`
`
`ITB J. Eng. Sci. Vol. 42, No. 2, 2010, 103-128 103
`
`
`
`Behavior of Shear Link of WF Section with Diagonal Web
`Stiffener of Eccentrically Braced Frame (EBF) of Steel
`Structure
`Yurisman, Bambang Budiono, Muslinang Moestopo & Made Suarjana
`
`Civil Engineering Department, Institute of Technology Bandung.
`Email: Yurisman_pdg@yahoo.com
`
`Abstract. This paper presents results of numerical and experimental study of
`shear link behavior, utilizing diagonal stiffener on web of steel profile to increase
`shear link performance in an eccentric braced frame (EBF) of a steel structure
`system. The specimen is to examine the behavior of shear link by using diagonal
`stiffener on web part under static monotonic and cyclic load. The cyclic loading
`pattern conducted in the experiment is adjusted according to AISC loading
`standards 2005. Analysis was carried out using non-linear finite element method
`using MSC/NASTRAN software. Link was modeled as CQUAD shell element.
`Along the boundary of the loading area the nodal are constraint to produce only
`one direction loading. The length of the link in this analysis is 400mm of the
`steel profile of WF 200.100. Important parameters considered to effect
`significantly to the performance of shear link have been analyzed, namely flange
`and web thicknesses, thickness and length of web stiffener, thickness of diagonal
`stiffener and geometric of diagonal stiffener. The behavior of shear link with
`diagonal web stiffener was compared with the behavior of standard link designed
`based on AISC 2005 criteria. Analysis results show that diagonal web stiffener is
`capable to increase shear link performance in terms of stiffness, strength and
`energy dissipation
`in supporting
`lateral
`load. However, differences
`in
`displacement ductility’s between shear links with diagonal stiffener and shear
`links based on AISC standards have not shown to be significant. Analysis results
`also show thickness of diagonal stiffener and geometric model of stiffener to
`have a significant influence on the performance of shear links. To perform
`validation of the numerical study, the research is followed by experimental work
`conducted in Structural Mechanic Laboratory Center for Industrial Engineering
`ITB. The Structures and Mechanics Lab rotary PAU-ITB. The experiments were
`carried out using three test specimens with model and dimension identical to the
`model in the numerical study. Experimental testing apparently has shown results
`of the same behavior as predicted in the numerical study. However, when it is
`compared to the shape of the hysterical curve, a slight difference is apparent.
`This is due to the influence of stiffness of bolt joints and the supports which is
`difficult to model precisely in the numerical studies.
`
`Keywords: cyclic loading; diagonal web stiffener; ductility; energy dissipation;
`monotonic loading; shear link; stiffness; strength.
`
`Received June 22nd, 2010, Accepted for publication July 12th, 2010.
`
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`Introduction
`1
`Indonesia is located in a tectonic area with high occurrences of earthquakes.
`This has resulted in many efforts to reduce risk created by this situation. Most
`fatalities due to earthquakes are caused by building collapse. To prevent such
`risks, designs of earthquake resistant buildings are based on a prevention
`concept where in the case of a major earthquake, buildings may experience
`damages, and however people inside the building must remain unharmed. Based
`on Indonesia’s National Standard (SNI) for earthquake resistant buildings is
`designed by allowing the ductility concept. Based on this concept, in the event
`of a major earthquake, certain elements of a structure may undergo
`plastification. This plastification is a mechanism to dissipate earthquake energy
`on the structure, preventing the structure to collapse. To allow this, elements
`need to be designed to experience a stabile inelastic deformation during a major
`earthquake.
`
`A steel structure is regarded as an earthquake resistant structure with a
`remarkable performance. This is due to unique characteristics of steel. By
`relying on the ductility and high strength characteristics, steel is suitable to be
`applied in areas with high seismic activity. Under the steel structure’s category,
`there are three systems which are resistant to earthquakes, (1) Moment Resisting
`Frame (MRF); (2) Concentrically Braced Frame (CBF); and (3) Eccentrically
`Braced Frame (EBF). MRF has superiority in energy dissipation ability to
`achieve required ductility, however this structure lacks of strength and stiffness
`resulting the requirement of a larger surface area and an expensive double plate
`panel zone to fulfill drift requirements. CBF efficiently fulfills deformation
`limits through its framework action; however the stability in the mechanism of
`energy dissipation is limited [1]. The limitation of both structures has resulted in
`the development of a new structure system named Eccentrically Braced Frame
`(EBF) structures. The difference in the three steel structural systems is shown in
`Figure 1.
`
`P
`
`Δ
`
`Figure 1 Behavior Differences in Three Steel Structure’s System [2].
`
`Page 2 of 26
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`

