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Abstract

Buckling-restrained braces play a critical role as the first-defendant line in dissipating seismic energy and are often used in concrete frame structures to ensure that the main beam–column members are “undamaged” or significantly elastic during medium earthquakes. The design of the reinforced concrete frame structures with buckling-restrained brace is generally based on the assumption of shear deformation of the structure. The conventional seismic design considers the “second-defendant line design” based on the geometric relationship between the axial deformation and strength of buckling-restrained braces and stratified deformation. This article proposes iterative optimization of the buckling-restrained brace design method and layout scheme based on the nonlinear structural response of the calibrated numerical model, and then approximates the nonlinear structure scheme using a linear method. Time history analyses are performed to prove that the linear design method is highly conservative for estimating seismic intensity, and the proposed design method provides more efficient damage distributions in frame components. The results of the nonlinear performance evaluation and energy analysis indicate that the method proposed in this article can meet the performance design requirements achieving multi-performance criteria.

Keywords

Seismic analysis performance-based design buckling-restrained brace reinforced concrete frame numerical modeling

Introduction

Reinforced concrete (RC) moment frames have experienced severe damage and collapse during recent earthquakes, for example, Northridge Earthquake (1994), Kobe Earthquake (1995), and the Wenchuan Earthquake (2008). RC-braced frames using buckling-restrained braces (BRBs) (RC-BRB frames) are an effective seismic-resistant structural system. The nonlinear analyses of frame structures conducted by Sarno and Manfredi¹ suggested that in RC-BRB frames, BRBs maintain elasticity of the concrete frame through its own yielding. Compared with the bare moment frames, RC-BRB frames provide essential lateral stiffness and deformability to resist seismic loading, which was proven in the experimental study by Mazzolani.² The “two-stage and three-level” elastic design method of RC-BRB frames is specified in the practical design. Other available methods are energy-based methods,^3,4 displacement methods,^5,6 and plastic design methods.⁷ Kim and colleagues^3–6 research assumed that the beam and column were hinged. This assumption is suitable for buckling-constrained steel frame structures without a bending frame, but for RC-BRB frames, the bending stiffness of the beam–column joints cannot be ignored. Kim and colleagues^5,6 assumed that the shear force was entirely borne by the BRB, while Choi and colleagues^3,4 assumed that the energy was completely dissipated by the BRB, which makes it easy to determine the BRB core cross section, but this is unreasonable because the structural role of the framework cannot be ignored. Bai and Ou⁷ adopted the concept of BRB shear ratio, which indicates the ratio of shear force of the BRB to the total shear force of the structural base. Based on this idea, the RC-BRB structure is equivalent to the superposition of the BRB and frame systems. The concept of shear ratio considers the distribution of shear force between the main frame and the BRB and separately designs the cross section of the BRB system and the frame system according to the proportions of the distribution. However, the key design assumption according to this method is that the BRB has the same ratio of stiffness in each layer, which limits the flexibility of the BRB arrangement. For example, in actual engineering, BRBs tend to be placed on the bottom floors which experience greater seismic force, while the top floor does not include BRBs in the structural design.

In 2013, China implemented the “Technical specification for seismic energy dissipation of buildings (JGJ 297-2013),”⁸ which requires that the seismic fortification target of the new energy dissipation structure should not be lower than the current seismic requirements (undamaged in small earthquakes, repairable in medium earthquakes, and no collapse in strong earthquakes).⁹ In engineering practices, the RC-BRB frame structure should fulfill higher performance demands to give full play to the performance of BRB products. It means that the main structures under medium earthquakes remain undamaged, and the BRB dissipates energy by yielding. In fact, the BRB acts as the first-defendant line for the structure, reducing the damage to the main structural members. In the existing design method, the second-defendant line design is generally based on the geometric relationship between the axial deformation of the BRB and stratified deformation. Specifically, the inter-story displacement angle corresponding to the BRB yield displacement is adjusted to be smaller than the elastic inter-story displacement angle limit of the frame portion, thereby ensuring that the BRB yields prior to the frame system; however, this method is unreliable when subjected to maximum capacity earthquakes. The performance of RC-BRB frames considering flexural deformation has been studied by Yao et al.¹⁰ Based on their research, due to the influence of the flexural deformation, the true axial deformation of the BRB cannot be obtained only by the geometric relationship conversion. If it is necessary to establish an accurate relationship between the axial deformation of the BRB and the deformation of the frame story, the influence of the compressive stiffness of the frame column and other factors should also be considered. A finite element model of the rod system can comprehensively design the deformation coordination relationship between the components and account for the internal forces of each member. The nonlinear performance evaluation software, Perform-3D, can accurately and quickly determine the inter-story displacement angle once the yielding and plastic deformation occur in BRBs. Therefore, this article intends to adjust the BRB scheme using pushover’s nonlinear performance evaluation and apply the linear analysis method to approximate the structural reinforcement of the frame part, so as to propose a performance-based design method considering the second-defendant line.

