Research Article  Open Access
Kun Wang, Junwu Xia, Xiaomiao Chen, Bo Xu, Xiangzhou Liang, Jian Wang, "Performance of the ColdBending ChannelAngle BucklingRestrained Brace under Cyclic Loading", Advances in Civil Engineering, vol. 2019, Article ID 9710529, 12 pages, 2019. https://doi.org/10.1155/2019/9710529
Performance of the ColdBending ChannelAngle BucklingRestrained Brace under Cyclic Loading
Abstract
In this study, three restricted coldbending channelangle bucklingrestrained brace (CCABRB) specimens were experimentally characterised by a lowreversed cyclic loading test. Three specimens had steel cores with cruciform cross section. Two restraining units were assembled to form an external constraint member, each of which was composed of an equilateral coldbending channel and two equilateral coldbending angles via welding. A gap or a thin silica gel plate was set between the internal core and the external constraint member to form an unbonded layer. Several evaluation parameters on the seismic performance, hysteretic behaviour, and energy dissipation capability of the CCABRB was investigated, including hysteresis curve, skeleton curve, compression strength adjustment factor, measured and computed stiffness, energy dissipation coefficient, equivalent viscous damping ratio, ductility coefficient, and cumulative plastic deformation. The test results and evaluation indices demonstrated that the hysteretic performance of braces with a rigid connection was stable. A Ramberg–Osgood model and two model parameters were calibrated to predict, with fidelity, the skeleton curve of CCABRB under cyclic load. The initial elastic stiffness of the brace used in practice should contain overall portions of the brace instead of the yielding portion of the brace. Finally, all the tested CCABRBs exhibited a stable energy absorption performance and verified the specimens’ construction was rational.
1. Introduction
As a kind of structure system with excellent ductility, the braced frame is often used in seismic structures. However, the general brace itself will suffer from comprehensive problems such as strength stiffness degradation and lowcycle fatigue fracture after buckling when under the action of cyclic load. A bucklingrestrained brace (BRB) is an energy dissipation damper of metal yielding which has advantages of stable energy dissipation capacity, easy construction and fabrication with low cost, etc. [1]. A BRB can provide stable lateral stiffness and loadcarrying capacity for a frame structure. As a result, BRBs have been used extensively in existing and new structures to enhance the earthquake resistance [2–6].
Diverse experiments show that BRBs have a substantial energy absorption capability under cyclic loading [7, 8]. In 1976, an early bucklingrestrained attempt to propose a brace with dissipating energy yet does not buckle was reported in an experimental study [9]. The brace consisted of a single flat plate as the internal core and a square steel pipe filled with mortar as the external constraint member. Since then, various structural forms and experimental studies of traditional BRBs were proposed by investigators around the world [10–13]. However, there were a series of issues affecting the traditional BRBs, in which the core buckling restrained by steel tube filled with concrete or mortar, such as the need for higher precision control between the external concrete member and the core steel member, and the complex processes of wet concrete pouring, further increasing the complexity of component fabrication and prolonging the production cycle. Based on the above reasons, scholars have put forward various forms of allsteel BRBs [14–21], which only require clamping the inner core with section steel or composite steel members to impose constraints, and the allsteel BRBs have the advantages of simple construction, convenient assembly, and lighter weight. Kuwahara et al. proposed the first representative allsteel bucklingrestrained brace in 1993 of which circular steel tubes were used to support the inner core (the inner circular tube) and the outer constraint members (the outer circular tube) [14]. The allsteel BRBs had steel cores with rectangular cross sections and were studied through a uniaxial test program [15] or subassemblage testing [16, 17]. The allsteel BRBs with cruciform crosssection core are generally used to provide large lateral restraint force to frame structures, and several axial cycle tests have been conducted to study the hysteresis behaviour of the allsteel BRBs with cruciform crosssection core [18–21]. In addition, several shaking table tests have been conducted on concrete and steel frames equipped with BRBs [22, 23]. A novel type of BRB, called coldbending channelangle bucklingrestrained brace (CCABRB), has been proposed and tested by the authors. This paper describes the characteristics, hysteresis behaviour, and energy dissipation capability of the new BRB.
