Shake table tests of special concentric braced frames under short and long duration earthquakes

Engineering Structures 200 (2019) 109695

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Shake table tests of special concentric braced frames under short and long duration earthquakes Ali Hammad, Mohamed A. Moustafa

T

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Department of Civil and Environmental Engineering, University of Nevada, Reno, NV 89523-0258, United States

ARTICLE INFO

ABSTRACT

Keywords: Shake table tests Special concentric braced frames Low cycle fatigue Long duration ground motions

Several long duration and subduction earthquakes recently took place in different locations such as Chile (2015, 2014, and 2010), Japan (2011), China (2008), and Indonesia (2004). These earthquakes motivate the need to prepare for a possible long-duration, large-magnitude earthquake in the Cascadia subduction zone along the Pacific Northwest Coast of the United States. Although earthquake duration is expected to affect the response of structures and damage accumulation, current seismic design specifications do not consider duration effects. One reason might be the lack of sufficient experimental research to better understand the effect of the duration on structural performance. In this paper, an experimental program was conducted to investigate the influence of earthquake duration on structural response of steel special concentric braced frames (SCBFs). Three identical 1/ 2-scale one-story one-bay SCBFs with chevron brace configuration were tested on one of the University of Nevada, Reno shake tables under unidirectional short and long duration earthquakes. The overall objective was to investigate whether the duration of earthquake have an effect on the collapse capacity of SCBFs dictated by brace rupture. Test results showed that the earthquake duration affects the structural performance of SCBFs and can cause a premature failure, i.e. lower displacement capacity, because it is directly related to the low cycle fatigue life of the braces. The experimental data provided here can be used to verify fatigue damage and degradation numerical models for capturing duration effects, and support initiatives to incorporate the duration effect in future seismic design provisions and performance-based assessment frameworks.

1. Introduction Special concentrically braced frames (SCBFs) are widely used in seismic design. Their strength and stiffness result in an economical system that easily meets serviceability limit states and ideally work for performance-based seismic design (PBSD). During large earthquakes, SCBFs exhibit a nonlinear behavior and must provide sufficient ductility to assure the life safety and collapse prevention performance states. The desired inelastic nonlinear behavior is dominated by braces extensive yielding, buckling, and low-cycle fatigue induced fracture, which need to be accurately captured by analytical models for reliable PBSD and collapse risk assessment. Current analytical approaches used in practice might not be well-suited for modeling low-cycle fatigue associated with very long duration earthquakes. The reason is that many of the commonly used low-cycle fatigue models are not physics-based models, and are typically statistical or regression models determined from previous experimental data that is mostly from cyclic tests and lacks dynamic or realistic seismic tests. Thus, it might not be possible to accurately predict and assess the post-yield mechanisms, failure modes, and

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structural collapse risk of SCBF buildings in urban areas located in the Cascadia Subduction zones (e.g. Seattle, WA or Portland, OR) using current approaches. Several long duration earthquakes have recently taken place such as the 2014 M8.2 Iquique, Chile earthquake, the 2011 M9.0 Tohoku, Japan earthquake, and the 2010 M8.8 Maule, Chile earthquake. The size of the faults rupture controls the durations of the ground motions where a rupture over 500 km during the 2010 Chile earthquake for instance led to many sites across Chile experiencing ground motions lasting for up to 90 s. Similar scenarios of long duration earthquakes potential risk can occur in the United States especially at the Cascadia Subduction zone in the Pacific Northwest. A subduction event at the Cascadia may produce earthquakes with extended durations and affect several states and metropolitan areas such as Seattle. This triggered national initiatives such as Project 17 (2015) to potentially consider the duration as a mapped parameter for next generation national seismic hazard maps and in turn, be considered in building codes. Several analytical projects studied the effect of long duration earthquakes on steel and reinforced concrete buildings as briefly discussed in next

Corresponding author. E-mail address: [email protected] (M.A. Moustafa).

https://doi.org/10.1016/j.engstruct.2019.109695 Received 27 April 2019; Received in revised form 13 August 2019; Accepted 17 September 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

Engineering Structures 200 (2019) 109695

A. Hammad and M.A. Moustafa

paragraph. However, most of these studies did not verify existing models against proper experimental tests or consider special modeling to account for damage-accumulation and deterioration as it relates to the earthquake duration, and especially long duration events. Accordingly, the ongoing Project 17 efforts will not consider the duration issue yet for the new maps in the 2020 NEHRP Recommended Provisions for New Buildings and Other Structures, but the duration remains an active “long-term” issue for consideration as more research and test data become available. Recently, research studies were motivated by the larger number of recorded long duration motions after events such as the Tohoku earthquake and started investigating the effect of earthquake duration on different structures damage and collapse risk [1,2]. The issue of the earthquake duration effect has been considered from different aspects and perspectives. In one way, such effect can depend on the duration definition where more than 30 definitions of strong ground motion duration are available in the literature. Another aspect renders the duration effect highly dependent on the structural model and the engineering demand parameter or damage metric used in judging the performance. Some studies that used peak response have generally found no correlation between ground motion duration and structural damage [3–6], but others found strong correlation when using cumulative damage measures [3,7] or energy measures [8–10]. Moreover, seismologists have recently looked at different ways of simulating the Cascadia subduction zone and seismic hazards in the Pacific Northwest such as the M9 Project [11]. In the latter, seismologists produced suites of synthetic ground motions that simulates different Cascadia subduction rupture scenarios and additionally, account for basin effects such as in Seattle. In terms of structural performance assessment under long duration earthquakes, mostly analytical studies are available in the literature with less focus on experimental testing. Marsh and Gianotti [12] used artificial acceleration records representing the Cascadia subduction zone earthquakes as an input for inelastic response history analyses of single degree of freedom systems. They found that structures subjected to long duration motions accumulate damage as a result of repeated cycles. Raghunandan et al. [13] carried out nonlinear dynamic analyses on reinforced concrete buildings designed according to outdated and modern building codes to study the duration effect. They concluded that that the median collapse capacity of the ductile buildings is approximately 40% less when subjected to ground motions from subduction, as compared to crustal earthquakes, i.e. seismic performance assessment based on crustal motions may substantially underestimate the seismic risk in regions with a subduction hazard. Moreover, Chandramohan et al. [1,2] evaluated the effect of considering ground motion duration when selecting hazard-consistent ground motions for structural collapse risk assessment. They developed a procedure to compute source-specific probability distributions of the durations of ground motions anticipated at a site, and then applied it to quantify the effect of considering duration when estimating the collapse risk of a ductile reinforced concrete moment frame building. The study showed that the mean annual frequency of collapse in Seattle, WA and Eugene, OR is underestimated by 29% and 59%, respectively, when using typicalduration ground motions from the PEER NGA-West2 database. It is noted that the aforementioned studies focused on concrete buildings, but few studies also considered the duration effects on reinforced

