Low Post-yield Stiffness Research Articles

Study on self-centering mechanism of different yield strength hybrid buckling restrained braces

Conventional buckling-restrained braces (BRBs) exhibit stable compressive and tensile strengths and excellent energy dissipation characteristics. Nevertheless, the low post-yield stiffness limits the capacity of BRBs to control the peak displacement of the structure. This leads to large residual displacements in structures, which increases the probability of collapse under strong earthquakes. Consequently, introducing a reliable system that dissipates seismic energy, and provides an adequate self-centering capability, is necessary. This study has been carried out to investigate the hybrid BRBs response with different yield strengths (DY-HBRB) using numerical analysis. The cyclic responses, residual displacement, energy dissipation, and equivalent damping coefficient of the DY-HBRB models have been assessed. A simplified core-spring finite element model was utilized to model DY-HBRB elements. Moreover, an innovative trilinear kinematic hysteresis (TKH) model is proposed to simulate the cyclic behavior and facilitate the application of DY-HBRBs to seismic designs. The proposed model has been validated with the experimental investigation and numerical analysis results. The results indicate that selecting appropriate combinations of steel cores with different yield strengths in DY-HBRB provides a stable cyclic response with adequate energy dissipation and eliminates a significant part of the residual displacement. In addition, it was confirmed that the proposed TKH model could logically represent the double yield point of the DY-HBRBs with remarkable precision.

Seismic performance evaluation of steel buckling-restrained braced frames including SMA materials

The permanent deformation of the building after seismic excitations can be determined by the Maximum Residual Interstory Drift Ratio (MR-IDR), which may be used for measuring the damage states. Low-post yield stiffness of the steel buckling-restrained braced frame (BRBF) makes this system vulnerable to large MR-IDR after a severe earthquake event. To overcome this issue, this paper investigates the seismic limit state performances of low- to mid-rise BRBFs with two- to eight-story levels (i.e. 2-Story, 4-Story, 6-Story, and 8-Story) adopting different lateral force-resisting systems using Viscous Dampers (VDs) and Shape Memory Alloys (SMAs). For this purpose, BRBFs improved with different implementation of SMAs and VDs, and Incremental Dynamic Analyses (IDAs) were performed based on Maximum Interstory Drift Ratio (M-IDR) and MR-IDR demands. Results showed that VDs and SMAs can decrease the values of maximum moment and rotation of hinges of structural members. Implementing both SMAs and VDs can significantly improve the seismic performance level and collapse failure probability of BRBFs more effectively than using one of the VDs or SMAs; then, it can be recommended to control the MR-IDR of BRBFs. To use the results, graphical user interface has been developed to estimate the improvements in the M-IDR and MR-IDR demands.

Seismic performance analysis of multi-story steel frames equipped with FeSMA BRBs

Buckling-restrained braces (BRBs) have been widely used in seismic prone areas around the world. However, one major problem associated with the steel BRB frames is the excessive residual deformation under strong earthquakes, mainly due to the low post-yield stiffness ratio of the steel BRBs. Recently, the community has fabricated the iron-based shape memory alloy (FeSMA) BRBs, which exhibited full hysteresis with high post-yield stiffness ratios, but the seismic behavior of the FeSMA BRB frames still remains unknown. As such, this paper conducts seismic performance analysis of multi-story steel frames equipped with the FeSMA BRBs, through a comparison with those equipped with conventional steel BRBs. Incremental dynamic analysis (IDA) is further conducted to establish the probability seismic demand models. Based on the IDA data, bivariate fragility analysis is conducted to quantify the probability of exceedance, conditioned on various limitations of the maximum and residual interstory drift ratios. According to current analysis, it indicates that both the maximum interstory drift ratios and the maximum floor accelerations are comparable between these two types of BRB frames. The major advantage of the FeSMA BRBs over the steel BRBs is that the former can better control residual interstory drift ratios.