Design method

Configuration of BRB components

The BRB is a commonly used energy dissipating component in buildings due to its buckling can be restrained by infill concrete.^11–14 According to various constraints, the BRB can be divided into a grouting type, all-steel type, and enclosed RC type.^15–17 The general energy dissipation mechanism of a BRB is to restrain the core plate from buckling by the restraint unit and dissipate the seismic energy through the stable tension and compression deformation of the core plate. Taking the grouting type as an example, as shown in Figure 1, a steel tube and concrete constitute the constraint component for suppressing the buckling of the core plate. An un-bonded material is placed between the core plate and the concrete to eliminate the adverse effects caused by friction.

Figure 1.

Composition of buckling-restrained brace.

RC-BRB frame systems

In the conventional design of the RC-BRB frame structure, the BRB is required to yield before the main structure, so that the BRB acts as the first-defendant line against earthquakes, but sometimes it does not work. The first step is to establish the geometric relationship between the axial deformation of the BRB and stratified deformation, as shown in Figure 2. The geometric relationship between the two can be expressed as

$δ = d \cos θ$ (1)

where δ, d, and θ are the axial deformation of the BRB, the stratified deformation of the structure, and the horizontal inclination of the BRB, respectively.

From equation (1), the inter-story displacement angle corresponding to the BRB yield displacement can be further determined as

$α = \frac{(1 + λ) f_{y}}{E \sin 2 θ}$ (2)

where α is the inter-story displacement angle, λ represents the ratio of the yield segment length to the axis length of the BRB, and f_y and E denote the yield strength and elastic modulus of the core plate, respectively. If the BRB model and layout scheme are determined, the inter-story displacement angle corresponding to the BRB yield displacement can also be determined. For instance, if one assumes λ, f_y, E, and θ are defined as 0.5, 235 MPa, 206 GPa, and 45°, respectively, an α value of 1/584 can be calculated from equation (2). Generally, it is considered that the frame portion remains elastic when the inter-story displacement angle is less than 1/550. A value of 1/584 is less than 1/550 and shows that the frame portion remains elastic when the BRB yields.

Figure 2.

Relationship between stratified deformation and axial deformation of the BRB. (a) Graphic deformation pattern of a portal-braced frame and (b) contribution of BRB on the strengths of the braced frame system.

The above introduction is the conventional method to ensure BRB yields before the main structure. Obviously, the above derivation ignores the influence of the axial deformation of the frame column. When the axial force of the BRB is too large, the axial deformation of the frame column cannot be neglected, otherwise, the actual axial deformation of the BRB will be less than the theoretical value, as shown in Figure 3.

Figure 3.

Actual deformation of a BRB considering axial deformation of frame columns. (a) Ideal shear type, (b) axial deformation effect, and (c) realistic deformation.

The above prediction can also be verified using Pushover analysis. The BRBs in the structure shown in Figure 4 are designed according to equation (2). The lateral force distribution is analyzed by Pushover analysis with inverted triangles. When the overall inter-story displacement angle is 1%, the BRB of the upper floor has not yielded, and the flexural deformation occurs in the overall frame, which indicates that the conventional approach cannot fully guarantee that the BRB yields before the main structure.

Figure 4.