concrete bridges [14,15]. Other studies considered the effect of duration on steel buildings but did not show consensus in the significance of the duration effect. Foschaar et al. [16] investigated the effect of ground motion duration on the collapse capacity of a 3-story steel braced frame. To isolate the effect of the ground motion duration from other ground motion characteristics, they used two record sets, one with long duration records and the other with spectrally equivalent short duration records. They found that the duration affects the collapse capacity significantly. Using a similar approach, Tirca et al. [17] studied the effect of mega-thrust subduction records versus crustal records on moderately ductile steel office buildings located in Canada. However, this study showed that subduction records characterized by longer Trifunac duration did not affect demand parameters such as the peak or residual interstory drift different from crustal records. This variation in quantifying the duration effect on steel buildings might be attributed mainly to the modeling assumptions as explained next. Braced frames are vulnerable and particularly susceptible to low-cycle fatigue induced seismic damage that can be manifested in longer duration earthquake events, and in turn, is the focus of this study. Analytical and numerical studies are usually highly dependent on the modeling assumptions and their accuracy or validity. Failure of steel components in structural steel construction (e.g. braces) or reinforced concrete applications (e.g. reinforcing steel) under seismic loads is usually tied to low-cycle fatigue. However, the strain may not have constant amplitude under seismic loading [18], and many previous studies focused on this issue as noted here. Based on independent research by Coffin [19] and Manson [20], the Coffin-Manson relationship was developed to relate the plastic strain amplitude, εi at given cycle i, and the number of cycles to failure, Nf, as a linear logarithmic equation with slope m and coefficient ε0 for the equivalent single reversal strain as shown in Equation (1). The m and ε0 parameters are also known as the fatigue ductility exponent and fatigue ductility coefficient, respectively. In a popular platform heavily used for seismic analysis and performance assessment such as OpenSEES [21], the fatigue material or wrapper is commonly used to capture the fatigue-induced rupture of steel elements. Uriz [22] originally introduced this model for fiber-based beam-column elements to simulate the large displacement and inelastic buckling behavior of steel braces. The model requires the Coffin-Manson m and ε0 input parameters and uses a modified rainflow counting associated with a linear strain accumulation model (i.e. Miner’s Rule). Several studies suggest different values to use for the m and ε0 based on regression analysis of results from experimental data in the literature. Table 1 shows a summary of the different studies and recommended models or values for estimating the m and ε0 mainly valid for structural steel braces. Note that two of the listed studies in Table 1 provide equations (Eqs. (2) and (3)) for estimating ε0 rather than specific values as shown here. Readers are referred to Lignos and Karamanci [23] and Tirca and Chen [24] for the background behind such equations for braced frames. i

=

0 (Nf

(1)

)m

where number of cycles to failure and the strain amplitude experienced by a fiber in a cycle; εi: strain amplitude experienced by a fiber in a cycle; m and ε0: calibrated values, where m is the relationship between the number of cycles to failure (the slope of the log-log plot) and ε0 is an estimate of

Table 1 Different recommended values for the OpenSEES fatigue model parameters (m and ε0). Study

m

ε0

Study

m

ε0

Uriz [22] Lignos and Karamanci [23] Tirca and Chen [24] Chen and Mahin [25]

−0.5 −0.3 −0.5 −0.6

0.095 Equation (2) Equation (3) 0.090

Santagati et al. [26] Salawdeh and Goggins [27] Lai and Mahin [28]

−0.46 −0.50 −0.46

0.070 0.190 0.099

2

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A. Hammad and M.A. Moustafa

the strain at which failure occurs over one cycle; i: represents a cycle increment 0

0

= 0.291

kL r

pred. =0.006

0.484

kL r

w t

0.613

0.859

bo t

E Fy 0.6

earthquakes. Another objective of the conducted tests is to use the data for validating current SCBFs and fatigue modeling approaches, but this is the focus of another ongoing study by the authors and is not part of the scope of this paper. Thus, the next sections in this paper present the development of the experimental program, ground motions used for shake tale tests, a discussion of the test results divided between global response and local response, then a summary and concluding remarks.

0.3

(2)

E Fy

0.1

(3)

