Development of centrically fused braced frame (CFBF) for seismic regions

Soil Dynamics and Earthquake Engineering 127 (2019) 105856

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Development of centrically fused braced frame (CFBF) for seismic regions a,∗

Morteza Bastami , Roohollah Ahmady Jazany

T

b

a Structural Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), No.21, Arghavan St. North Dibaji, Farmaniyeh, Tehran, Iran b Department of Civil Engineering, Islamic Azad University (IAU), East Tehran Branch, Ghiamdasht, Emam Reza Blvd, Afsariye, Tehran, Iran

A R T I C LE I N FO

A B S T R A C T

Keywords: Concentrically braced frame (CBF) Mid-height gusset plate Rupture Out-of-plane buckling Structural fuse

This research presents an experimental study to develop a novel structural fuse for concentrically braced frame (CBF) system using ductile mid-height gusset plate by proposing the specified innovative detailing. This concept leads to concentrated inelastic deformation and the largest stress demand on a very thin mid-height gusset plate as an intentional weak point. Since other structural steel members including corner gusset plates, braces, beam and columns remain within the elastic range of steel material; this concept protects structural elements from damages and improves seismic performance of CBF. To demonstrate the efficacy of the improved CBF system, which is so called “Centrically Fused Braced Frame (CFBF)”, cyclic lateral test are conducted on four three-fourth scale braced frame test specimens using the proposed detailing of mid-height gusset plates. The results of experimental study indicate that CFBF can meet the criteria as desired by AISC codes for CBF; Also it is shown that increasing the thickness of mid-height gusset plate within a very limited range between 2 to 5 mm decreases the strength degradation by up to 40% however increases the relative out-of-plane displacement of the braces approximately by up to 5 times. Finally a design method is suggested to enhance the cyclic behavior of CFBF system.

1. Introduction Special concentrically braced frames (SCBFs) are one of the wellknown lateral load resisting systems that are utilized in a seismic zone because of their inherent ability in achieving the required strength and stiffness. The gusset plates of SCBF are proportioned to accommodate large inelastic deformation after brace buckling happens although the braces play most important role in controlling the excessive lateral drift of braced frame system [1]. At the beginning of the twenty first century, the design concept of “weak gusset plate-strong brace” for SCBF was investigated by many researchers [2-3] and the results of these research works indicated that the above-mentioned design concept provides larger post-buckling compressive loads compared to conventionally designed subassemblies; however, using this concept may result in gusset plate rupture due to tension [2-3]. Uriz and Mahin [4] and Yoo et al. [5] showed that excessive postbuckling deformation of the braces results in fracture of gusset plate and braces and leads to poor seismic behavior of SCBF. In a study by Lehman et al. [6], it was indicated that overstrength characteristics of gusset plate connection can considerably affect the maximum strain demand of the beam and columns under strong earthquake. Ariyaratana and Fahnestock [7] implied that combining moment frame and ∗

Buckling-Restrained Braced Frame (BRBF) as a dual lateral load resisting system in braced frames provide considerable reserved strength and has significant impact on seismic behavior and performance of braced frames. Roeder et al. [8,9] proposed a practical approach for designing of SCBF in which the tensile yielding of braces or brace buckling are balanced against the corner gusset plates yield mechanisms. In a follow-up experimental study by Lumpkin et al. [10], it was shown that composite action of concrete slab should be considered for designing of beams in a chevron configuration in AISC design method [11]. Furthermore, it was revealed that the innovative design method suggested by Roeder et al. [8,9] provides more seismically compact mid span gusset plates and also leads to greater overall ductility in the SCBFs. Hisao et al. [12] proposed an analytical model simulating the seismic behavior of corner gusset plate connection as well as predicting post-buckling and buckling capacity of the brace with acceptable precision. Chen and Chang [13] studied the effect of Low Yield Point (LYP) of steel gusset plate on seismic resistance of gusset plate where the gusset plate is designed based on weak gusset plate-strong brace concept. They illustrated that the pinching effect in the cyclic response of braced frame due to buckling of the conventional thin corner gusset plate can be alleviated by using steel material with LYP. Chou et al. [14] investigated the cyclic

Corresponding author. E-mail addresses: [email protected] (M. Bastami), [email protected] (R. Ahmady Jazany).

https://doi.org/10.1016/j.soildyn.2019.105856 Received 7 July 2019; Received in revised form 4 September 2019; Accepted 5 September 2019 0267-7261/ © 2019 Elsevier Ltd. All rights reserved.