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`Behavior of Shear Link of WF Section
`
`105
`
`
`
` 2
`
`The Objective of Research
`
`The article presented in this paper is part of a Doctor’s student research
`conducted in Civil Engineering Department of Institute of Technology Bandung
`(ITB) division of structural engineering. The specimen of the study is to obtain
`an EBF structure with maximum performance through increasing performance
`of link elements. To achieve the specimen, this study is aims to: 1) Understand
`mechanism of earthquake energy dissipation in eccentric braced frame steel
`framework structure. 2) Determine parameters which significantly affect link
`element behavior in eccentric braced frame, 3) examine each parameter in
`resulting an improvement of performance link, 4) examine the usage of
`diagonally placed web stiffeners on link element increasing link performance in
`EBF.
`
`Literature Study
`
`3
`3.1 General Overview of Eccentric Braced Frame (EBF)
`Structure System
`Eccentric braced frame (EBF) structure system is a development from the two
`previous lateral force resistant systems, which are MRF and CBF. MRF has
`superiority as it is very ductile and it capable of for large energy dissipation
`capacity, but low in stiffness, while CBF has high stiffness but a small energy
`dissipation capacity. Therefore EBF was developed to perfect both MRF and
`CBF systems. Figure 2 illustrates forms of EBF system which are generally
`applied [3].
`
`EBF system joins each advantage from both structure systems, and decrease the
`weakness. The EBF characteristics are: 1) has a high elastic stiffness; 2) has a
`stable inelastic response under lateral cyclic loading; 3) has a high ductility and
`energy dissipation ability.
`
`In EBF, absorbance of earthquake energy is carried out through a mechanism of
`plastic joint formation on link elements. Link elements are part of the beam
`which is assigned to dissipate energy in the event of a large earthquake. Plastic
`hinges occurring on link elements can be in a form of shear or flexural yielding.
`The type of yielding is dependent on link length.
`
`Page 3 of 26
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`106
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`Yurisman, et al.
`
`b
`
`d
`
`c
`
`b
`
`a
`
`a
`
`b
`
`c
`
`b
`
`d
`
`d
`
`c
`
`c
`
`d
`
`a
`
`b
`
`d
`
`a
`
`b
`
`b
`
`d
`
`c
`
`c
`
`a
`
`a
`
`d
`
`d
`
`b
`
`c
`
`b
`
`c
`
`b
`
`c
`
`b
`
`a
`
`a
`
`c
`
`b
`
`c
`
`c
`
`a
`
`a
`
`b
`
`d
`
`d
`
` d
`
`d
`
`d
`
`d
`
`d
`
`d
`
`a = link
`b = beam segment outside of
`link
`c = diagonal brace
`d = column
`
`
`
`
`Figure 2 Eccentrically Braced Frame Configurations [3].
`
`Link Element Characteristic in EBF System
`3.2
`Link is an element inside EBF system which behaves as a short (deep) beam
`and on both sides apply shear forces with opposite directions along with the
`corresponding flexures (see Figure 3).
`
`Plastification occurring on link element is caused by both forces above;
`therefore link element behavior in overall can be classified into two types
`namely; 1) Moment (flexural) link and 2) Shear link. Link is classified as
`shear link if yielding is caused primarily by shear, and is classified as
`moment link if the yielding is caused by flexural moment.
`
`M
`
`V
`
`M
`
`V
`
`Figure 3 Shear Forces on Link Element [4-5].
`
`
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`Page 4 of 26
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`
`Behavior of Shear Link of WF Section
`
`107
`
`Deformation after yielding occurred of a link beam is caused by either shear
`yielding or flexural yielding or combination of both. By applying a simple
`analytical model, it can be determined the exact limit between flexural and
`shear mechanisms. This limit can be described by using a shear span which
`simultaneously yields in both flexure and shear condition [6].
`
`d
`
`t f
`
`b f
`
`P
`
`a
`
`
`Figure 4 Shear Span and Surface of A Simple Cantilever Beam [7-8].
`
`Shear span is a comparison between moment with shear on a point or spacing
`between point M=0 (inflection point) with a maximum moment point with no
`increase in load between both points. Shear span in its simplest form is
`described as a cantilever beam loaded on its end, as seen in Figure 4. Behavior
`of link in EBF system during mechanism situation is described with the same
`concept, which is a simple shear span as in Figure 4. A balance strength ratio is
`achieved when shear span experiences both flexural and shear yielding
`simultaneously.
`Ma
`=
`V
`Where a = length of cantilever beam shear span, M = moment working on