2. Experimental program development

where k:buckling factor; L: brace length; r: brace section radius of gyration; w: HSS section width; t: section wall thickness; E: steel Young’s modulus; Fy: steel yield stress. One limitation of the OpenSEES fatigue model is that it can be reasonably accurate only within few cycles of loading and might not be suitable to properly capture longer duration ground motions with large number of loading cycles. This is mainly because the Coffin-Mason equation is less accurate for large strain-range and number of cycles. Moreover, the large variability in the fatigue model input values shown in Table 1 can significantly affect the interpreted structural response from the analysis in terms of the onset of failure and the overall global behavior of the structural system. This observation has been demonstrated by the authors in a recent sensitivity analysis for SCBF buildings as they relate to the fatigue modeling parameters [29]. That study presented a new perspective of investigating the effects of SCBFs modeling uncertainties and variability on their seismic response with a special focus on earthquake duration. A sensitivity analysis was conducted for two SCBFs configurations: single diagonal brace and double X-bracing under cyclic loading and two sets of ground motions covering a wide range of significant duration. Tornado diagrams were considered to rank the effect of the considered modeling parameters and present the model sensitivity through their range of effect. The study showed that the different recommended values for m and ε0 may result in a large variation of results, and rendered the need for further validation or calibration using more test data. That study does not recommend yet the use of this fatigue modeling approach solely to understand the effect of duration on SCBFs before further validation, which motivated the experimental program conducted and presented in this paper. In summary, several studies considered the effect of the duration and the overall conclusion from these studies is that earthquake duration affects the structural performance and need to be properly accounted for in the design or assessment process in the future. However, more work, especially experimental testing, is still needed to better understand and/or quantify the effect of duration or provide the data needed to validate many of the numerical models and approaches. This study relates to the first need with focus on SCBFs by conducting largescale shake table tests for SCBFs under short and long duration earthquakes. Therefore, the overall goal of this study is to provide better understanding of the effect of earthquake duration. The two specific objectives are: (1) conduct three ½-scale one-story one-bay SCBF unidirectional shake table tests: two tests under spectrally-matched short and long duration ground motions and third test under another long duration ground motion; and (2) report and compare the seismic response of the identical frames, mainly global response: force, displacement, and acceleration, and local response: brace buckling, fatigue, and rupture, under the different short and long duration

This section presents the different aspects of the experimental program starting with the prototype selection and specimen design, then material properties and specimens’ fabrications, test setup, and instrumentation. 2.1. Prototype and specimen selection Three identical one-story one-bay SCBF with chevron brace configuration were used in this study. The test specimens for this study were adopted from a prototype building from 2006 IBC Structural/ Seismic Design Manual (Volume 3). The objective of starting the specimen design from a prototype building was to obtain actual design forces and floor mass, which was then scaled to design the specimen as explained in the next section. On the other hand, all the results of the conducted tests in this study were meant to be interpreted comparatively to understand effect of duration. Thus, reflecting test results on a prototype building or study the design implications of longer duration earthquakes is beyond the scope of this study. For determining the specimen design loads, the aforementioned prototype was used which featured a floor plan 49 m × 36.5 m and used bracing on the four sides of the building. The basement panel was chosen to determine the specimen forces. According to the shake table dimensions available at the Earthquake Engineering Laboratory at the University of Nevada, Reno and the height of the mass rig that can be attached to the specimen, a geometric scale of 1/2 was used to determine the design forces using the relevant laws of similitude [30] as summarized in Table 2. The designed specimen with all the dimensions and the members used is shown in Fig. 1 and details of design are discussed next. 2.2. Specimen design The design of the specimens was carefully done to be consistent and representative of the current practice (e.g. current codes and technical discussion with local consulting firms) within testing constraints. The standard codes and design recommendations used include mainly the AISC LRFD Manual [31] and AISC LRFD Seismic Provisions for Structural Steel Buildings [32]. The design process for each structural element is provided next. However, it is noted that several methods are usually available in the AISC standards [33] for instance for designing the gusset plate connections. The Uniform Force Method (UFM) was the one adopted here based on the wide use of such method. The prototype building used for determining the specimen forces was designed for a location in Seattle, WA, using Seismic Design Category D with soil Site Class C. The building was designed to meet ASCE-7 design spectrum. A response modification factor equals to 6 was used in the design. The

Table 2 Similitude scale factors for SCBF shake table tests. Parameter Length (L) Young’s modulus (E) Stress (σ) Strain (ε) Density (ρ) Force (F)

Relationship SL SE Sσ = SE Sε = Sσ/SE Sρ = Sσ/SL SF = SL2.Sσ

Model/Prototype

Parameter

1/2 1.0 1.0 1.0 2.0 1/4

Mass (m) Stiffness (k) Time (t) and period (T) Displacement (d) Velocity (v) Acceleration (a)

3

Relationship 3

Sm = Sρ.SL Sk = SE.SL St = (Sm/Sk)1/2 Sd = SL Sv = SL/St Sa

Model/Prototype 1/4 1/2 0.707 1/2 0.707 1.0

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limitation would not affect the overall objective of the study, i.e. the relative comparison of the tested SCBFs and small-scale braces behavior under short and long duration ground motions. Beam Design: The axial load capacity of the beam was designed considering the maximum axial load that could be delivered to the beams by the link. Consistent with the AISC [31], the beam design considered a vertical unbalanced load from the braces and W18x46 was selected. The beam flanges satisfied current seismic requirements, but the beam web does not satisfy current height-to-thickness requirements for highly ductile sections [31]. Column Design: Columns were designed following the same basic load assumptions as before. Additional gravity loads tributary to the columns were considered for the design but were not applied during testing. Similar to the beam, the column section satisfies seismic design requirements but the web and flanges do not satisfy current width-tothickness requirements for highly ductile sections [31]. The design was meant to represent real projects and construction limitations. As the brace has to be connected to a gusset plate, which in turn would be connected to the column flange and the base plate, a large gusset plate footprint was required on the base plate. This resulted in a large base plate area with a large moment arm between the anchor bolts that was not practical to be considered as a hinged base connection. Therefore, this connection was design to be fixed, which resulted in attracting around 20% of the horizontal load. These loads were taken in to account while designing the columns. Connections Design: Specimen connections were designed according to the above referenced AISC (2010a) guidelines. The connection and gusset plates details were sized based on the expected capacity of the braces. The gusset plates were fillet welded to the beams and columns, and similarly, the braces were fillet welded to the gusset plates. A linear clearance of (2 t), at the brace-to-column connection was applied and a horizontal clearance of (8 t) was applied as well at the brace-to-beam connection. Slotted connection between the HSS brace and gusset plates was used, i.e. there was a region of the brace having a reduced net section. As required by current provisions (AISC 2010a), reinforcement at these locations was designed. Shear tabs were bolted to the beams but welded to columns to be compatible with the welds used for the gusset-to column interface. Four bolts were used in each shear tab connection. Column-to-baseplate connections were designed based on the yield moment capacity of the column with fillet weld all around to provide a fixed condition at the column base. Fig. 2 shows all the connections details.

