels a similar analytical study of the effect of flange width-to-thickness ratio on WF EBF link rotation capacity by Richards and Uang [18], which also considered experimental data from Okazaki et al. [20]. Similar analytical models and failure criteria are chosen for this study for the purpose of maintaining consistency such that implementation of links with tubular cross sections may be efficiently achieved. The flange width–thickness requirement for links is the same as that used for steel moment frames and is justified by work done by Kasai and Popov [3]. They developed a conservative bound for the plastic buckling stress of a link flange. Web restraint to flange buckling was conservatively neglected.

Link Shear (kN) 

Link Rotation p (rad) 

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© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)

Fig. 12. Comparison of numerical and experimental link shear versus rotation hysteresis curves [19]

By modelling the finite element method, calibration of models on existing results of experiments can be performed which can replace the expensive experiments to great extent. The experiments tend to be performed on small specimen due to economic profitability. However, the model calibration is not possible without the conducted experiments.

5 CONCLUSIONS

In this study, the nonlinear inelastic analysis of short seismic links constructed of rolled sections was studied using the finite element method. The main aim was to investigate the behavior of short links with different number of intermediate web stiffeners, i.e. without any stiffener on the seismic link length, with one, two and three couples of web stiffeners. Design equations and requirements have been proposed and verified by numerical analysis. Shear-Rotation relationships for all four types of seismic links with different number of stiffeners were obtained. Web stiffeners do not affect the elastic stiffness, i.e. behaviour of seismic links with different number of web stiffeners in elastic region is identical. By adding the web stiffeners, the shear force increases at the link where the nonlinear inelastic deformation occurs. It can be concluded that the design model of plastic shear resistance is applicable to short seismic links without web stiffeners while for seismic links with web stiffeners the design model must be corrected with a correction factor. Energy absorbing takes place by the link beam web when the beam works in shear and placing proper stiffeners on web leads to the complete use of strain hardening. Flanges and stiffeners do not have any role in absorbing energy but they help the web for better functioning and the failure is ductile. The finite element model of four types of short seismic links was developed using Solid 3D (8-nodal brick) elements and showed good agreement with the experimental results in terms of behaviour and deformations.

6 ACKNOWLEDGMENT

Research presented in this paper was partly sponsored by the University of Rijeka, Croatia, within Research Project: "Development of structures with increased reliability with regard to earthquakes" No. 402-01/14-01/11.

REFERENCES

[1] Roeder C.W., Popov E.P., “Eccentrically Braced Steel Frames for Earthquakes”, Journal of the Structural Division, 104(3), 391-412, 1978.

[2] Hjelmstad K.D., Popov E.P., “Seismic Behavior of Active Beam Links in Eccentrically Braced Frames”, Report No. UCB/EERC-83/15, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1983.

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© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)

[3] Kasai K., Popov E.P., “General Behavior of WF Steel Shear Link Beams”, Journal of the Structural Division, 112(2), 362-382, 1986.

[4] Kasai K., Popov E.P., “Cyclic web buckling control for shear link beams”, Journal of the Structural Division, 112(3), 505-523, 1986.

[5] Hjelmstad K.D., Lee S.G., “Lateral Buckling of Beams in Eccentrically-Braced Frames”, J. Constr. Steel Research, 14, 251-272, 1989.

[6] Kasai K., Popov E.P., “A Study of Seismically Resistant Eccentrically Braced Steel Frame Systems”, Report No. UCB/EERC-86/01, Earthquake Engineering Research Center, University of California, Berkeley, 1986.

[7] Malley J.O., Popov E.P., “Design Considerations for Shear Links in Eccentrically Braced Frames”, Report No. UCB/EERC-83/84, Earthquake Engineering Research Center, University of California, Berkeley, 1983.

[8] Mazzolani F.M., Piluso V., “ECCS Manual on Design of Steel Structures in Seismic Zones”, European Convention for Constructional Steelworks, TC 13 Seismic Design, Naples, 1994.

[9] Chegeni B., Mohebkhah A., “Rotation capacity improvement of long link beams in eccentrically braced frames”, Scientia Iranica A, 21(3), 516-524, 2014.

[10] ABAQUS, Manual, SIMULIA, Rising Sun Mills, 2007.

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[12] Malley J.O., Popov E.P., “Shear Links in Eccentrically Braced Frames”, Journal of Structural Engineering. ASCE, September, 1984.

[13] Engelhardt M.D., Popov E.P., “On Design of Eccentrically Braced Frames”, Earthquake Spectra 5(3), 495-511, 1989.

[14] Causevic M. “Interaction of Eurocode 8 and Eurocode 3 in eccentrically braced steel frame design”, European Earthquake Engineering, Journal of the European Association for Earthquake Engineering, Patron Editore Publisher, 2, 3-7, 1998.

[15] Mazzolani F.M., Gioncu V., (editors), “Behaviour of Steel Structures in Seismic Areas”, Proceedings of the International workshop organised by ECCS, E&FN SPON, An Imprint of Chapman & Hall, London, 1994.

[16] European Committee for Standardization (CEN). EN 1998 - Eurocode 8: Design of structures for earthquake resistance, Brussels, 2004.

[17] Rossi P.P., Lombardo A. “Influence of the link Overstrength factor on the seismic behaviour of Eccentrically Braced Frames”, Journal of Constructional Steel Research, 63, 1529-1545, 2007.

[18] Richards P.W., Uang C.M., “Effect of flange width thickness ratio on eccentrically braced frames link cyclic rotation capacity”, J Struct Eng, 131(10), 1546–52, 2005.

[19] Berman J.W, Bruneau M., “Tubular Links for Eccentrically Braced Frames. I: Finite Element Parametric Study”, J. Struct. Eng., 134, 692-701, 2008.

[20] Okazaki T., Arce G., Ryu H.C., Engelhardt M.D., “Experimental study of local buckling, overstrength, and fracture of links in eccentrically braced frames”, J. Struct. Eng., 131(10), 1526–1535, 2005.