Soil Dynamics and Earthquake Engineering 127 (2019) 105856

M. Bastami and R. Ahmady Jazany

behavior of dual-gusset-plate connections in compression for BRBFs. They indicated that the proposed method for estimating the ultimate capacity of gusset plate as desired by AISC [11] cannot precisely predict the ultimate capacity of dual-gusset-plate connections. Shen et al. [15] analytically studied the seismic demand of inverted-V braced and two story X-braced systems. They showed that braces in two-story X-braced systems experience large inelastic deformation at story drift angle ranging between 0.02 and 0.04 radians and they highlighted the role of inelastic deformation of brace-intersected beams to provide required ductility for the brace and brace connections. Fang et al. [16] carried out an analytical study to estimate the postbuckling capacity of gusset plate connection with respect to initial imperfection and strain hardening. Then regarding the results of these parametric analyses, they proposed a method for estimating the gusset plate ultimate strength using plate analogy concept. Siekierski [17] proposed a simple method to estimate the normal and equivalent stresses of bridge gusset plate under service load using shell element in Finite Element Method (FEM). They showed that the suggested method can estimate the above-mentioned stress values with acceptable accuracy but there is not a precise estimation of stress concentration close to the outermost of beam elements. Sen et al. [18] conducted an experimental study program to examine the design concept of Non-Ductile Concentrically Braced Frames (NCBFs) for different chevron configurations. The results indicated that NCBFs develop a mechanism in which the beam yields, deforms plastically, and this mechanism limits tensile elongation of the brace so yield mechanism of beam provides adequate lateral strength and deformation capacity of the braced frame. Bradley et al. [19] experimentally investigated the failure mechanisms and overall collapse of low-ductility steel CBFs. The outcomes of this research confirmed that Ordinary Concentrically Braced Frame (OCBF) as one of the low-ductility CBFs has low reserved capacity after buckling of braces and gusset plate weld fracture. Salawdeh et al. [20] preformed comprehensive experimental study using shaking table test to better understand the gusset plate configuration effects on seismic performance of CBF. They concluded that balanced design approach improves the seismic performance of CBF in term of story drift ratio; moreover, using nonlinear clearance rule in the gusset plate connection design controls the out-of-plane buckling of brace efficiently and thus affects the post-bulking failure mode of the braces considerably. In a key research, Costanzo et al. [21] carried out a comprehensive numerical study to compare the seismic behavior of Vbraced frames designed based on European and North American codes. They implied that the design criteria established by North American codes for the braces and gusset plate connections provide greater dissipated energy capacity under seismic loads compared to European codes, e.g. E8 [22], by establishing a balanced yield mechanism of the braces in tension and compression. In a follow-up study, these researchers [23] proposed some design criteria to provide the required ductility for chevron system and showed that these criteria improve dissipated energy and seismic performance of chevron CBFs. In a similar study by Azad et al. [24], the results demonstrated that AISC 341–10 [25] is capable of providing larger plastic demand for the braced frame compared to those designed based on European code e.g. E8 [22]. Also, the seismic response of SCBFs is usually influenced by nonlinear behavior of the braces; therefore, AISC provisions [11,25] aim at assuring that the braces sustain the required inelastic capacity during large seismic loading. It can be concluded that both brace and the corner gusset plate must tolerate the controlled inelastic deformations during strong earthquake while other structural elements do not experience significant large deformation [11,22and25]. In a more recent study, Bastami and Ahmady Jazany [26], i.e. the author of present research, conducted 9 experiments to develop an innovative structural system, which is so called Eccentrically Inter-connected Braced Frame (EIC-BF), which proposed innovative Structural Fuse (FS) at mid-height gusset plate (which is hereinafter so called M − H gusset plate). In EIC-BF, the brace segments are connected

Fig. 1. Comparison of structural behavior of M − H gusset plates in EIC-BF and CBF systems.

eccentrically to M − H gusset plate [26] (See Fig. 1(a)). They implied that using a very thin M − H gusset plate having specified details as the proposed Structural Fuse (SF) provides acceptable seismic performance as desired by AISC 341–16 [25] and also the suggested Structural Fuse (SF) prevents other braced frame elements including beam, column and corner gusset plate from entering the inelastic phase of steel material. Using similar concept as the above-mentioned study, the authors of present research, conducted four experiments to propose a new structural system, which is so called Centrically Fused Braced Frame (CFBF). In this newly proposed system, concentric brace segment at M − H gusset plate having specified detail as an efficient Structural Fuse (SF) is used instead of eccentric braced configuration at M − H gusset plate which was employed in previous research [26]. These two proposed structural systems, i.e. EIC-BF and CFBF, are conceptually similar to each other except for presence of braces eccentricity in EIC-BF system. The above-mentioned eccentricity leads to differences in M − H gusset plate structural behavior which in turn influences the braced frame inelastic behavior. In EIC-BF system, the eccentricity of brace segments leads to shear behavior in M − H gusset plate by establishing shear panels (See Fig. 1(a)) while, in CFBF system, compressive and tensile stress zones in M − H gusset plate (See Fig. 1(b)), considering buckling stress of M − H gusset plate and nonlinear behavior of material, can change the cyclic behavior of the proposed SF which is discussed in this study. The present study aims to employ “weak gusset plate-strong brace” design concept in CBF by providing SF element in M − H gusset plate. In order to control the large inelastic deformation in M − H gusset plate as a structural fuse element, the specified details are proposed and the design criteria are established based on test observations and measured experimental cyclic responses. This research reports experimental investigation results elaborately.

2. Description of experimental program 2.1. Test set up Four laboratory tests were conducted on one-story, single-bay braced frame using a specific lateral quasi-static cyclic load as described 2

Soil Dynamics and Earthquake Engineering 127 (2019) 105856

M. Bastami and R. Ahmady Jazany

Fig. 2. (a) Front view of test set up and studied braced frame (CFBF) (b) Schematic view of test specimen (C1 to C4 test specimens), lateral support, the locations of strain gages and displacement transducers.

in the following sections to gain more insight in the cyclic behavior of CFBF suggested by the present study. The experimental program was performed at the structural laboratory of the structural research center, International Institute of Earthquake Engineering and Seismology (IIEES). Fig. 2(a) shows the test set up including lateral support and reaction frame. Fig. 2(b) illustrates the schematic view of test setup, the test specimen and the location of installed measuring devices including displacement transducers and strain gages. A 50-Ton hydraulic actuator having stroke up to ± 150 mm was utilized in order to impose the cyclic load pattern to the one of top corners of the studied test specimens as shown in Fig. 2(b). U-Channel (UNP) sections and Wide flange I-section (IPE), according to DIN-1025 [27], were chosen as shown in Fig. 2(b) for the braces, the columns and the beam of test specimens respectively. Pinned connection was employed to connect beam to columns as well as columns to reaction support, (see Fig. 2(b)). The latter pinned connections were fabricated by bolt and shank as the bolted connections; but the connections between gusset plates and the braces as shown in Fig. 2(a) and (b) were assigned by slip-critical bolted connections (see the connection between M − H gusset plate /corner gusset plates and

Table 1 Material properties of the test specimens. Type

IDa

Fyb (MPa)

FUb(MPa)

Elongation(%)

1

Plates

2

Hot rolled Sections

3 4

Bolts Weld

2mm 3mm 4mm 5mm 10mm 20mm UNP 160 UNP 220 IPB240 8.8 7018

310.5 307 307.3 313 283 295.3 302.3 324.5 330.0 640.0 4950

543.2 542.2 534.5 543.0 543.2 532.3 532.3 543.4 532.4 830 6700

22 23 22 23 18 19 18 19 19 12 1.5

a ID refers to plate thickness, steel hot rolled section, bolt grade marking and electrode type for the first to the fourth row of this table respectively. b Fy and FU are yield stress and ultimate stress of steel material respectively.

