Cumulative Ductility Research Articles

Interstitial-Free Bake Hardening Realized by Epsilon Martensite Reverse Transformation

By investigating a metastable high-entropy alloy, we report a latent strengthening mechanism that is associated with the thermally-induced epsilon-martensite-to-austenite reverse transformation. We show this reversion-assisted hardening effect can be achieved in the same time-scale and temperature range as conventional bake-hardening treatment, but leads to both improved strength and cumulative ductility. Key mechanisms are discussed considering transformation kinetics, kinematics, strengthening and ductilization modules.

Assessing and quantifying the earthquake response of reinforced concrete buckling-restrained brace frame structures

Due to the stable hysteretic behavior, buckling-restrained braces (BRB) have been increasingly adopted in reinforced concrete (RC) frame structures to develop a dual structural system. This investigation aims to quantify the seismic behavior of newly-constructed reinforced concrete BRB frames (RC-BRBFs). The force–deformation characteristic of dual RC-BRBFs is firstly presented and the yield displacement is derived using the story shear ratio resisted by BRB system. The seismic design procedure of dual systems for different BRB configurations (including single diagonal, V-type and inverted V-type), is developed using the performance-based plastic design approach by considering BRB postyield behavior, design target drift and global yield mechanism. 126 RC-BRBF structures corresponding to different story numbers, BRB configurations and story shear ratios are designed. The influence of story shear ratios on the design results is analyzed. The seismic response of structures subjected to 22 ground motions is investigated and compared in terms of yield mode, maximum interstory drift ratio, BRB maximum ductility and cumulative ductility, and residual drift ratio. The relationship between actual and design normalized story shear of BRBs is demonstrated and a fitting equation is proposed to quantify the actual story shear ratios. The analytical results of the present study can provide quantified insights to the seismic design of RC-BRBF structures.

Development of Ductile Truss System Using Double Small Buckling-Restrained Braces: Analytical Study

Introdution: This paper proposed a Small Buckling-Restrained Brace (SBRB) for the ductile truss moment frames and is called here as the Double Braced Truss Moment Frames (DB-TMF). The braces are located at the edge of the truss girder and are only placed around the building perimeter. The braces work in pair as a weak element (structural fuses) and is expected to effectively absorb the seismic energy. The proposed DB-TMF system is an extended development of the Knee Braced Truss Moment Frames (KB-TMF). The DB-TMF system is expected to carry the whole seismic loads, while the rest of the frame is designed to carry only the gravity loads. Methods: To study the performance of the proposed DB-TMF system, non-linear finite element analysis was carried out using the DRAIN-2DX package. From the analysis with various time history records, it was found that the drift ratio of the DB-TMF system is lower than the allowed story drift. The roof-top displacement shows an asymptotic behavior. The shape of the hysteresis curve tends to have a pinching shape. However, the cumulative ductility of the proposed system satisfies the requirements as a hysteretic structure. In the event of an earthquake, only the SBRB and the chords adjacent to the column element are damaged while the rest of the structural elements remain elastic which is expected. Results and Conclusion: Based on the performance evaluation of the DB-TMF system, the DB-TMF system is suitable for moderate seismic region and has smaller dimension steel sections compared to the KB-TMF system.

A modified DEB procedure for estimating seismic demands of multi-mode-sensitive damage-control HSSF-EDBs

The core objective of this research is to develop a modified dual-energy-demand-index-based (DEB) procedure for estimating the seismic demand of multi-mode-sensitive high-strength steel moment-resisting frames with energy dissipation bays (HSSF-EDBs) in the damage-control stage. To rationally quantify both the peak response demand and the cumulative response demand which are essential to characterise the damage-control behaviour of the system subjected to ground motions, the energy factor and cumulative ductility of modal single-degree-of-freedom (SDOF) systems are used as core demand indices, and the contributions of multi-modes are included in the proposed method. A stepwise procedure based on multi-mode nonlinear pushover analysis and inelastic spectral analysis of SDOF systems is developed. Based on the numerical models validated by test results, the proposed procedure is applied to prototype structures with a ground motion ensemble. The satisfactory agreement between the estimates by the proposed procedure and the results determined by nonlinear response history analysis (NL-RHA) under the ground motions indicates that the modified DEB procedure is a promising alternative for quantifying the seismic demands of tall HSSF-EDBs considering both peak response and cumulative effect, and the contribution of multi-modes can be reasonably estimated.

