# Shaking Table Test for Evaluating the Seismic Performance of Steel Frame Retrofitted by Buckling-Restrained Braces

Authors: Tingting Wang; Jianhua Shao; Chao Zhao; Wenjin Liu; Zhanguang Wang
Journal: Shock and Vibration
 (2021)

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## Abstract

To investigate the seismic performance of buckling-restrained braces under the earthquake action, the shaking table test with a two-story 1/4 scale model is carried out for the ordinary pure steel frame and the buckling-restrained bracing steel frame with low-yield-point steel as the core plate. The failure modes, dynamic characteristics, acceleration response, interstory drift ratio, strain, shear force, and other mechanical properties of those two comparative structures subjected to different levels of seismic waves are mainly evaluated by the experiment. The test results show that under the action of seismic waves with different intensities, the apparent observations of damage occur in the pure frame structure, while no obvious or serious damage in the steel members of BRB structure is observed. With the increase in loading peak acceleration for the earthquake waves, the natural frequency of both structures gradually decreases and the damping ratio gradually increases. At the end of the test, the stiffness degradation rate of the pure frame structure is 11.2%, while that of the buckling-restrained bracing steel frame structure is only 5.4%. The acceleration response of the buckling-restrained bracing steel frame is smaller than that of the pure steel frame, and the acceleration amplification factor at the second story is larger than that at the first story for both structures. The average interstory drift ratios are, respectively, 1/847 and 1/238 for the pure steel frame under the frequent earthquake and rare earthquake and are 1/3000 and 1/314 for the buckling-restrained bracing steel frame, which reveals that the reduction rate of lateral displacement reaches a maximum of 71.71% after the installation of buckling-restrained brace in the pure steel frame. The strain values at each measuring point of the structural beam and column gradually increase with the increase of the peak seismic acceleration, but the strain values of the pure steel frame are significantly larger than those of the buckling-restrained bracing steel frame, which indicates that the buckling-restrained brace as the first seismic line of defense in the structure can dramatically protect the significant structural members. The maximum shear force at each floor of the structure decreases with the increase in height, and the shear response of the pure frame is apparently higher than that of the buckling-restrained bracing structure.


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## Body

## 1. Introduction

In order to ensure the safety of the construction structure, many adverse factors need to be considered in the design, such as earthquake, strong wind, and the impact of human-induced vibration on the structure; among these, the most obvious effect on the structural damage is the earthquake action [1–3]. The earthquake engineering researchers have developed a feasible technology of passive energy dissipation systems, which can absorb seismic energy through utilizing the energy dissipating devices so as to reduce the influence of earthquakes on the building structures. One of the most widely applied types for the passive energy dissipation systems is the concentrically braced frame [4, 5]. The braced frame is universally provided with X-shaped crossing braces, single-inclined braces, inverted V-shaped braces, K-shaped braces, and so on. However, most of the braces in building structures are single construction types and cannot meet the higher seismic requirements of the structure. Therefore, the earthquake researchers have developed an innovative type of devices, such as buckling-restrained braces to immensely dissipate the energy from the earthquake action [6, 7].The buckling-restrained brace (BRB) is mainly composed of steel bracing inner core, outer covering restraint component, and nonbonding material or gap arranged between those two components [8–10]. Compared with ordinary braces, the enormous difference lies in that the inner core component reaches the full section yield under compression or tension and achieves the purpose of energy dissipation through the yield hysteresis due to the constraint action of the outer covering component for the buckling-restrained braces. Through the reasonable design of buckling-restrained brace, seismic energy can be absorbed and dissipated to a large extent, and the damage caused by the earthquake to the structure is reduced [11–13]. A remarkable essential factor for energy dissipation in buckling-restrained brace support is the choice of material for the inner core component. In recent years, one of the most effective materials for core elements in the buckling-restrained brace has been found to be low-yield-point (LYP) steel [14, 15]. The LYP steel possesses extremely low yield strength, low yield ratio, and high elongation capacity much larger than that of conventional structural steel. It also exhibits excellent strain hardening characteristics when subjected to cyclic loads. With a low yield ratio, the structure that utilizes LYP steel can redistribute the inelastic stress easily and provides a larger plastic zone [16–22]. Although the research on the properties and application of LYP steel is on the rise, there are extremely few researches focused on its combination with buckling-restrained brace, especially the shaking table test of LYP steel buckling-restrained bracing structure.The research achievement derived from scholars found that the reasonably constructed buckling-restrained brace possesses excellent energy dissipation capacity and can provide additional stiffness during large deformations. The vertical resistance and horizontal resistance of the buckling-restrained brace are relatively independent, and its working performance exhibits remarkable stability in the innovative structural system [23–25]. The buckling-restrained brace is further optimized and improved by some scholars proposing a novel type of BRB with a modularized inner core that can be adjusted flexibly according to building requirements. A method of replacing the BRB inner core and reducing the length of outer covering restraint component is put forward, and the corresponding specimen is designed to perform the experimental research with favourable results. The performance-based design method of gusset plates in buckling-restrained braces is proposed, the mechanical performance is investigated, and the corresponding seismic design recommendations for gusset plates are summarized [26–29]. It is found from the research on seismic performance that buckling-restrained braces can effectively dissipate the seismic energy under earthquakes, reduce structural response, and provide additional stiffness and damping for the building structure. The buckling-restrained brace can enter the elastoplastic state before the main structure, which improves the seismic ultimate bearing capacity of the overall structure [7, 30–36].Some previous achievements have been made in the research and analysis of buckling-restrained bracing structure, which promotes the application and development for building systems. However, these researches are restricted to focus on the static or cyclic loading tests and finite-element numerical simulations at a component level of braces. Any new in-depth study on time-history dynamic characteristics investigation of an overall structure combined with additional buckling-restrained braces is rarely carried out, let alone the shaking table tests of structures.In order to investigate the mechanical performance of buckling-restrained bracing structure, a two-story 1/4 scale model of this brace fabricated using LYP steel with a yield strength of approximately 100 MPa as the inner core was designed and manufactured in this study. The comparison in the dynamic characteristics of pure steel frame and buckling-restrained bracing steel frame was made by shaking table test. Three seismic waves were used to perform shaking table loading tests for these two different kinds of structures, and the mechanical properties such as the failure mode, dynamic characteristics, acceleration response, interstory drift ratio, strain, and interstory shear response under different intensity levels of seismic waves were investigated, and the seismic performance of buckling-restrained braces was analyzed and evaluated. The comprehensive test results provide novel and practical insights and act as a new technical reference on the engineering application and theoretical analysis for this kind of metallic brace.


## 2. Design of the Shaking Table Test

The shaking table test of structural model is an important method for simulating earthquakes in the laboratory, which is primarily utilized to analyze the damage mechanism, failure mode, and weak parts of structure under the earthquake action from a macro perspective, to evaluate the overall seismic resistance and to measure the effectiveness of shock absorption and isolation. After the shaking table test, the seismic performance and failure mode of the components under different earthquake intensity levels can be accurately achieved by collecting and analyzing the measured data.


### 2.1. Specimen Design

Two models used for the shaking table test include the single-span two-story pure steel frame (hereinafter referred to as pure frame) and single-span two-story buckling-restrained bracing steel frame (hereinafter referred to as BRB frame), which were designed in accordance with the Chinese Code for Seismic Design of Buildings (GB 50011–2010) under the seismic fortification intensity of 8 degrees [37]. Due to the limitation of working parameters, such as size of platform, anchor bolt spacing, lifting height, and bearing capacity, provided by shaking table facility, it was eventually determined that spatial structural test model of both the pure frame and BRB frame was designed and fabricated in accordance with 1/4 scale. According to the Buckingham theory and dimensional analysis method, the similitude ratios of significant physical parameters for the model structure are obtained, as shown in Table 1. The experimental results of the scaled model were then converted by the corresponding similitude ratios to achieve the dynamic responses of the prototype structure.Table 1
Scaling factors of the model structure.
Physical quantitiesSimilarityratiosPhysicalquantitiesSimilarityratiosStress1Stiffness1/4Length1/4Acceleration1.8Strain1Mass0.0347Elastic modulus1Period0.373Bending moment1/64Frequency2.68The additional mass blocks with a weight of 2 tons were mounted on each story of the specimen to simulate the weight distribution of the prototype structure accurately. Taking the mass blocks into consideration, the total weights of specimen, including the mass of the steel columns, beams, braces, and connecting plates, were approximately 4.26 tons and 4.29 tons for the pure frame and BRB frame, respectively. The plane size of two specimens with a height of 0.8 m at each story, shown in Figure1, was 1.2 × 1.2 m considering the limited size and loading capacity of the shaking table. Hot-rolled H-shaped steel with type specification of H100 × 100 × 6 × 8 mm was adopted for all the frame columns (FC), and the I-shaped steel of I10 was used for all the main beams (MB) and secondary beams (SB). BRB was welded from multiple steel plates. The inner core plate in BRB was made of low-yield-strength steel, whereas ordinary Q235B steel was applied in all other steel components. A cantilever splicing section located at the weak axis of the frame column was connected with the main frame beam by the full penetration butt weld to ensure the rigid beam-column joint, as shown in Figure 2. The bottom of the steel column in Figure 3 was strengthened using multiple stiffeners to achieve sufficient strength and stiffness, in order to prevent the column base from any premature formation of local buckling or plastic hinge during the tests.Figure 1
Plane and elevation layouts of the specimen (mm). (a) Plane layout of both models. (b) Elevation of the pure frame. (c) Elevation of the BRB frame.
(a)(b)(c)Figure 2
Beam-column connection. (a) 3D connection of the pure frame. (b) 3D connection of the BRB frame. (c) Plane of connection. (d) Section a2-a2. (e) Section b2-b2.
(a)(b)(c)(d)(e)Figure 3
Detailed connections at the bottom of columns (mm). (a) 3D. (b) Plane. (c) Section A-A.
(a)(b)(c)