3

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M. Bastami and R. Ahmady Jazany

enter the inelastic range of force-displacement curves; whereas, the M − H gusset plate as the structural fuse element were designed to experiences large inelastic deformations. The ratio of yield strength of M − H gusset plate to yield strength of the braces (i.e. Aw.Fyg/Ab.Fyb) was considered in the range of 0.24 to 0.34 (see Table 2). Predetermined cyclic loading pattern specified by ATC 24 [30] was used for the cyclic loading of the experiments of this research (See Fig. 5). This general loading protocol is appropriate for CBF.

Table 2 M − H gusset plate and AST tie specifications and detailing. Test Specimen

M − H gusset plate thickness (cm)1

AST tie sthickness (cm)

Strength Ratio (Aw.Fyg/Ab.Fby)

C1 C2 C3 C4

0.2 0.3 0.4 0.5

0.5 0.5 0.5 0.5

0.24 0.27 0.30 0.34

2.3. Instrumentation braces in Fig. 2(a) and (b)). The welding electrode of E7018 was used to add the required stiffeners to beam and corner gusset plates. The E7018 welding electrode provides the absorbed energy of 70 J at temperatures of −30 °C [28]. The steel member material properties and material specifications of bolts and weld metal are presented in Table 1. The lateral support was provided to prevent lateral torsional buckling of the beams and this lateral supports consisted of inverted U-shaped frame which strongly surrounded the beam flanges of the test specimens at two specified locations (See Fig. 2(b)). Four test specimens of present research, which are called C1 to C4 test specimens, consisted of a singlebay one-story braced frame having X configuration and M − H gusset plate having specified details. The structural elements of studied test specimens including braces, columns; beams and corner gusset plate had similar section sizes and dimensions except for the M − H gusset plates that had different thickness (See Table 2).

In order to monitor the strain values on structural steel elements, 13 uni-axial strain gages designated as S1 to S13 (see Fig. 2(b)) were fixed to the beam, columns, braces and corner gusset plates of each test specimens; and also five tri-axial strain gages designated as S14 to S18 (see Fig. 3(b)) were fixed to M − H gusset plate and AST ties of each test specimen. For all studied test specimens, six displacement transducers (LVDTs) were installed on the one of the braces (see Fig. 2(b)), the M − H gusset plates center and AST ties designated as d1 to d6 (see Figs. 3(c) and 4(d)) respectively to measure the out-of-plane displacements of above-mentioned structural elements. 3. Description of experimental results The experimental outcomes of C1 to C4 test specimens are discussed in this section.

2.2. Experimental models 3.1. Test observations For all studied three-fourth scale test specimens, the beams length reached up to 264 cm and columns height up to 220 cm and also IPE240 and 2UNP 220 sections were utilized for constructing beam and columns respectively as shown in Fig. 2(b). Brace element section were 2UNP160 with slenderness ratios of the braces (about main axes of the brace section) λy = KyL/ry = 34 and λx = KxL/rx = 27. Four rectangular steel plates having dimension of 65 × 75 cm and 0.2, 0.3, 0.4, 0.5 cm thickness values were employed for M − H gusset plates of C1, C2, C3 and C4 test specimens respectively (See column 2 of Table 2). Furthermore, in order to stop the propagation of the possible crack in the M − H gusset plate center and prevent the M − H gusset plate total fracture, four steel narrow plates, which is hereinafter called “Adjoined Steel Tension tie (AST tie)” (See Figs. 3(a) and 4(a) to (c)), with specified dimensions of 11x37 × 0.5 cm and 11x17 × 0.5 cm having round corners were utilized (See Fig. 3(a)). M − H gusset plate and AST ties were connected using bolts. The relative out-of-plane deformation between M − H gusset plate and AST ties was prevented using bolted connection at mid-length of each AST ties as shown in Fig. 3(a). Table 2 presents AST ties thickness, thickness of M − H gusset plate and ratio of yield strength of M − H gusset plate, which is obtained by multiply Whitmore section [6] area by yield stress of steel material of M − H gusset plate [6] to yield strength of the brace (i.e. Aw.Fyg/Ab.Fyb). With regard to this ratio, the parameters of Aw, Ab, Fgy and Fyb are Whitmore section area [6] in the M − H gusset plate, the section area of braces, the expected yield stress of steel material of the M − H gusset plate and expected yield stress of the brace material respectively. Since the Whitmore section includes the section area of AST ties, yield strength of the AST ties contributes to the above-mentioned ratio (i.e. Aw.Fyg/ Ab.Fyb). The beam, column, brace elements and corner gusset plate connections of the studied test specimens were proportioned to remain in elastic range of steel material, and also meet the requirements of Special Concentrically Braced Frame (SCBF) to meet the criteria of AISC 341–16 [25] while M − H gusset plates of proposed system were designed to sustain large inelastic deformation and experience limited damage as a structural fuse element. By using pushover analysis [29], the brace design forces were calculated based on the maximum force corresponds to yield mechanisms of the M − H gusset plate, also the corner gusset plates and braces were proportioned such that they do not