2. Layouts of the CCABRB
Each CCABRB consists of an internal steel core, external constraint members, and an unbonded layer between them (Figure 1). The steel core is subjected to the axial load while constraint members provide lateral support to the steel core and prevent the core from buckling. The external constraint members of the CCABRB are composed of two restraining units, each of which consists of an equilateral coldbending channel and two equilateral coldbending angles via welding (Figure 2). The ratio of web height to flange plate width of the channel is 2 : 1. Each CCABRB has the steel core with cruciform cross section which consists of three portions: a yielding portion, a transition portion, and a connection portion (Figure 3). A gap must be present between the internal core and the external constraint members while the gap can be adjusted to form an unbonded layer. The thin layer of unbonded material along the internal steel core eliminates shear transfer during the elongation and contraction of the core and also accommodates its lateral expansion when in compression.
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Figure 3 shows the crosssectional schematic diagram of the CCABRB and the dimension parameters: h_{c} denotes the width and t_{c} the thickness of the steel core; h_{cc} denotes the web height, b_{cc} the flange width, and t_{cc} the thickness of the coldbending channel steel; h_{ca} denotes the vertical limb height, b_{ca} the horizontal width and t_{ca} the thickness of the coldbending angle steel.
3. Component Testing
3.1. Specimen Design
The geometric dimension parameters of the specimens are listed in Table 1, and the meaning of each parameter is shown in Figure 3, in which L_{y} represents the yielding portion length of the core, L_{tr} the transition portion length of the core, L_{con} the connection portion length of the core, L_{total} the total length of the core, and L_{em} the length of the external constraint members.

A construction drawing of the BRB1 specimen is shown in Figure 4. The internal steel core of CCABRB is composed of three flat plates via fullfillet welding by carbon dioxide arc welding. The core of CCABRB was a Q235 steel member with a variable cross section, in which the dimensions of the yielding portion section were 68 mm × 68 mm × 8 mm and connection portion section 128 mm × 128 mm × 8 mm. The yielding portion length L_{y} of the core was 800 mm, the transition portion length L_{tr} 100 mm (50 mm on each side), the connection portion length L_{con} 300 mm (150 mm on each side), and the total length of the core L_{total} 1200 mm. The external restraining members of CCABRB are composed of two coldbending channels and four coldbending angles in which all components were made of Q235 steel. The crosssection dimensions of the channel were 140 mm × 70 mm × 5 mm and the angle 60 mm × 60 mm × 5 mm. The design length of all restraining components L_{em} was 1160 mm which is shorter than the core 40 mm; that is, each side is reserved the axial compression space of 20 mm to meet the 2% compressive strain (each end splits an average of 1% deformation) of the core and left a certain margin to consider the machining error. Each channel and two angles were bound via fillet welds.
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Note that 1 mm gap was set between the internal core and the external constraint members of the specimens on each side with pasting 1millimeterthick silica gel plate along the yielding portion of the core to reduce the friction when in compression. A 25millimeterthick square plate was welded at the end of the core via full penetration weld, and the dimensions of the plate were 200 mm × 200 mm. Based on the realistic consideration of the test fixture, a 18millimeterthick holding plate (the dimensions of the holding plate were 150 mm × 100 mm) and the square end plate were bound via fillet weld to form a fixed joint to satisfy test loading.
3.2. Experimental Setup
Figure 5 indicates the experimental setup of the specimens. Both the ends of the specimens are connected to a PWS500 electrohydraulic servo actuator at the Jiangsu Key Laboratory of Environmental Impact and Structural Safety in Engineering of China University of Mining and Technology by which an axial cyclic load was applied. The actuator had a cyclic load capacity of ±500 kN and a displacement capacity of ±200 mm. To observe the axial deformation, two displacement meters were set at the upper end of the specimens and two at the lower end.