Fig. 1. Typical ½-scale test specimen.

calculated period was found to be 0.12 s. The design loads and calculations were first made based on the full scale prototype, then scaling factors were applied to obtain the corresponding values for the scaled specimen design. The gravity load used was 3.64 kN/m2 on the typical floor and 3.5 kN/m2 for the roof. Loads from the exterior curtain wall and steel studs were taken as 0.96 kN/m2 with exterior wall height of 4 m. The total mass on floor was approximately 7140 kN, distributed along two sides of bracing and each has three vertical bracing systems. The scaled mass on each frame was approximately 300 kN. To simulate this mass for the shake table test, two concrete blocks (each weighs approximately 90 kN) were added to the mass rig frame, which weighs about 90 kN. The additional concrete block weight along with the specimen weight and the rigid link that connects the mass rig to the specimen all together provide a very close equivalent to the required 300 kN of weight needed to model the required mass of 30.58 kN sec2/m. Brace Design: The braces member size was designed based on the force-based design criteria. The response spectrum for Seattle, WA was used and the corresponding force was divided by the overstrength factor R specified in the ASCE-7 (2010). The selected member size is HSS was 2.5 × 2.5 × 3/16 (size in US units). The resulting brace slenderness (KL/r) is 72, which is substantially less than the maximum permitted for current provisions for SCBFs [31]. The brace width-tothickness (b/t) ratio is 11.4 which satisfies the current limit for SCBFs [31], calculated as 0.55(E/Fy)0.5 = 13.8. It is worth mentioning that the braces size used in this study might not be representative of full-scale braces typically used in actual buildings. While a brace size is known to affect its fatigue and fracture properties, the authors believe that this

2.3. Material properties and specimens fabrication A local vendor in the Reno-Tahoe area was hired to provide all the

Fig. 2. Typical connection details shown for: (a) south base, (b) brace-gusset slot connection, and (c) South beam-column connection and column strengthening at mass rig rigid link connection location. 4

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Fig. 3. (a) Schematic diagram showing the details of the shake table test setup, (b) Schematic diagram showing out-of-plane restraining system.

steel fabrication and the field welds were placed by certified welders. All welds were specified as notch-tough [AWS-A5.20 (AWS 2005): E71T9C dual shield 7100 Ultra]. Each specimen contained both welded and bolted connections. A325 3/4″ diameter bolts were used to connect framing elements to each other. All bolted connections were pretensioned connections (in accordance with RCSC Specifications) with threads excluded for the shear plane. A992 steel grade was used for both beams and columns; A500-B grade for braces; and A572 grade was used for plates. Nominal values of Fy and Fu were used for design calculations according to the grade of steel, and nominal values for member sizes and geometries were used for all calculations for the design of the specimens. The actual brace dimension was found to be 63.5 mm with a thickness approximately equals to 4.67 mm (average of several measured spots).

under unidirectional earthquake loading. Fig. 3a shows schematic details of the full shake table test setup. In order to represent the inertial mass, each specimen was attached laterally to the mass rig system, which was designed by Laplace et al. [34] and has been commonly used at the Earthquake Engineering Laboratory for unidirectional single degree of freedom tests. The mass rig was connected to the column flange using a rigid link to apply the lateral force to the specimen. Four threaded high strength rods were used to connect the special link with the mass rig. The total inertial mass was 300 kN represented by own weight, connections, mass rig, and two concrete blocks as previously mentioned. Due to the mass rig and concrete blocks height, there was some eccentricity of about 23.50 cm between the centerline of the link and that of the beam. This eccentricity was assumed to have a minor effect on the overall behavior of the frames because horizontal and diagonal stiffeners were added between the column flanges to create a load path for the horizontal load as illustrated in Fig. 3a.

2.4. Test setup The three SCBFs were tested on one of the shake tables at the Earthquake Engineering Laboratory at the University of Nevada, Reno 5

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2.5. Instrumentation

increase the scale until failure is captured (final number of runs and testing scales are discussed in the next section). It is noted that other ground motion scaling schemes such as scaling to a given FEMA P-695 performance level was not adopted because the objective of testing is to understand the behavior at failure rather than assessing seismic performance at a given hazard level. To directly determine whether the earthquake duration affects the seismic capacity of the tested specimens, the short duration ground motion was spectrally matched to one of the two long duration ground motions. This is to test the frames under approximately similar force and acceleration demands and leave it for the low-cycle fatigue accumulated damage to determine the force and displacement capacity of the frames. It is noted that the specimens were designed according to downtown Seattle response spectrum. However, the rupture of the SCBF braces was dictated mainly by the low-cycle fatigue damage accumulation rather than force demands, which is the typical design philosophy for SCBFs. The third specimen was tested under another long duration ground motion to provide more data on seismic performance of SCBFs under long duration subduction earthquakes. Both long duration ground motions were adopted from the 2011 Tohoku, Japan earthquake. For the two spectrally-matched ground motions, an actual record from Tohoku earthquake, i.e. as originally recorded without modification, was used for the long duration case and a short duration record from the PEER NGA West 2 database was selected and matched in two steps. First, the online PEER NGA [38] matching tool was used to obtain a close matching record to the selected long duration record. Then, another matching tool was used to alter the frequency content of the short duration record such that the response spectrum would closely match the one for the long duration record within a range of periods of interest. The later matching tool is SeismoMatch [39] and the specified range of periods of interest varied from 0.05 to 0.6 s, which well encompassed the specimen’s fundamental period and the expected period elongation due to inelastic response. Fig. 8 shows the acceleration time histories for both the original and modified record after matching. The figure shows that the matched record did not change compared to the original record. The reason is that the motion was already selected to mostly match the long duration record spectrum and SeismoMatch was used only to slightly alter the frequency content so that both records would produce same demand when considering the period range of interest. The actual records and characteristics are listed in Table 3. Moreover, Fig. 7a shows the acceleration histories of the short and long duration ground motions used for testing after time scaling for similitude (see Table 2 above). Fig. 7b shows the 5% damping-ratio response spectra of the original and matched short record as compared to that of