Based on the test observations of the present study, the first yielding in C1, C2, C3 and C4 test specimens were measured at the center of M − H gusset plate at the 7th, 9th, 11th and 11th cycle of the predetermined load pattern respectively (corresponding to drift angles of 0.008, 0.01 and 0.012 and 0.012 radians); subsequently, the out-ofplane deformation with x-shaped pattern were appeared at the M − H gusset plate of C1 and C2 test specimens. This was followed by maximum out-of-plane bucking at the center of M − H gusset plate for C1 to C4 test specimens reaching up to 5.40, 3.58, 2.24, 1.47 cm respectively at story drift ratio of 1.2, 1.2, 1.5 and 2% radians (see Fig. 6); then, the vertical and horizontal AST ties of C1 to C4 underwent the considerable out-of-plane buckling value reaching up to 3.30, 2.79, 2.19, 1.21 cm (see Table 3). At these stages, C1 and C2 test specimens experienced ductile rupture located at center of M − H gusset plate (See growth of cracks in Fig. 7(a) and (b)); whereas, in the case of C3 test specimen, a small crack located at the M − H gusset plate in vicinity of horizontal AST tie without any growth was appeared at story drift ratio of 2.1% as shown in Fig. 7(c) and test was stopped at story drift ratio of 3% to prevent some damages to the test set up apparatus. In the case of test specimens of C1 and C2, the above-mentioned cracks were then extended towards the proximity of AST ties (See Fig. 7(a) and (b)) at story drift ratios up to 2.3 and 3% respectively and the experiments were finished at these stages due to considerable strength degradation. In spite of observed fracture mode of C1 to C3 test specimens, i.e. cracking at M − H gusset plate, C4 test specimen did not experience any rupture at M − H gusset plate till the end of loading sequences and the experiment was ended ((See Fig. 7(b) and (d)) at story drift ratio of 3% to prevent damage to equipments of the laboratory. 3.2. Assessment of measured strains and displacements 3.2.1. Measured strain value at M − H gusset plate The measured strain demand and displacement of steel elements are useful experimental data to get better perception about the actual seismic behavior of CFBF system and its proposed detailing. Tri-axial strain gages measures the strain values in two orthogonal and one diagonal directions in which these strain values were used to calculate the 4

Soil Dynamics and Earthquake Engineering 127 (2019) 105856

M. Bastami and R. Ahmady Jazany

Fig. 3. Details of M − H gusset plate, AST Ties, corner gusset plates and the locations of fixed measuring devices.

strength, buckling strength and stiffness of the M − H gusset plates with larger thickness which decreases microstrain demand in M − H gusset plate.

principle stresses at the M − H gusset plate connection. Fig. 8(a) and (b) illustrate the maximum strain at M − H gusset plate (see the location of S14 in Fig. 3(b)) and AST ties (See the location of S15 to S18 in Fig. 3(b)) in the case of C1 to C4 test specimens versus story drift ratio for both tension and compression. Based on Fig. 8(a), maximum strain demand at M − H gusset plate center for C1, C2, C3 and C4 test specimens reached up to 23612, 17223, 9320, 6932 microstrains respectively. This revealed that the thicker M − H gusset plate has smaller peak microstrains demand. Table 3 presents a summary of experimental results including M − H gusset plates out-of-plane buckling and as well as maximum measured strain demand in AST ties and M − H gusset plate. Regarding Fig. 8(a), the maximum measured microstrain demand of all test specimens at the M − H gusset plate center in compression are lower comparing with the corresponding values in tension. By comparing the microstrain demand of M − H gusset plate center in the studied test specimens (see Fig. 8(a)), it is found that the difference between measured maximum strain demand in compression and tension decreases if the thickness of M − H gusset plate increases (e.g. see strains values of C4 test specimen). This is due to increase of the tensile

3.2.2. Measured strain values in AST ties Similar to evaluation of M − H gusset plate strain demand in previous section, the measured microstrain demanded by cyclic loading in AST ties of M − H gusset plate for C1 to C4 test specimens are compared as shown in Fig. 8(b). By comparing Fig. 8(a) and (b), it is found that the microstrain demand at the AST ties of C1 and C2 test specimens suddenly rises up to 9140 and 8690 microstrains in tension concurrent with extending the crack at the M − H gusset plate and decreasing the strain demand on the M − H gusset plate respectively (see Table 3). This implies that the AST ties act as parallel force transferring systems when the M − H gusset plate cannot tolerate the stress demand imposed by cyclic loading because of cracks extension and local rupture. Also regarding Fig. 8(b), it is demonstrated that increase of the M − H gusset plate thickness results in decrease of the differences between the measured peak microstrain demands of AST ties in tension and 5

Soil Dynamics and Earthquake Engineering 127 (2019) 105856

M. Bastami and R. Ahmady Jazany

compression. In this research, the installed rosette strain gage S14 was used to measure the maximum shear microstrains demand in center of M − H gusset plate. Fig. 8(c) shows that shear strain demand increases in M − H gusset plate center if the gusset plate thickness decreases (See Table 3). 3.2.3. Measured strain value in the braced frame elements As it was previously explained, 13 strain gages which are illustrated by S1 to S13 in Fig. 2(b), were installed on studied C1 to C4 test specimens to measure the microstrain demand on braces, corner gusset plates, beam and columns. Based on the measured microstrains demand recorded by installed strain gages (see Table 4), it is found that the maximum microstrains demand, which were measured for all structural elements except for M − H gusset plate, did not go beyond the value of yield strain for C1, C2 and C3 test specimens. This confirms that M − H gusset plates behaves as a structural fuse element and protect structural members including, braces, beam and column against damages. Whereas, in the case of C4 test specimen, the microstrains demand at the braces, which were measured by strain gages of S1, S2, S3 and S4, surpassed the value of yield strain; this revealed that the M − H gusset plate of C4 test specimen did not prevent the damages to the braces.

Fig. 4. (a) M − H gusset plate of CFBF (b) Vertical AST ties and (c) Horizontal AST ties (d) Location of fixed displacement transducers (LVDTs).