Equivalent static loads for double-layered domes supported by multistorey buckling-restrained braced frames

Curved gridshells are excited not only in the horizontal direction but also experience large anti-symmetric vertical accelerations when subjected to horizontal earthquake ground motions. In addition to the coupled response, gridshells exhibit closely spaced modes and substructure-roof interaction. Nevertheless, previous studies have proposed elastic horizontal and vertical equivalent static seismic forces considering these complex dynamic response characteristics. These are determined from the input horizontal acceleration at the substructure’s roof level, an assumed acceleration distribution, nodal roof masses and amplification factors derived from the dynamic characteristics of the dome and substructure. To extend this methodology to nonlinear substructures with displacement-dependent damping devices, this paper investigates the applicability of ductility reduction factors (or Rμ factors) to estimate the inelastic response spectra and an alternative equivalent linearisation approach to compute the peak horizontal acceleration of multistorey substructures with buckling-restrained braces. This is achieved by modelling the curved roof as a rigid mass for the substructure model, and using its idealised base shear-roof displacement relationship obtained from modal pushover analyses. The peak horizontal acceleration of the substructure is then used to obtain the equivalent static loads of the curved roof using amplification factors, and the accuracies are verified against the results from nonlinear response history analyses. It was confirmed that the Rμ [Formula: see text]factors combined with the roof amplification factors provide a simple way to estimate the peak roof response with sufficient accuracy for preliminary design of domes with multistorey substructures having low post-yield stiffness.

Quantification of higher mode effects of steel frame and control method using dual self-centering variable friction damper brace

Self-centering energy dissipation braced frames (SCEDFs) have been developed to satisfy the requirements of resilience. However, low post-yield stiffness in such systems often leads to a higher mode effect, resulting in a significant deformation concentration that may exceed the design objectives. A novel dual self-centering variable friction damper (DSC-VFD) brace with high post-yield stiffness and enhanced energy dissipation capability was proposed. Its hysteretic behavior, characterized by a loading stiffness that is larger than the unloading stiffness, was developed by incorporating the C++ language into the OpenSees platform. To evaluate the higher mode effect in different types of frames, a quantification measure based on the higher mode results of the steel frames, considering the seismic responses around the peak value, was therefore established. Then, the seismic responses of the DSC-VFD frames (DSC-VFDFs) using the proposed uniaxial material were calculated and compared with those of the traditional moment resisting frame (MRF) and SCEDF with the same design process. Finally, the four parameters, including the first stiffness modification coefficient α1, second stiffness ratio α2, strength ratio β, and fourth stiffness ratio α4, were considered to evaluate their influences on nonlinear seismic responses and the higher mode effect of the DSC-VFDF by the above-mentioned quantification measures. The results indicate that the influence of higher modes should not be ignored in the design of self-centering braced frames, and the higher mode quantification results of base shear are more sensitive than those of effective displacement. The DSC-VFD brace can more effectively improve the seismic responses and control the higher mode effect than the traditional SCEDF.

A novel all-steel buckling restrained brace for seismic drift mitigation of steel frames

Buckling restrained braces (BRBs) as metallic dampers can supply stable and balanced hysteretic response. While BRBs exhibit outstanding energy dissipation capacity, their low post-yield stiffness contributes to large residual drift concentration in simply supported buckling restrained braced frames. The present study introduces a novel all-steel tube-in-tube BRB composed of a short-length hybrid core serially connected to a non-yielding robust member. The hybrid core includes short-length yielding members made up of circular hollow sections surrounded by an all-steel encasing system. High strain hardening capacity of short-length hybrid core enhances the post-yield stiffness, thus reducing the residual drift in simply supported buckling restrained braced frame. In this paper, first the components of proposed brace are represented in detail. Subsequently, the design procedure and stability analysis results are provided. The feasibility of conceptual hybrid BRB is evaluated by finite element analysis method. Afterwards, the global response of prototype buckling restrained braced frames comprising conventional and proposed braces are appraised via pushover and nonlinear time history analyses. The analyses results designated the significant efficiency of proposed braces to help mitigate inter-story and particularly residual drifts in buckling restrained braced frames.