Pushover analysis of BRBs in a RC-BRB frame model (red indicates BRB yielding).

From the perspective of performance-based design, the design requirements of the second-defendant line can be further converted into quantitative performance targets, as shown in Table 1, which can be described as “the main structure under the medium earthquake remains undamaged, and the BRB dissipates energy by yielding.” The values of the inter-story displacement angle limits in Table 1 refer to the current seismic code provisions 3.10.3.,⁹ where Δu_py/h indicates the inter-story displacement angle when the BRB yields.

Table 1.

Seismic design parameters of RC-BRB frames with various performance levels.

Earthquake level		Frequent earthquake	Design earthquake	Rare earthquake
Performance level	Frame	Undamaged	Undamaged	Slight damage
Performance level	BRB	Undamaged	Slight damage	Moderate damage
Story drift angle		Δu_py/h	1/550	1/300
Column		Elasticity	Elasticity	No yield
Beam		Elasticity	Elasticity	Slight yield
BRB		Elasticity	Yielding	No failure

BRB: buckling-restrained braces.

Design process

This article proposes that in order to achieve the design of the second-defendant line and the performance objectives shown in Table 1, the results of the Pushover analysis of the structure should be used as the design basis. The specific design process is as follows:

1. Determine the initial design scheme based on the method recommended by the specification.⁹

Considering the earthquake action using the matrix decomposition reaction spectrum method, the maximum value of the seismic influence coefficient is determined according to predetermined earthquake prevention measures.

Replace the BRB with a box-section steel support, ignoring the stability check of the support.

The BRB layout scheme is adjusted so that the displacement angles of each layer of the structure are less than 1/550, thereby ensuring that the structure satisfies the performance requirements of multiple earthquakes and fortified earthquakes in Table 1.

At this time, the structural scheme BRB maintains elasticity under the fortification earthquake, and it cannot guarantee that the BRB yields before the frame part and form an obvious two-way line of defense. Therefore, the BRB layout scheme should be further optimized.

2. Establish a nonlinear model of the initial scheme based on Perform-3D.

To meet the performance requirements of a medium earthquake, the concrete tensile strain is selected as the performance index. The beam–column component uses a fiber section model to monitor the tensile strain of the concrete at critical sections. In Perform-3D, the fiber section model divides the section into several fiber units along the longitudinal direction of the member. Each unit support defines the specific material properties. Based on the flat section assumption and the section curvature, the strain of each element can be obtained, and then the fiber stiffness is used to obtain the section. The BRB can be simulated with a special BRB composite component consisting of a BRB nonlinear unit, an elastic rod, and an end rigid domain.

3. Perform Pushover analysis on the above nonlinear model using the inverted triangle lateral force distribution. Adjust the BRB type and layout scheme based on the analysis results until: (a) the displacement angles of the layers are less than 1/550 and (b) all BRBs are fully yielded. If necessary, the beam–column section can also be adjusted.

4. Modify the linear calculation model in step (1) based on the final BRB type and layout scheme, use the linear design software, PKPM, to implement the section design of the frame part, and then determine the section reinforcement of the beam and column.

It should be noted that although BRBs have yielded in the design process of the main structure, this article does not recommend considering the additional damping caused by nonlinear energy dissipation because the actual nonlinear deformation of the BRB affected by a moderate earthquake is difficult to accurately estimate. It may lead to overestimation of the damping effect of the BRB, causing the structural scheme to be dangerous.

Seismic analysis and model validation

Design details

Using the structural design of a teaching building as an example, the seismic fortification intensity is 8° (0.2 g), the earthquake group is the first group, and the site classification is class II. The peak value of the horizontal seismic influence coefficient is 0.16 and 0.45 g under a small earthquake and medium earthquake, respectively. The characteristic period is 0.35 s and the damping ratio is 5%. The dead load of the roof, the dead load of the floor, the uniform live load of the roof with no crowd load, the live load of the floor, the live load of the corridor, and the basic wind pressure are, respectively, 7, 5, 0.5, 2.5, 3.5, and 0.35 kN/mm², and the terrain roughness is class B. The plane axis net of the teaching building is shown in Figure 5. The horizontal direction is 7 × 7800 mm, the longitudinal side span is 10,800 mm, and the middle span is 2600 mm. There are 15 stories in the height direction. The first floor is a lecture hall with a height of 5.4 m and the height of the other stories is 3.9 m.