3.2.4. Measured out-of-plane displacement at M − H gusset plate Based on Fig. 9(a) and (b), the largest out-of-plane buckling value in M − H gusset plate of C1 and C4 test specimens having the smallest and the largest thickness reached up to 5.04 and 1.47 cm respectively (see Table 3). Moreover, the corresponding values for AST ties reached up to 3.30 and 1.21 cm respectively. This confirmed that C1 test specimen with smaller thickness values had maximum out-of-plane displacement at M − H gusset plate compared to the corresponding values of other test specimens. This is due to smaller buckling strength values that are provided by thinner M − H gusset plate, e.g. C1 test specimen. Fig. 10 shows the relative displacements between the braces end at the M − H gusset plate. By comparing Figs. 6 and 10 (see Table 3), it is indicated that the test specimen with the smallest thickness (e.g. C1 test specimen), which experienced the largest out-of-plane buckling value in M − H gusset plate centre, underwent the smallest braces segments end relative displacements. Whereas, C4 test specimen with the largest thickness experienced the smallest out-of-plane buckling value at M − H gusset plate center as well as the largest relative displacement of brace segments end. This is due to larger buckling strength provided by thicker M − H gusset plate, e.g. in the case of C4 test specimen, comparing with thinner M − H gusset plates, e.g. C1 test specimen. Furthermore, increasing the M − H gusset plate thickness from C1 to C4 test specimens changes the deformation mode form out-of-plane buckling at M − H gusset plate center to relative displacement between M − H gusset plate edges.

Fig. 5. Applied cyclic loading pattern [30].

3.3. Assessment of experimental cyclic responses Fig. 11 illustrates the cyclic behavior of C1 to C4 test specimens. It is shown that the ultimate strength of the C1, C2, C3, C4 test specimens reached up to 132, 183, 393 and 443 KN respectively. Table 5 summarizes the experimental results including reason of test termination, initial stiffness, peak strength, ultimate strength, total story drift ratio and strength degradation. Based on this table, it is shown that the thickness of M − H gusset plate has considerable effects on initial stiffness, peak strength and ultimate strength of CFBF system. In other words, a decrease in thickness of M − H gusset plate by up to 60%, by changing the thickness of M − H gusset plate of C4 to C1 test specimens, leads to a decrease of initial stiffness, ultimate and peak strength by up to 62%, 70% and 46% respectively. Based on AISC 341–16 [25], gusset plate connections should at least be capable of accommodating an inter-story drift angle of 0.025 radians in Special Concentrically Braced Frame (SCBF), if both beam and column were connected to the gusset plate directly. Based on Fig. 11 and Table 5, all test specimens

Fig. 6. (a) (b) (c) and (d) Front view of M − H gusset plate of C1, C2, C3 and C4 test specimens showing out-of-plane buckling of M − H gusset plates and AST ties during experiments.

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Table 3 Maximum measured strain demand and out-of-plane displacement of M − H gusset plate. Test Specimen

Maximum strain (microstrains)a M − H Gusset plate

C1 C2 C3 C4 a b

Out-of-plane displacementb (cm) AST ties

Tension

Compression

Tension

Compression

23612 17223 9320 6932

9503 7021 8011 5312

9140 8690 4302 3490

4120 4090 4022 2910

M − H Gusset plate

AST tie

5.04 3.58 2.24 1.47

3.3 2.79 2.19 1.21

Maximum microstrain is measured by rosette strain gage installed at M − H gusset plate center and AST ties(See Fig. 3). Maximum out-of-plane displacement at M − H gusset plate and AST ties are measured by LVDTs d2 to d6 (See Fig. 3).

[31]. In this study, the envelope of hysteresis loops were provided for all experimental models to compute the elastic strength demand, ultimate displacement, yield displacement and design strength based on ATC-19 [31]. R-factor, for C1 to C4 test specimens are presented in Table 6 based on Allowable Stress Design (ASD) and Load and Resistance Factor Design (LRFD) [25]. In ASD, R-factor can be also computed by multiplying the ductility (Rw ) by redundancy (Y) and overstrenght (Ω) as follows [31]:

RASD = Rw ΩY

(1)

In LRFD method, R-factor is calculated by multiplying overstrength (Ω) by ductility (Rw ) however redundancy (Y) is not considered in the above-mentioned equation:

RLRFD = Rw Ω

(2)

The ductility (Rw ) ratio is obtained by dividing maximum base shear coefficient (Ceu) that develops in a structure, if it were to remain elastic by base shear coefficient (Cy) corresponding to the actual yielding of a structure (See Fig. 12). Overstrength (Ω) is also calculated by dividing base shear coefficient (Cy) corresponding to the actual yielding of the structure by the code-prescribed factored design base shear coefficient (CW) which corresponds to formation of first plastic hinge (See Fig. 12). The redundancy factor (Y) is the ratio of the code-prescribed factored design base shear coefficient (CW) to the code-prescribed un-factored design base shear coefficient (CS) in a structural system (See Fig. 12). Redundancy factor (Y) is obtained with respect to the yield and tensile strength of M − H gusset plate [31] (See Table 6) because it is expected that only the M − H gusset plate endures the inelastic behavior. Overstrength (Ω) and ductility (Rw ) are obtained based on ATC-19 [31] using envelope of cyclic behavior of C1 to C4 test specimens. Table 6 presents R-factor for the studied test specimens. Based on this table, it is confirmed that C1 test specimen, having thinner M − H gusset plate, provides the smallest ductility value with respect to the others. This is due to presence of extensive cracks at the center of M − H gusset plate in smaller story drift ratios which extended to corners and edges of M − H gusset plate while C4 test specimen, having the largest M − H gusset plate thickness, did not experience the above-mentioned cracking. In other words, decrease of thickness of M − H gusset plate by up to 250%, by changing M − H gusset plate of C4 to C1 test specimens result in decrease of R-factor by up to 25%. However increase of thickness of M − H gusset plate over 4 mm, i.e. M − H gusset plate thickness of C4 test specimen, leads to increase of the stress demand of the braces beyond the yield stress of steel material thus the preliminary assumption for the establishing fused structural system by M − H gusset plate is not satisfied. The hysteresis curves of the studied experiments (See Fig. 11) were employed to calculate the absorbed energy [29]. Based on Table 7 which presents dissipated energy for the studied test specimens, C3 test specimen has the largest dissipated energy. Considering Fig. 11 and Tables 6 to 7, it is found that, in general, an increase in the ultimate strength results in an increase in dissipated energy except for C4 test specimen, which has the largest ultimate force, but not the largest