Seismic performance of fish-bone shaped buckling-restrained braces with controlled damage process

A new type of all-steel fish-bone shaped buckling-restrained braces (FB-BRBs) with large maximum ductility and cumulative ductility have been proposed, and their excellent seismic performance and failure mechanism have been verified through a series of experiments in a previous study. The proposed FB-BRBs can fully utilize ductility of a material through a multiple-neck deformation mechanism. This mechanism can achieve a well-controlled damage process of different segments of the FB-BRBs. In addition, the proposed FB-BRBs can sustain tensile load-carrying capacity even after rupture of the core plate, which is owing to the interaction between the multiple stoppers of the core plate and corresponding filling plates. Both experimental and numerical studies have been conducted. However, the previous study failed to achieve the expected failure mechanism due to unexpected failure at the stoppers of the FB-BRBs. This paper aims to experimentally investigate the optimal values of the design parameters of the FB-BRBs, and further clarify the failure mechanism. Quasi-static cyclic loading tests were carried out using eight specimens with different configurations. Different failure modes of the newly proposed FB-BRBs are verified, and high seismic performance of the dampers is proved through the experimental results.

Collapse Prevention seismic performance assessment of new buckling-restrained braced frames using ASCE 41

This paper presents the results of a seismic performance assessment using ASCE 41-13 for six buckling-restrained braced frames (BRBFs) designed in accordance with the 2012 International Building Code. The correlation between ASCE 7-10 and ASCE 41-13 is investigated to compare the seismic performance anticipated by the two standards. Three archetype buildings (4-, 8-, and 16-story) with BRBFs along one principal direction are designed for seismic effects: (1) once using the equivalent lateral force (ELF) procedure and (2) a second time using the response spectrum analysis (RSA) procedure. Performance assessments are conducted using four analysis procedures, static and dynamic analyses performed under both linear and nonlinear analysis regimes. Linear analysis results indicate minor performance deficiencies in the columns and the braces. Surprisingly, the nonlinear analysis results indicate more performance deficiencies in the braces, which is opposite of the general expectation that a more sophisticated analysis would yield a less conservative result. The contributing factors to the performance deficiencies are investigated. Recommendations are made on how to alter the performance outcome such as using alternative ground motion selection approaches (e.g., conditional mean spectrum) and having acceptance criteria based on cumulative ductility demands.

Flexural Properties of Buckling-Restrained Brace Connections

Buckling-restrained braces (BRBs) achieve large peak and cumulative ductility capacities by restricting yielding to an encased core, while maintaining global stability. However, stability is often governed by the connections and is sensitive to the end fixity provided by the adjacent framing and gusset, and flexural continuity between the neck and restrainer. This paper presents simple analytical methods to determine the flexural properties of these key components. Full-depth gusset stiffeners are found to be highly effective in increasing the out-of-plane rotational stiffness (KRg), equivalent to doubling the thickness. An equivalent connection is proposed to account for the adjacent framing (KRf), but this may be neglected if KRf > 10∙KRg. This is typically satisfied if a diaphragm slab and transverse beam are provided, but may exceed beam torsional bracing requirements. The restrainer end moment transfer capacity is extended to mortar-filled RHS restrainers, confirming that neck insert ratios of Lin/Bn > 2.0 are required for full continuity.

Experimental and numerical studies of hysteretic response of triple-truss-confined buckling-restrained braces

A new type of BRBs, namely a triple-truss-confined BRB (TTC-BRB) is proposed, and its hysteretic response is investigated experimentally and numerically in this paper. The TTC-BRB is formed through introducing an additional structural system of rigid trusses to the outside of a common BRB to effectively increase its external restraining flexural stiffness and its overall load-carrying capacity, especially when it is utilized as a long-span and a heavily axially loaded brace. The TTC-BRB may be adopted innovatively as diagonal braces in mega-frame structures of high-rise buildings and in long-span spatial structures. A total number of two TTC-BRB specimens have been designed and the hysteretic responses of the two TTC-BRB specimens are experimentally investigated under a combination of standard and fatigue loading protocols. The obtained experimental results indicate that both the TTC-BRB specimens have excellent hysteretic responses as well as being able to attain stable and ample hysteretic curves under cyclic loads, with both cumulative ductility and total accumulated cycles of loading, being well above the requirements specified respectively in the AISC seismic provisions and the Chinese code GB50010 for seismic design of buildings. The experimental results obtained are compared with those obtained by numerical analysis from a simplified FE model consisting of BEAM188 element, indicating that the FE model provides good correlations with the experimental results. Moreover, relevant failure mechanism and design suggestions of the TTC-BRB specimens are discussed and provided based upon the FE results. At last, as a mega brace, the influence of its self-weight, length and imperfection are investigated numerically to reveal the performance of the TTC-BRBs under cyclic loads.