Evaluation of approximate methods for estimating residual drift demands in BRBFs

Nowadays, Buckling Restrained Braced Frame (BRBF) system is extensively used for the seismic design of new buildings. This system is composed of Buckling Restrained Braces (BRBs) that do not buckle under compression forces, and have high energy-dissipation capacity. However, low post-yield stiffness of the brace core in BRBs may cause large residual drifts after the occurrence of an earthquake. In this study, four approximate methods for estimating residual drift demands in BRBFs are evaluated. These methods include the FEMA P-58 method, the method proposed in this study, the method proposed by Erochko et al. and the coefficients method introduced by Ruiz-García and Chora, calibrated in this study for BRBFs. To evaluate the estimated residual drifts of BRBFs according to these approximate methods, 2-, 4-, 6-, 8-, 10- and 12-story BRBFs are designed. Nonlinear dynamic analyses are performed on the BRBFs using 78 ground motion records scaled to different ground motion intensity levels. The results show that the proposed method is more accurate than the FEMA P-58 and Erochko et al. methods that are conservative for estimating the median and mean residual drifts of BRBFs, respectively. Moreover, the coefficients method, which estimates the median of maximum residual drifts, is the most accurate method among the four methods considered. However, it does not provide information about the height-wise distribution of residual drifts.

Experimental investigation of a multistage buckling-restrained brace

While buckling-restrained braces offer excellent energy dissipation characteristics, their low post-yield stiffness may result in large residual drifts and interstory drift concentration when used in simply supported frames. This paper introduces a new multistage buckling-restrained brace to help mitigate these design challenges. The proposed device features two low yield point (LYP) cores with LY225 and short yield lengths, and one high yield point (HYP) core with SA440B and a longer yield length. In a design level event, the LYP cores dissipate energy, while the parallel HYP core provides an elastic restoring force. At large drifts, the HYP core yields and the device acts similar to a high-capacity, ductile, conventional BRB.A 384 kN specimen was tested at up to 1.5% strain and the individual core contributions recorded using strain gauges attached to the elastic core segments inside the restrainer. The multistage response matched the predicted trilinear backbone, achieving 10 to 20% equivalent damping prior to yielding the HYP core, and a fatigue capacity exceeding three times the AISC 341-16 acceptance criteria. Interaction between the decoupled cores was studied using a 3D finite element model, indicating that minor detailing changes could further improve performance.

Analytical and experimental studies on buckling-restrained brace with gap-supported tendon protection

This paper proposes a new brace called TP-BRB, composed of a conventional buckling-restrained brace (BRB) with a gap-supported tendon protection (TP) in parallel. The gap-supported tendon protection remains inactive before the deformation of TP-BRB reaches a threshold value, while obtaining a high axial stiffness after the threshold value is exceeded. Under strong earthquake, the TP-BRB is expected to provide structures with effective energy dissipation capacity and mitigate the risks of global collapse caused by low post-yield stiffness of the conventional BRB. As the earliest part of the research on the TP-BRB, this paper firstly presents both the stiffness characteristics of the hysteretic curve and a theoretical formula of residual deformation. Secondly, a quasi-static test is conducted, the results of which illustrate that TP-BRB shows a stable hysteretic behavior, a skeleton curve with significant tri-linear characteristic, and a smaller residual deformation than a conventional BRB. Finally, parametric studies based on numerical models show that, with the reduction of the threshold value (u0) and the increase of the ratio (γ) between the axial stiffness of BRB and gap-supported tendon protection, both the residual deformation and the equivalent damping ratio of TP-BRB decrease, but the secant stiffness of TP-BRB increases.