Figure 5.

Plane and elevation views of a generic RC-BRB frame.

The BRB layout of the structure is shown in Figure 5. Frame dimensions and BRB models are determined according to general design methods. The BRB information of the initial design scheme is shown in Table 2. The initial design is then optimized based on the performance-based design method proposed in this article. The beam–column size or BRB type is adjusted so that the structure meets the seismic performance index and all the BRB can fully yield. The BRB information of the final design scheme is shown in Table 3.

Table 2.

BRB information for the initial design.

Type	Core area(mm²)	Length(mm)	Bearing capacity (kN)	Yielddisplacement (mm)	Initial stiffness(KN/mm)	Steelquantity (t)	Quantity
BRB1	2000	3500	480	3.6	133.2	0.192325	60
BRB2	1600	3000	384	3.09	124.32	0.13188	72
BRB3	2000	4000	480	4.11	116.55	0.2198	8
BRB4	1600	3500	384	3.6	106.56	0.15386	40
BRB5	1000	3000	240	3.09	77.7	0.082425	60
					Total	33.89316	240

BRB: buckling-restrained braces.

Table 3.

BRB information for the final design.

Type	Core area(mm²)	Length(mm)	Bearing capacity (kN)	Yield displacement (mm)	Initial stiffness(KN/mm)	Steelquantity (t)	Quantity
BRB1	2000	3500	480	3.6	133.2	0.192325	12
BRB2	4000	3000	384	3.09	310.8	0.3297	96
BRB3	2000	4000	480	4.11	116.5	0.2198	8
BRB4	1600	3500	384	3.6	106.5	0.15386	24
BRB5	1000	3000	240	3.09	77.7	0.082425	36
BRB6	4000	3500	384	3.6	266.4	0.38465	64
					total	66.995	240

BRB: buckling-restrained braces.

Simplified numerical model of BRB components

Perform-3D supports the definition of a BRB compound component, which is obtained by connecting the BRB unit, the elastic rod, and the rigid region, in series. Among them, the BRB unit is used to simulate the elasto-plastic material behavior of the BRB components, including the skeleton curve and hardening parameters, and supports the definition of two types of skeleton curves (E-P-P type and trilinear type).

The BRB involved in this article is the concrete grouting type. To accurately simulate the numerical characteristics of the BRB in nonlinear analysis, the author carried out a set of static loading tests and summarized the hysteresis curves of three specimens. The general rule of determining the basic parameters of the BRB numerical model is given. In this test, a 150 T MTS electric-hydraulic servo system in the Structural Engineering Laboratory of Shanghai Normal University was used as the loading equipment. The BRB specimens were placed vertically and connected to the connecting piece through the end plate, as shown in Figure 6.

Figure 6.

Dimensions and test details of BRB specimens. (a) Configuration of BRB components and (b) test setup of axial loading system.

The typical hysteresis curves of the experiment are shown in Figure 7. The general rule of the hysteresis curve in the BRB test is as follows: (1) The hysteresis curve can reflect the stiffness of the brace. From the hysteresis curve, it can be found that after the brace yields, the tangential stiffness in the direction of tension and compression is slightly inconsistent. The tangential stiffness of the compression brace is slightly larger than that of the tension brace so that the axial force of the brace at the same displacement amplitude is slightly larger than the brace tensile force. This phenomenon exists in each stage of the loading cycle, and as the displacement amplitude increases, the imbalance of the brace output becomes more obvious. (2) The hysteresis curve can reflect the unbalanced characteristics of the tensile and compressive bearing forces of the brace. On the basis of the hysteresis curve, the compressive bearing capacity adjustment coefficient β can be calculated, and the maximum coefficient of 13 specimens is 1.18. (3) The hysteresis curve can reflect the ductility of the brace. The maximum ductility coefficient among the specimens is 22.8 based on the hysteresis curve and the maximum deformability is 3%. Table 4 summarizes the design parameters of BRB test specimens, where K_c (K_c = EA/L) is the initial axial linear stiffness based on calculation, K_e is the initial axial linear stiffness from test results, P_yc is the calculated yielding strength, P_y is the measured yielding strength, β is the adjustment coefficient of compressive bearing capacity, Δ_max is the maximum deformation capacity, D is the ductility factor, CPD is the cumulative plastic deformability, and CPE is the cumulative energy dissipating capacity. K_c can be calculated as follows: K_c = EA/L, where E, A, and L are the elastic modulus, cross-sectional area, and length of the brace, respectively.