3.3. Loading Protocol
The loading protocols adopted in this lowreversed cyclic loading test are shown in Figure 6. The parameter used to define the test program was the core axial strain, and three loading protocols were adopted corresponding to three specimens. Corresponding to the specimen BRB1, two loading cycles were performed to an amplitude increment in the core axial strains of 0.5%, 1.0%, and 1.5% followed by five loading cycles of 2% strain to complete the experiment (see the loading protocol 1). Corresponding to the specimen BRB2, two loading cycles were performed with 0.5%, 1.0%, and 1.5% core axial strain followed by five loading cycles of 2% strain to complete the experiment (see the loading protocol 2). The difference of loading protocols between BRB1 and BRB2 was the loading type of BRB1 traction after compression and BRB2 compression after traction. According to the requirements of GB500112010 [24], the parameter corresponding to the specimen BRB3 was defined at levels of 1/300, 1/200, 1/150, and 1/100 bracing length under tensioncompression three times (see the loading protocol 3). On the basis of the loading protocols, when the specimens BRB1 and BRB2 completed five 2% axial strain loadings, the value of CPD, which is a normalized expression of the cumulative plastic deformation, was measured at 212 which satisfies the plastic deformation capability requirements on the BRB specified in ANSI/AISC 34110 [25]. The core axial displacement loading protocol of each specimen is shown in Table 2. The core length was 1200 mm, and the core yielding portion length was 800 mm.
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3.4. Material Properties
Based on the request of GB/T228.12010 [26], the material properties tests of the internal steel core and external constraint members of varying thicknesses were measured. The corresponding material property index is shown in Table 3, in which E denotes elastic Young’s modulus, f_{y} the steel yield strength, f_{u} the steel tensile strength, and f_{y}/f_{u} the steel yieldtensile strength ratio.

4. Test Results and Performance Analysis
4.1. Hysteresis Curve
The hysteresis curves of the specimens are plotted with the recorded axial force in the brace as ordinate against the axial displacement measured across the entire brace including connections as abscissa (Figure 7). The vertical coordinate is the measured axial load of the specimens, and its sign convention is positive tension and negative compression. The horizontal coordinate is the measured axial deformation, and the sign convention is the same. It is noteworthy that the flexibility of the connections contributes only slightly to the overall displacement; further, the axial deformation measured by the displacement meter mainly reflects the axial deformation of the yielding segment of the brace.
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The hysteresis loops resulting from the lowreversed cyclic loading test show that all the test braces exhibited stable hysteretic behaviour for all displacement amplitudes, with a plump hysteresis curve and substantial energy absorption capability. It can be seen that there was no significant stiffness or strength degradation when the test completed, and the loading and unloading stiffnesses were basically the same. In addition, the forcedisplacement loops showed a distinct cyclic hardening characteristic and an asymmetrical feature between tension and compression. It must be pointed out that the BRB with a rigid connection produce a moment on the loading setup which should be considered in the structural design of the frame.
4.2. Skeleton Curve
The skeleton curves of the specimens are shown in Figure 8, in which the curves are almost identical. It is seen that the skeleton curves of three specimens present distinct bilinear characteristics, and there is an obvious inflexion between the elastic stage and the plastic stage. The core of each specimen has a noticeable strengthened segment after entering the plastic stage.
In order to concise the variation law of the skeleton curve of the CCABRB, the Ramberg–Osgood model [27] is used to fit the skeleton curves of the specimens. The formula of the Ramberg–Osgood model is given bywhere Δε represents total strain amplitude; Δε_{e} and Δε_{p} represent, respectively, elastic strain amplitude and plastic strain amplitude; Δσ represents stress amplitude; K′ and n represent, respectively, cyclic hardening coefficient and cyclic hardening exponent. The fitting parameters of the Ramberg–Osgood model are shown in Table 4.

Figure 9 plots the fitting skeleton curves. It is seen that the fitting curve was little different from that of test points curve, indicating that the Ramberg–Osgood model can be used to simulate the skeleton curve of CCABRB under cyclic loading.
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4.3. Compression Strength Adjustment Factor
Due to the Poisson effect, the lateral cross section of the internal core tended to increase under compression; thus, the internal core may contact the external constraint member. Further, a frictional force at the contact surface was generated to increase the axial force of the core under the compression stage. In addition, the bearing capacity under compression is greater than that under tension, affecting the asymmetry characteristic of tension and compression of a brace.