Multiple types of instruments were used for each test to measure forces, displacements, strains and accelerations. In addition, high-definition video cameras were used to capture damage propagation. A summary of the different instrumentation types and layout is shown in Fig. 5. The load was measured using load cells at the lateral rigid link connecting the specimen with the mass rig and also from the shake table actuator, and used for capacity estimation. The deformed shape and lateral displacement of the frame was measured using several string potentiometers at the north column at two locations (column top and mid-height). Each brace was connected to two string potentiometers in the mid-span to measure in- and out-of- plane displacements and buckling. To capture the deformation of the gusset plates, two linear variable differential transformers (LVDTs) were attached to the bottom gusset plates and four LVDTs were attached to the upper middle gusset plate. Fig. 5a shows the layout and orientation of the string pots and LVDTs. Eight accelerometers were also used to measure the accelerations at different locations, two at the column top, two at the column midheight, two on the base plates, one on the table, and one at the beam mid span as shown in Fig. 5a. Strains in the braces and gusset plates were also measured using about 40 linear and rosette strain gages per specimen (all gages had a nominal gage factor of 2.14 and 6-mm gage length). Fig. 5b shows the layout of the strain gages for each specimen. It is also noted that target-tracking digital image correlation (DIC) was applied for the tested SCBFs), which explains the black and white targets shown in Fig. 4. However, the DIC work is part of another ongoing study on dynamic response monitoring and structural system identification [35,36]. Thus, results from DIC are not shown in this paper and not part of the scope but the distribution of DIC targets and coordinate identification for one of the SCBFs is shown in Fig. 6 for completeness. More information and full details on the specimens detailing, test setup, and instrumentations can be found in [37]. 3. Ground motion selection The experimental program involved three identical specimens that were tested under different ground motions. To achieve the overall goal of this study, i.e. study the effect of ground motion duration on seismic response of SCBFs and specifically the low-cycle fatigue capacity of the braces, one short crustal and two long duration subduction ground motions were used for testing (see Fig. 7 and Table 3). The intensity (scale) of each ground motion was increased until both braces ruptured. No particular number of runs was specified for each specimen as the criteria was to start from 100% of the ground motion and incrementally

Fig. 4. Different views of actual test set-up and general layout. 6

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Fig. 5. Schematic layout of: (a) LVDTs, string potentiometers, and accelerometers, (b) strain gages.

the long duration record. For the third test, as second long duration Tohoku ground motion was used, but the record was selected such that the velocity and/or displacement pulses, if existed, are shifted from the peak acceleration or pulse. There was not a specific objective for such selection other than just demonstrating another long duration record with different characteristics, and see whether the shifted displacement pulse affect the low-cycle fatigue damage accumulation. Table 3 lists the three ground motions used for the three specimens along with the acceleration, velocity, and displacement time histories of the third ground motion where the anticipated shift in the pulses or simply peak values is illustrated. A final note is that the two long duration records were handpicked using several trials and extensive pretest analysis following simple criteria: (1) ground motions with relatively long 5–95% significant duration, i.e. longer than 100 s for the uncompressed motion; (2) ground motions that do not have any site-specific properties or pulses so that the focus is mainly on the duration effect; (3) the feasibility of adopting a reasonably scaled short duration ground motion for the comparative nature of this part of the study, and (4) keeping the expected force and acceleration demands all the way through braces rupture within the allowable shake table and actuators limits, i.e. 720 kN and 4.0 g;.

4.1. Test progression and mode of failure To conduct the desired shake table tests, the first step was to properly tune the shake table control parameters for best performance given the stiff nature of the test specimens. An adaptive closed-loop control is generally adopted for shake table testing where the performance of the table is usually enhanced after few tests based on the feedback control adjustments. Overall, the shake table reproduced the desired target signals for all three tests for both long and short duration ground motions. Fig. 9 shows a comparison between the target command and actual shake table feedback for one of S2 tests. The figure shows that the shake table would slightly overshoot in some of the peaks, but the signals are reasonably matching overall without significant time delays. As previously mentioned, the exact number of runs and scales until brace rupture for each tested specimen was hard to determine before the tests. In the meantime, every ground motion run after the onset of buckling directly contribute to the fatigue life and need to be properly assessed. Therefore, it was desired to achieve brace buckling around the original 100% ground motion level so that the following larger scale runs would have meaningful contribution to the fatigue life and in turn, the rupture could be achieved within few number of runs. One challenge associated with the fixed base of the frames columns is the distribution of the lateral dynamic forces between the columns and braces. Thus, it was not easy to determine what percentage of the force goes to the braces to calculate buckling loads for estimating the best ground motion scale. Accordingly, a small scale of the long duration ground motion was conducted first, and using the strain gages attached to each brace at three different sections, the force in the braces was estimated and related to the total lateral force measured in the rigid link. Next, while the approximate force required to cause buckling could be estimated, the equivalent total link force was back calculated and related to the original ground motion to find the intensity scale. This procedure was adopted mainly for the first long duration ground motion and similar scale factors were used for other tests for direct comparison purposes.

4. Test results and discussions: Global response Test results and discussion with focus on the global seismic response, i.e. force, displacement, and acceleration are presented in this section. The force-deformation relationship for each frame and the stiffness degradation as testing progressed are also presented here. A summary of the key test results is provided at the end of this section, which can be used for model calibration/verification in future studies. A more detailed discussion on the braces buckling and fatigue is presented under local response in the next section.

Fig. 6. DIC targets attached to one of the tested SCBFs and the corresponding 2D coordinates (mm) for the spatial targets locations. 7

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Fig. 7. (a) Acceleration time histories of the long and modified short duration records, (b) 5%-damping ratio response spectra of the original and matched short duration record versus the long duration record.