### 2.2. Design of the BRB Element

Only the inner core plate in buckling-restrained brace designed for the shaking table test is connected to the main members of the structure, and all the transferred loads are born by the core plate made of LYP steel. The external restraint steel plate with the gap of 7.5 mm between the core plate and restraining element only limits the inner core to buckling under compression. The 3D diagram of BRB member is shown in Figure4.Figure 4
3D diagram of BRB.Considering the ultimate loading capacity of the shaking facility, and the stiffness and bearing capacity of specimen, the detailed cross-sectional dimensions of each plate in the buckling-restrained brace with the inner core of 5-mm thickness are eventually determined as shown in Figure5. The BRB is connected to the main frame by welding the connecting plate on the frame beam and column in advance. A certain number of equally spaced stiffeners are set at the connecting joint located in flange of frame beam to prevent local shear buckling of the beam web caused by the axial force of BRB, as shown in Figure 6.Figure 5
Details of BRB (mm). (a) Overall drawing of BRB. (b) Restraining plate 1 with a thickness of 10 mm. (c) LYP core with a thickness of 5 mm. (d) Restraining plate 2 with a thickness of 11 mm.
(a)(b)(c)(d)Figure 6
Detailed connection of BRB (mm). (a) Connection of BRB. (b) Gusset plate 1. (c) Gusset plate 2.
(a)(b)(c)


### 2.3. Material Property Test

The uniaxial tensile test on steel coupons had been carried out to obtain fundamental mechanical properties of the materials, including the yield strength, ultimate tensile strength, modulus of elasticity, elongation, and yield ratio. The material of typical steel coupons designed as the shape of the plate required for the steel tensile test was cut from the base material. Three tensile coupons were tested for the LYP steel with the nominal yield strength of 100 MPa.These steel coupons for tensile tests were respectively installed on the electrohydraulic universal material-testing machine, which can automatically record the maximum load, yield strength, and ultimate strength at the end of the test. The tensile coupons of LYP steel were observed to stretch considerably long, from the initial elasticity to the yield and then to the strain hardening stage until the necking fracture. The cross-sectional area was reduced to a sufficiently small section, and the fractured surface was uneven and jagged after tensile fracture of LYP steel coupons, which indicates that this LYP steel exhibits superior ductile performance.Table2 presents the different mechanical behaviors of LYP and ordinary steel specimens under quasistatic tensile tests. In comparison, the ratios of yield strength, ultimate tensile strength, and yield ratio of LYP steel to Q235 steel were approximately 0.41, 0.64, and 0.63, respectively, whereas the elongation of LYP steel was approximately 1.36 times that of Q235 steel.Table 2
Results of the material test.
SpecimenMaximum loadF(kN)Yield strengthfy(MPa)Tensile strengthfu(MPa)Modulus of elasticityE(MPa)Elongation(%)Yieldratiofy/fuMaterialNumberLYP steelM147.42100.59250.6819863946.360.40M247.1394.74248.9620873448.180.38M347.0490.76248.7620097448.180.36Ordinary steel (Q235)74.26234.91391.2120015235.100.60


### 2.4. Facility and Installation of the Specimen

A series of shaking table tests under three seismic waves, with the scaled amplitude modulation of peak acceleration, was carried out to investigate the overall damage process of pure frame and BRB structure subjected to the different intensity levels of earthquake records. The geometric working size was 4.0 × 6.0 m for the loading test of the shaking table facility with a maximum capacity of up to 250 kN, operating frequency range of 0.1–50 Hz, and maximum velocity of ±6 mm/s. The shaking table could produce a maximum acceleration of 3.0 g at the nonload condition and 1.5 g at the loading condition of 250 kN, with a maximum displacement of ±250 mm, as shown in Figure7.Figure 7
Shaking table.All the steel components in the specimen were fabricated and connected in the factory. The welded connection was adopted in the beam-column joints to possess a rigid stiffness. The bottom plate with a thickness of 20 mm was welded to the end of the steel column, which was firmly attached to the shaking table surface with the high-strength bolt of 36-mm diameter and 300-mm hole spacing. After being transported to the structural laboratory, the whole specimen was hoisted to the shaking table surface by a bridge crane in the laboratory and fixed by the anchor bolt. Then, artificial counterweights of additional mass blocks in the form of rubber isolation bearings, and steel plates were deployed and bolted to the steel floor slab with a thickness of 5 mm in order to ensure that no slipping could be occurred throughout the test, as shown in Figure8.Figure 8
Installed specimen. (a) Pure frame. (b) BRB frame. (c) Enlarged BRB connection.
(a)(b)(c)


### 2.5. Measuring Instrument and Arrangement of the Monitoring Point

The strain and displacement responses measured by the experiment were utilized to analyze and evaluate the indicators of seismic performance for these two structures under different seismic intensity levels of different seismic waves. The resistance strain gauges were adopted to investigate the strain variance of steel members during this test after the additional mass blocks were mounted on each story of the specimen (as shown in Figure9(a)). The LVDT displacement sensors were mounted on the model to monitor the interstory drift ratios (see Figure 9(b)). The corresponding dynamic signal processing system was used for data acquisition and analysis (see Figure 9(c)).Figure 9
Layout of measuring instrument. (a) Placement of mass block. (b) Displacement sensor. (c) Data acquisition system.
(a)(b)(c)The monitoring point arrangement of specimen includes the arrangement of strain gauges and displacement sensors. Four strain measuring points are arranged on each beam and column member of each frame, that is, one strain gauge is provided on each of the top and bottom flanges on both sides of the column, and one strain gauge is arranged on each of the upper and lower flanges at both ends of the beam. A total of 48 strain gauges are arranged for the uncontrolled pure frame structure, while for the controlled BRB structure, two additional strain gauges need to be set on each BRB, and a total of 64 strain measurement points are arranged. A displacement meter is arranged at the connection between the beams and column on each floor of the structure, and the measuring point layout is shown in Figure10.Figure 10
Layout of measuring points. (a) Pure frame. (b) BRB frame.
(a)(b)