`beam, V = shear force working on beam. Meanwhile length of cantilever in
`balanced plastic condition can be translated in the formula:
`
`
`
`
`
`(1)
`
`
`
`a
`b
`
`=
`
`M
`V
`
`p
`
`
`
`(2)
`
`where:
`
`=
`
`M
`p
`=ba
`
`p
`.
`FZ
`x
`
` ,
`
`V
`
`p
`
`y
`
`.6,0=
`
`.
`.
`tdF
`y
`
`w
`
`
`
` Comparison of balance strength ratio
`
`Page 5 of 26
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`108
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`Yurisman, et al.
`
`Mp = plastic moment, Vp = plastic shear force, Zx = surface modulus x axis
`direction, d = height of beam surface profile WF, tw = thickness of web profile
`WF, Fy = yield stress.
`
`The cantilever beam will yield caused by shear if the cantilever’s length is less
`than ab and will yield caused by flexure if the length of cantilever exceeds ab.
`From the perspective criteria, link design is considered as a confined beam on
`both ends, balanced link length can be given in the formula:
`
`
`
`e
`b
`
`2
`a=
`b
`
`=
`
`
`
`p
`
`(3)
`
`M
`2 p
`V
`where: eb = balance link length.
`Based on the yield mechanism occurring in link beams, link is divided into two
`namely moment link and shear links depending on flexural and shear yields
`mechanism. However, there is no apparent limit between shear link and
`moment link. To identify a link yields caused by moment or shear, experiments
`are required.
`
`Pure shear occur during link length (e) maximum 80 % from shear span length
`in equilibrium (eb); thus e ≤ 80% eb = 0, 8.2ab = 1,6Mp/Vp. While pure flexural
`condition is considered to occur when “e” exceeds 5Mp/Vp
`
`Behavior of beam link between both conditions is illustrated by applying
`strength ratio Mp/Vp as follows: 1) pure shear link if: e < 1,6Mp/Vp, 2)
`dominant shear link if 1,6Mp/Vp < e < 2,6Mp/Vp, 3) flexural dominated link if:
`2,6Mp/Vp < e < 5,0Mp/Vp, 4) pure flexural link if: e > 5Mp/Vp.
`
`Effects of Web Stiffener towards Shear Link Performance
`3.3
`Due to the high ductility demand on short links, the flange area of the link
`surface (WF profile) might experience buckling phenomena; therefore it is
`required to install web stiffeners. If these web stiffeners are not installed, a large
`premature torsional buckling may occur on the web which in turn might cause
`lateral torsional buckling on the link. Figure 6 shows shear link WF profile with
`a spacing to web stiffener as far as “a” where “a” is web stiffener spacing.
`Experiments conducted by Ghobarah [9] on short links has shown links with
`web stiffeners result in bigger shear ability, along with wider and more stabile
`hysteric loops. Other researchers such as Kasai and Popov [10,12] have
`determined a few simple requirements regarding web stiffener spacing with a
`maximum inelastic rotational angle (γp) to the beginning of web torsional
`buckling, which are as follows :
`
`Page 6 of 26
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`
`
`Behavior of Shear Link of WF Section
`
`109
`
`a = 29tw – d/5 then γp = ± 0. 09 rad.
`a = 38tw – d/5 then γp = ± 0.06 rad.
`a = 29tw – d/5 then γp = ± 0.03 rad.
`a = web stiffener spacing, d = beam height, tw = web thickness.
`
`a
`
`a
`
`a
`
`a
`
`bf
`
`d
`
`tw
`
`
`
`Figure 5 Shear Link with Spacing of Intermediate Web stiffener ”a” [11].
`
`The current code of practice of web stiffener spacing is listed in AISC 2005,
`intermediate web stiffener for shear links cannot be less than (30tw – d/5) and
`the thickness of web stiffener cannot be less than tw or 10 mm.
`
`Method of Research
`4
`This research was conducted with two methods, namely, (1) numerical study
`and (2) experimental study. Numerical study is aimed to examine behavior of
`shear link under cyclic and monotonic load, also to determine parameters which
`influence significantly under the performance of shear link. Numerical study
`was conducted with non linear finite element using MSC/NASTRAN software
`where link is modeled using element of Shell CQUAD4. Element models, up
`until shear links WF profile were made. These were fixed on both ends, where
`one end was given 1 DOF in direction of the Z axis, which can be seen in
`Figure 6. The load given to test specimen was in the form of static monotonic
`and cyclic load under displacement control.
`
`Parameters analyzed in this numerical study were: flange thickness, web
`thickness, web stiffener thickness, spacing of web stiffener, also thickness and
`geometric model of diagonal web stiffener. Next an experimental study was
`conducted to perform a validation towards results of numerical study.
`
`
`
`
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`Page 7 of 26
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`