190% scale and the south brace ruptured at 200% scale. It is noted that the lateral force capacity of the tested frames was reached early in the first few runs of testing when brace buckling took place. Increasing the ground motion scale after that point did not cause an increase in the force demands but induced larger displacements and testing continued until the ultimate displacement capacity was captured. Given the comparative nature especially for S1 and S2, the ground motion scale does not really mean a lot and only the equivalent runs and sequence that cause failure is what mattered. In other words, the problem at hand is a low-cycle fatigue problem and in turn, the same ground motion scale that caused buckling could have been applied as many times as needed until the brace rupture. For Specimen S2 that was tested under the matched short duration ground motion, reaching an equivalent 200% scale as the long duration ground motion did not accumulate enough damage and no rupture was observed. However, testing of S2 continued until failure, i.e. brace rupture, did not happen until the ground motion was scaled up to 225% (run #16). It is worth mentioning that during for Specimen S2 (run #2) a slip occurred at one of the base plates and the table interlocked as the allowable slippage was limited to 0.5 cm as a safety precaution to prevent any yielding in the shake table anchor holes. The overall force versus the drift ratio, i.e. hysteretic relationship, for S1 and S2 along with the displacement history at the SCBF top are shown in Fig. 11. The backbone curves for both specimens are also shown in Fig. 12 with the sequence of brace buckling and rupture identified. From that figure, it is observed that failure in case of the long duration earthquake occurred at lower drift ratio compared to the short

For the purpose of test results discussion, the first run reported here is the first run to cause inelastic buckling with the assumption that the contribution from the few small-scale trials, conducted to properly tune the shake table and adjust the scale, towards the fatigue life of the braces can be neglected. The justification of this assumption is that low-cycle fatigue is usually sensitive to small amount of cycles in the inelastic range, unlike the high-cycle fatigue that depends on large number of cycles in the elastic range. The testing procedure was successfully achieved and inelastic buckling was observed at the intended intensity levels adjusted as part of the ground motion selection process. The inelastic buckling simply refers to the residual buckling or end state after the completion of a given earthquake run, which continued to increase until full rupture took place. Fig. 10 shows the inelastic brace buckling and the complete brace rupture for one of the three tested frames. 4.2. Force-displacement response The first aspect of the seismic response is the number of runs and ground motion amplification scale required to reach failure. Regardless of the scale values, this was a comparative study so whatever scale factors needed to fail the SCBF under the first long duration earthquake were applied in same order using the short duration one. The first specimen tested under the first long duration earthquake, designated as specimen S1 throughout the rest of this discussion and noted in Table 3, required seven incremental runs until the complete brace rupture was reached at 200% scale of the original ground motion. For S1, the north brace ruptured at

Table 3 Characteristics of the selected ground motions for all three test specimens and time histories of the third specimen ground motion (velocity and displacement pulses shifted from acceleration peak).

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Fig. 8. (a) Acceleration time histories of the original (black) and matched (red) short duration record. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

duration ground motion, which is about 0.85% versus 1.25% for long and short duration cases, respectively. This is an important observation which means about 40% reduction in the intended displacement capacity due to the effect of the longer duration earthquake. The force versus drift ratio for the third specimen, S3 that was tested under the second long duration record with shifted velocity and acceleration peaks/pulses, is shown in Fig. 13. The figure shows that similar to S1, a lower displacement capacity was observed from this test at 1% drift ratio. This is slightly higher than the 0.85% capacity for S1 but still much lower than the 1.25% observed for S2, which again confirms the reduction in displacement capacity due to the duration effect. During S3 tests, after the force demand was capped when the frame reached its ultimate force capacity, one of the larger scale runs caused a sudden increase in the shake table actuator force and the table interlocked as illustrated in Fig. 13. The interlock caused a large displacement cycle (Fig. 13) which was accounted for as part of the fatigue life as discussed later. In such case, a relatively smaller test scale was applied to ensure the shake table actuator force is back within limits and the shake table was tuned again which can be observed in Fig. 13 in the displacement values of the 7th run that followed the interlock. It is also noted that for S3, the final force demand recorded when the failure occurred was only about half of the frame force capacity. The scaled 5–95 significant duration for specimen S3 was 64 s, which is considered more than eight times longer compared to the short duration record. The shifted velocity and displacement pulses were thought to be the reason the record caused high displacements at failure although the fact that the force demands and acceleration reported at

the last two runs were relatively small. The increased frame displacement caused higher accumulation of strains in the brace fibers causing complete brace rupture. The noticed feature of the long duration records compared to short duration, is the high number of small cycles with relatively low amplitude compared to the PGA. These cycles showed experimentally their significant effect accumulation damage in the brace fibers leading to quicker brace damage accumulation. This is discussed later in the paper showing the fatigue counting for both records S1 and S2. It is noted that the displacements values reported in the three tests are relatively low compared to common multi-story structures. This is mainly because of the single story set-up that worked best within the laboratory and shake table limitations in addition to the base fixity considered as part of designing the specimen to be in the first story. On the other hand, in a multi-story building, lateral displacements will be higher specially at higher floor levels and this will cause higher out of plane demands on the braces causing more strains and fatigue damage. Another factor is the brace local slenderness (b/t) ratio, where in the tested braces, (b/t) is relatively small compared to the common sizes used in a multi-story structure. As noticed during the test that the first stage in brace fracture is the brace wall local buckling, when the (b/t) ratio becomes higher, it is expected to observe local buckling earlier and eventually experience earlier brace rupture as well as loading cycles continue. This can always be related to main shocks and aftershocks, where a main shock may cause brace buckling, then a following aftershock may cause brace fatigue accumulation and cause full rupture.

Fig. 9. Comparison of shake table command signal and achieved feedback for one of S2 tests. 9

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Fig. 10. Typical test progression: (a) inelastic buckling, (b) complete brace rupture.

