Cyclic behavior studies on I-section inverted V-braces and their gusset plate connections

Journal of Constructional Steel Research 67 (2011) 407–420

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Cyclic behavior studies on I-section inverted V-braces and their gusset plate connections Wenyuan Zhang a,∗ , Mingchao Huang a , Yaochun Zhang a , Yusong Sun b a

School of Civil Engineering, Harbin Institute of Technology, Harbin, 150090, China

b

Northeast Electric Power Design Institute, Changchun, 130021, China

article

info

Article history: Received 1 February 2010 Accepted 28 September 2010 Keywords: Special concentrically braced frame Inverted V-brace Gusset plate connection Cyclic behavior Experimental investigation Low-cycle fatigue fracture

abstract Inverted V-braces and their central gusset plate connections are popular patterns of brace arrangements for special concentrically braced frames (SCBF). To improve the understanding of their seismic performances and promote their applications in seismic designs, the hysteretic behavior of nine I-section inverted V-braces and their gusset plate connections subject to inelastic cyclic loading is examined through experiments and analytical simulations. It is found that the clearance at the brace end on the gusset plate, the locations of the intersection point of bracing members, and the ratio of the free edge length to the gusset plate thickness are the key parameters. The loading capacities of braced frames show no decrease before the brace low-cycle fatigue fracture, but a longer plateau at a lower load level exists in the hysteretic loops. Although specimens with a linear clearance exhibit better seismic behaviors, a negative clearance is also acceptable as long as the gusset plate does not fracture prior to the braces. A brace intersection point with moderate eccentricity is preferable for its better behavior and its economical dimension of the gusset plate, but the brace point location in the gusset plate could induce out-of-plane deformations in the gusset plate and cause the system ductility to deteriorate. Based upon test results, a suggested limitation of the ratio of the free edge length to thickness for the gusset plates is presented. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction The inelastic lateral response of concentrically braced frames is mastered by axial yielding and post buckling deformation of the braces, and to assure appropriate inelastic performance of the frames, special concentrically braced frames (SCBFs) are introduced by recent seismic guidelines [1]. The braces are typically connected to the beams and columns of the frame through gusset-plate connections. Under severe earthquakes, the gusset-plate connections may tolerate large inelastic deformations and rotations after the brace buckling, and they must also support the loading induced by tensile yielding or post buckling of the braces. Fracture of a gusset plate will most likely result in considerable loss of strength and stiffness of the braced frame. Therefore, the governing failure mode of the gusset plate connections in seismic applications should be a yielding failure mode, but not a fracture mode [2]. In the past twenty years, much more attention has been paid to the bolted or welded connections of diagonal braces to beams and columns (shown in Fig. 1) subjected to monotonic or cyclic

∗

Corresponding author. E-mail address: [email protected] (W. Zhang).

0143-974X/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2010.09.012

loading. The majority of the load-carrying capacity researches on gusset plate connections focused on the elastic or inelastic stress distribution models and strength checking methods, such as the widely used Whitmore effective area concept [3–5] and the block shear concept [6–9]. When gusset plates are subjected to compressive loads, the buckling of the gusset plate at its free edges and local buckling near the end of the splicing members have also been examined [10–13]. The buckling capacity of the gusset plate could be estimated to be the compressive resistance of the imaginary column strips with the specified effective length factors by the proposed simplified methods [14–16]. The range of effective length factors were thought to be from 0.65 to 1.2, depending on the gusset plate configuration and supported conditions. But some results also showed that, in buckling restrained braced frames, an effective length factor that is no less than 1.5 should be considered for the design of the gusset plate without edge stiffeners [17]. To investigate the ductility and energy dissipation capability of the bracing elements during severe earthquakes, models including the interaction of gusset plate and brace member were employed in some recent experimental and analytical studies under cyclic loading [18–22]. When the brace buckles out-of-plane, two plastic hinges will form on the gusset plates at each end of the brace, and one plastic hinge will form at the brace midspan. It was proposed that an adequate 2tp (double thickness of gusset plate) free length of gusset plate, between the brace end (or splice end)

408

W. Zhang et al. / Journal of Constructional Steel Research 67 (2011) 407–420 Column p 2t

Column I-Section Brace

HSS Brace Gusset Plate

Double Angles on Each Flange

Double Angles

Gusset Plate

8t p Shear Tab

W.P.

Double Angles

W.P.

Beam

(a) Diagonal braced frame.

(b) Linear clearance.

Beam

(c) Elliptical clearance.

Fig. 1. Diagonal braced frame and the corner gusset plate connections.

Beam

Beam nt

p

W.P.

e

CJP Plastic Hinge Curve Gusset Plate Splice Plates

St iffener

I-Section Brace

(a) Inverted V-braced frame.

Gusset Plate

I-Section Brace

(b) Central gusset plate.

(c) Detailed issues in design.

Fig. 2. Inverted V-braced frame and the central gusset plate connections.

and the restrained line of the gusset plate, shown in Fig. 1(b), was necessary to ensure the free formation of plastic hinges and no prior occurrence of damage accumulation at the gusset connections [20–22]. In these researches, various kinds of brace sections (double angle, square hollow and circular hollow sections) were studied to prove the availability of plastic rotation around the linear clearance on the gusset plate, and the braces were able to dissipate energy until they fractured at the midspan plastic hinge. However, achieving this free rotation at brace ends often results in large and uneconomical gusset plate connections in practical seismic applications. A modified approach was proposed, in which the yield mechanism of the brace was balanced with that of the connection to achieve a target yielding hierarchy and suppress unwanted connection failure modes [23–25]. The elliptical clearance model with an 8tp clearance, shown in Fig. 1(c), was regarded as a balanced value, and could maximize the ductility of the structural system while limiting premature damage. Inverted V-bracing (i.e., chevron type bracing) is a very popular pattern of arranging braces for SCBFs, as shown in Fig. 2(a). Until recently, however, relatively little attention has been given to the behaviors of inverted V-braces and their central gusset plate connections [2,17], as shown in Fig. 2(b). The inverted V-braces are much different from diagonal braces, due to the combined action on the central gusset plate caused by tension in one brace and compression in the other. Firstly, there is only one restrained edge connection of the central gusset plate to the beam, while there are two restrained edges connecting the corner gusset plate to the beam and column respectively. If there are no stiffeners on the gusset plate, the former would have weaker out-of-plane rotational stiffness than the latter. Secondly, both tensile and compressive fields exist simultaneously in the central gusset plate, and the stress state will become even more complex after the compressed bracing member buckling. We still don’t know if and how the tensile field will give any help to sustain the stability of the compressive field on the gusset plate. Thirdly, the length of free edge on the central gusset plate is much longer than that on the corner gusset plate, but the compressive stress only exists in the half length of the free edge near the compressed