### 2.6. Loading Scheme

More than three different seismic waves are generally required to be utilized in the shaking table test for evaluating the seismic performance of the structural model. Three factors of seismic wave, including the effective peak value, duration, and spectral characteristics, should be considered in the selection of earthquake waves. Three ground excitations, representative of actual earthquake records, which conform to the dynamic characteristics of the standardized response spectrum put forward by the GB 50011–2010, are selected to input to the shaking table instrument: El Centro wave (Imperial Valley earthquake, 1940), Kobe wave (Hyogoken-Nanbu earthquake, 1995), and Taft wave (California earthquake, 1952). The representative seismic waves and corresponding frequency spectra, derived from converting the input time domain into the frequency domain by fast Fourier transform under the peak ground acceleration (PGA) of 0.3 g, as an example for three ground records, are shown in Figures11 and 12.Figure 11
Loading earthquake waves. (a) El Centro wave. (b) Kobe wave. (c) Taft wave.
(a)(b)(c)Figure 12
Corresponding frequency spectra of waves. (a) El Centro wave. (b) Kobe wave. (c) Taft wave.
(a)(b)(c)In the shaking table test, acceleration similarity ratio is the significant control parameter of applying the dynamic load of seismic wave. Considering the numerous different factors, such as the noise of shaking table, maximum bearing capacity of equipment, and section size of specimen, and based on the previous test experience, this scaling factor of acceleration adopted in the test was determined to be 1.8. The specimen was designed according to the seismic fortification intensity of 8 degrees given in the GB 50011–2010, and the corresponding acceleration peaks of the specimen under the frequent earthquake, occasional earthquake, and rare earthquake were 0.126 g, 0.36 g, and 0.72 g, respectively.In order to investigate the energy dissipation and shock absorbing ability of the buckling-restrained brace under different earthquake intensity levels, the peak acceleration of three seismic waves was increasingly scaled amplitude during loading. The loading-scaled PGAs of input El Centro and Taft waves were increased from 0.1 g to 1.0 g, with each case increased by 0.1 g, whereas the Kobe wave was scaled up to 1.6 g due to the different maximum oil pressures caused by the individual dynamic characteristics of seismic waves. The white noise signal with PGA of 0.05 g was used to sweep the frequency of the structural model before the test and the loading of each level of seismic wave. The specific loading conditions of the test are shown in Table3.Table 3
Seismic loading plan.
CaseEarthquakePGA (g)CaseEarthquakePGA (g)CaseEarthquakePGA (g)CaseEarthquakePGA (g)1White noise0.054White noise0.057White noise0.0510White noise0.05El Centro0.1El Centro0.4El Centro0.7El Centro1.0Kobe0.1Kobe0.4Kobe0.7Kobe1.0Taft0.1Taft0.4Taft0.7Taft1.02White noise0.055White noise0.058White noise0.0511White noise0.05El Centro0.2El Centro0.5El Centro0.8Kobe1.1Kobe0.2Kobe0.5Kobe0.812Kobe1.2Taft0.2Taft0.5Taft0.813Kobe1.33White noise0.056White noise0.059White noise0.0514Kobe1.4El Centro0.3El Centro0.6El Centro0.915Kobe1.5Kobe0.3Kobe0.6Kobe0.916Kobe1.6Taft0.3Taft0.6Taft0.9During the test, as the set peak acceleration increases gradually, the set value of the peak acceleration of each seismic wave will be different from the actual loading value because the oil supply pressure of the shaking table equipment provided by pipeline is slightly insufficient. Therefore, when the structural performance analysis is performed using the measured acquisition data, the loading actual peak acceleration shall prevail. The actual loading PGA, which is slightly larger than each seismic level, is taken as the basis of this level for the seismic performance evaluation. The loading cases under frequent earthquake, occasional earthquake, and rare earthquake for the structural performance analysis correspond to case 2 with PGA of 0.2 g, case 4 with PGA of 0.4 g, and case 8 with PGA of 0.8 g, respectively.


## 2.1. Specimen Design

Two models used for the shaking table test include the single-span two-story pure steel frame (hereinafter referred to as pure frame) and single-span two-story buckling-restrained bracing steel frame (hereinafter referred to as BRB frame), which were designed in accordance with the Chinese Code for Seismic Design of Buildings (GB 50011–2010) under the seismic fortification intensity of 8 degrees [37]. Due to the limitation of working parameters, such as size of platform, anchor bolt spacing, lifting height, and bearing capacity, provided by shaking table facility, it was eventually determined that spatial structural test model of both the pure frame and BRB frame was designed and fabricated in accordance with 1/4 scale. According to the Buckingham theory and dimensional analysis method, the similitude ratios of significant physical parameters for the model structure are obtained, as shown in Table 1. The experimental results of the scaled model were then converted by the corresponding similitude ratios to achieve the dynamic responses of the prototype structure.Table 1
Scaling factors of the model structure.
Physical quantitiesSimilarityratiosPhysicalquantitiesSimilarityratiosStress1Stiffness1/4Length1/4Acceleration1.8Strain1Mass0.0347Elastic modulus1Period0.373Bending moment1/64Frequency2.68The additional mass blocks with a weight of 2 tons were mounted on each story of the specimen to simulate the weight distribution of the prototype structure accurately. Taking the mass blocks into consideration, the total weights of specimen, including the mass of the steel columns, beams, braces, and connecting plates, were approximately 4.26 tons and 4.29 tons for the pure frame and BRB frame, respectively. The plane size of two specimens with a height of 0.8 m at each story, shown in Figure1, was 1.2 × 1.2 m considering the limited size and loading capacity of the shaking table. Hot-rolled H-shaped steel with type specification of H100 × 100 × 6 × 8 mm was adopted for all the frame columns (FC), and the I-shaped steel of I10 was used for all the main beams (MB) and secondary beams (SB). BRB was welded from multiple steel plates. The inner core plate in BRB was made of low-yield-strength steel, whereas ordinary Q235B steel was applied in all other steel components. A cantilever splicing section located at the weak axis of the frame column was connected with the main frame beam by the full penetration butt weld to ensure the rigid beam-column joint, as shown in Figure 2. The bottom of the steel column in Figure 3 was strengthened using multiple stiffeners to achieve sufficient strength and stiffness, in order to prevent the column base from any premature formation of local buckling or plastic hinge during the tests.Figure 1
Plane and elevation layouts of the specimen (mm). (a) Plane layout of both models. (b) Elevation of the pure frame. (c) Elevation of the BRB frame.
(a)(b)(c)Figure 2
Beam-column connection. (a) 3D connection of the pure frame. (b) 3D connection of the BRB frame. (c) Plane of connection. (d) Section a2-a2. (e) Section b2-b2.
(a)(b)(c)(d)(e)Figure 3
Detailed connections at the bottom of columns (mm). (a) 3D. (b) Plane. (c) Section A-A.
(a)(b)(c)


## 2.2. Design of the BRB Element

Only the inner core plate in buckling-restrained brace designed for the shaking table test is connected to the main members of the structure, and all the transferred loads are born by the core plate made of LYP steel. The external restraint steel plate with the gap of 7.5 mm between the core plate and restraining element only limits the inner core to buckling under compression. The 3D diagram of BRB member is shown in Figure4.Figure 4
3D diagram of BRB.Considering the ultimate loading capacity of the shaking facility, and the stiffness and bearing capacity of specimen, the detailed cross-sectional dimensions of each plate in the buckling-restrained brace with the inner core of 5-mm thickness are eventually determined as shown in Figure5. The BRB is connected to the main frame by welding the connecting plate on the frame beam and column in advance. A certain number of equally spaced stiffeners are set at the connecting joint located in flange of frame beam to prevent local shear buckling of the beam web caused by the axial force of BRB, as shown in Figure 6.Figure 5
Details of BRB (mm). (a) Overall drawing of BRB. (b) Restraining plate 1 with a thickness of 10 mm. (c) LYP core with a thickness of 5 mm. (d) Restraining plate 2 with a thickness of 11 mm.
(a)(b)(c)(d)Figure 6
Detailed connection of BRB (mm). (a) Connection of BRB. (b) Gusset plate 1. (c) Gusset plate 2.
(a)(b)(c)


## 2.3. Material Property Test

The uniaxial tensile test on steel coupons had been carried out to obtain fundamental mechanical properties of the materials, including the yield strength, ultimate tensile strength, modulus of elasticity, elongation, and yield ratio. The material of typical steel coupons designed as the shape of the plate required for the steel tensile test was cut from the base material. Three tensile coupons were tested for the LYP steel with the nominal yield strength of 100 MPa.These steel coupons for tensile tests were respectively installed on the electrohydraulic universal material-testing machine, which can automatically record the maximum load, yield strength, and ultimate strength at the end of the test. The tensile coupons of LYP steel were observed to stretch considerably long, from the initial elasticity to the yield and then to the strain hardening stage until the necking fracture. The cross-sectional area was reduced to a sufficiently small section, and the fractured surface was uneven and jagged after tensile fracture of LYP steel coupons, which indicates that this LYP steel exhibits superior ductile performance.Table2 presents the different mechanical behaviors of LYP and ordinary steel specimens under quasistatic tensile tests. In comparison, the ratios of yield strength, ultimate tensile strength, and yield ratio of LYP steel to Q235 steel were approximately 0.41, 0.64, and 0.63, respectively, whereas the elongation of LYP steel was approximately 1.36 times that of Q235 steel.Table 2
Results of the material test.
SpecimenMaximum loadF(kN)Yield strengthfy(MPa)Tensile strengthfu(MPa)Modulus of elasticityE(MPa)Elongation(%)Yieldratiofy/fuMaterialNumberLYP steelM147.42100.59250.6819863946.360.40M247.1394.74248.9620873448.180.38M347.0490.76248.7620097448.180.36Ordinary steel (Q235)74.26234.91391.2120015235.100.60