A dual-energy-demand-indices-based evaluation procedure of damage-control frame structures with energy dissipation fuses

The primary objective of this research is to extend energy balance concept in seismic behavior evaluation of low-to-medium rise frame systems with energy dissipation fuses dominated by racking deformations. At its core, energy demand indices under ground motions considering both peak responses and cumulative responses are quantified to develop a dual-energy-demand-indices-based procedure for damage-control behavior evaluation. Firstly, based on the experimentally validated hysteretic feature and representative ground motion ensembles, a parametric study is conducted considering the demand indices of the energy factor and the cumulative ductility. Results of the indices distribution and dispersion are presented in detail. Subsequently, a stepwise procedure that accounts for the peak demand and the cumulative demand is constructed. Then, the procedure is applied in prototype structures for validation. Results indicate that the consideration of dual energy demand indices is necessary for evaluation of systems with fuses, and these indices are influenced by structural nonlinear parameters and ground motions properties. The procedure based on the dual energy demand indices can be used to evaluate the structural damage-control behavior with satisfactory accuracy considering the peak response, the cumulative response, and the energy distribution along stories.

Cumulative Ductility and Hysteretic Behavior of Small Buckling-Restrained Braces

Cumulative ductility is defined as a ratio of total energy to elastic energy which is dissipated by an element of the structural system during cyclic loading. An element of the structural system is categorized hysteretic if the cumulative ductility factor fulfills certain criteria. This study investigated both analytically and experimentally Small Buckling-Restrained Braces (SBRBs). The core of bracings was modeled using Menegotto-Pinto and bilinear functions. The restrained bracing members were in the shape of square hollow steel section. They were made of the assembly of two L-shaped steel sections. From the experimental study on four SBRB specimens, it was proven that the proposed SBRBs have performed relatively stable hysteretic curves up to two percent of strain and the cumulative ductility factor of 199–450. This value is sufficient for the Buckling-Restrained Brace (BRB) elements as elastoplastic structural components. The comparisons of the hysteretic behaviors resulted by SBRB specimens using the Menegotto-Pinto functions and experiments exhibited good agreements, while the amount of energy dissipated by the SBRB specimens using the bilinear model agreed well with the experimental results. Based on the behavior of the experimental hysteretic, implementing the proposed SBRBs as components in ductile truss system is recommended.

Seismic behavior of coupled column bridge RC piers: Experimental campaign

This paper focuses on presenting an experimental campaign devised at the Laboratory of Earthquake and Structural Engineering (LESE) of Faculty of Engineering of University of Porto (FEUP), and some of its earlier stage results. The scope of said campaign consists of exploring the seismic behavior of a double-column reinforced concrete bridge bent frame with a short-spanned beam, which was designed to be applied on the construction of the Portuguese High-Speed Railway Line.As is the norm on HSRL bridges due to restricting code deformation limits, this particular application presents high stiffness to horizontal transverse loads. It is, therefore, predictable, that seismic demand on this bridge bent frame will be met with a structural performance associated with high shear load not only on the piers, but in the short-spanned beam as well, which can be a limiting factor on the global ductility achieved by the structure.In order to study this situation, reduced scale specimens were built, sharing a design goal of maximizing the shear ductility in the short-spanned beam. As such, the design approach was similar to that used in coupling beams of shear walls, for which several recommendations exist in the literature. Additionally, a new test setup is also presented, which was prepared at the LESE laboratory to accommodate the challenges of testing a frame structure under constant axial load and cyclic horizontal imposed displacements, on the specific context of this experimental campaign. The obtained results confirmed that shear ductility in the beams is a critical factor for the design of this type of structure, independent of the reinforcement layout, and that shear dominated failure is likely to occur, for lateral drift levels under 3.00%. Nonetheless, it also showed that specimens that adopt an adequate beam reinforcement layout for improved cyclic shear performance exhibit more than double the cumulative ductility of those that do not. In contrast, the columns were observed to experience relatively low damage outside the interface surfaces with the heavy shear damaged beams.