4.3. Stiffness degradation/period elongation

FRF is sometimes referred to “transfer function”. Fig. 14 shows the FRF for S1, S2 and S3 from three different white noise tests: an initial test before any seismic runs, a test after both braces buckled, and a test after rupture was observed. The reduction in the detected fundamental frequency, illustrated in Fig. 14, means period elongation and reflects stiffness reduction or degradation. Similar trend and values are observed for the other two specimens in the same figure. From the figure, it is shown that the fundamental frequency shifted from 8.5 Hz to about 4.5 Hz, which corresponds to period elongation from 0.12 s to 0.23 s when both braces completely ruptured. Another way of presenting the stiffness degradation is shown in Fig. 15. The figure presents the estimated stiffness values, as obtained from linear regression on the force-displacement curve from each seismic test, against the corresponding estimated period. For the linear regression, the average coefficient of determination (R2) was found to be 0.90, 0.96 and 0.89 for the three specimens, respectively. The figure shows the stiffness degradation for all three specimens and confirms that the identical frames had very comparable stiffness estimates and vibration periods, which are mainly governed by brace buckling and rupture and independent from the earthquake duration. This is another important observation because it suggests that accurate numerical models will need to properly capture the buckling and damage

As tests progressed and the braces of a given specimen buckled, the overall frame’s stiffness degradation was observed with changing contribution from a buckled brace when it is in tension or compression. However, SCBFs typically suffer major stiffness loss with the first brace (s) buckling then after a complete brace rupture given that all other components, e.g. columns, remain elastic. Two different ways were used to report the stiffness degradation. The first method is an indirect way through capturing the change in the specimens’ fundamental period as testing progress. For this purpose, a white noise excitation was applied after each seismic test and the recorded accelerations were used to calculate the Frequency Response Function (FRF). It is noted that it is not practical to reproduce an actual white noise through the shake table. Thus, the so-called white noise refers to a low amplitude excitation (less than 0.02 g) that is adopted from a more formal white noise signal. Such excitations do not cause any significant frame displacements or accumulate damage, and in turn, structural response under these low-amplitude excitations is not included in the discussion expect for the FRF estimates. The FRF is a frequency based measurement function used to identify the resonant frequencies of a physical structure by relating an output acceleration to the input, and in turn,

Fig. 11. Force versus drift ratio for S1 and S2 (left), and top displacement history for both tests (right). 10

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Fig. 12. The backbone curves for S1 and S2 with both braces buckling and rupture identified.

accumulation through fracture rather than considering macro-models or hysteretic degradation models for SCBFs.

2.64 cm, which is considered around 40% higher when compared to Specimen S1. It was noted that the force demands and the recorded acceleration at the last two runs decreased significantly to ∼ 460 kN and 1.65 g, respectively, although the PGA level was almost the same (1.65 g) as previous runs. For S2, the peak brace out-of-plane displacements were reported to be 8.26 and 15.80 cm for the north and south brace, respectively. Specimen S3 was tested under another long duration record, where the force capacity was almost similar to the first two specimens at about 640 kN. During run #6, the shake table interlocked due to a sudden increase in the force in the shake table actuator beyond the allowable limit. Thus, the values reported during that run were not representative because of the mechanism of the interlock caused a sudden impact in the shake table for that reported large value for the force demand. However, it is noted that the strain history and cycles accumulated during this run was still fully considered in the low cycle fatigue counting and fatigue life estimate. The maximum displacement reported for S3 frame during the test was about 1.98 cm, which still lower than the displacement capacity exhibited under the short duration record. Again the main reason is thought to be the high number of cycles accumulated in both braces during less number of tests under the long duration record compared to the short duration one. It was noticed that failure occurred at lower force demands and acceleration, however, the amount of strains accumulated during the eight runs were enough to cause brace rupture. The maximum out-of-plane brace displacement were reported to be 5.69 and 13.18 cm for the north and south braces of S3, respectively.

4.4. Summary of key test results A comprehensive summary of key test results is provided in Table 4 for all the runs for the three specimens, and can be readily used in future studies to validate numerical models to properly capture the effect of earthquake duration. The table reports values for the peak top accelerations, peak force demand in each run, frame displacements, brace out of plane buckling, and the residual displacements. The force and displacement capacities for each specimen are highlighted in the table as well. It is shown that force capacity is approximately the same for all three specimens and this is dictated mainly by the inelastic brace buckling so it is insensitive to the earthquake duration. However, the displacement capacity, as discussed before, is mainly dictated by the brace rupture, which is dictated by the low-cycle fatigue and in turn, sensitive to the earthquake duration. For specimen S1 tested under long duration record, The frame reached its lateral capacity at almost 660 kN and stayed at the same force level even with the increased seismic intensity and displacement demands. On the other hand, the top displacements increased with a maximum reported value of 1.90 cm. The maximum reported out-ofplane buckling was almost 15 cm, i.e. about 2.3 times the brace width. Only for S1, it was not possible to record the out-of-plane buckling in the last three tests due to instrumentation damage. However, new instrumentation was properly installed and attached in a secured way to fully capture the out-of-plane buckling in S2 and S3 tests all the way through rupture as shown in the table. As the three specimens were identical, the second specimen exhibited the same lateral force capacity (∼670 kN). However, the maximum displacement reported was

5. Test results and discussions: Local behavior This section complements the discussion above and focuses on the

Fig. 13. Force versus drift ratio (hysteretic behavior) for S3 (left), and top displacement history (right). 11

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Fig. 14. FRF and identified fundamental frequency for S1, S2 and S3 from white noise after three seismic tests.

local behavior in terms of brace buckling and damage propagation, fatigue life estimated based on the outer most fiber of the brace, and gusset plate behavior during loading. A brief discussion on the low cycle fatigue damage accumulation until failure is also presented.

5.1. Brace buckling Gusset plates’ deformation was observed during the tests and reported after the out-of-plane brace buckling occurred. Both gusset plates connecting the braces to the beam and the columns deformed as

Fig. 15. Stiffness degradation with respect to fundamental period for tested specimens S1, S2, and S3. 12

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Table 4 Summary of key test results for all runs and specimens.

Fig. 16. (a) Out-of-plane brace buckling, (b) upper gusset deformation, (c) lower gusset deformation, (d) upper brace white wash flakes.