## 2.4. Facility and Installation of the Specimen

A series of shaking table tests under three seismic waves, with the scaled amplitude modulation of peak acceleration, was carried out to investigate the overall damage process of pure frame and BRB structure subjected to the different intensity levels of earthquake records. The geometric working size was 4.0 × 6.0 m for the loading test of the shaking table facility with a maximum capacity of up to 250 kN, operating frequency range of 0.1–50 Hz, and maximum velocity of ±6 mm/s. The shaking table could produce a maximum acceleration of 3.0 g at the nonload condition and 1.5 g at the loading condition of 250 kN, with a maximum displacement of ±250 mm, as shown in Figure7.Figure 7
Shaking table.All the steel components in the specimen were fabricated and connected in the factory. The welded connection was adopted in the beam-column joints to possess a rigid stiffness. The bottom plate with a thickness of 20 mm was welded to the end of the steel column, which was firmly attached to the shaking table surface with the high-strength bolt of 36-mm diameter and 300-mm hole spacing. After being transported to the structural laboratory, the whole specimen was hoisted to the shaking table surface by a bridge crane in the laboratory and fixed by the anchor bolt. Then, artificial counterweights of additional mass blocks in the form of rubber isolation bearings, and steel plates were deployed and bolted to the steel floor slab with a thickness of 5 mm in order to ensure that no slipping could be occurred throughout the test, as shown in Figure8.Figure 8
Installed specimen. (a) Pure frame. (b) BRB frame. (c) Enlarged BRB connection.
(a)(b)(c)


## 2.5. Measuring Instrument and Arrangement of the Monitoring Point

The strain and displacement responses measured by the experiment were utilized to analyze and evaluate the indicators of seismic performance for these two structures under different seismic intensity levels of different seismic waves. The resistance strain gauges were adopted to investigate the strain variance of steel members during this test after the additional mass blocks were mounted on each story of the specimen (as shown in Figure9(a)). The LVDT displacement sensors were mounted on the model to monitor the interstory drift ratios (see Figure 9(b)). The corresponding dynamic signal processing system was used for data acquisition and analysis (see Figure 9(c)).Figure 9
Layout of measuring instrument. (a) Placement of mass block. (b) Displacement sensor. (c) Data acquisition system.
(a)(b)(c)The monitoring point arrangement of specimen includes the arrangement of strain gauges and displacement sensors. Four strain measuring points are arranged on each beam and column member of each frame, that is, one strain gauge is provided on each of the top and bottom flanges on both sides of the column, and one strain gauge is arranged on each of the upper and lower flanges at both ends of the beam. A total of 48 strain gauges are arranged for the uncontrolled pure frame structure, while for the controlled BRB structure, two additional strain gauges need to be set on each BRB, and a total of 64 strain measurement points are arranged. A displacement meter is arranged at the connection between the beams and column on each floor of the structure, and the measuring point layout is shown in Figure10.Figure 10
Layout of measuring points. (a) Pure frame. (b) BRB frame.
(a)(b)


## 2.6. Loading Scheme

More than three different seismic waves are generally required to be utilized in the shaking table test for evaluating the seismic performance of the structural model. Three factors of seismic wave, including the effective peak value, duration, and spectral characteristics, should be considered in the selection of earthquake waves. Three ground excitations, representative of actual earthquake records, which conform to the dynamic characteristics of the standardized response spectrum put forward by the GB 50011–2010, are selected to input to the shaking table instrument: El Centro wave (Imperial Valley earthquake, 1940), Kobe wave (Hyogoken-Nanbu earthquake, 1995), and Taft wave (California earthquake, 1952). The representative seismic waves and corresponding frequency spectra, derived from converting the input time domain into the frequency domain by fast Fourier transform under the peak ground acceleration (PGA) of 0.3 g, as an example for three ground records, are shown in Figures11 and 12.Figure 11
Loading earthquake waves. (a) El Centro wave. (b) Kobe wave. (c) Taft wave.
(a)(b)(c)Figure 12
Corresponding frequency spectra of waves. (a) El Centro wave. (b) Kobe wave. (c) Taft wave.
(a)(b)(c)In the shaking table test, acceleration similarity ratio is the significant control parameter of applying the dynamic load of seismic wave. Considering the numerous different factors, such as the noise of shaking table, maximum bearing capacity of equipment, and section size of specimen, and based on the previous test experience, this scaling factor of acceleration adopted in the test was determined to be 1.8. The specimen was designed according to the seismic fortification intensity of 8 degrees given in the GB 50011–2010, and the corresponding acceleration peaks of the specimen under the frequent earthquake, occasional earthquake, and rare earthquake were 0.126 g, 0.36 g, and 0.72 g, respectively.In order to investigate the energy dissipation and shock absorbing ability of the buckling-restrained brace under different earthquake intensity levels, the peak acceleration of three seismic waves was increasingly scaled amplitude during loading. The loading-scaled PGAs of input El Centro and Taft waves were increased from 0.1 g to 1.0 g, with each case increased by 0.1 g, whereas the Kobe wave was scaled up to 1.6 g due to the different maximum oil pressures caused by the individual dynamic characteristics of seismic waves. The white noise signal with PGA of 0.05 g was used to sweep the frequency of the structural model before the test and the loading of each level of seismic wave. The specific loading conditions of the test are shown in Table3.Table 3
Seismic loading plan.
CaseEarthquakePGA (g)CaseEarthquakePGA (g)CaseEarthquakePGA (g)CaseEarthquakePGA (g)1White noise0.054White noise0.057White noise0.0510White noise0.05El Centro0.1El Centro0.4El Centro0.7El Centro1.0Kobe0.1Kobe0.4Kobe0.7Kobe1.0Taft0.1Taft0.4Taft0.7Taft1.02White noise0.055White noise0.058White noise0.0511White noise0.05El Centro0.2El Centro0.5El Centro0.8Kobe1.1Kobe0.2Kobe0.5Kobe0.812Kobe1.2Taft0.2Taft0.5Taft0.813Kobe1.33White noise0.056White noise0.059White noise0.0514Kobe1.4El Centro0.3El Centro0.6El Centro0.915Kobe1.5Kobe0.3Kobe0.6Kobe0.916Kobe1.6Taft0.3Taft0.6Taft0.9During the test, as the set peak acceleration increases gradually, the set value of the peak acceleration of each seismic wave will be different from the actual loading value because the oil supply pressure of the shaking table equipment provided by pipeline is slightly insufficient. Therefore, when the structural performance analysis is performed using the measured acquisition data, the loading actual peak acceleration shall prevail. The actual loading PGA, which is slightly larger than each seismic level, is taken as the basis of this level for the seismic performance evaluation. The loading cases under frequent earthquake, occasional earthquake, and rare earthquake for the structural performance analysis correspond to case 2 with PGA of 0.2 g, case 4 with PGA of 0.4 g, and case 8 with PGA of 0.8 g, respectively.


## 3. Experimental Observations

The uniaxial loading shaking table tests subjected to three different seismic waves were performed on the pure frame and BRB structure, respectively. After the entire loading cases with the increasing earthquake intensity levels were successfully completed, the apparent observations of damage occurred in the pure frame structure, while no obvious or serious damage in the steel members of BRB structure was observed. The experimental phenomenon is shown in Figure13.Figure 13
Test phenomena. (a) Scattered dust. (b) Dropped rust spots. (c) Tension texture. (d) Crack of weld.
(a)(b)(c)(d)Before the loading case 2 of frequent earthquake, no visual and acoustical evidence of all the steel components for both pure frame and BRB structure was demonstrated in the test model. When the input excitation increased from case 3 to case 4 of occasional earthquake, the overall sway of pure frame structure was relatively obvious and the slight tremor phenomenon occurred at the mass block composed of many steel plates on the second floor, accompanied by a small amount of dust, as shown in Figure13(a). However, no obvious observations occurred in the BRB structure.Under the loading cases 5 to 6, more obvious tremor and noise were observed from the additional upper mass on the second floor of pure frame structure, and the lower mass on the first floor began to appear the slight sloshing. Meanwhile, dust was seriously scattered from the specimen during the test, and rust spots at the welds of beam-column connection dropped obviously, as shown in Figure13(b). The mass block on the second floor of BRB structure appeared as the obvious tremor and noise, but the structure maintained no obvious damage phenomenon.Under the further earthquake action from loading case 7 to case 8 of rare earthquake, the mass blocks of pure frame appeared the noticeable tremor and occurred larger noise. During the test, the displacement meter erected on the column was deflecting due to the large vibration amplitude, resulting in falling off. The falling phenomenon of rust spot was more obvious, and a considerable area of uneven tension texture appeared on the steel beams and columns, as shown in Figure13(c). The mass blocks on the second floor of BRB structure trembled more clearly and caused the loud noise; meanwhile, the mass blocks on the first floor also began to appear as the apparent tremor. The rust spots on the steel beam dropped down and the tension texture appeared on the surface of steel column.When subjected to the loading cases 9 to 10, the trembling amplitude of mass blocks on the first and second floors of pure frame increased significantly, accompanied by continuous loud sound, and the crack of welds at the beam-column joints was obvious, as shown in Figure13(d). The mass block on the second floor of BRB structure trembled extremely, and the mass block on the first floor also appeared as the obvious tremor. A small number of displacement sensors mounted on the model broke and dropped down, and some connecting wires of strain gauges fell off.Under the earthquake action of loading cases 11 to 16 for the Kobe wave, the mass blocks on each floor of both pure frame and BRB structure occurred as extreme tremor, accompanied by excessively loud and continuous noise and a considerable amount of dust drifting down. Meanwhile, loosening of the high-strength bolts at the column bases incurred.