Numerical comparison on the efficiency of conventional and hybrid buckling-restrained braces for seismic protection of short-to-mid-rise steel buildings

Buckling-restrained brace (BRB) is a specific kind of bracing system which has an acceptable energy dissipation behavior in a way that would not be buckled in compression forces. However, considerable residual deformations are noticed in strong ground motions as a result of the low post-yield stiffness of the BRBs. The seismic performance of a modern lateral load resisting system, which is called the hybrid BRB, and its conventional counterpart are assessed and compared in this paper. Multiple plates with different stress–strain behavior are used in the core of this new innovative system, and this is its difference with the existent BRBs. Nonlinear static and incremental dynamic analyses are carried out for three building frames with different structural heights, which use conventional and hybrid BRB systems. To carry out response history analyses, the FEMA P695 far-field earthquake record set was adopted in different hazard levels. The hybrid BRBs are shown to have superior seismic performance in comparison with the conventional systems based on the response modification factor and the damage measures including residual displacements and inter-story drift ratios.

Multi-material core as self-centering mechanism for buildings incorporating BRBs

Conventional buckling restrained braces used in concentrically braced frames are expected to yield in both tension and compression without major degradation of capacity under severe seismic ground motions. One of the weakness points of a standard buckling restrained braced frame is the low post-yield stiffness and thus large residual deformation under moderate to severe ground motions. This phenomenon can be attributed to low post-yield stiffness of core member in a BRB. This paper introduces a multi-core buckling restrained brace. The multi-core term arises from the use of more than one core component with different steel materials, including high-performance steel (HPS-70W) and stainless steel (304L) with high strain hardening properties. Nonlinear dynamic time history analyses were conducted on variety of diagonally braced frames with different heights, in order to compare the seismic performance of regular and multi-core buckling restrained braced frames. The results exhibited that the proposed multi-core buckling restrained braces reduce inter-story and especially residual drift demands in BRBFs. In addition, the results of seismic fragility analysis designated that the probability of exceedance of residual drifts in multi-core buckling restrained braced frames is significantly lower in comparison to standard BRBFs.

Damage Concentration Effect of Multistory Buckling‐Restrained Braced Frames

Due to the low postyield stiffness of buckling‐restrained braces (BRBs), multistory buckling‐restrained braced frames (BRBFs) subjected to earthquakes are prone to lateral deformations and damage concentrations at certain stories, which is deemed a damage concentration effect (DCE). A series of nonlinear pushover analyses and response history analyses are conducted to investigate the key factors affecting the DCE of BRBFs. Two comparisons of the DCE are performed for different types of structures and different beam‐to‐column connections in the main frame (MF). These comparisons show that BRBFs equipped with BRBs as the main earthquake resistance system have a more serious DCE than the traditional moment‐resisting frame or conventional braced frame and that the MF stiffness significantly affects the structural residual displacement and DCE. Then, parametric analyses are performed to investigate the influence of two stiffness distribution parameters (in the horizontal and vertical directions) on the DCE of a 6‐story BRBF dual system designed according to the Chinese seismic code. The results show that increasing the MF stiffness and avoiding abrupt changes in the BRB stiffness between stories can effectively mitigate the DCE of BRBFs. Finally, the correlations between various damage performance indices are analyzed. A low statistical correlation between the peak and residual drift responses can be observed in BRBFs. Therefore, it is recommended that the DCE be considered in BRBF design.

Numerical Investigation of Seismic Response of Hybrid Buckling Restrained Braced Frames

The Conventional buckling restrained braces used in concentrically braced frames are expected to yield in both tension and compression without major degradation of capacity under severe seismic ground motions. One of the weakness points of a standard buckling restrained braced frame is the low post-yield stiffness and thus large residual deformation under moderate to severe ground motions. This phenomenon can be related to the low post-yield stiffness of the core segment in comparison to its elastic stiffness. This paper investigates the application of stainless steel as the core material in a hybrid buckling restrained brace. The “hybrid” term arises from the use of more than one core component with different steel materials, including high strength high-performance steel and stainless steel (304L) with high strain hardening in the core of buckling restrained brace. Nonlinear dynamic time history analyses were conducted on a variety of diagonally braced frames with different heights, in order to compare the seismic performance of standard (non-hybrid) and hybrid buckling restrained braced frames. The results showed that the proposed hybrid buckling restrained braces reduce the inter-story and specially the residual drift demands in buckling restrained braced frames.