brace end. Although Astaneh-Asl [2] reported results of cyclic load tests of three gusset plate specimens representing the V-braced connections, they were gusset plate tests rather than assemblage or braced system tests, and the impact of braces buckling or yielding could not be considered in these tests. To explore the seismic behavior of the braced systems assembled with inverted V-braces and their gusset-plate connections, a series of one-storey, one-bay braced systems were tested at the Harbin Institute of Technology. These assemblages were subjected to a cyclic displacement history, which consisted of monotonically increasing drift cycles. Nine specimens were designed to investigate the effects of interesting key issues, shown in Fig. 2(c), such as the clearance model of the plastic hinge on the gusset plate, the thickness of the gusset plate, the location of the intersection point of bracing members, the function of stiffeners on the gusset plate, etc. To support and extend the experimental research, and to obtain the complex stress distribution that could not be measured in detail on the gusset plate in the tests, nonlinear analyses were performed using the ANSYS program. The stress studies were performed to bring forward a reasonable model of the plastic hinge curve on the gusset plate. The proposals for the central gusset plate connection designs in inverted V-braced systems to meet specific performance objectives are also presented in this paper. 2. Experimental program 2.1. Test setup As all the mentioned facts approved the importance of studying the seismic behavior of braced systems, a test setup of one storey and one bay plane frame including the columns, beams, inverted V-braces and gusset plate was designed particularly, as shown in Fig. 3. Welded steel beams and columns were used for assemblage convenience. To study the hysteretic behaviors of the inverted V-braces and their connections without the inelastic interference by the other members and connections, the fourhinge frame was employed here, and the beams and columns

W. Zhang et al. / Journal of Constructional Steel Research 67 (2011) 407–420 Out-of-Plane Support Out-of-Plane Su pport

Upper Beam

Hydraulic Actuator 2

18 5

1

Greased Interface

A C Column

Tested Specimen

B

Gusset Plate Hinge C

I-Section Brace Out-of-Plane Hinge In-Plane Hinge 4 Supporting Beama

Lateral Support Out-of-Plane Support System

Hinge

Lo ad Cell

Strong Wall

Material: Q235B(Chinese Standard) Supporting Beam: Box 493X350X12X24 Upper Beam: I 200X150X8X16 Columns: I 190X150X10X10 Hinges Ground Anchors: Bar D120 Hinges: Bar D30 LV DT String Potentiometer

698

Rigid Column

3

409

Ground Anchor 1886

Lateral Support

Fig. 3. Test setup of braced four-hinge frame.

which should work in an elastic state during all the tests were designed strong enough. Based on the same reason, the corner connection of the studied I-section brace to the column and lower beam was specially designed with two hinges that allowed brace end rotation both in-plane and out-of-plane. The I-section brace web was placed in the tested frame plane to assure the braces could buckle out-of-plane around their weak axes, which is very popular in engineering. The lower support beam was fixed on the ground. A 300 kN hydraulic actuator, applying predetermined horizontal displacements, was mounted on the upper beam of the four-hinge frame. Consequently, the inverted V-braced systems would be subjected to mainly push–pull loading, a simulation of actual loading of bracing members due to earthquakes. Two out-of-plane lateral supports were set up on the upper beam to assure the braced frame could be only loaded and deformed in-plane. 2.2. Test specimens The experimental program consisted of testing of nine I-section inverted V-braced systems under reversed cyclic loading. Two bracing members and their gusset plate connections were involved in each specimen, shown in Fig. 4. Each gusset plate was fillet welded (leg size 4 mm) to an end plate (thickness 12 mm), which was bolted with high strength bolts to the lower flange of the upper beam at midspan. The flanges and web of each brace were both connected to the gusset plate by the welded splices. It should be noted that there was a slot on the flange splice where the gusset plate was welded, while the brace flange was welded to the other part of the splice. The required strength of all the other connections, including splices, welds and bolts, was equal to Ry AFy , the nominal axial yield strength (product of section area A and yield stress Fy ) of the brace multiplied by the ratio (Ry ) of the expected yield strength to the minimum specified yield strength, according to both the AISC and Chinese seismic provisions [1,26]. The tensile capacities of the gusset plate in all the specimens were checked beforehand, based on the limit states of rupture of the Whitmore effective net section [1,3] and block shear rupture [1,8]. The local buckling capacity with the effective length factor 1.2, was also calculated to assure it was greater than the overall buckling capacity of the braces in compression [2]. The brace sections were fixed on the same size (shown in Fig. 4) for all the specimens. The nine specimens were designed with variable parameters on the gusset plate connections, shown in Fig. 4 and the column 3 to 8 of Table 1, which are the potential key issues influencing the behavior of the braced systems. The eccentricity e between the beam axis and the intersection point

of the inverted V-brace axes in column 3 is one of the important factors determining the connection size. Greater eccentricity may usually result in a more compact gusset plate, and the behavior and ductility of these specimens would be tested here. The zero or negative clearance in column 5 (the value of c) means that the specimen does not satisfy the clearance requirement for 2tp ∼ 3tp [2,20]. These specimens were used to explore if the clearance rule is applicable to the central gusset plate connections. The pair of stiffeners, which could once supposedly prevent the free edge buckling of the gusset plate, was used to reduce the ratio of free edge length to thickness, b1 /tp (see the Node 4 in Table 1). The specimens with variable b1 /tp were designed to evaluate the rationality of the limitation of b/tp proposed by Astaneh-Asl [2] under cyclic load, expressed as b1 /tp ≤ 0.75 E /Fy .