## 4. Experimental Results and Analysis

### 4.1. Natural Vibration Properties

Before the loading intensity levels of seismic waves are input, the specimen model is scanned by white noise signal, and the response information collected under the excitation of white noise is processed to achieve the transfer function of frequency response and draw the response amplitude-frequency characteristic diagram. The frequency corresponding to the peak point is the natural vibration frequency of the structural model. Then, the damping ratio of the structure is calculated by adopting the half-power bandwidth method of the following formula, and the dynamic characteristics of the two specimens under the excitation of each white noise are obtained, as shown in Table4:(1)ξ=f2−f12f,where ξ is the damping ratio, f is the frequency corresponding to the peak amplitude Amax of the transfer function, and f1 and f2 are, respectively, the frequencies corresponding to the value equal to 0.707 Amax.Table 4
Natural frequency and damping ratio of the specimen.
Number of the white noise12345678910Pure framef (Hz)10.0610.04109.989.929.839.7339.649.579.48BRB framef (Hz)23.1223.0823.0123.0122.8622.7922.7622.7122.6422.49Pure frameξ (%)2.062.132.192.352.442.552.682.772.842.92BRB frameξ (%)2.782.912.973.133.223.293.343.573.723.86It can be known from Table4 that as the peak acceleration of the earthquake action increases, the natural frequency of these two structures including pure frame and BRR frame decreases, whereas the damping ratio increases. The initial natural frequency and damping ratio of pure frame were 10.06 Hz and 2.06%, respectively. However, those of BRB structure were 23.12 Hz and 2.78%, respectively. At the end of the test, the damping ratio of pure frame increased to 2.92%, whereas that of BRB frame increased to 3.86%, which indicates that the buckling-restrained brace can increase the damping ratio of the structure and improve its seismic performance under the earthquake action.According to the calculating formula of fundamental natural frequencyf=1/2πk/m, under the condition that the structural mass is unchanged, the structural stiffness k is proportional to the square of the natural vibration frequency f; therefore, the change of structural stiffness can be reflected by the variation in natural frequency. The expression of stiffness degradation rate λ is as follows:(2)λ=Δkk0=k0−kk0=f02−f2f02,where k0 and k are the initial structural stiffness in the beginning of test and the stiffness when a certain loading case is completed. f0 and f are the initial natural frequency of structure and the measured frequency at the end of loading under a certain working condition.The stiffness degradation rate obtained using equation (2) is shown in Figure 14. It can be seen from Figure 14 that the stiffness degradation rates of pure frame and BRB structure under the action of frequent earthquake represented by case 2 are basically the same. Under the action of moderate earthquake represented by case 4, there is little difference in stiffness degradation rate λ between these two structures. The stiffness degradation rate of pure frame is 1.58% and that of BRB structure is 1.01%. However, the stiffness degradation rate of the uncontrolled pure frame is significantly higher than that of the buckling-restrained bracing structure under the action of a rare earthquake represented by case 8. The degradation rate of pure frame reaches 8.18%, whereas that of BRB structure is only 3.55%. From the overall analysis, with the increase in peak acceleration, the stiffness trend of the uncontrolled frame structure degrades significantly, especially after loading case 5, the structural stiffness is extremely reduced, and the maximum degradation rate reaches 11.2%. However, the stiffness degradation trend of BRB structure basically changes linearly, and the maximum stiffness degradation rate is only 5.4% at the end of the test, indicating that the buckling-restrained brace has absorbed a large amount of energy during the test. Until the end of the test, the BRB structure still possess a strong lateral stiffness and exhibits the excellent seismic performance.Figure 14
Stiffness degradation of the specimen.


### 4.2. Acceleration Response

In the shaking table test, the acceleration amplification factor is used to represent the dynamic amplification characteristics of the structural model under different seismic conditions, which is the ratio of the measured peak acceleration of each structural story to that of the shaking table surface in the corresponding direction. The acceleration amplification factors of frame structure and BRB structure under three different loading seismic waves for frequent earthquake, occasional earthquake, and rare earthquake are shown in Figure15.Figure 15
Acceleration amplification factor of the specimen. (a) Frequent earthquake. (b) Occasional earthquake. (c) Rare earthquake.
(a)(b)(c)Figure15 shows that all acceleration amplification factors at the second story of structure are significantly higher than those at the first story subjected to the three earthquake records. The acceleration response of the BRB structure is smaller than that of the pure frame under the same loading case. The dynamic amplification effect derived from different seismic waves on the structure was obviously different under the action of the same seismic intensity, and the seismic effect caused by EL Centro wave was slightly lighter than the other two seismic waves, which indicates that the seismic waves with different dynamic characteristics, such as duration and frequency, have a significant influence on the seismic response of structure. With the increase of earthquake action, the acceleration amplification coefficients of two structures decreased, and especially decreased significantly for the pure frame, which shows that the lateral stiffness of the frame structure is extremely degraded after the action of rare earthquake. On the other hand, it also shows that the buckling-restrained brace possess a certain beneficially protective effect on the acceleration response.