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`110
`
`V1
`C1
`
`V1
`C1
`
`
`
`
`
`
`
`
`
`
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`A
`
`Y
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`Z
`
`X
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`C
`
`Y
`
`Z
`
`X
`
`Yurisman, et al.
`
`V1
`L1
`C1
`
`V1
`C1
`
`B
`
`Y
`
`Z
`
`X
`
`D
`
`Y
`
`Z
`
`X
`
`Figure 6 Finite element model of shear link with various type of stiffner
`[4,5,7,8].
`
`Experimental study was conducted in Structural Mechanic Laboratory Center
`for Industrial Engineering ITB. In this study, three test specimens were created
`in the form of shear link with and without diagonal web stiffeners. Shape and
`dimension of the three test specimens were adjusted with element models until
`ones analyzed in numerical study. The test specimens was created from profile
`WF 200.100.5,5.8 (as in numerical study profile), the thickness of web stiffener
`was 10 mm, while the thickness of diagonal web stiffener were made in two
`variations, 8 mm and 4 mm as seen in Figure 7.
`
`After creating test specimens, loading frames and the software were then
`prepared along with tools to perform testing. Each test specimen is placed on
`support of test specimen and connected to the actuator with joint plates 40 mm
`thick, connection of joint plates to actuator is using 27 mm bolts.
`
`
`
`
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`Page 8 of 26
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`
`Behavior of Shear Link of WF Section
`
`111
`
`(b)
`(a)
`Figure 7 The form of specimens of shear link with and without diagonal web
`stiffener.
`
`Loading pattern given on test specimens is based on load patterns in AISC
`2005. Applied load are cyclic loads with displacement control. Figure 9 shows a
`graph of load pattern applied on the test specimen.
`
`Loading
`frame
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`LVDT
`Specimen
`
`Actuator for
`applied of
`load to
`specimen
`Support of
`specimen
`
`Figure 8 Set up of equipment and specimen of shear link.
`
`
`
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`Page 9 of 26
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`112
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`Yurisman, et al.
`
`
`
`
`40
`
`30
`
`20
`
`10
`
`0
`
`displacement (mm)
`
`Typical Quasi-static Cyclic Loading
`(AISC 2005)
`
`
`
`
`
`
`
`
`
`
`
`
`
`Figure 9 Quasi-static cyclic loading pattern were subjected to the specimens
`according with AISC 2005.
`
`-10
`
`-20
`
`-30
`
`-40
`
`loading cycle
`
`Numeric Study Results
`5
`Results of numerical study have shown parameters which significantly affect
`the performance of shear link. These parameters are: thickness of diagonal
`stiffener and the geometric model of the stiffener. A few parameters such as
`spacing and thickness of web stiffener, has no significant effect on link
`performance. Other parameters, such as thickness of flange and thickness of
`web, is kept constant in this analysis because these parameters cannot be
`modified in the field due to the applied WF profile which is default from the
`factory. Therefore this research analysis topic is focused on diagonal stiffener
`and vertical stiffener where those parameters could be modified easily to
`increase performance of shear link.
`
`Effect of Web stiffener on Shear Link Performance
`5.1
`AISC 2005 regulated intermediate web stiffener spacing for shear link to not be
`less than (30tw – d/5) and the thickness to not be less than tw or 10 mm. This
`research applies a spacing of stiffener to be 100 mm and thickness of stiffener
`10 mm. To examine effect of spacing and thickness to the performance of shear
`link, observation of three stiffener’s spacing variation as much as 200 mm (2
`spacings); 133.3 mm (3 spacing’s) and 100 mm (4 spacing’s) was conducted.
`Thickness of stiffener was done in three variations: 4 mm, 6 mm, and 10 mm.
`
`Page 10 of 26
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`load (N)
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`
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`
`Behavior of Shear Link of WF Section
`
`113
`
`Load-Displacement Curve of Shear Link with Various Stiffener Spacing
`(100 mm, 133 mm, 200 mm)
`
`
`d = 100 mm
`
`d = 133 mm
`
`d = 200 mm
`
`300000
`
`250000
`
`200000
`
`150000
`
`100000
`
`50000
`
`load (N)
`
`0
`
`0
`
`5
`
`10
`
`20
`15
`displacement (mm)
`
`25
`
`30
`
`35
`
`Figure 10 Link Performance with difference vertical web stiffener spacing.
`
`Load-Displacement Curve of Shear Link with Various
`the Thickness of Verical Web Stiffener
`
`300000
`
`250000
`
`200000
`
`150000
`
`100000
`
`50000
`
`0
`
`0
`
`t = 6 mm
`
`t = 8 mm
`
`t = 10 mm
`
`5
`
`10
`
`20
`15
`displacement (mm)
`
`25
`
`30
`
`35
`
`Figure 11 Link Performance with difference vertical web stiffener thickness.
`
`Page 11 of 26
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`114
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`Yurisman, et al.
`
`Results of non linear finite element analysis are presented in the form of load
`vs. displacement curves. Load vs. displacement curve in Figure 10 shows
`effects of web stiffener spacing on performance of shear link. The nonlinear
`analysis shows that the spacing of stiffener does not have a significant effect,