Assessment of design parameters influencing seismic collapse performance of buckling-restrained braced frames

Buckling Restrained Braced Frames (BRBFs) are widely used as seismic force-resisting systems due to their significant ductility and energy dissipation capacity. However, owing to their modest overstrength and relatively low post-yield stiffness, BRBFs subjected to seismic loading may be susceptible to concentrations of story drift and global instability triggered by P-∆ effects. Due to the use of simplistic methods that are based on elastic stability, current code-based design provisions do not address seismic stability rigorously and do not consider the unique inelastic characteristics of different systems. Supplemental strategies may be used to prevent undesirable seismic response of BRBFs, such as story drift concentration and large residual drift. This study employed the FEMA P695 framework to evaluate the response of BRBFs designed according to current codes in the United States and to study the effect on seismic stability of three additional parameters: BRBF column orientation, gravity column continuity, and dual systems. Results from nonlinear static and dynamic analyses provide insight into seismic behavior, and collapse performance evaluation quantifies the relative performance of various BRBF designs and supplemental strategies for enhancing seismic stability.

Probabilistic seismic demand assessment of steel frames braced with reduced yielding segment buckling restrained braces

Buckling-restrained braces have adequate seismic performance characteristics such as high energy absorption due to their symmetric behaviour in compression and tension. However, low post-yield stiffness is one of the main disadvantages of these braces. The stiffness values of buckling-restrained brace frames can highly degrade when the core segments are yielded. Reducing the length of the yielding segments of buckling-restrained braces is being proposed and investigated by many researchers, considering the high strain capacity of steel in the post-elastic region. This article focuses on a type of buckling-restrained brace called reduced yielding segment buckling restrained brace or in short, ‘reduced length buckling restrained brace’. In such frames, the length of the yielding part is reduced and placed in one end of the brace element. In this research, the seismic performances of the above-mentioned buckling-restrained braces were investigated through probabilistic approach and compared with those of conventional buckling-restrained braces. Their performances were quantitatively assessed in terms of two limit states, immediate occupancy and collapse prevention. The fragility curves, the mean annual limit states frequencies and the seismic demand hazard curves of the frames were plotted using probabilistic seismic demand analysis. According to the results obtained for immediate occupancy limit state, the frames braced with reduced length buckling restrained braces show better seismic performances compared to those braced with conventional buckling-restrained braces. However, for collapse prevention limit state, it is hard to comment accurately because in some cases, reduced length buckling restrained braced frames show enhanced seismic performance while in other cases, conventional ones exhibit improved response.

The effect of mainshock-aftershock on the residual displacement of buildings equipped with cylindrical frictional damper

Recently, Friction dampers become popular due to the desirable performance in the energy dissipation of lateral loads. A lot of research which has been conducted on these dampers results in developing friction dampers with low sensitivity to the number of cycles and temperature increases. Friction dampers impose high residual drifts to the buildings because of low post-yield stiffness of the damper which results from increasing lateral displacement and period of buildings. This issue can be more critical under strong aftershocks which results in increasing of structural damages. In this paper, in addition to the assessment of aftershock on steel buildings equipped with friction dampers, methods for controlling residual drifts and decreasing the costs of retrofitting are investigated. Utilizing rigid connections as a lateral dual system and activating lateral stiffness of gravity columns by adding elastic braces are as an example of effective methods investigated in this research. The results of nonlinear time history analyses on the low to medium rise steel frames equipped with friction dampers illustrate a rise in residual drifts as the result of aftershocks. In addition, the results show that different slip loads of friction damper can affect the residual drifts. Furthermore, elastic stories in comparison to rigid connections can reduce residual drifts of buildings in an effective fashion, when most slip loads of friction dampers are considered.