### 4.3. Interstory Drift Responses

Interstory drift ratio is an important structural design index in the seismic design. By controlling the interstory lateral displacement of the structure, the seismic design goal of “not collapsing in rare earthquake” can be achieved to ensure that the overall structure does not collapse. The maximum interstory drift ratio of the structure can be obtained from analyzing and processing the data collected by the displacement sensors arranged at the monitoring points of each story of the specimen. Only the displacement data within the PGA of 0.9 g were recorded because one part of the displacement sensors mounted on the steel column fell down when PGA reached 1.0 g. For the BRB structure, the displacement data collected by the displacement sensors ranged from case 1 to case 9 for both El Centro wave and Kobe wave and from case 1 to case 8 for Taft wave. However, for the pure frame structure, those ranged from case 1 to case 9 for all the three loading seismic waves.Figure16 shows that the variation trend of maximum interstory drift ratio θ for pure frame and BRB structure under the action of three different seismic waves with the increasing loading earthquake intensity. It can be seen from Figure 16 that, with the increase in seismic acceleration, the interstory drift ratios of two structures increase gradually, whereas the measured θ of frame structure is obviously higher than that of BRB structure under the same earthquake action. The growth trend of interstory drift ratios for two structures under the first four loading cases of three seismic waves was basically the same, showing a linear change. However, the different seismic waves induced the different effects on maximum interstory drift ratios of the structure when subjected to the larger peak acceleration actions of loading case 5 to 6. The maximum interstory drift ratio response caused by Kobe wave was obviously larger than the El Centro wave and Taft wave under the same earthquake intensity. The maximum θ reached 1/334 for the frame structure, while 1/400 for the BRB structure under the PGA of 0.6 g. However, compared with other two seismic waves, El Centro wave caused the largest influence on the displacement response of the structure when subjected to the further increasing PGA of 0.7 g to 0.9 g. The maximum θ reached 1/198 for the frame structure under the PGA of 0.9 g, while 1/263 for the BRB structure. The results based on the above comprehensive analysis show that the maximum interstory drift ratio response of structure caused by different seismic waves was dramatically different, and maximum θ of pure frame was significantly higher than that of BRB structure under the same loading seismic wave.Figure 16
Interstory drift ratios of the specimen under different waves.Table5 lists the measured interstory drift ratios of two structures and its reduction rates of BRB structure relative to the pure frame under the action of different intensity levels of three seismic waves. As can be seen from Table 5, under the frequent earthquake corresponding to the loading case 2 with PGA of 0.2 g in this test, the maximum and average interstory drift ratios among three input earthquake records were 1/727 and 1/847 for the frame structure and were 1/2400 and 1/3000 for the BRB structure, which was far less than the elastic limit value of 1/250 for the multistory steel structure given by the GB 50011-2010. This indicates that the test structures meet the specific seismic fortification goal of “no damage under minor earthquakes.” Furthermore, under the action of rare earthquake corresponding to the loading case 8 with PGA of 0.8 g, the maximum and average interstory drift ratios among three input earthquake records were 1/233 and 1/238 for the frame structure and were 1/303 and 1/314 for the BRB structure, indicating a satisfactory performance within the elastic-plastic allowable limit value of 1/50 described in this code. This also indicates that the structure meets another required goal of “no collapsing under strong earthquakes.”Table 5
Interstory drift ratios of the specimen.
PGA (g)0.10.20.30.40.50.60.70.80.9El Centro waveFrame1/27501/10321/7521/6111/4991/4151/3401/2521/198BRB1/85001/36001/17141/13841/10001/6321/4341/3271/263η (%)69.4471.3356.1355.8550.1034.3421.6622.9424.71Kobe waveFrame1/23571/8401/6711/5561/4541/3341/2781/2331/216BRB1/76001/32721/20001/12861/6321/4001/3711/3031/283η (%)73.8174.3366.4556.7728.1616.5025.0723.1023.67Taft waveFrame1/21331/7271/6331/5321/4811/4031/3171/2441/219BRB1/45001/24001/15651/12411/7661/5451/3491/313—η (%)52.6469.7159.5557.1337.2126.069.1722.04—Average valueFrame1/23801/8471/6801/5651/4761/3801/3091/2381/211BRB1/63631/30001/17421/13011/7721/5071/3811/3141/273η (%)64.6571.7160.8556.6138.1524.9618.8622.7022.76The reduction rateη of interstory drift ratio of the BRB structure relative to the frame structure can be defined as follows:(3)η=θ1−θ2θ1×100%,where θ1 and θ2 are the maximum interstory drift ratios of the frame structure and BRB structure under the action of three seismic waves, respectively.The reduction rates of interstory drift ratio subjected to the El Centro, Kobe, and Taft waves were from 21.66% to 71.33%, 16.50% to 74.33%, and 9.17% to 69.71%, respectively. This clearly demonstrates that the maximum interstory drift ratio induced by the earthquake action can be effectively reduced when the buckling-restrained brace is appropriately applied in the building structure.


### 4.4. Strain Responses

The maximum tensile and compressive strains at each measuring point of the structural model can be derived from the time-history data of strains collected by the strain gauges glued on the flange of the frame beam or column at each story. Figures17 and 18, respectively, present the time-history curves of strains at the bottom of the column and end of the first-story beam for the frame structure and BRB structure, as an example under the rare earthquake with PGA of 0.8 g for three seismic waves. For the frame structure, the strain responses of column and beam subjected to the Kobe wave were the maximum compared with other two seismic waves. The corresponding envelope values of tensile and compressive strains were, respectively, 452.48με and −439.03με at the bottom of column and were 457.82με and −486.8με, respectively, at the end of beam. However, for the BRB structure, the maximum tensile strain was 188.54με under the Kobe wave, and compressive strain was −206.17με under the El Centro wave at the bottom of column; the maximum tensile strain was 138.30με under El Centro wave and compressive strain was −127.43με under Kobe wave at the end of beam. Those achieved envelope values were less than the yield strain of 1140με deduced from the measured yield strength of Q235 ordinary steel in Table 2, indicating that the steel columns and beams of two structures were still in the elastic stage under a rare earthquake. The strain result clearly demonstrates that the strain responses are inconsistent, even when PGA is scaled to adjust at the same level for different ground excitations, due to the individually essential factors of motion including the duration and spectrum characteristics.Figure 17
Time-history curves of stain at the bottom of column. (a) El Centro wave. (b) Kobe wave. (c) Taft wave.
(a)(b)(c)Figure 18
Time-history curves of stain at the end of beam. (a) El Centro wave. (b) Kobe wave. (c) Taft wave.
(a)(b)(c)In order to investigate the strength reduction and seismic protection of the main structure after the applied additional buckling-restrained brace, the maximum strains of steel columns and beams for two structures subjected to the different intensity levels of three seismic waves were obtained by arranging numerous strain gauges at the appropriate monitoring positions, as shown in Figure19. It can be seen that the strain values of frame structure are significantly higher than those of BRB structure at the same location, and this difference between two structures becomes more obvious as the loading earthquake acceleration increases. The strains in the steel columns and beams increase steadily with the increment in earthquake intensity levels for two structures, whereas the maximum strain of beams in the structure is apparently higher than that of columns. This indicates that the designed specimen in this test accords with the seismic design requirements of strong columns and weak beams. It is found from comparison of strains at different stories of two structures that the maximum strain value at the first-story column is significantly higher than that at the second-story column subjected to three different seismic waves, whereas the strain value of the first-story beam is slightly greater than that of the second-story beam, illustrating that the column base is the weakest compared with the components at the other locations of the column.Figure 19
Comparison of maximum strains for these two specimen under different earthquake waves. (a) El Centro wave. (a1) Column. (a2) Beam. (b) Kobe wave. (b1) Column. (b2) Beam. (c) Taft wave. (c1) Column. (c2) Beam.
(a)(b)(c)Under the first four loading cases with PGA of less than 0.4 g, the strain values of two structures are relatively small, the strain difference between these two structures is not obvious, and the overall growth trend of strains maintains approximately linear. However, when subjected to the further earthquake action with increasing PGA from 0.5 g to 1.0 g, the strain growth of pure frame is extremely large, while the BRB structure is still small, and the strain difference between these two structures is significantly obvious. Under the continuous increasing PGA from 1.1 g to 1.6 g of Kobe wave, the strain values of two structures continue to increase rapidly, but the increasing amplitude of BRB structure is still much smaller than that of pure frame structure. The maximum strain of beam for the pure frame reaches 1131με under PGA of 1.6 g, while that is only 267με for the BRB structure. It can be concluded from the intensive comparison that the maximum strains of pure frame are dramatically higher than those of BRB structure under the same action of seismic wave, indicating that the buckling-restrained brace can effectively protect the main structure and improve the overall seismic capacity.


### 4.5. Structural Shear Response

The magnitude of seismic force caused by the earthquake action can be reflected by the structural response of shear force. When subjected to the earthquake load, the shear force of structural floor can be obtained by the following formula:(4)Vitmax=−∑j=1nmjajtmax,i=1,2……,where n is the total number of floors and aj and mj are the induced acceleration response and concentrated mass of the floor j, respectively.Figure20 shows the comparison diagram of the maximum shear force at each floor between pure frame and BRB structure under the loading case 2 of frequent earthquake, case 4 of occasional earthquake and case 8 of rare earthquake. With the increase in seismic intensity level, the floor shear force of two structures increased to varying degrees, whereas the shear response of pure frame was apparently higher than that of BRB structure subjected to the same earthquake intensity. This analysis reveals that the buckling-restrained brace is the first seismic line of defense to resist the horizontal load when subjected to the earthquake, which will significantly decrease the floor shear force and reduce the vibration or impact influence on the main structure by the earthquake action.Figure 20
Comparison of floor shear force. (a) El Centro wave. (b) Kobe wave. (c) Taft wave.
(a)(b)(c)