`due to the vertical stiffener attached on IWF web profile which only delays
`local buckling occurring on the web. Generally encountered IWF profile in the
`market has a compact surface characteristic resulting in minimizing the effect of
`local buckling occurring on the section. The same applies to stiffener spacing;
`variation of stiffener thickness also does not have a significant effect on the
`performance of shear link. Plot on Figure 11 illustrates the effect of stiffener
`thickness on the performance of shear link.
`
`5.2
`
`Increase of Shear Link Performance through Installation on
`Diagonal Stiffener
`Based on the previous analysis, there is no significant effect on the variety of
`stiffener thickness and spacing of web stiffener to the performance of shear link,
`although regulations regarding stiffener thickness and spacing of web stiffener
`have been regulated in AISC 2005 [3] and from previous researches.
`
`Table 1 Models of Shear Links for Cyclic Analysis.
`The thickness
`of Diagonal
`Plate
`(mm)
`
`The thickness of
`Vertical Plate
`(mm)
`
`Sketch
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`10
`
`
`10
`
`
`10
`
`
`8.0
`
`
`
`
`
`4.2
`
`
`Model
`
`
`DV8
`(spec.I)
`
`
`WS3
`(spec.II)
`
`
`DV42
`(spec.III)
`
`
`In this analysis, an innovation to increase performance of shear link through the
`installation of diagonal web stiffener on web area was attempted. The
`hypothesis the research is by installing a diagonal stiffener, a change in surface
`properties may occur. These changes include increase of inertia moment and
`
`Page 12 of 26
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`
`
`Behavior of Shear Link of WF Section
`
`115
`
`shear surface. The installation is also predicted to prevent local buckling on link
`element. Although there is yet a code or previous research results which
`regulate the design of diagonal stiffener on link, numerical and experimental
`studies to further determine shear link behavior with diagonal stiffener on the
`web area was conducted. Table 1 shows a sketch model of the analyzed
`specimens with cyclic loading.
`
`Based on the results of initial studies which have been performed numerically, it
`was found an indication that the installation of diagonal bracing on the web
`profile of WF on the link element can increase link capacity of lateral force
`resistance, and improve the ability of shear link in the energy dissipation.
`Indicators ability shear links in the energy dissipation is expressed in the form
`of hysteretic curve Force vs. Displacement relationship obtained from the quasi-
`static loading (cyclic) as shown in Figure 12.
`
`5.00
`
`10.00
`
`15.00
`
`600000
`
`500000
`
`400000
`
`300000
`
`200000
`
`100000
`
`0
`0.00
`-100000
`
`-200000
`
`-300000
`
`-400000
`
`-15.00
`
`-10.00
`
`-5.00
`
`load (N)
`
`-500000
`displacement (mm)
`
`WS3
`
`DV42
`
`DV8
`
`
`
`Figure 12 Comparison of shear link hysteretic curve with thickness variation of
`diagonal bracing and shear link under AISC-2005 standards.
`
`Experimental Study Results
`6
`Experimental tests conducted on three specimens of each link namely link
`without diagonal stiffener, diagonal stiffener link with 4.2 mm thick and a link
`
`Page 13 of 26
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`116
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`Yurisman, et al.
`
`with a diagonal stiffener of 8 mm. All specimens were steel profile of WF
`200.100.5, 5.8 and 400 mm in length.
`
`The first specimen (Specimen I) is capable to withstand large lateral force at
`failure. This is because the influence of the diagonal stiffener increasing the
`stiffness and the strength of the specimens. However, thicker diagonal stiffener
`can inhibit plastification of the web leading to brittle failure mechanism. The
`amount of the maximum load that can be resisted for specimen 1 is 517.222 N
`in compression and 403.466 N in tension whilst the value of the corresponding
`maximum displacement of the specimen is 11.76 mm in tension and 10.94 mm
`in compression.
`
`Specimen II is the standard shear link complying with the AISC 2005 is capable
`to withstand the lateral force of 353.755 N in compression and 310.409 N in
`tension, whilst the value of the corresponding maximum displacement of
`specimens is 24.68 mm in compression and 25.38 mm in tension. The failure
`mechanism, however, is more ductile compared to the first Specimen.
`
`Specimen III is a shear link with diagonal stiffener of 4.2 mm thick, underwent
`plastification on the flange, web and diagonal stiffener before collapse. Because
`the thicknesses of the diagonal stiffeners are relatively thin with lower yield
`stress, buckling has occurred in the diagonal stiffener before the collapse of the
`specimen. Maximum load that can be retained by the specimen is 446.992 N in
`compression and 326.323 N in tension, whilst the corresponding maximum
`displacement is 16.58 mm in compression and 18.04 mm in tension. The failure
`mechanism is close to Specimen with comparable ductility.
`
`
`
`
`
`
`
`
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`
`
`Figure 13 Cracks in the flange of the Specimen I in the top of the welded
`joints, no buckling occurred in the diagonal stiffener during collapse.
`
`Page 14 of 26
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`