Probabilistic seismic demand assessment of residual drift for Buckling-Restrained Braced Frames as a dual system

The main drawback of Buckling-Restrained Braced Frames (BRBFs) is low post-yield stiffness of steel cores that leads to concentrate large residual drift in a story after earthquakes. Residual drifts not only cause serviceability issues but also increase the potential damage during aftershocks or future events. In this study seismic demands of low and mid-rise BRBFs and Dual-BRBFs were studied using the Probabilistic Seismic Demand Analysis (PSDA). By comparing demand hazard curves of frames it was concluded that using of BRBFs as a dual system could reduce the residual drift demand significantly. It can improve the revival capacity of such structures after earthquakes with low repairing cost. In the other part of this study, two different nonlinear models including a deteriorating model and a non-deteriorating model were used to explore the effect of degradation on Dual-BRBFs seismic demands. It was observed that the residual deformations are more sensitive to degradation than maximum deformations. Although the deterioration is not serious because of large BRBs stiffness which keeps MRFs in low range of nonlinearity.

Response modification factor of the frames braced with reduced yielding segment BRB

In this paper, overstrength, ductility and response modification factors are calculated for frames braced with a different type of buckling restrained braces, called reduced yielding segment BRB (Buckling Restrained Brace) in which the length of its yielding part is reduced and placed in one end of the brace element in comparison with conventional BRBs. Forthermore, these factors are calculated for ordinary BRBF and the results are compared. In this regard incremental dynamic analysis (IDA) method is used for studying 17 records of the most known earthquakes happened in the world. To do that, the considered buildings have different stories and two bracing configurations: diagonal and inverted V chevron, the most ordinary configurations of BRBFs. Static pushover analysis, nonlinear incremental dynamic analysis and linear dynamic analysis have been performed using OpenSees software. Considering the results, it can be seen that, overstrength, ductility and response modification factors of this type of BRBF(Buckling Restrained Braced Frame) is greater than those of conventional types and it shows better seismic performance and also eliminates some of conventional BRBF's disadvantages such as low post-yield stiffness.

Evaluation of buckling-restrained braced frame seismic performance considering reserve strength

Buckling-restrained braced frame (BRBF) systems are used extensively for resisting lateral forces in high seismic regions of the United States. Numerical and large-scale experimental studies of BRBFs have shown predictable seismic performance with robust ductility and energy dissipation capacity. However, the low post-yield stiffness of buckling-restrained braces (BRBs) may cause BRBFs to exhibit large maximum and residual drifts and allow the formation of soft stories. Thus, reserve strength provided by other elements in the lateral-force-resisting system is critical to improving seismic performance of BRBFs. This reserve strength can be provided in two primary ways: (1) moment-resisting connections within the BRBF and (2) a steel special moment-resisting frame (SMRF) in parallel with the BRBF to create a dual system configuration. These two approaches to providing reserve strength can be used together or separately, leading to a variety of potential system configurations. In addition, special attention must be given to the connections within the BRBF since moment-resisting connections have been observed experimentally to limit drift capacity due to undesirable connection-related failure modes. This paper presents nonlinear dynamic analysis results and evaluates performance of BRBF and BRBF–SMRF systems using moment-resisting and non-moment-resisting beam–column connections within the BRBF. Reserve strength is shown to play a critical role in seismic behavior and performance of BRBFs.

Reducing residual drift of buckling-restrained braced frames as a dual system

Buckling-restrained braced frames (BRBFs) have been shown to exhibit very favorable energy-dissipating characteristics. Nevertheless, low post-yield stiffness of the braces leave the system vulnerable to unfavorable behavioral characteristics such as large permanent drift. This paper presents results of a study conducted to investigate the potential benefit of using buckling-restrained braces in a dual system to minimize permanent deformations. Results from nonlinear time-history analyses demonstrate significant improvements in reducing residual story drifts using the dual system.