Figure 7.

Axial force versus displacement hysteresis curves of various BRB components.

Table 4.

Main seismic performance parameters of test specimens.

Specimen	K_c (kN/mm)	K_e (kN/mm)	K_c/K_e	P_yc (kN)	P_y (kN)	P_yc/P_y	β	Δ_max	D	CPD	CPE
BRB1	196.34	159.11	1.23	333.95	348.45	0.96	0.93	0.015	13.62	226.21	79.11
BRB2	196.34	167.37	1.17	333.96	325.38	1.03	0.95	0.009	8.29	110.62	29.34
BRB3	196.34	189.76	1.03	333.96	330.69	1.01	1.06	0.019	16.44	235.66	148.73
BRB6	126.00	108.53	1.16	208.73	209.29	0.99	0.83	0.026	22.80	547.88	187.32
BRB8	126.00	111.45	1.13	208.73	190.61	1.09	0.99	0.016	14.67	298.89	93.57
BRB10	104.01	118.74	0.88	316.85	314.21	1.008	0.77	0.021	10.28	170.89	54.85
BRB11	161.68	172.00	0.94	506.96	505.55	1.003	0.99	0.018	8.68	93.81	47.56
BRB12	104.01	98.07	1.06	316.89	317.14	0.99	1.22	0.025	11.94	245.65	147.31
BRB13	161.68	163.71	0.99	506.96	517.27	0.98	1.18	0.030	14.72	447.95	394.10
Average	–	–	1.07	–	–	1.01	0.99	–	–	–	–

CPD: cumulative plastic deformability; CPE: cumulative energy dissipating capacity; BRB: buckling-restrained braces.

From the hysteresis behavior, a practical BRB numerical model should satisfy the following conditions: (1) satisfy the actual hardening model; (2) reflect the unbalanced relationship between compression and tension; and (3) demonstrate the ductility and fatigue life of the component. On the basis of the actual parameters of different specimens, it is proposed to design the BRB components based on the following provisions. From the test results, most of the specimens lost axial resistance at 1/100 deformation, so the ultimate displacement of the BRB can take 1/100 of the length of the brace, which is considered to be conservative. The test results indicate that the ratio of the actual value of the initial axial stiffness of the BRB to the calculated value is close to 1. If the gap and the unbonded material are reasonable, the initial axial stiffness value can be approximately equal to the initial axial stiffness calculation. Then, the ratio of the actual yield strength to the theoretical yield strength of the core material determined by the test is about 1. If the gap and the unbonded material are properly set, the yield strength of the seamless in-line BRB can be approximated as the yield strength of the material.

To verify whether the above design suggestions are reasonable, we use the Trilinear skeleton curve to determine the hysteresis curve of Perform-3D based on the above design proposal and fit of the test hysteresis curve. In Perform-3D, the BRB nonlinear component, the elastic rod, and the end rigid domain simulate the core yield section, elastic section, and gusset of the BRB, respectively. The actual performance of BRB can be well simulated by adjusting the relevant parameters. Taking BRB13 as an example, the constitutive behavior of BRB adopts a trilinear kinematic hardening model. First, set BRB information on the basis of experimental results, such as length, stiffness, key points of the constitutive curve, and the hysteretic loading system. Then, the hysteresis curve information of the BRB can be obtained by Perform-3D, as shown in Figure 8.

Figure 8.