The asymmetry between tension and compression of a brace is generally expressed by the compression strength adjustment factor β [28], which is defined bywhere and represent the maximum axial compression and the maximum axial tension, respectively, during the ith hysteresis loop.
The values of compression strength adjustment factor during the distinct loading displacement amplitudes are shown in Table 5. Based on the requirements of ANSI/AISC 34110, the compression strength adjustment factor of a BRB must not exceed 1.3. It can be seen that the increase factors of BRB1 and BRB2 were 1.092 and 1.118, respectively, which remained lower than the limit value 1.3 of the code under the loading amplitude of 2% core axial strain. The coefficient value of BRB3 was 1.050 which is still below 1.3 when the core axial strain remained within 1.5%. The abovedescribed indicated that the CCABRB still exhibited a stable and symmetrical hysteretic behaviour, with an adequate energy dissipation capacity even when the core axial strain reached 2%.

4.4. Measured and Computed Stiffness Values
Based on the experimental data, the initial elastic stiffness and the secondary stiffness which are of interest in the mechanical characterization of the brace are identified in this section. As shown in Figure 3(c), the core of the brace with a cruciform cross section consists of a yielding portion, a transition portion, and a connection portion throughout, with the cross section of the yielding stage smaller than the cross sections of the transition portion and the connection portion. The total elastic stiffness of the brace is the summation in series of the individual stiffness of the segments described above. The formula for the total elastic stiffness of the core is given bywhere represents the total elastic stiffness, represents the elastic stiffness of the yielding portion, represents the elastic stiffness of the transition portion, and represents the elastic stiffness of the connection portion.
The values of computed elastic stiffness for the yielding portion, the transition portion, and the connection portion are, respectively,where A_{y} and A_{con} represent, respectively, the crosssectional area of the yielding portion and the connection portion. Based on the above values given by equations (4)–(6), the total elastic stiffness , given by equation (3), is 200.8 kN/mm.
Table 6 lists the computed stiffness, measured stiffness, and the difference between these values for each specimen. The computed elastic stiffness values given in columns 2, 3, 4, and 5 were obtained from equations (3)–(6), respectively. The measured stiffness values given in columns 6 and 7 were computed by fitting the tensile section of the skeleton curve (using a double broken line model) of each brace. Column 6, labelled , corresponds to the slope of the axial forcedisplacement relationship measured for the elastic portion of the fitting skeleton curve, whereas, column 7, labelled K_{2}, corresponds to the slope measured for the plastic portion of the fitting skeleton curve.
As can be seen from Table 6, the computed total elastic stiffness value given by equation (3) is in close accordance with the value measured from the test data. In theory, the stiffness values used in the design should contain the entire portions of the brace. If the stiffness value for yielding portion be used in the design instead of the overall stiffness, then the stiffness value is overestimated by 37%. In addition, if assuming that the cross area over the entire length is equal to A_{y}, then the stiffness value is calculated to be 171.5 kN/mm and the stiffness value is still figured to be undervalued by 15%.
4.5. Secondary Stiffness
The secondary stiffness which usually can also be written as postyielding stiffness is of interest for the mechanical properties of the BRB and depends in general on the loading course. The measured values of secondary stiffness and postyielding ratio, , of each specimen are given in columns 7 and 8 of Table 6, respectively. Column 8, labelled α, corresponds to the ratio of elastic stiffness to secondary stiffness.