(1)

If the brace physical length L, between the splice end on the central gusset plate and out-of-plane hinge at the other brace end (shown in Fig. 4), is assumed to be the out-of-plane effective length of the braces, there are a little differences among the brace slenderness ratios for each specimen due to the detailed requirements of the studied parameters. But the differences among the specimens in the same groups or the specimens to be compared in the following are so small that its effect on the low-cycle fatigue life of the braces is ignored in this paper. The average material properties of the steel plates used for the braces and gusset plates, as shown in Table 2, are obtained by tensile coupon tests. The gauge length and width of the coupons are prepared and tested according to the Chinese Standard GB/T 2282002 [27]. Because the rolled times for the relatively thinner steel plates used here would be much more than the normal thickness plate, the yield stresses in Table 2 are higher than the normal value (Fy = 235 MPa). But the elongation rates show all the plates have good ductility behaviors which can meet the test material requirements. 2.3. Measuring instrumentation and test procedure The measuring instruments are also shown in Fig. 3. The cyclic loads applied to the braced frames were measured using the 300 kN load cell located between the actuators and the upper beam end. Two strain gauge rosettes were attached on the gusset plate (point A in Fig. 3: the re-entrant corner on the gusset plate, and point B in Fig. 3: the gusset plate at the splice end), where the worst stress state would occur. Four pairs of strain gauges to measure the brace strain were placed on each free out-stand of the brace flanges at the first quarter of brace length (cross-section C in Fig. 3), where little additional stress would be caused by the constraint of the

I-Section Brace

tp

50

70

40 A- A

Flange Splice a

18

0

h

A

3

883

A

3

L

Stiffener

120 s

3

c

Gusset Plate Splices

10 0

W. Zhang et al. / Journal of Constructional Steel Research 67 (2011) 407–420 e

410

Out-of-Plane Hinge

tp

b Gusset Plate

78 3

783

Fig. 4. Test specimen and influence parameters. Table 1 Specimen descriptions and measured dimensions. Group

Specimen

e (mm)

tp (mm)

c (mm)

Stiffeners

b (mm)

b1 /tp

L (mm)

a (mm)

h (mm)

s (mm)

G1

KZ-1 FKZ-1 KJH

100 100 100

3.92 3.92 5.70

10 (2.5tp ) −20 (−5tp ) 15 (2.5tp )

Without Without Without

183 183 183

46.7 46.7 32.1

796 826 791

322 322 322

157 157 157

52 83 47

G2

KZ-2 FKZ-2 KJL

0 0 0

3.92 3.92 3.92

10 (2.5tp ) 0 (0tp ) 10 (2.5tp )

Without Without With

301 301 301

76.8 76.8 38.4

764 774 764

431 431 431

140 140 140

52 62 52

G3

KZ-3 FKZ-3

157 157

3.92 3.92

10 (2.5tp ) −16 (−4tp )

Without Without

119 119

30.4 30.4

797 823

300 300

190 190

52 78

G4

KZ-4

50

3.92

10 (2.5tp )

Without

219

55.9

798

322

134

52

Note: 1. The brace sections in each specimen are all welded I-sections, I70 × 40 × 3 × 3 (A = 432 mm2 ), and the web and flanges are welded together by gas shielded arc welding with effective throat depth of 3 mm. 2. The symbol meanings in this table are given in Fig. 4. 3. The stiffener plate size is 140 × 60 × 4. 4. For the gusset plate with the stiffeners, the free edge length b1 is equal to b/2; and without stiffeners, b1 is equal to b. 5. The minimum slenderness ratio is 88.6 for KZ-2, and the maximum is 95.8 for FKZ-1. Table 2 Dimensions and results of coupon tests.

Nominal thickness t (mm)

Actual thickness t (mm)

Young’s modulus E (MPa)

Yield stress fy (MPa)

Tensile stress fu (MPa)

Poisson ratio ν

Elongation rate εu (%)

h l l0 (mm) (mm) (mm)

3 4 6

2.87 3.92 5.70

2.05 × 105 2.06 × 105 2.06 × 105

316 295 267

451 404 410

0.272 0.278 0.265

23.3 27.4 25.8

40 40 50

brace end or the local buckling of the brace midspan. Two LVDTs (named 1 and 2) were installed at each end of the upper beam to measure the horizontal deformation, and one LVDT (named 3) was installed at the upper beam midspan to measure the vertical deformations. Another one (named 4) was installed at the end of the support beam to obtain the possible support deformation. Two string potentiometers linked to the brace web at midspan (named 5 and 6) were used to measure the out-of-plane displacements after brace buckling. A typical loading sequence for each specimen is shown in Fig. 5. Pursuant to the JGJ 101-96 [28], the tested specimens were initially subject to monotonically increasing load cycles, until one of the inverted V-braces buckled firstly under compression. The increasing amplitude load in each cycle was equal to 10 kN. These elastic load cycles could allow for an instrumentation calibration check and provide a good opportunity to ensure the test frame assembly was operating safely. Once one compressed brace buckled, the specimen would be loaded reversely to the position where the other brace buckled too. And then, the increasing amplitude drift in every two loops would be equal to 1δ = 5 mm, as shown in Fig. 5 until the components (braces or gusset plate) of the specimen failed as a result of fracturing.