Comparison of the hysteresis curve in Perform-3D and test.

The fitting results are shown in Figure 8. From the above fitting results, we can find that the numerical model and parameter design suggestions of the BRB are reasonable. This shows that the BRB unit in Perform-3D can accurately reflect the mechanical properties of the actual BRB component with appropriate parameter settings.

Seismic analysis for design verification

Seismic waves and spectral analysis

The main difficulty in the design of an RC-BRB frame structure is to accurately estimate the earthquake action of the frame part under the premise of BRB yield deformation, thus completing the section reinforcement. When the RC-BRB frame structure satisfies the performance goal of the BRB without plastic deformation under small earthquakes, the structure affected by a medium earthquake should be a weakly nonlinear structure system. Therefore, the response spectrum method of the traditional linear analysis can also effectively estimate the frame part. Figure 9 is a comparison of seven seismic waves within the specification spectrum.

Figure 9.

Comparison of seven seismic waves within the specification spectrum.

To verify the accuracy of the response spectrum method based on the current seismic code 5.1.2.,⁹ the time history analysis results of seven seismic waves were selected for comparison, including five natural waves and two artificial waves. The characteristic periods of the seven seismic waves are close to 0.35 s. It can be seen from Figure 10 that the response spectrum method overestimates the seismic response on the lower floor compared with the average of the time history analyses, which is easy to understand because the response spectrum method ignores the nonlinear characteristics of the BRB. The higher floors (2–9 floors) estimated by the response spectrum method are exactly the floors on which the BRBs are centrally arranged. However, this also suggests that it is feasible to estimate the seismic action of the RC-BRB frame structure using linearization methods in the design, as conservative design results are advantageous for structural safety.

Figure 10.

Relation of shear force versus floor of RC-BRB frames. (a) x-direction and (b) y-direction.

Story drift angle

The nonlinear model of Perform-3D was determined on the basis of the final structural design. Figure 11 shows the inter-story drift angle of the performance-based design scheme under moderate earthquakes. It shows that the average inter-story displacement angle of the seven waves is consistent with the design value in stories 1–12, satisfying the story drift angle limitation of 1/550 under medium earthquakes. Since the BRB is not arranged, the deformation of the upper floor is larger. Considering the influence of the flexural deformation, the unfavorable inter-story displacement angle of the top floor may not be obvious.

Figure 11.

Inter-story drift angle of ductile design scheme along the x-direction (medium earthquake).

To verify the above assumptions, the tensile strain performance of the concrete on the surface of the column is extracted. As can be seen from Figure 12, the cracking condition of the 13-story column is more severe, while the 14 and 15 story columns are essentially uncracked. It indicated that the 13-story column is greatly affected by shear deformation, and the lateral stiffness should be strengthened. Overall, the frame column is less cracked, indicating that the design method of this article generally meets the performance targets of the medium earthquake.

Figure 12.

JG0393 wave column cracking performance (red represents cracking).

Figure 13 illustrates that the performance-based design scheme can generally meet the present performance of the inter-story displacement angle of 1/300 affected by large earthquakes, indicating that the ductile structural measures can be reduced. It can be seen from Figure 13 that the deformation of the structure under JGR18 ground motion is the most unfavorable. The performance of the main structure was evaluated by extracting the performance state of the structure along the x-direction of the JGR18 ground motion. Life safety, referred to as LS, is a performance standard defined by US standards. This level is equivalent to “repairable” in the Chinese specifications. Perform-3d can represent the performance parameters of structures using different colors. Blue, green, orange, and red represent 0.25 LS, 0.5 LS, 0.75 LS and 1.0 LS, respectively. It can be seen from Figure 14 that the part of the beam hinge under the JGR18 ground motion is between 0.25 and 0.5 times the LS, and the column hinge is less than 0.25 times the LS, which meets the predetermined performance goal.

Figure 13.

Inter-story drift angle along the x-direction of the performance-based design scheme.

Figure 14.

Component deformations subjected to a JGR18 wave-type large earthquake (blue indicates 0.25 times LS).