Fig. 7. (a), (b) Front view of M − H gusset plate of C1 and C2 test specimens showing X-shaped cracking pattern at M − H gusset plate center (c) Crack initiation of C3 test specimen and (d) C4 test specimen without any crack after experiment.

tolerated a total inter-story drift ratio of 2.5% which is recognized as the qualifying criterion of SCBF system based on AISC seismic provisions [25] except for C1 test specimen which experienced extensive cracks in M − H gusset plate center at story drift ratio of 2.3 %. Considering Fig. 11 and tests observations (See Figs. 6 to 7 and 10), it is indicated that increase of relative out-of-plane displacement of braces in proximity of M − H gusset plate results in an increase in the pinching of hysteresis loops. For example, cyclic response of C4 test specimen which experienced larger relative out-of-plane displacement between the end of braces to M − H gusset plate connection (See Fig. 10) in proximity of M − H gusset plate, has considerable pinching (See Fig. 11) compared to C1 test specimen having smaller relative out-ofplane deformation of brace segments end to M − H gusset plate connection. The strength degradation of C1 and C2 test specimens, having larger out-of-plane deformation at M − H gusset plate center, were almost 43 and 44% (See Table 5) at the story drift ratios of 2.3 and 3% radians respectively, but C3 and C4 test specimens, in which M − H gusset plate experienced smaller out-of-plane deformation, demonstrated negligible strength degradation (See Figs. 6 and 11). 4. Assessment of CFBF using R-factor and absorbed energy Response reduction factor (R), which is hereinafter called R-factor, represents the capacity of a structure to absorb the induced energy by seismic loading through inelastic behavior and reflects the reliability of a structure to withstand excessive loading. R-factor includes the effects of ductility, redundancy and overstrength of a structure, and is calculated by dividing the equivalent elastic strength by the design strength 7

Soil Dynamics and Earthquake Engineering 127 (2019) 105856

M. Bastami and R. Ahmady Jazany

Table 4 The largest measured strain demand value on columns, beam, braces and corner gusset plates (S1 to S13). Test Specimen

Beam (S11 to S13)b

Columns (S5 to S6)b

Brace segment (S1 to S4)b

Corner gusset plates (S7 to S10)b

C1 C2 C3 C4

323 412 412 213

453 431 561 612

932 912 1192 1466 > a

1011 1123 1241 1364

a The yield strain limit values of column, beam, brace and corner gusset plates are 1545, 1571, 1432 and 1406 respectively. b S1 to S13 refer to strain gages location as shown in Figs. 2(b) and 3.

Fig. 9. (a)Measured out-of-plane displacement at M − H gusset plate center versus story drift angle (b) Maximum measured out-of-plane displacement at AST ties versus story drift angle.

Fig. 8. (a) Measured microstrain at the M − H gusset plate center (b) The largest measured microstrain in AST ties (c) Measured shear microstrain at the M − H gusset plate center versus story drift.

8.01. This shows that the proposed structural fuse is able to improve the seismic performance of CBF sufficiently.

dissipated energy. This is due to considerable pinching observed in hysteresis loops of C4 test specimen in comparison with other specimens. Based on experimental findings (See Fig. 11), the pinching phenomenon is the most important factor affecting the dissipated energy of the studied test specimens. Therefore, in spite of the largest ultimate strength compared to other test specimens, C4 test specimen dissipated smaller energy value imposed by cyclic load than corresponding value of C3 test specimen. Finally, it is worth noting that 5.5 R-factor value is proposed by IBC code [32] for SCBF system based on LRFD method [25] while based on this study the corresponding value for CFBF varies ranging from 6.41 to

5. Design methodology for M − H gusset plate of CFBF Based on the experimental results and test observations, some design criteria for M − H gusset plate were proposed in this section to control the observed dominant rupture modes, out-of-plane and excessive in-plane deformation of M − H gusset plate. Using these criteria could also prevent the structural members including columns, beam, braces as well as connections such as corner gusset plates from experiencing the inelastic behavior. Based on this concept, yielding mechanism in tension and M − H gusset plate out-of-plane buckling in 8

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M. Bastami and R. Ahmady Jazany

slenderness along L1 to L3, i.e. KtL1/rg, KtL2/rt and KtL3/rt, Kt is buckling length factor and is considered as 1 and rg is gyration radius of the section having width of 1 cm and the height is equal to the thickness of M − H gusset plate. Also rt is gyration radius of the section having the width of 1 cm and the height value is equal to sum of thickness of M − H gusset plate and AST tie thickness. Table 8 summarizes the design parameters including slenderness along the specified lengths of L1 to L3 (See Fig. 13(b)), the peak strength of M − H gusset plate (FGP), yield strength of AST tie (FT) and ratio of peak strength of M − H gusset plate (FGP) to yield strength of the braces (Fb) and ratio of yield strength of AST tie (FT) to yield strength of the brace. Since C1 test specimen did not tolerate a story drift ratio of 2.5% as desired by AISC [25], the M − H gusset plate of C1 test specimen did not provide satisfactory results as a structural fuse; Moreover, regarding Table 4, the braces of C4 test specimen experienced nonlinear behavior as well as the cyclic behavior of C4 test specimen demonstrated considerable pinching, so M − H gusset plate could not satisfactorily behave as a qualified structural fuse to protect the main structural elements. Therefore M − H gusset plate of C1 and C4 test specimens did not behave as the qualified structural fuse. Whereas, founded on experimental observation and test results, the M − H gusset plate of C2 and C3 test specimens could efficiently act as structural fuses. Fig. 13(c) and (d) illustrate the schematic view of load paths in M − H gusset plate before and after cracking of M − H gusset plate center. Based on Fig. 13(c), two structural fuses including M − H gusset plate and AST tie concurrently transfer the force by tension action; however, since buckling strength of M − H gusset plate and AST tie are infinitesimal, the contribution of the braces in transferring the lateral load in compression is not considerable. Regarding Fig. 13(d), in the cases of C1 and C2 test specimens, after the M − H gusset plate experienced extensive X-shaped crack (See Fig. 7 (a) and (b)), the load paths were changed through AST ties. Regarding the main assumption of this research about seismic behavior of the structural fuse, the M − H gusset plate should buckle to prevent the braces buckling. Considering