55 60 90

45 50 75

3. Experimental results 3.1. Response and failure mode In all specimens, the initial yield mechanism was one of compressed brace buckling out-of-plane when the increasing horizontal cyclic load reached a certain value. Although the brace buckling caused a little out-of-plane rotation on the gusset plate, there was no visible local buckling or flaking of the red-paint, indicating no plasticity on the gusset plate just at the beginning of the brace buckling. In the reversed half of the loading loop, the other brace which was to be compressed in turn, buckled under approximately the same load level. With the following drift cycles, the two braces would be compressed buckling out-of-plane and tensioned straight alternately. With additional drift demand, the out-of-plane deformation of the compressed brace increased gradually and the local buckling on the brace flange near midspan (shown in Fig. 6(a)) would occur due to the developed great cyclic plastic strain. At the same time, the rotation of the brace end increased and flaking of the red-paint owing to the accumulated plasticity could be observed on the gusset plate. In all test specimens, the low-cycle fatigue

W. Zhang et al. / Journal of Constructional Steel Research 67 (2011) 407–420

Fig. 5. A typical loading sequence.

fracture occurred always in a tension cycle on the brace flanges near midspan where the severest local buckling and cyclic plastic stress had developed, as illustrated in Fig. 6(b, c). There were no fractures that could be observed on the gusset plates or their weld zone, although the gusset plates had been bent or tensioned to yield long before the tearing of the brace midspan. Fig. 7 provides the gusset plate deformation of all the specimens after the tests. Because the test ceased when one of the braces was tensioned to fracture and the other compressed was under buckling, the rotated deformation on one part of the gusset plate connecting the tensioned brace was restored, while there was obviously plastic rotation on the other part connecting the compressed brace. No local buckling was observed in the gusset plates in the course of all the tests. There was also no obvious free edge buckling for all the specimens except KZ-1, although the ratio of free edge length to gusset plate thickness varied greatly for these specimens. The free edge buckling appeared in large drift cycles for KZ-1, but it had no obvious effect on the seismic behavior of the specimen which will be also discussed in the following Section 5.3. It should be noted, at the end of tests for the specimens of KZ3 and FKZ-3, markedly out-of-plane plastic rotation of the whole gusset plates around the restrained edge could be found, shown in Fig. 7(g, h). For both of these specimens, the intersection points of the brace axes was located in the gusset plates with the maximum eccentricity e in the all specimens. The reason of these phenomena will be discussed further in the following Section 5.2. The failure sequence of the braces and connections are well in agreement with the hierarchical order of desirability that is well covered in the literature and design specifications [1,2,24]. Generally, the failure modes and their sequence could be described as: (1) Buckling of the bracing members; (2) Plastic out-of-plane rotation of the gusset plates; (3) Yielding of the bracing members; (4) Yielding of the gusset plates; (5) Free edge buckling of the gusset plate; (6) Fracture of the bracing members. The ductile failure modes, such as yielding of bracing members or connections, occurred prior to the brittle failure modes, such as fracture of connections. In this way the specimen can be in great ductility and can dissipate energy as much as possible. 3.2. Summary of hysteretic behavior The solid lines in Fig. 8 show the force–deflection behavior of the nine specimens. For the diameters of the two perpendicular pin bolts connecting the brace to the support beam were designed about 2–3 mm smaller than the pin holes to assemble easily, there were some slippage in each cyclic loop even before the brace buckling. But this slippage did not influence the strain behavior of the brace and gusset plate, except the maximum drift ratio or ductility. For this reason, the slippage that could be detected in force–deflection curves was subtracted from the tested drift in the following results.

411

The hysteretic behavior of the inverted V-braced system in the tests is much different from a single bracing member. There are enough load-carrying capacities in both positive and negative directions and the envelope of hysteretic curves shows no decrease until one of the braces fracture, for the existence of tension bracing member at anytime in the cyclic loops. But a longer plateau at a lower load level, which is not more than 30 kN or not more than 30% of the capacity corresponding to initial brace buckling, can be found in the hysteretic loops. The reason is, in the course of reversed loading from zero (the state A in one of the hysteretic loops for specimen KZ-2 in Fig. 9), the brace ‘‘II’’ that began once more to be compressed would buckle soon (the state B in Fig. 9) for the degradation in compressive capacity after the initial outof-plane buckling cycle, while at this time there was no stiffness on the other brace ‘‘I’’ that had buckled previously and now tended to be tensioned straight. The state of loss of tangent stiffness, in which the two braces were both curving (shown by the state C in Fig. 9), would not end until the brace ‘‘I’’ was tensioned to be straight (the state D in Fig. 9). Then due to the contribution to storey stiffness by the tensioned braces, the capacities of the braced frames would reach to the maximum values in the range of 124–150 kN for different specimens (shown by the state E in Fig. 9). 3.3. Performance of the tested specimens Data for all of the 9 specimens, averaged test results of positive and negative directions, are summarized in Table 3. The following data are reported for the cyclic loading tests: (1) Ke = lateral elastic frame stiffness before brace buckling, (2) Pcr = loading applied corresponding to the brace original buckling, (3) Pu1 and Pu2 = assumed ultimate load-carrying capacities for the inverted V-braced frames in the first and second reversed loops corresponding to storey drift ratio 1/30, (4) µ= ductility ratio, i.e., the maximum storey drift divided by the brace-buckling storey drift. (5) θu = maximum storey drift ratio, i.e., the maximum storey drift divided by storey height, (6) Σ Ei /Ep = normalized dissipated energy, i.e., the summation of energy dissipated up to the point of strength loss normalized by the area enclosed by horizontal deflection axis and the secant of envelope curve at the point of storey drift ratio 1/30 (calculated as the product of the Pu1 and 883 mm/30), and (7) δu /L= ratio of the maximum out-of-plane deformation at the brace midspan to the brace length L referring to Fig. 4 and Table 1. There is not much difference about the storey elastic stiffness Ke , exclusive to specimen KJH whose gusset plate (thickness 5.7 mm) was much thicker than the others (thickness 3.92 mm). For the difference of initial imperfection and set-up dimension errors in fabrication and assemblage, the inequality force distributing in the tensile and compressive bracing members can cause much difference in the storey buckling capacities Pcr as shown in Table 3. But these factors have no obvious effect on the storey assumed ultimate strength Pu , for these errors are diminished by the large inelastic post-buckling deformation in braces and gusset plates. For each specimen, the ultimate strength Pu2 in the second load cycles shows a marked decrease, approximately 16% of the initial Pu1 . This is a typical response of braced systems to inelastic cyclic loading and can be attributed to two effects: residual out-of-plane displacement in the compressive bracing member at the start of the following tension cycle and accumulative damage in the two bracing members and gusset plate. Though the clearance requirements are not provided in some specimens (FKZ-1, FKZ-2 and FKZ-3), there is enough ductility in each specimen, shown from the ductility ratio µ and maximum storey drift ratio θu . The minimum value of θu (0.0358 for specimen FKZ-2) greatly exceeds the storey deformation demand (1/50 = 0.02) in severe earthquakes pursuant to the GB50017 code [26].