`

`
`
`
`Behavior of Shear Link of WF Section
`
`117
`
`All of the specimens have the same failure modes starting with the occurrence
`of cracks on the flange around the joint at the supported area. High stresses
`concentration due to thick welded joints in these positions causes the vicinity
`becomes brittle and it is prone to crack or fracture. This phenomenon
`accelerates the collapse of the specimen and the cracking (fracture) of the
`specimen. However, this behavior is difficult to model in numerical studies.
`Figures 13 to 15 show cracks that occurred in the third Specimen at failure.
`
`
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`
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`
`
`
`
`
`
`
`
`
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`
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`
`
`Figure 14 Fracture in the flange of the Specimen II at the top of the welded
`joints at the time of collapse.
`
`Figure 15 Fracture in the flange on the third specimen in the top of the welded
`joints at the time of the collapse.
`
`Page 15 of 26
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`

`

`118
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`Yurisman, et al.
`
`Perbandingan Respons Tiga Benda Uji Dalam Menahan Beban Siklik
`Hingga Mengalami Keruntuhan
`
`10
`
`20
`
`30
`
`600000
`
`400000
`
`200000
`
`0
`
`0
`
`-200000
`
`-400000
`
`-20
`
`-10
`
`-30
`
`load (N)
`
`-600000
`displacement (mm)
`spec 1
`spec 2
`
`spec 3
`
`
`
`Figure 16 Hysteretic curves of three specimens.
`
`Response of Three specimens of shear links under cyclic loading
`(rotation 0.03 radian)
`600000
`
`5
`
`10
`
`15
`
`400000
`
`200000
`
`0
`
`0
`
`-200000
`
`-400000
`
`-600000
`displacement (mm)
`
`-10
`
`-5
`
`-15
`
`load (N)
`
`thickness of stiffner 4 mm
`
`no stiffner
`
`
`Figure 17 Response of specimens under stable condition (rotation of 0.03
`radiant).
`
`thickness of stiffner 8 mm
`
`Page 16 of 26
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`