Fig. 10. (a) (b) (c) and (d) Side view of M − H gusset plate of C4, C3,C2 and C1 test specimens showing relative displacements between the braces end respectively.

compression are considered as two main controlling seismic behaviors in CFBF. Fig. 13 (a) and (b) illustrate the schematic view of widths of Whitmore section [10] and the buckling lengths at M − H gusset plate which are utilized for calculating the slenderness of M − H gusset plate. Based on Fig. 13(a), the thickness of Whitmore section includes M − H gusset plate and AST ties thicknesses (See Fig. 13(a)). Also regarding Fig. 13(b), the considered buckling lengths at M − H gusset plate includes the length between the edges of Whitmore widths (L1), the lengths between brace ends (See L2 and L3 in Fig. 13(b)). To calculate

Fig. 11. (a)–(c) Cyclic behavior of experimental models C1, C2, C3 and C4. 9

Soil Dynamics and Earthquake Engineering 127 (2019) 105856

M − H gusset plate fracture M − H gusset plate fracture No failure occurred up to 0.03 radians No failure occurred up to 0.03 radians

Table 6, the slenderness of braces both in out-of-plane and in-plane directions of braced frame should be smaller than M − H gusset plate slenderness along L1 to L3 (See Fig. 13(b)). Based on the calculated maximum and minimum ratios of M − H gusset plate slenderness along the buckling lengths to the slenderness of the braces for the case of C2 and C3 test specimens as qualified SCBFs (see the colored row in Table 8), The following criteria (Eqs. (3) and (4)) can be established:

( ) 12 < max ( kt l1 rg

M − H gusset plate

)

kx ,lx ky ly , r rx y brace

< 16.5

( )

kt l2, 3 rt AST tie

1.35 <

max

(

kx ,lx ky ly , r rx y

)

(3)

< 3.3

brace

43 44 – –

Wn = (La + 2Lb ∗ tan (30) − 2db)

238.5 306.6 393 443

Peak strength (KN) Ultimate strength (KN)

R < FGP

(8)

Where ϕu is 0.9 in LRFD [11,25] method, Fgy, Fty and W are expected yield stress of M − H gusset plate, expected yield stress of steel material of AST ties and width of Whitmore section (W=Wn+2db). Column 5 of Table 8 also presents sum of projected yield strength of horizontal and vertical AST ties along the brace main axis (FT) for C1 to C4 test specimens. FT is the vector addition of FV and Fh (See Fig. 13(d)) and FV and Fh are yield strength of vertical and horizontal AST ties. FT is calculated as follows:

214.28 305.21 414.34 563.2

Initial stiffness (KN/Cm)

(7)

Where R is base shear demand of a braced frame which is obtained by elastic analysis using factored loads based on IBC-2006 [32]. Regarding Table 8, FGY is yield strength of braced frame which is equal to projected yield strength of M − H gusset plate along braces main axis and is calculated as follows:

132 183 393 443

(4) (3)

(6)

Where ϕn is 0.75 in LRFD method [11,25,33], tg, tt, Fgu, Ftu and θ are M − H gusset plate thickness, AST tie thickness, expected tensile stress of M − H gusset plate, expected tensile stress of AST tie and the angle which is made up of brace main axis and M − H gusset plate’s weak axis (See Fig. 13 (c)). Based on column 4 of Tables 5 and 8, it is found that there is good agreement between peak strength of braced frame (FGP) calculated by equation (6) and obtained experimental results (See Fig. 11). To prevent failure of CFBF, the following expression should be satisfied:

FGY = ϕu . W . (tg . Fgy + tt . Fty ). Cos(θ)

(2)

(5)

Where La, Lb and db are center-to-center distances of the holes and bolt diameter respectively (See Fig. 13(a)). Since the compressive (Fc) and buckling strength of M − H gusset plate are not considerable, the peak strength of braced frame (FGP) (See Table 8), which is equal to projected peak strength of M − H gusset plate along the brace main axis (see Fig. 13 (c)), is calculated as follows (see column 4 of Table 8):

FGP = ϕn . Wn. (tg . Fgu + tt . Ftu ). Cos(θ)

Sin (θ))

(9)

Where d1 and d2 are widths of horizontal and vertical AST ties respectively. Since the force transferring path of M − H gusset plate after cracking is changed through AST ties, yield strength of (FT) should be

C1 C2 C3 C4

Test Specimen

FT = ϕu . (FH . Cos (θ) + FV Sin (θ)) = ϕt . Fty .. (tt + tg ) . (d1 Cos (θ) + d2

(1)

Table 5 Summary of the tests results.