412

W. Zhang et al. / Journal of Constructional Steel Research 67 (2011) 407–420

(a) Local buckling of KZ-1.

(b) Specimen FKZ-3 after test.

(c) Details of two braces of FKZ-3.

Fig. 6. Buckling deformation and fracture mode of the braces.

(a) KZ-1.

(b) FKZ -1.

(c) KJH.

(d) KZ-2.

(e) FKZ-2.

(f) KJL.

(g) KZ-3.

(h) FKZ-3.

(i) KZ-4.

Fig. 7. Deformation of the gusset plates. Table 3 Summary of measured and simulated results for the nine specimens. Group Specimen

Measured results

Simulated results

µ

θu

Σ Ei /Ep

δu /L

Pcr ,S /Pcr

Pu1,S /Pu1

Pu2,S /Pu2

15.3 16.1 14.1

0.0528 0.0482 0.0388

12.27 8.74 7.35

0.147 0.157 0.172

1.121 1.478 0.854

0.966 0.953 0.934

1.043 1.126 1.053

9.31 7.11 7.34

0.0468 0.0358 0.0407

8.58 4.89 6.61

0.130 – 0.150

0.604 0.622 0.610

0.863 0.844 0.871

1.007 0.934 1.015

120.7 113.6

10.8 9.41

0.0418 0.0447

8.69 8.64

0.123 –

0.717 1.099

0.901 0.949

0.983 1.045

104.3

19.0

0.0496

9.94

0.122

1.060 0.907 0.314

0.928 0.912 0.045

1.066 1.030 0.049

Ke (kN/mm) Pcr (kN)

Pu1 (kN)

Pu2 (kN)

G1

KZ-1 FKZ-1 KJH

38.3 38.1 57.3

112.4 76.6 144.8

128.2 128.9 132.1

110.4 102.6 111.8

G2

KZ-2 FKZ-2 KJL

34.7 37.6 37.8

171.5 166.7 175.8

133.0 136.9 135.2

107.1 118.0 110.9

G3

KZ-3 FKZ-3

41.4 42.9

159.9 99.9

139.8 133.6

G4 KZ-4 37.5 98.2 127.5 Averages of variations for the predicted-to-test ratios Coefficient of variations for the predicted-to-test ratios

The structural response in severe earthquakes also depends closely on the capability of energy dissipation by the assemblages in the braced frame. Although the hysteretic loops are not very full as shown in Fig. 8, the low-cycle fatigue life is so long that the tested braced frame can also dissipate much energy by the many hysteretic loops with large plastic deformation, proved by

the normalized dissipated energy Σ Ei /Ep . This result can also demonstrate why the SCBFs have a predominant earthquakeresistance behavior compared to the ordinary concentrically braced frames (OCBFs). The brace out-of-plane deformation after buckling governs the curvature of the bracing member, and the maximums δu /L obtained in the tests are also presented in Table 3.

W. Zhang et al. / Journal of Constructional Steel Research 67 (2011) 407–420 150

50 0 -50

50 0 -50

-100

-100

-150

-150 -6

-4

-2

0

2

4

-4

-2

2

4

6

-6

0 -50

50 0 -50 -100

-150

-150 0

2

4

-6

-4

-2

0

2

4

50 0 -50

-100

-100

-150

-150 -2

0

-4

2

4

150 Lateral force (kN)

Lateral force (kN)

0

-4

-6

0

2

6

4

6

Test (KZ-4) FEM (KZ-4)

100 50 0 -50 -100 -150

-6

6

-4

-2

Storey drift ratio (%)

0

2

4

6

-6

Storey drift ratio (%)

(g) KZ-3.

-2

Storey drift ratio (%)

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4. Simulation by finite element analysis (FEA) 4.1. Finite element model To obtain the detailed results such as the complicated strain, the load-carrying capacity, etc., a numerical investigation of the

cyclic behavior for the test specimens was conducted using the nonlinear finite element program ANSYS. The effects of stiffness of braces and gusset plate, nonlinear material behavior and initial out-of-straightness imperfection were considered in the finite element simulation. To simplify the computing model and increase computational efficiency, the upper loading beam and the two columns were replaced by the constraint conditions as illustrated

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Fig. 10. Constraint conditions and detailed meshes in FEA.

Fig. 11. Simulated deformation of specimen FKZ-2.

in Fig. 10. The end plate and the beam lower flange were so thick and they were connected with so many high strength bolts, that they could be regarded as one body and the bolts used here didn’t need to be modeled in the FEA. In order to model the brace pinned end, a cover plate was used and defined as a rigid surface in the ANSYS program. The finite element model was constructed using four-node quadrilateral shell elements for all of the members (Shell 181). After a mesh refinement study, the maximum mesh (10 mm by 10 mm) was used as shown in Fig. 10, to ensure convergence and accuracy of the finite element solution and simultaneously to optimize the execution time. The measured material properties were used in the FEA (Table 2). A large-displacement formulation was used to simulate buckling, and the kinematic hardening plastic material model was adopted to simulate the inelastic behavior of steel under cyclic loading. Each model was subjected to the specified cyclic loading history strictly according to the test sequence. The Newton–Raphson iterative method is used in solving nonlinear equations. 4.2. Comparisons with test results Plastic local buckling of the brace midspan would occur following the development of out-of-plane deformation of the brace. It would have a significant impact on the response of overall braced frame so that simulating it exactly was important. Fig. 11 shows that good comparison was obtained between the computed and physically observed buckling of compressed brace and local buckling of its midspan for specimen FKZ-2 at the same drift of the frame. The experimental and simulated relations between the lateral load and displacement for all the nine specimens are shown in Fig. 8 and Table 3. In general, the FEA results closely approximated all aspects of the measured response, such as the buckling of the bracing members, the load-carrying capacities and the characteristics of bracing member deformation in hysteretic loops. The top views of finite element analysis results in each state for one of hysteretic loops are also illustrated in Fig. 9. The stiffness differences between the test and FEA results in the course of