Fig. 17. Out-of-plane brace deformation for S2 north (left) and south (right) braces.

shown in Fig. 16. According to the AISC design criteria, the gusset plates should stay elastic during extreme events, which was observed in these tests even after the inelastic brace buckling. Fig. 16b and 16c show the deformation of upper and lower gusset plates that followed the out-of-plane brace buckling (Fig. 16a). Fig. 16d shows a line crack that can approximately represent the rotation axis for the buckling

brace. Figs. 17 and 18 show the out-of-plane brace buckling for specimens S2 and S3 as measured at the brace mid-span using wire potentiometers. For S3 that was tested under the second long duration earthquake, the two braces buckled in opposite directions as seen in Fig. 18. It is worth noting that towards the end of S1 tests, the brace wire potentiometers slipped and the string wires were cut so reliable 13

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Fig. 18. Out-of-plane brace deformation for S3 braces and view of the opposite buckling directions.

Fig. 19. Stages of brace failure: (a) local buckling, (b) crack initiation, (c) crack propagation, (d) fracture.

that exceed the yield strain value. The figure illustrates that the long duration runs generated significantly larger number of strain cycles than the short duration runs mainly in the low strain ranges. This explains why failure occurred at a lower ground motion scale for the long duration relative to the short one, i.e. 200% versus 225%. When the 40% reduction in the displacement capacity observed in the long duration test is also considered, the overall effect of longer duration can be interpreted as premature failure for two reasons: (1) failure happened at smaller earthquake intensity for case of long duration motion; and (2) the observed capacity was also lower than what would be intended from typical short duration earthquakes due to the larger damage accumulation in case of the longer duration earthquakes. In a case of a multi-story SCBF, this can be alarming as the damaging effect of the large number of low range strain cycles associated with longer duration earthquakes could induce brace rupture at lower inter-story drifts than what is anticipated from the seismic design or performance-based assessment. Another way of looking at the fatigue life and damage accumulation is presented in Fig. 21b, which shows a comparison between the estimated damage index (DI) as it built up with the different strain ranges for S1 and S2. The DI was calculated by running each strain range with its equivalent number of cycles, i.e. results in Fig. 21a, through the Coffin-Manson relationship then apply Miner’s rule to reach failure, i.e. DI = 1. As explained before, Coffin-Manson requires input for m and ε0, which was estimated based on the empirical values obtained from Eq. (3) in Table 1. The goal here is not to assess the validity of existing values or determine new values for m and ε0, but rather provide a consistent means of comparing the damage accumulation between S1 and S2. The figure confirms that S1 accumulated more damage (higher DI) at the lower strain ranges than S2, which let to the full failure (DI = 1) reached earlier in S1. The difference in the strain range at DI = 1 between S1

brace buckling data were not recorded towards the end and not shown here. In terms of damage propagation for braces, Fig. 19 shows the different stages of brace failure. First, local brace buckling occurs, then tiny cracks start to from at the buckled face near the HSS edges. The crack propagates continuously until it makes a complete rupture in the brace cross-section. 5.2. Low-cycle fatigue and brace rupture A fair discussion of the low-cycle fatigue and models for capturing its effect for steel braces was previously provided in the introduction section. Results from the global response suggest that low-cycle fatigue induced rupture can be related to earthquake durations. Accordingly, the objective of this section is to provide a sample of the strain data measured in one of the tests and relate this data to fatigue life. Four strain gages were used at three different locations for each brace and distributed around the HSS 4 sides to accurately measure the outermost strains (Fig. 20). It is noted that at the brace mid-span (location B in Fig. 20), fibers 1 and 3 experienced the largest strain values and experienced the initial fatigue cracks that led to the full rupture. Fig. 20 shows the strain history for one of S3 braces at the three different sections and at each face of the HSS brace as a sample. As shown in the figure, the strains are drifting and this is due to the residual inelastic strains accumulated at the end of each test run. All the strains measured during the tests (e.g. the sample shown in Fig. 20) were used to do strain counting using the rainflow scheme as one way of interpreting fatigue life as it relates to the earthquake duration effects. The number of cycles corresponding to different strain ranges was calculated for the two specimens tested under the spectrally matched short and long duration earthquakes, i.e. S1 and S2, and shown in Fig. 21a. These numbers were counted from the accumulated strain from all runs, i.e. until failure, and using different strain ranges 14

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Fig. 20. Strains all over the brace at sections shown for Specimen S1.

and S2 again confirms that long duration earthquakes can cause failure before the full anticipated displacement or strain capacity from a typical short duration earthquake is reached. In summary, the above results preliminarily show that it is not a matter of how severe the ground motion is, in terms of ground accelerations, but rather the accumulated “low range” strain cycles with longer duration earthquakes that could matter for SCBFs seismic performance.

5.3. General notes For completeness, few general notes about the tests are provided. No yielding or flaking or any signs of deformation was reported in the beam at the location of the unbalanced forces of the braces. This confirms that the SCBF beams remained elastic even after the brace rupture as required by design. However, few signs of deformation were observed near the column connection to the base. Welding cracks were also reported at one single location, at the edge of the weld line of the 15

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Fig. 21. (a) Number of cycles for different strain ranges as accumulated from all S1 and S2 runs until failure; (b) representation of how outermost brace fiber accumulated damage from different strain ranges.

bottom gusset plate with the column. At the mass rig to the south column rigid link connection, some hair lines appeared in the white wash at the column flange at the location of the stiffening plates.

premature seismic failures or lower capacities, which provides more confidence for future initiatives to consider duration effects as part of the seismic design provisions. The tests also highlight the importance of the fatigue role in dictating SCBFs seismic capacities and the need for well verified numerical models for low-cycle fatigue. The experimental data provided in this paper can help in future verification studies. However more research that considers more cases and configurations is also needed to comprehensively address the duration effects on the structural safety and collapse capacity of SCBFs.

6. Summary and conclusions Due to the widespread use of SCBFs in the United States and the increasing risk from a large-magnitude long duration earthquake in the Pacific Northwest, this study focused on investigating the seismic response of SCBFs as it relates to the duration of the earthquake. In this study, experimental results of three shake table tests of identical ½-scale SCBF with chevron brace configuration under short and long duration records are presented and discussed. Two of the specimens were tested under spectrally matched short and long duration ground motions, and the third specimen was tested under another long duration record. Concluding remarks from the tests are as follows:

Declaration of Competing Interest The authors declared that there is no conflict of interest. References

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