## 4.1. Natural Vibration Properties

Before the loading intensity levels of seismic waves are input, the specimen model is scanned by white noise signal, and the response information collected under the excitation of white noise is processed to achieve the transfer function of frequency response and draw the response amplitude-frequency characteristic diagram. The frequency corresponding to the peak point is the natural vibration frequency of the structural model. Then, the damping ratio of the structure is calculated by adopting the half-power bandwidth method of the following formula, and the dynamic characteristics of the two specimens under the excitation of each white noise are obtained, as shown in Table4:(1)ξ=f2−f12f,where ξ is the damping ratio, f is the frequency corresponding to the peak amplitude Amax of the transfer function, and f1 and f2 are, respectively, the frequencies corresponding to the value equal to 0.707 Amax.Table 4
Natural frequency and damping ratio of the specimen.
Number of the white noise12345678910Pure framef (Hz)10.0610.04109.989.929.839.7339.649.579.48BRB framef (Hz)23.1223.0823.0123.0122.8622.7922.7622.7122.6422.49Pure frameξ (%)2.062.132.192.352.442.552.682.772.842.92BRB frameξ (%)2.782.912.973.133.223.293.343.573.723.86It can be known from Table4 that as the peak acceleration of the earthquake action increases, the natural frequency of these two structures including pure frame and BRR frame decreases, whereas the damping ratio increases. The initial natural frequency and damping ratio of pure frame were 10.06 Hz and 2.06%, respectively. However, those of BRB structure were 23.12 Hz and 2.78%, respectively. At the end of the test, the damping ratio of pure frame increased to 2.92%, whereas that of BRB frame increased to 3.86%, which indicates that the buckling-restrained brace can increase the damping ratio of the structure and improve its seismic performance under the earthquake action.According to the calculating formula of fundamental natural frequencyf=1/2πk/m, under the condition that the structural mass is unchanged, the structural stiffness k is proportional to the square of the natural vibration frequency f; therefore, the change of structural stiffness can be reflected by the variation in natural frequency. The expression of stiffness degradation rate λ is as follows:(2)λ=Δkk0=k0−kk0=f02−f2f02,where k0 and k are the initial structural stiffness in the beginning of test and the stiffness when a certain loading case is completed. f0 and f are the initial natural frequency of structure and the measured frequency at the end of loading under a certain working condition.The stiffness degradation rate obtained using equation (2) is shown in Figure 14. It can be seen from Figure 14 that the stiffness degradation rates of pure frame and BRB structure under the action of frequent earthquake represented by case 2 are basically the same. Under the action of moderate earthquake represented by case 4, there is little difference in stiffness degradation rate λ between these two structures. The stiffness degradation rate of pure frame is 1.58% and that of BRB structure is 1.01%. However, the stiffness degradation rate of the uncontrolled pure frame is significantly higher than that of the buckling-restrained bracing structure under the action of a rare earthquake represented by case 8. The degradation rate of pure frame reaches 8.18%, whereas that of BRB structure is only 3.55%. From the overall analysis, with the increase in peak acceleration, the stiffness trend of the uncontrolled frame structure degrades significantly, especially after loading case 5, the structural stiffness is extremely reduced, and the maximum degradation rate reaches 11.2%. However, the stiffness degradation trend of BRB structure basically changes linearly, and the maximum stiffness degradation rate is only 5.4% at the end of the test, indicating that the buckling-restrained brace has absorbed a large amount of energy during the test. Until the end of the test, the BRB structure still possess a strong lateral stiffness and exhibits the excellent seismic performance.Figure 14
Stiffness degradation of the specimen.


## 4.2. Acceleration Response

In the shaking table test, the acceleration amplification factor is used to represent the dynamic amplification characteristics of the structural model under different seismic conditions, which is the ratio of the measured peak acceleration of each structural story to that of the shaking table surface in the corresponding direction. The acceleration amplification factors of frame structure and BRB structure under three different loading seismic waves for frequent earthquake, occasional earthquake, and rare earthquake are shown in Figure15.Figure 15
Acceleration amplification factor of the specimen. (a) Frequent earthquake. (b) Occasional earthquake. (c) Rare earthquake.
(a)(b)(c)Figure15 shows that all acceleration amplification factors at the second story of structure are significantly higher than those at the first story subjected to the three earthquake records. The acceleration response of the BRB structure is smaller than that of the pure frame under the same loading case. The dynamic amplification effect derived from different seismic waves on the structure was obviously different under the action of the same seismic intensity, and the seismic effect caused by EL Centro wave was slightly lighter than the other two seismic waves, which indicates that the seismic waves with different dynamic characteristics, such as duration and frequency, have a significant influence on the seismic response of structure. With the increase of earthquake action, the acceleration amplification coefficients of two structures decreased, and especially decreased significantly for the pure frame, which shows that the lateral stiffness of the frame structure is extremely degraded after the action of rare earthquake. On the other hand, it also shows that the buckling-restrained brace possess a certain beneficially protective effect on the acceleration response.


## 4.3. Interstory Drift Responses

Interstory drift ratio is an important structural design index in the seismic design. By controlling the interstory lateral displacement of the structure, the seismic design goal of “not collapsing in rare earthquake” can be achieved to ensure that the overall structure does not collapse. The maximum interstory drift ratio of the structure can be obtained from analyzing and processing the data collected by the displacement sensors arranged at the monitoring points of each story of the specimen. Only the displacement data within the PGA of 0.9 g were recorded because one part of the displacement sensors mounted on the steel column fell down when PGA reached 1.0 g. For the BRB structure, the displacement data collected by the displacement sensors ranged from case 1 to case 9 for both El Centro wave and Kobe wave and from case 1 to case 8 for Taft wave. However, for the pure frame structure, those ranged from case 1 to case 9 for all the three loading seismic waves.Figure16 shows that the variation trend of maximum interstory drift ratio θ for pure frame and BRB structure under the action of three different seismic waves with the increasing loading earthquake intensity. It can be seen from Figure 16 that, with the increase in seismic acceleration, the interstory drift ratios of two structures increase gradually, whereas the measured θ of frame structure is obviously higher than that of BRB structure under the same earthquake action. The growth trend of interstory drift ratios for two structures under the first four loading cases of three seismic waves was basically the same, showing a linear change. However, the different seismic waves induced the different effects on maximum interstory drift ratios of the structure when subjected to the larger peak acceleration actions of loading case 5 to 6. The maximum interstory drift ratio response caused by Kobe wave was obviously larger than the El Centro wave and Taft wave under the same earthquake intensity. The maximum θ reached 1/334 for the frame structure, while 1/400 for the BRB structure under the PGA of 0.6 g. However, compared with other two seismic waves, El Centro wave caused the largest influence on the displacement response of the structure when subjected to the further increasing PGA of 0.7 g to 0.9 g. The maximum θ reached 1/198 for the frame structure under the PGA of 0.9 g, while 1/263 for the BRB structure. The results based on the above comprehensive analysis show that the maximum interstory drift ratio response of structure caused by different seismic waves was dramatically different, and maximum θ of pure frame was significantly higher than that of BRB structure under the same loading seismic wave.Figure 16
Interstory drift ratios of the specimen under different waves.Table5 lists the measured interstory drift ratios of two structures and its reduction rates of BRB structure relative to the pure frame under the action of different intensity levels of three seismic waves. As can be seen from Table 5, under the frequent earthquake corresponding to the loading case 2 with PGA of 0.2 g in this test, the maximum and average interstory drift ratios among three input earthquake records were 1/727 and 1/847 for the frame structure and were 1/2400 and 1/3000 for the BRB structure, which was far less than the elastic limit value of 1/250 for the multistory steel structure given by the GB 50011-2010. This indicates that the test structures meet the specific seismic fortification goal of “no damage under minor earthquakes.” Furthermore, under the action of rare earthquake corresponding to the loading case 8 with PGA of 0.8 g, the maximum and average interstory drift ratios among three input earthquake records were 1/233 and 1/238 for the frame structure and were 1/303 and 1/314 for the BRB structure, indicating a satisfactory performance within the elastic-plastic allowable limit value of 1/50 described in this code. This also indicates that the structure meets another required goal of “no collapsing under strong earthquakes.”Table 5
Interstory drift ratios of the specimen.
PGA (g)0.10.20.30.40.50.60.70.80.9El Centro waveFrame1/27501/10321/7521/6111/4991/4151/3401/2521/198BRB1/85001/36001/17141/13841/10001/6321/4341/3271/263η (%)69.4471.3356.1355.8550.1034.3421.6622.9424.71Kobe waveFrame1/23571/8401/6711/5561/4541/3341/2781/2331/216BRB1/76001/32721/20001/12861/6321/4001/3711/3031/283η (%)73.8174.3366.4556.7728.1616.5025.0723.1023.67Taft waveFrame1/21331/7271/6331/5321/4811/4031/3171/2441/219BRB1/45001/24001/15651/12411/7661/5451/3491/313—η (%)52.6469.7159.5557.1337.2126.069.1722.04—Average valueFrame1/23801/8471/6801/5651/4761/3801/3091/2381/211BRB1/63631/30001/17421/13011/7721/5071/3811/3141/273η (%)64.6571.7160.8556.6138.1524.9618.8622.7022.76The reduction rateη of interstory drift ratio of the BRB structure relative to the frame structure can be defined as follows:(3)η=θ1−θ2θ1×100%,where θ1 and θ2 are the maximum interstory drift ratios of the frame structure and BRB structure under the action of three seismic waves, respectively.The reduction rates of interstory drift ratio subjected to the El Centro, Kobe, and Taft waves were from 21.66% to 71.33%, 16.50% to 74.33%, and 9.17% to 69.71%, respectively. This clearly demonstrates that the maximum interstory drift ratio induced by the earthquake action can be effectively reduced when the buckling-restrained brace is appropriately applied in the building structure.