unloading and at the beginning of reversed loading (state A or B in Fig. 9) are mainly caused by the four-hinge frame facility in which the released elastic deformation would accelerate the unloading rate of bracing members. The stress results for braces and gusset plate were detected by monitoring the strain development of some key points shown in Fig. 3 (point A, B and section C). Fig. 12 shows the strain comparisons between the test results and the predictions by the FEA for specimen KZ-2. Because the plastic strain became so large that some strain gauges stopped working after brace buckling, attention is mainly concentrated on the elastic range where the test data are reasonable and available. It can be found that the strain values and their trends in development predicted by FEA are in great accordance with those of the recorded test results. The strains at these key points remained in the elastic range before the brace buckling, but large plastic strain could be developed quickly as soon as brace buckling occurs. There are some the strain accumulations in the test results shown at point A in Fig. 12(a) when unloading to zero in each loop. Although these accumulations could have been produced by the test setup fabrication errors illustrated in Section 4.3 and cannot be simulated well by the employed FE model here, the predicted peak points in each loop by FEA have a better agreement with test results. 4.3. Reasons for some errors The discrepancies of brace initial buckling resistance between the measured and simulated results are mainly owing to the brace compressive capacity in the inverted V-bracing members caused by the brace initial imperfection and set-up fabrication errors as discussed in Section 3.3. If the compressed brace can share more lateral loads before buckling, the initial buckling resistance measured will be greater than the simulated, such as for the specimens KZ-2, FKZ-2, FJL and KZ-3. Contrarily, if the compressed brace has a lower capacity, the tensioned brace will yield soon after the compressed brace buckling, and the measured results would be lower than the simulated, such as for KZ-1, FKZ-1, FKZ-3 and KZ-4. The geometry imperfection influence can be illustrated by Fig. 13(a) for specimen KZ-2, in which the smaller brace outof-straightness (OOS) perpendicular to the test frame means the

W. Zhang et al. / Journal of Constructional Steel Research 67 (2011) 407–420 Average Strain

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compressed brace will share more lateral force before buckling. The initial buckling resistance of the braced frame, with brace outof-straightness to be equal to 1/4000 times brace length, is 21% greater than that with out-of-straightness to be 1/500. But the post buckling resistances will tend to be identical for all these frames with different values of brace out-of-straightness. The other reason resulting in the greater measured resistance may be the gaps, caused by brace negative length errors between the end plate and beam lower flange, were forced to be close before the test by tightening the high strength bolts. In this way some given pretensioned forces would be induced to the inverted V-braces for these specimens. The influence of this pre-tension is shown in Fig. 13(b), where the different values of brace axial pre-tensioned deformation (PD) is used. When PD is equal to 0.2 mm, the ratio of the produced stress to yield stress can reach 0.17. It can be found that great brace pre-tensioned force can be established with very small axial deformation (0.2–0.4 mm), and this kind of pre-tension can obviously improve the frame resistance. If the brace geometry imperfection is very small and at the same time there is some pre-tension in the braces (such as PD = 0.3 and OOS = 1/6000 in Fig. 13(b)), the frame lateral resistance can become markedly greater than the prediction without these considerations.

For the predominant behavior of the tensioned brace in the loops after the initial brace buckling, the contribution of the compressed brace to the storey lateral resistance decreased greatly, which are also expressed well in the simulated results. The coefficient of variations for the predicted-to-test ratios (Pu1,S /Pu1 or Pu2,S /Pu2 ) are reduced to no more than 5% from 31.44% (Pcr ,S /Pc ) corresponding to the original brace buckling, as shown in Table 3. It means the effects of imperfections decrease obviously after the original brace buckling. However, additional attention should be paid to the greater deviation of initial buckling resistance induced by brace out-of-straightness or pre-tensioned force in the pair of V-bracing members in the design and construction of the boltconnected V-braced frames. 5. Effect of design variables Although the general trends and characteristics with respect to all the experiments and simulations are summarized in the previous section, in this section the detailed effects of the clearance at the brace end on the gusset plate, the location of the intersection point of bracing members, and the ratio of free edge length to

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∑Ei/Ep

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Fig. 14. Dissipated energy ratio and ductility ratio versus clearance.

gusset plate thickness on the braced frame performance are to be investigated further. It should be recognized that the tests presented here are not enough to establish the quantitative formulas for the gusset plate design, but can indeed gain some qualitative assessment and guidelines in design. A rigorous system performance assessment is needed to accurately establish acceptability criteria for the central gusset plate connections. Such an assessment is outside the scope of this paper. 5.1. Effect of gusset plate clearance As shown in Table 3, the lateral elastic stiffness of the frame without 2.5tp clearance on the gusset plate is a little greater than those with 2.5tp clearance in the first three groups respectively, mainly due to the effect of splices which extended the brace actual length. There were longer splices for the specimens without 2.5tp clearance. These negative clearance specimens were schemed out to explore the plastic stress distribution on the gusset plate and to investigate how they could effect on the behavior of braced systems. Although overall the 9 specimens failed as a result of fracturing at the brace central plastic hinge, the effect of gusset plate clearance on the system energy dissipation or ductility could be compared to find some constructive results. In each group, most of the specimens with 2.5tp linear clearance exhibit better ductility and have greater storey drift ratios than those with zero or negative clearance, as shown in Fig. 14 and Table 3. It can also be found that the specimens with 2.5tp linear clearance have a more significant amount of normalized dissipated energy in each group. These advantages for the specimens with 2.5tp linear clearance are in virtue of the powerful and explicit yield mechanism of plastic hinges on both gusset plate and brace midspan. The relatively free rotation round the linear clearance can release the constraint of gusset plate to the brace end, and the brace with the greater slenderness ratio shows the growth of low-cycle fatigue life. To demonstrate this phenomenon in more detail, accumulated dissipated energy versus storey deformation for these three tested groups are employed in Fig. 15. More cyclic loops can be loaded on the specimens with 2.5tp linear clearance, especially for KZ-1 and KZ-2. Although the dissipated energy for specimen KZ-1 in each loop is less than FKZ-1 under the same grade level, there are much more loops before bracing member fracturing for KZ-1, and the accumulated dissipated energy will become eventually greater than FKZ-1. It is a fact that the behavior of specimens without linear clearance is not better than those with linear clearance. But the negative clearances could also be accepted in the tested