`

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`
`Behavior of Shear Link of WF Section
`
`119
`
`The comparisons among the hysteretic curves of Specimens are showed in
`Figure 16. The curves show that the link with the diagonal stiffener has the
`ability to withstand greater lateral force, but less inelastic deformation. To
`achieve the ability to the link with optimal performance, the thickness and
`material properties of diagonal stiffener must be design in such a way as to not
`impede the plasticity process of the web. The Figure also shows that the shear
`link with a thinner thickness of the stiffener has fatter hysteretic curve
`indicating a better performance despite the lateral force is slightly lower.
`
`Hysteretic curves in Figure 16 cannot be used directly to compare the
`performance of individual specimens because failure occurs at different load. In
`order to compare the performance of the samples individually stable condition
`should be chosen rather than at failure. Stable condition in this case is defined
`as a condition whereby the three specimens were already experiencing inelastic
`deformation without collapse of any parts of the specimens or stable inelastic
`condition. In this test a stable inelastic condition occurs when the rotation is
`0.03 radians or displacement of 12.00 mm as shown in Figure 17.
`
`7
`
`Cyclic Analysis towards Performance of Shear Link
`Specimens
`Cyclic analyses of the three specimens were conducted to compare the shear
`link performance of the three specimens for strength, stiffness, energy
`dissipation, and ductility based on the results of both experimental work and
`numerical model.
`
`Strength is defined as the maximum lateral force (shear force) that can be
`retained by the specimens in each stage of loading (load step). Load vs.
`displacement curve in Figures 18 and 19 show the comparison of the strength of
`three specimens from the results of experimental tests and numerical studies.
`Load vs. displacement curves in the figure shows that Specimen I (shear link
`with diagonal bracing of 8 mm thick) obtained the highest strength in a lateral
`withstanding tension and compression compared to Specimens II and III.
`
`Stiffness is defined as secant stiffness is the ratio between the maximum lateral
`force and displacement at each stage of loading (load step). Similar to the
`analysis of strength, the secant stiffness for the three models of the specimens
`were observed in the tension and compression. Figure 20 shows the relationship
`between the stiffness vs. displacement of the experimental tests. Specimen I has
`the highest secant stiffness, despite it is more brittle compared to Specimens II
`and III. In numerical studies, the earlier failure phenomenon cannot be picked
`up modeled with computer software used. The results of numerical studies
`
`Page 17 of 26
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`

`

`120
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`Yurisman, et al.
`
`shown in Figure 21 are in a good agreement with the experimental work that the
`use of the diagonal stiffener improves the stiffness of the shear link.
`
`spec.1(DV8)
`
`spec. 2 (WS3)
`
`spec. 3 (DV42)
`
`450000
`
`400000
`
`350000
`
`300000
`
`250000
`
`200000
`
`load (N)
`
`150000
`
`100000
`
`50000
`
`
`
`
`
`0
`0.00
`
`2.00
`
`4.00
`
`10.00
`8.00
`6.00
`displacement (mm)
`
`12.00
`
`14.00
`
`16.00
`
`(a)
`
`spec.1 (DV8)
`
`spec. 2 (WS3)
`
`spec. 3 (DV42)
`
`600000
`
`500000
`
`400000
`
`300000
`
`200000
`
`100000
`
`load (N)
`
`0
`0.00
`
`2.00
`
`4.00
`
`10.00
`8.00
`6.00
`displacement (mm)
`
`12.00
`
`14.00
`
`16.00
`
`(b)
`Figure 18 Comparison of shear strength of three model specimens of shear
`link, the experimental results in tension (a) and the compression (b).
`
`Page 18 of 26
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`

`

`
`
`
`Behavior of Shear Link of WF Section
`
`121
`
`
`
`
`
`spec.2 (WS3)
`
`spec.3 (DV42)
`
`spec.1 (DV8)
`
`450000
`
`400000
`
`350000
`
`300000
`
`250000
`
`200000
`
`force (N)
`
`150000
`
`100000
`
`50000
`
`0
`0.00
`
`2.00
`
`4.00
`
`8.00
`6.00
`dispalcement (mm)
`
`10.00
`
`12.00
`
`14.00
`
`(a)
`
`spec.2 (WS3)
`
`spec.3 (DV42)
`
`spec.1 (DV8)
`
`500000
`
`450000
`
`400000
`
`350000
`
`300000
`
`250000
`
`200000
`
`150000
`
`100000
`
`50000
`
`force (N)
`
`0
`0.00
`
`2.00
`
`4.00
`
`8.00
`6.00
`displacement (mm)
`
`10.00
`
`12.00
`
`14.00
`
`(b)
`Figure 19 Comparison of shear strength of three model specimens of shear link,
`the results of numerical studies on the condition of tension (a) and the
`compression (b).
`
`Page 19 of 26
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`