(4)

Where kx and ky are buckling length factor about main axes of the braces section which is considered as 0.5 and 0.75 respectively [33]; Lx and Ly are buckling lengths of the braces respectively and finally rx, ry are gyration radiuses about main axes of the braces section respectively. In order to calculate M − H gusset plate peak strength, the effective width of Whitmore section (Wn) (See Fig. 13(a)) is calculated as follows:

2.3 3 3.1 3

Strength degradation (%) Total story drift ratio (%)

Test termination reason

(6) (5)

(7)

M. Bastami and R. Ahmady Jazany

10

Soil Dynamics and Earthquake Engineering 127 (2019) 105856

M. Bastami and R. Ahmady Jazany

Table 6 Calculated R-factor of the studied test specimens based on LRDF and ASD. Test Specimen

Overstrenght

Redundancy factor

Ductility

Response reduction factor(LRFD)a

Response reduction factor(ASD)1

C1 C2 C3 C4

1.58 1.79 1.80 1.83

1.25 1.25 1.25 1.25

4.06 4.23 4.33 4.38

6.41 7.57 7.79 8.01

8.01 9.45 9.74 10.01

a

ASD and LRFD refer to Allowable Stress Design and Load Resistant Factor Design [25,33].

larger than peak strength of M − H gusset plate (FGP) to assure that there is a reliable force transferring path during earthquake to prevent structural collapse.

FT > FGP

As it was discussed in this section, the details of M − H gusset plate for C2 and C3 test specimens provide the requirement of SCBF as desired by AISC [11–25] as well as prevent the damages to main structural members. In this regards, columns 6 and 7 of Table 8 present the ratios of peak strength of M − H gusset plate (FGP) to yield strength of braces (Fb) and yield strength of AST ties (FT) to yield strength of braces (Fb) respectively. Based on Table 8, to achieve the satisfactory seismic performance for CFBF, the above-mentioned ratios should fall between the following specified ranges (See colored rows in columns 6 and 7 of Table 8):

Fig. 12. Typical envelope of cyclic response and utilized parameters for calculation of response reduction factor. Table 7 Calculated dissipated energy values of the studied test specimens. Test Specimen

Dissipated Energy (N.m)

C1 C2 C3 C4

1.7x105 3.43x105 4.45x105 4.05x105

(10)

0.2 <

FGP < 0.22 Fb

(11)

0.23 <

FT < 0.26 Fb

(12)

Fb = ϕt . Ab . Fby

(13)

Because the above-mentioned design methodology, adopted for CFBF, was verified by the experiment, this method is able to adjust the yielding sequences in M − H gusset plate and AST ties and provide practical guide line for design of CFBF as an innovative structural system. 6. Conclusions In this research, four three-fourth scale specimens were tested to examine the cyclic behavior of proposed CFBF system. Furthermore, the adequacy of the proposed details for M − H gusset plate was evaluated with respect to the main assumption of this study “ductile M − H gusset plate as structural fuse element”. Based on the test results and experimental observations, the following conclusions are drawn: 1. The test observations demonstrated that CFBF with specified details can accommodate the required story drift ratio of SCBF by more than 2.5% as the qualifying criterion for CBF addressed by AISC [11,25] and M − H gusset plate acts as an energy dissipation device (i.e. structural fuse) and protect the sub-structural elements against structural failure. 2. Considering the measured strain values in structural elements and test observations, it is illustrated that AST ties can sufficiently prevent the extension of cracks observed in thinner M − H gusset plates towards gusset plate edges by acting as a parallel force transferring path at M − H gusset plate of CFBF. 3. The experimental results also exhibited that increase of the M − H gusset plate thickness by up to 2.5 times (i.e. ratio of M − H gusset plate thickness in C4 specimen to that of C1 specimen) decreases AST ties and center of M − H gusset plate out-of-plane buckling by up to 63 and 70%; however, increases the relative displacement between the brace segments end and M − H gusset plate connections by up to approximately 12 times. 4. The results (see Table 5 in section 3.3) illustrated that increase of

Fig. 13. (a) Calculation method of Whitmore section at M − H gusset plate connection to brace segment end (b) specified buckling lengths at M − H gusset plate (c) Schematic view of tensile and compressive force transmitted through M − H gusset plate before rupture of M − H gusset plate (d) Schematic view of tensile force transmitted through AST tie after rupture of M − H gusset plate center.

11

Soil Dynamics and Earthquake Engineering 127 (2019) 105856

M. Bastami and R. Ahmady Jazany

Table 8 Required design parameters for CFBF. 1

2

Test specimen

C1 C2 C3 C4

3

4

5

6

7

M − H gusset plate Slenderness

Brace Slenderness

M − H gusset plate

Yield strength of tension ties (FT) KN

FGP/Fb

FT/Fb

Ktl1/r1

Ktl2/r2

Ktl3/r2

KxL/rx

KyL/ry

peak strength (FGP) KN

Yield Strength (FGY) KN

831 554 415 332

129 113 100 90

59 52 46 42

27 27 27 27

34 34 34 35

251 286 317 358

83 124 165 211

301 340 383 433

0.17 0.20 0.22 0.25

0.21 0.23 0.26 0.30

M − H gusset plate thickness by up to 2.5 times (i.e. ratio of M − H gusset plate thickness in C4 specimen to that of C1 specimen) results in an increase in the initial stiffness and ultimate force by up to 2.63 and 3.28 times. 5. The outcomes of this study revealed that decreasing the thickness of M − H gusset plate by up to 60% leads to decrease of the dissipated energy and R-factor by up to 58 and 20%. 6. The developed design methodology of CFBF can provide practical guideline and establish a reliable structural fuse. Based on the proposed design criteria for CFBF, the ratios of peak strength of M − H gusset plate (FGP) to yield strength of braces (Fb) and yield strength of AST ties (FT) to yield strength of braces (Fb) should fall between 0.20 to 0.22 and 0.23 to 0.26 respectively so that satisfactory seismic performance could be achieved.

[10]

[11] [12]

[13]

[14]

[15]

Acknowledgement

[16]

This research was supported by IIEES (International Institute of Earthquake Engineering and Seismology). The authors would like to express their sincere appreciation to all staff and lab technician for their valuable assistance.Special thanks also go to Dr. A. Kalantari and A.S, Moghadam, the present and former director of the Structural Engineering Research Center (SERC) at IIEES for their sincere assistance.

[17]

[18]

[19]

[20]

Appendix A. Supplementary data

[21]

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.soildyn.2019.105856.

[22]

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