connections from the fact of fracturing at the brace midspan hinges for all the 9 specimens, but not on the gusset plate. When the clearances reduce from zero to the negative, the gusset plate dimension will become compact economically. After the brace out-of-plane buckling, the brace end rotation can result in plastic hinge curves but not plastic hinge lines on these gusset plates. The plastic strain diagrams simulated by FEA are shown in Fig. 16(a) and (b). The result here is also proved reasonable by the previous studies providing an elliptical clearance model on corner gusset plates [23–25]. The curvature of the plastic hinge curve will increase with the increasing of extension of the brace end into the gusset plate. The greater the magnitude of negative clearance (i.e., the greater the brace end extension into the gusset plate), the more concentrated the strain will be formed on the gusset plate. In this way, there should be a limitation for the negative clearance, out of which the gusset plate would have a lower life than the bracing member under cyclic loading. For the limited numbers of the specimens in tests, however, it has not been found when the gusset plate would fracture prior to the brace following the increase of magnitude of negative clearance. 5.2. Effect of intersection point location of inverted V-braces To compare the behaviors influenced by the intersection point location of the inverted V-braces, four specimens (KZ-1, -2, -3 and -4) with the same linear clearance were employed. The storey lateral stiffness Ke mainly depends upon the brace length L, the angle between brace and column, and the gusset plate dimensions. Although there was no eccentricity between the brace intersection point and beam centerline for KZ-2, the shorter brace length L and the larger gusset plate dimensions make its lateral stiffness smaller than the others. From the ductility ratio µ, maximum storey drift ratio θu and the normalized dissipated energy Σ Ei /Ep shown in Table 3, it can be found that the specimens (KZ-1 and KZ-4) with moderate eccentricity e have the more preferable behaviors than the specimen (KZ-2) without eccentricity and the specimen (KZ3) with a much greater eccentricity that exceeds half of the beam height. The same conclusion can also be obtained by the comparison of the accumulated dissipated energy shown in Fig. 17. Currently, the concentric joint in specimen KZ-2 is the most popular design pattern for V-braced frames, but this specimen behaved in a relatively undesirable manner. KZ-2 has the longest length of gusset plate (a = 431 mm shown in Table 1), whereas it has the narrowest width of gusset plate (h = 140 mm). The brace forces applied to the gusset plate are distributed in a relatively small area near the end of bracing member, so that the inelastic zones on the gusset plate of KZ-2 are relatively more concentrated than the others, as the calculated results show in Fig. 16(c). Most of the areas on the gusset plate are in a much lower stress state in all the loading loops, except the plastic hinge line that is shortest in all the specimens. This disadvantage behavior for the concentric joint is exactly consistent with Astaneh-Asl studies [2] on cyclic load tests of three gusset plate specimens representing the V-braced connections. But for the specimen KZ-3 with the brace intersection point located in the gusset plate, the conclusion is exactly contrary to Astaneh-Asl results [2]. For only the gusset plate was involved in Astaneh-Asl tests, the interaction of gusset plate and bracing member could not be taken into account. There was no brace buckling that could induce the out-of-plane rotation of the gusset plate in Astaneh-Asl tests, and the brace force could be directly balanced in the gusset plate with fully developed plasticity, so that the specimen with the brace intersection point in the gusset plate generally behaved in a very ductile manner. However, if the

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(c) KZ-2. Fig. 16. Plastic hinge line and plastic hinge curve on gusset plates.

interaction could be considered in the tests like the specimens in this paper, there should be an out-of-plane force on the support of brace end (i.e., the gusset plate) to maintain the equilibrium of the out-of-plane buckled brace. Once the brace point is located within the gusset plate like the specimen KZ-3 or FKZ-3, an outof-plane moment and its corresponding rotation would occur on the gusset plate around restrained edge (i.e., the weld line connecting with the end plate), as shown in Fig. 18. The simulated

out-of-plane deformation of gusset plate for specimen FKZ-3 shown in Fig. 19(a) is identical with the physically observed deformation shown in Fig. 7(h). On the gusset plate of FKZ-3, a third plastic hinge line can be found along the restrained edge besides the two plastic hinge curves at brace ends. The simulation result is shown in Fig. 19(b) and (c). This unexpected deformation could deteriorate the ductility of storey drift and the capability of energy dissipation.

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If the brace buckling is considered in gusset plate tests, there are two important issues that should be mentioned about the stress state on gusset plates. Firstly, if the tensioned stresses in the gusset plate and bracing member can both reach yielding simultaneously in ideal design, the compression stress in the reversed loop in the gusset plate must not reach yielding due to the buckling of this bracing member. And in the following brace post-buckling cycles, the compression stress in the gusset plate will be further greatly reduced to no more than 1/3 times the initial brace buckling stress, according to the reduction of brace post-buckling resistance [1,26]. Secondly, the compression stress only exists in the half length of the free edge near the compressed brace end. As shown in Fig. 16(c), even in the compression part the strain distribution is non-uniform. Except the plastic strain on the clearance strip coacted by both bending moment and compression, a majority of free edge length is in relatively low compression strain or in a tension strain condition. Hence, the limited compression stress cannot induce buckling on the free edge, although the ratios of free edge length to thickness are much greater than formula (1). The buckling capacity Fcr of the compressed brace can be derived from Pcr through mechanical equilibrium at the node of brace and beam. Because there was no substantial free edge buckling in tests, Fcr can be conservatively regarded as the lower limitation of free edge buckling strength. The design principle usually requires the buckling capacity of the free edge of the gusset plate to be approximately equal to that of the bracing member to achieve an economical aim. In this way, the buckling capacities of free edge of gusset plates in the Refs. [2,29,30] can be assumed to be the maximal buckling capacity Fcr of the supposed bracing member. In this way, the available test data are shown in Fig. 20(b). Compared to the dashed line suggested by Astaneh-Asl in formula (1), a more reasonable equation (2) is presented here, which takes the brace buckling strength into account and shows a good agreement with test results. If there is no buckling in a bracing member, Fcr will approach to Fy , and Eq. (2) will become identical with Astaneh-Asl’ formula (1). Within the Eq. (2), buckling of the free edge can be prevented. b1 /tp ≤ 0.75 E /Fcr .