4.6. Energy Dissipation Index
Energy dissipation capacity is an important index for evaluating the performance of CCABRB. In this section, the energy dissipation capacity of each specimen is evaluated via parameters which contain energy dissipation coefficient and equivalent viscous damping ratio. The parameters of the specimens were obtained from the hysteresis curves and are listed in Table 7. According to Section 4.5.6 of JGJ/T1012015 [29], the values for the energy dissipation coefficient and the equivalent viscous damping ratio are calculated by, respectively,where S_{BEDFB}, as shown in Figure 10, represents the hysteresis loop area of a brace enveloped by one displacement amplitude, S_{△OAB} and S_{△OCD} represent the area of triangle OAB and triangle OCD, respectively. It can be seen from Table 7 that the energy dissipation coefficient and the equivalent viscous damping ratio of each specimen show a trend of gradual increase with the increase of loading displacement amplitude. Further, the gradual increasing trend of energy dissipation indices indicates that the brace has a substantial and repeatable capability to absorb earthquake energy.

4.7. Ductility Coefficient
The deformation capacity which determines the maximum displacement of a brace is an important index for evaluating the seismic performance of CCABRB and is expressed via the ductility coefficient. The ductility coefficient of a brace refers to the ratio of the maximum displacement to the yield displacement of the brace before the obvious strength degradation of the hysteresis curve. The coefficients of each specimen are listed in Table 7. According to Section 4.5.4 of JGJ/T1012015 [29], the formula is given bywhere d_{max} and d_{y} represent maximum displacement and yield displacement, respectively, of the brace. It can be seen from Table 7 that the ductility coefficient values of BRB1 and BRB2 appear to be 11.4 and 12.4, respectively, once the core axial strain reaches 2.0%, and the value of BRB3 appears to be 7.4, once the core axial strain reaches 1.5%. In addition, the specimens have a large and substantial plastic deformation capability.
4.8. Cumulative Plastic Deformation Capability
An index used in practice to evaluate the plastic deformation capability of a brace is the cumulative plastic strain or, alternatively, the cumulative plastic deformation. The cumulative plastic deformation [30] of the brace can be defined bywhere and represent the absolute values of the maximum tensile displacement and the maximum compressive displacement, respectively, during each visit i into the inelastic range. The last column of Table 7 lists the cumulative plastic deformation values of each specimen. It can be seen from Table 7 that the values of BRB1 and BRB2 appear to be 311 and 327, once the core loading displacement amplitude reaches the axial strain of 2.0%, and the value of BRB3 appears to be 167.6, once the core loading displacement amplitude reaches the axial strain of 1.5%. Further, it is noted that the cumulative plastic deformation values of BRB1 and BRB2 during the testing protocol exceed the requirement of the minimum limit (200) set by the ANSI/AISC 34110, indicating that the brace has an excellent plastic deformation capability.
5. Conclusions
In this study, lowreversed cyclic loading tests of three CCABRB specimens under three loading protocols were conducted to consider the seismic performance, hysteretic behaviour, and energy dissipation capability of CCABRBs. Based on the experimental results and several evaluation indices, the main conclusions drawn are the following:(1)The observed hysteretic behaviour of the CCABRB with a rigid connection was excellent for all displacement amplitudes, indicating that the brace had a stable capability to absorb seismic energy.(2)The skeleton curves of three CCABRB specimens present distinct bilinear characteristics. The Ramberg–Osgood model was adopted to approximate the skeleton curve of the brace, and two model parameters were found to fit the skeleton curves with little difference, indicating that the Ramberg–Osgood model can be used to simulate the skeleton curve of CCABRB under cyclic load.(3)The computed initial elastic stiffness was in close agreement with the value measured from the test data, indicating that the stiffness used in the design should contain overall portions of the brace.(4)All CCABRB specimens showed a stable energy absorption performance to enhance the resistance of existing and new structures during strong earthquake shaking.
Appendix
Derivation of Equation (5)
Schematic diagram of the derivation of equation (5) is shown in Figure 11. The elongation d(Δl) of microsegment dx can be given bywhere the crosssectional area A(x) can be given by
With integrating equation (A.1), the elongation of transition region can be obtained as
With transforming equation (A.3), the stiffness of transition region can be given by
Data Availability
All the data used to support the findings of this study are included within this article.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by grants from the Fundamental Research Funds for the Central Universities (2018ZDPY04) and The Open Fund from Jiangsu Collaborative Innovation Center for Building Energy Saving and Construction Technology (SJXTQ1521).
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Copyright © 2019 Kun Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.