## 4.4. Strain Responses

The maximum tensile and compressive strains at each measuring point of the structural model can be derived from the time-history data of strains collected by the strain gauges glued on the flange of the frame beam or column at each story. Figures17 and 18, respectively, present the time-history curves of strains at the bottom of the column and end of the first-story beam for the frame structure and BRB structure, as an example under the rare earthquake with PGA of 0.8 g for three seismic waves. For the frame structure, the strain responses of column and beam subjected to the Kobe wave were the maximum compared with other two seismic waves. The corresponding envelope values of tensile and compressive strains were, respectively, 452.48με and −439.03με at the bottom of column and were 457.82με and −486.8με, respectively, at the end of beam. However, for the BRB structure, the maximum tensile strain was 188.54με under the Kobe wave, and compressive strain was −206.17με under the El Centro wave at the bottom of column; the maximum tensile strain was 138.30με under El Centro wave and compressive strain was −127.43με under Kobe wave at the end of beam. Those achieved envelope values were less than the yield strain of 1140με deduced from the measured yield strength of Q235 ordinary steel in Table 2, indicating that the steel columns and beams of two structures were still in the elastic stage under a rare earthquake. The strain result clearly demonstrates that the strain responses are inconsistent, even when PGA is scaled to adjust at the same level for different ground excitations, due to the individually essential factors of motion including the duration and spectrum characteristics.Figure 17
Time-history curves of stain at the bottom of column. (a) El Centro wave. (b) Kobe wave. (c) Taft wave.
(a)(b)(c)Figure 18
Time-history curves of stain at the end of beam. (a) El Centro wave. (b) Kobe wave. (c) Taft wave.
(a)(b)(c)In order to investigate the strength reduction and seismic protection of the main structure after the applied additional buckling-restrained brace, the maximum strains of steel columns and beams for two structures subjected to the different intensity levels of three seismic waves were obtained by arranging numerous strain gauges at the appropriate monitoring positions, as shown in Figure19. It can be seen that the strain values of frame structure are significantly higher than those of BRB structure at the same location, and this difference between two structures becomes more obvious as the loading earthquake acceleration increases. The strains in the steel columns and beams increase steadily with the increment in earthquake intensity levels for two structures, whereas the maximum strain of beams in the structure is apparently higher than that of columns. This indicates that the designed specimen in this test accords with the seismic design requirements of strong columns and weak beams. It is found from comparison of strains at different stories of two structures that the maximum strain value at the first-story column is significantly higher than that at the second-story column subjected to three different seismic waves, whereas the strain value of the first-story beam is slightly greater than that of the second-story beam, illustrating that the column base is the weakest compared with the components at the other locations of the column.Figure 19
Comparison of maximum strains for these two specimen under different earthquake waves. (a) El Centro wave. (a1) Column. (a2) Beam. (b) Kobe wave. (b1) Column. (b2) Beam. (c) Taft wave. (c1) Column. (c2) Beam.
(a)(b)(c)Under the first four loading cases with PGA of less than 0.4 g, the strain values of two structures are relatively small, the strain difference between these two structures is not obvious, and the overall growth trend of strains maintains approximately linear. However, when subjected to the further earthquake action with increasing PGA from 0.5 g to 1.0 g, the strain growth of pure frame is extremely large, while the BRB structure is still small, and the strain difference between these two structures is significantly obvious. Under the continuous increasing PGA from 1.1 g to 1.6 g of Kobe wave, the strain values of two structures continue to increase rapidly, but the increasing amplitude of BRB structure is still much smaller than that of pure frame structure. The maximum strain of beam for the pure frame reaches 1131με under PGA of 1.6 g, while that is only 267με for the BRB structure. It can be concluded from the intensive comparison that the maximum strains of pure frame are dramatically higher than those of BRB structure under the same action of seismic wave, indicating that the buckling-restrained brace can effectively protect the main structure and improve the overall seismic capacity.


## 4.5. Structural Shear Response

The magnitude of seismic force caused by the earthquake action can be reflected by the structural response of shear force. When subjected to the earthquake load, the shear force of structural floor can be obtained by the following formula:(4)Vitmax=−∑j=1nmjajtmax,i=1,2……,where n is the total number of floors and aj and mj are the induced acceleration response and concentrated mass of the floor j, respectively.Figure20 shows the comparison diagram of the maximum shear force at each floor between pure frame and BRB structure under the loading case 2 of frequent earthquake, case 4 of occasional earthquake and case 8 of rare earthquake. With the increase in seismic intensity level, the floor shear force of two structures increased to varying degrees, whereas the shear response of pure frame was apparently higher than that of BRB structure subjected to the same earthquake intensity. This analysis reveals that the buckling-restrained brace is the first seismic line of defense to resist the horizontal load when subjected to the earthquake, which will significantly decrease the floor shear force and reduce the vibration or impact influence on the main structure by the earthquake action.Figure 20
Comparison of floor shear force. (a) El Centro wave. (b) Kobe wave. (c) Taft wave.
(a)(b)(c)


## 5. Conclusion

Based on the shaking table test with a two-story 1/4 scale model of the ordinary pure steel frame and the buckling-restrained bracing steel frame with low-yield-point steel as the core plate subjected to the different intensity levels of earthquake records, the following significant conclusions can be drawn from the experimental studies:(1)
After the entire loading cases were successfully completed, the apparent observations of damage occurred in the pure frame structure, while no obvious or serious damage in the steel members of BRB structure was observed. The trembling amplitude of the mass blocks on each floor of two structures increased dramatically as the further increasing earthquake intensity levels, accompanied by excessively loud and continuous noise and a considerable amount of dust drifting down. Meanwhile, the crack of welds at the beam-column joints was obvious and loosening of the high-strength bolts at the column bases incurred.(2)
The initial natural frequency and damping ratio of pure frame were 10.06 Hz and 2.06%, respectively. However, those of BRB structure were 23.12 Hz and 2.78%, respectively. At the end of the test, the damping ratio of pure frame increased to 2.92%, while that of BRB frame increased to 3.86%, which indicates that the buckling-restrained brace can increase the damping ratio of the structure and improve its seismic performance under the earthquake action.(3)
The acceleration response of BRB structure was smaller than that of pure frame under the same loading case. The dynamic amplification effect derived from different seismic waves on the structure was obviously different under the action of the same seismic intensity, which indicates that the seismic waves with different dynamic characteristics such as duration and frequency have a significant influence on the seismic response of structure. With the increase in earthquake action, the acceleration amplification coefficients of two structures decreased.(4)
The measured interstory drift ratios of frame structure were obviously higher than that of BRB structure under the same earthquake action. Under the frequent earthquake, the maximum and average interstory drift ratios among three input earthquake records were 1/727 and 1/847 for the frame structure and 1/2400 and 1/3000 for the BRB structure, which was far less than the elastic limit value of 1/250. This indicates that the test structures meet the specific seismic fortification goal of “no damage under minor earthquakes.” Furthermore, under the action of rare earthquake, the maximum and average interstory drift ratios among three input earthquake records were 1/233 and 1/238 for the frame structure and 1/303 and 1/314 for the BRB structure, indicating a satisfactory performance within the elastic-plastic allowable limit value of 1/50. This also indicates that the structure meets another required goal of “no collapsing under strong earthquakes.”(5)
The column base was the weakest compared with the components at the other locations of the column. The maximum strain of beam for the pure frame reached 1131με under PGA of 1.6 g, while that was only 267με for the BRB structure. It can be concluded from the intensive comparison that the maximum strains of pure frame were dramatically higher than those of BRB structure under the same action of seismic wave, indicating that the buckling-restrained brace can effectively protect the main structure and improve the overall seismic capacity.(6)
The shear response of pure frame was apparently higher than that of BRB structure subjected to the same earthquake intensity. This analysis reveals that the buckling-restrained brace is the first seismic line of defense to resist the horizontal load when subjected to the earthquake, which will significantly decrease the floor shear force and reduce the vibration or impact influence on the main structure by the earthquake action.



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*Source: 6654201-2021-09-07.xml*