Fig. 18. Out-of-plane rotation of gusset plate for specimen KZ-3 and FKZ-3.

5.3. Effect of free edge length to thickness ratios In the tests, the ratios of free edge length to thickness (b1 /tp in Table 1) are much greater than the result of formula (1) proposed by Astaneh-Asl (19.8 and 20.8 for the gusset plates with thickness 3.92 mm and 5.70 mm respectively). But there was no obvious free edge buckling for all the specimens except KZ-1, on the gusset plate of which free edge buckling only appeared near the finial drift cycles. Impressively, the behavior of KZ-1 did not deteriorate by this kind of buckling, but proved almost to be the best one in all the specimens. As shown in Fig. 20(a), there are no obvious influences of b1 /tp on the lateral resistance (Pcr , Pu1 and Pu2 ) of the frames. It seems that the limitation proposed by Astaneh-Asl [2] under cyclic load is very strict for the central gusset plate connections. Why? Astaneh-Asl’s limitation was formulated on the criterion that the stress in the free edge of the gusset plate could reach the steel yield point Fy prior to the free edge buckling. As discussed earlier, there were no considerations of buckling of bracing members in his tests and his reference tests [29,30], so that the gusset plates were loaded with some very short and never buckling members. This condition can only exist in some extreme cases, such as buckling restrained braces or the braces with very small slenderness ratio in some trussed girders. However, the bracing members that may buckle under severe earthquakes are commonly permitted in design and widely used in SCBFs.

(2)

If the brace buckling strength Fcr is small, the corresponding compressed stress on the gusset plate and the required buckling capacity of the gusset plate will be small too. In this way, the required ratio b1 /tp of free edge length to thickness will be quite large. However, it does not mean the gusset plate would become more slender, because the tension strength and block shear strength should be checked besides the buckling strength, to assure the gusset plate has a higher strength than the tensioned brace. The behaviors of specimen KJH (with additional thicker gusset plate) and KJL (with additional stiffeners) did not show much more advantages than the others in each group respectively, as indicated in Table 1. The gusset plate must be strong enough to support the capacity of the brace, but additional strength and stiffness will reduce the system ductility. This point was also supported by Yoo’s analytical research result about corner gusset plate connections [23]. 6. Summary and conclusion The experimental and analytical studies on the inelastic, seismic performance of I-section inverted V-braces and their central gusset plate connections are conducted to improve the performance relative to the current design provisions, and simultaneously to improve the constructability of SCBF systems. The investigations focus on the deformation characteristic of brace and gusset plate, the detailed failure modes, the hysteretic behaviors of braced systems, the clearances on the gusset plate at the brace end, the

W. Zhang et al. / Journal of Constructional Steel Research 67 (2011) 407–420

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locations of brace points, and the ratios of the free edge length to thickness for the gusset plate. The conclusions include the following. (1) For the existence of a tension bracing member at anytime in the cyclic loops, the envelope of hysteretic curves have no decrease in both positive and negative directions before fracture of the plastic hinge at brace midspan. But a longer plateau at a lower load level can be found in the hysteretic loops. (2) Before tearing at the midspan of the out-of plane buckled braces, there are no fractures that can be observed on

the gusset plates or their weld connections. The gusset plates designed according to the given principles can have great ductility and can dissipate energy generated in severe earthquakes with enough low-cycle fatigue life. (3) For the powerful and explicit yield mechanism of plastic hinges on both gusset plate and brace midspan, the specimens with 2.5tp linear clearance exhibit better seismic behavior than those without that clearance. But in the range of the parameters in this paper, the negative clearances can also be accepted from the fact of ductile fracture at the hinge of brace

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midspan. When the clearances reduce from zero to negative, the brace end rotation will result in plastic hinge curves but not lines on gusset plates. (4) The specimens whose brace intersection points are between the beam center line and lower flange (with moderate eccentricity) have a more preferable behavior than the others. If the brace point is located within the gusset plate, an outof-plane additional force and its corresponding rotation can induce the third plastic hinge line on the gusset plate around beam-restrained edge. (5) If brace buckling is considered, the lesser compression stress (in value and its distributed region) on gusset plates cannot induce buckling on the free edge, although the ratios of free edge length to thickness may be great. From test results, the suggested conservative limitation of the ratio of the free edge length to thickness is presented. Acknowledgements The authors gratefully acknowledge the financial support from the National Science & Technology Pillar Program under Grant No. 2006BAJ01B02-01-04. References [1] AISC. Seismic provisions for structural steel buildings. Chicago (IL): American Institute of Steel Construction; 2005. [2] Astaneh-Asl A. Seismic behavior and design of gusset plates, Steel tips. Structural Steel Educational Council; 1998. [3] Whitmore RE. Experimental investigation of stresses in gusset plates. Bulletin no. 16. Engineering Experiment Station. University of Tennessee May 1952. [4] Bjorhovde Reidar, Chakrabarti SK. Tests of full-size gusset plate connections. Journal of Structural Engineering 1985;111(3):667–84. [5] Walbridge SS, Grondin GY, Cheng JJR. Gusset plate connections under monotonic and cyclic loading. Canadian Journal of Civil Engineering 2005;32: 981–95. [6] Hardash SG, Bjorhovde R. New design criteria for gusset plates in tension. Engineering Journal AISC 1985;22(2):77–94. [7] Kulak Geoffrey L, Grondin Gilbert Y. AISC LRFD rules for block shear—a review. AISC Engineering Journal 2001;38(4):199–203. [8] Topkaya Cem. Block shear failure of gusset plates with welded connections. Engineering Structures 2007;29:11–20. [9] Huns Bino BS, Grondin Gilbert Y, Driver Robert G. Tension and shear block failure of bolted gusset plates. Canadian Journal of Civil Engineering 2006;33: 395–408.

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