Hysteresis energy distributions

As described in the design flow of section “Seismic analysis for design verification,” the initial design scheme adopts the traditional elastic design method, and the second-defendant line design is considered on the basis of equation (2). The final design is obtained by iteratively optimizing the solution according to the performance state of Pushover analysis. Here, the optimization effect of the method is proven by comparing the energy analysis of the above two schemes.

Figure 15 shows the BRB energy consumption time history of the two structural schemes under the JG0393 wave corresponding to a medium earthquake. The abscissa indicates the seismic wave loading time history, and the ordinate indicates the percentage of max energy (maximum value is 100). The yellow portion represents the x-direction BRB energy dissipation, and the red portion shows the energy dissipation of other units except for the BRB in the x-direction. By comparing Figure 15(a) and (b), it can be found that the structure is elastically deformed at 0–10 s, and no hysteresis energy is generated in both the BRB and frame; at 10–15 s, the total energy consumption of the initial design is less than 13%, mainly based on beam and column energy dissipation; however, the total energy consumption of the final design is 85%, of which BRB energy consumption attains 48%. It can be clearly seen from Figure 15(b) that the energy consumption of BRB is close to the total energy consumption during 10–12.5 s, indicating that the final model BRB consumes energy before the frame.

Figure 15.

Time history hysteresis energy of BRBs along the x-direction affected by a JG0393 wave (medium earthquake). (a) Initial design and (b) final design.

Figure 16 shows the energy dissipation ratio of each component of the two structural schemes under the JGR18 wave (large earthquake). In the initial design stage, beam components dissipate 48% of the total earthquake input energy, and 38% for BRBs, but in the final design, BRBs contribute the majority, 62%, of the total energy. It indicates that the proposed design procedure can effectively avoid the premature plastic deformations in the beam and column components. Figure 17 shows the time history BRB energy dissipation of the two structural schemes under the JGR18 wave corresponding to a large earthquake. It can be seen from Figure 17 that the structure generates plastic-induced energy from 2 s. During 2–10 s, the BRB energy consumption in the initial scheme accounts for 29%, and the energy consumption is mainly carried by beams and columns. In contrast, during the 2- to 8-s time period, the energy in the final design was mainly consumed by BRB, and the energy consumption ratio was 38%. It can be seen that in the final design BRB consumes energy before the frame, which meets the requirements of the second line of defense.

Figure 16.

Energy dissipation ratio of each component affected by a JGR18 wave (large earthquake). (a) Initial design and (b) final design.

Figure 17.

Time history hysteresis energy of BRBs along the x-direction affected by a JGR18 wave (large earthquake). (a) Initial design and (b) final design.

Conclusion

This study proposed a new design method for RC-BRB braced frames to achieve two levels of performance criteria. The distribution of BRB components in the frame is initially designed by the response optimization based on the Pushover model analysis. Then, a typical RC-BRB braced frame model was built and validated in terms of the experimental data of the BRB components. For the conventional weakly nonlinear structural systems, the seismic effect estimated by the conventional method is slightly higher than the average results of the time history analysis under natural seismic waves, but it is conservative and reliable in terms of the proposed design method. In addition, the RC-BRB frame model designed by the method in this article meets the performance goals and significantly improves the seismic redundancy of the full-plastic deformations developed in BRB components, ensuring an unchanged mainframe affected by medium earthquakes.

Footnotes

Handling Editor: Vittorio Memmolo

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: The first and the corresponding authors are grateful to the financial support from the “Fundamental Research Funds for the Central Universities” (Grant No. xjj2017174 and xjj2017037),additionally,the corresponding author is a research fellow awarded by the Alexander von Humboldt Foundation in Germany.

ORCID iDs

Yanchao Yue

Yongtao Bai

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Seismic design and analysis of reinforced concrete buckling-restrained braced frame buildings with multi-performance criteria

Abstract

Keywords

Introduction

Design method

Configuration of BRB components

RC-BRB frame systems

Design process

Seismic analysis and model validation

Design details

Simplified numerical model of BRB components

Seismic analysis for design verification

Seismic waves and spectral analysis

Story drift angle

Hysteresis energy distributions

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iDs

References