`

`
`
`
`
`122
`
`Yurisman, et al.
`
`spec.1 (DV8)
`
`spec.2 (WS3)
`
`spec.3 (DV42)
`
`120000
`
`100000
`
`80000
`
`60000
`
`40000
`
`20000
`
`stiffness (N/mm)
`
`0
`0.00
`
`2.00
`
`4.00
`
`10.00
`8.00
`6.00
`displacement (mm)
`
`12.00
`
`14.00
`
`16.00
`
`(a)
`
`spec.1 (DV8)
`
`spec.2 (WS3)
`
`spec.3 (DV42)
`
`120000
`
`100000
`
`80000
`
`60000
`
`40000
`
`20000
`
`stiffness (N/mm)
`
`0
`0.00
`
`2.00
`
`4.00
`
`10.00
`8.00
`6.00
`displacement (mm)
`
`12.00
`
`14.00
`
`16.00
`
`(b)
`Figure 20 Comparison of secant stiffness of the specimens of experimental
`work in tension (a) and compression (b).
`
`Page 20 of 26
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`

`

`Behavior of Shear Link of WF Section
`
`123
`
`WS3
`
`DV42
`
`DV8
`
`2.00
`
`4.00
`
`8.00
`6.00
`displacement (mm)
`
`10.00
`
`12.00
`
`14.00
`
`(a)
`
`WS3
`
`DV42
`
`DV8
`
`2.00
`
`4.00
`
`8.00
`6.00
`displacement (mm)
`
`10.00
`
`12.00
`
`14.00
`
`
`
`
`
`180000
`
`160000
`
`140000
`
`120000
`
`100000
`
`80000
`
`60000
`
`40000
`
`20000
`
`stiffness (N/mm)
`
`0
`0.00
`
`180000
`
`160000
`
`140000
`
`120000
`
`100000
`
`80000
`
`60000
`
`40000
`
`20000
`
`stiffness (N)
`
`0
`0.00
`
`(b)
`Figure 21 Comparison of secant stiffness of three numerical model of
`specimens in tension (a) and compression (b).
`
`
`
`
`
`
`Page 21 of 26
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`

`

`124
`
`Yurisman, et al.
`
`spec.2 (WS3)
`
`spec.1 (DV8)
`
`spec.3 (DV42)
`
`2
`
`4
`
`6
`
`8
`
`10
`
`12
`
`14
`
`16
`
`displacement (mm)
`
`(a)
`
`2.00
`
`4.00
`
`6.00
`
`8.00
`
`10.00
`
`12.00
`
`14.00
`
`displacement (mm)
`spec.2 (WS3)
`spec.1 (DV8)
`
`spec.3 (DV42)
`
`
`
`
`
`30000000
`
`25000000
`
`20000000
`
`15000000
`
`10000000
`
`5000000
`
`energy of dissipation (N.mm)
`
`0
`
`0
`
`-5000000
`
`35,000,000
`
`30,000,000
`
`25,000,000
`
`20,000,000
`
`15,000,000
`
`10,000,000
`
`5,000,000
`
`energy of dissipation (N.mm)
`
`0
`0.00
`-5,000,000
`
`(b)
`Figure 22 Comparative performances of three specimens in the dissipation of
`energy of the experimental test results (a) and the results of numerical studies
`(b).
`
`Page 22 of 26
`
`

`

`
`
`
`Behavior of Shear Link of WF Section
`
`125
`
`In this study, the amount of energy dissipation in the specimen of the shear link
`is expressed by the area under cyclic hysteretic curves in terms of the force vs.
`displacement relationship. Calculate the area of hysteretic curve analysis is
`conducted using the incremental method where the curve is divided into small
`triangle. The amount of energy dissipation is the result of a cumulative sum of
`the total hysteretic curve generated in each stage of loading. Cumulative energy
`dissipation curve vs. displacement in the Figure 22a shows the amount of
`energy dissipation capacity of shear links due to cyclic loading.
`
`From the experimental results showed that the shear link with diagonal stiffener
`4.2 mm has the highest energy dissipation (Specimen III), while the link with 8
`mm thick diagonal stiffener (Specimen I) in the early stages of loading is
`capable to achieve the highest energy dissipation among the three specimens,
`however, this specimen collapse in the early stage of loading. The failure is
`because of fracture occurred on the flange in the support.
`
`The curve in Figure 22b is the result of numerical study. The curve indicates
`that the shear link with diagonal stiffener 8 mm (Specimen I) has the best
`performance in terms of energy dissipation. As shown in Figure 22b, the
`numerical result is slightly different with the experimental tests for Specimen I.
`This is