Seismic loss assessment of a structure retrofitted with slit-friction hybrid dampers

In this study a hybrid energy dissipation device is developed by combining a steel slit plate and friction pads to be used for seismic retrofit of structures, and its effectiveness is investigated by comparing the life cycle costs of the structure before and after the retrofit. A hybrid damper is manufactured and is tested under cyclic loading. It is observed that the damper shows stable hysteretic behavior throughout the loading history, and that the cumulative ductility ratio obtained from the experiment far exceeds the limit value required by the AISC Seismic Provisions. The probabilities of reaching various damage states are obtained by fragility analysis to evaluate the margin for safety against earthquakes, and the life cycle costs of the model structures are computed using the PACT (Performance Assessment Calculation Tool). According to the analysis results the slit-friction hybrid damper shows superior performance to the slit damper with the same yield strength for seismic retrofit of structures. The analysis results also show that the probabilities of reaching the limit states are minimized by the seismic retrofit with hybrid dampers combined with increasing column size. The combined seismic retrofit method also results in the lowest repair cost and shortest repair time.

Effect of Surface Modification on Cumulative Tensile Ductility of AZ31 Magnesium Sheet

Wire brushing and annealing (WBA) process was developed, optimized and utilized to modify the surface layer microstructure of AZ31 automotive magnesium sheet material. The process was carried out using softer brass wire brushes to mitigate the effect of wire brushing on surface quality and damage. The influence of modified surface grain structure and crystallographic texture was studied by continuous uniaxial tension test as well as by a newly proposed multi-step uniaxial stretching and annealing (MUSA) process to assess cumulative uniaxial tensile ductility of AZ31 sheet. A rotational speed of 2800 revolutions per minute for the wire brush with a near-zero depth of cut followed by annealing at 473 K (200 °C) for 60 minutes resulted in acceptable surface quality with a refined grain layer of depth 30 μm, and a modified crystallographic texture on the surface. Material flow behavior, grain microstructure, and texture evolution of WBA-processed material during subsequent MUSA process were analyzed to assess the role of wire brushing in enhancing the MUSA response of AZ31 sheet. Original fully annealed AZ31 sheet (in the non-WBA condition) was also subjected to identical MUSA process for comparison purposes. The results showed improvement in terminal uniaxial tensile ductility of WBA-MUSA-processed material compared to Standard-MUSA material. The ductility improvement is attributed to non-basal texture development and re-distribution of the texture, as well as to grain refinement within the highly deformed surface layer from the combination of WBA and MUSA processes.

Collapse prevention seismic performance assessment of new special concentrically braced frames using ASCE 41

This paper presents the results of a seismic performance assessment using ASCE 41-06 for six special concentrically braced frames (SCBFs) designed in accordance with the 2012 International Building Code. The correlation between ASCE 7-10 and ASCE 41-06 is investigated to compare the seismic performance anticipated by the two standards. Three archetype buildings (4-, 8-, and 16-story) with SCBFs along one principal direction are designed for seismic effects: (1) once using the equivalent lateral force (ELF) procedure and (2) a second time using the response spectrum analysis (RSA) procedure. Performance assessments are conducted using four analysis procedures, static and dynamic analyses performed under both linear and nonlinear analysis regimes. Linear analysis results indicate minor performance issues in the columns and no performance issues in the braces. In contrast, the nonlinear analysis results indicate that the braces consistently fail to meet the assessment criteria. The contributing factors to the noted performance issues with regards to ASCE 41 are investigated. Recommendations are made on how to alter the performance outcome such as using alternative ground motion selection approaches (e.g., conditional mean spectrum), using higher fidelity brace models, and having acceptance criteria based on cumulative ductility demand or energy dissipation.

Earthquake-resistant design of buckling-restrained braced RC moment frames using performance-based plastic design method

In this study, a performance-based plastic design (PBPD) method for dual system of buckling-restrained braced reinforced concrete moment-resisting frames (RC-BRBFs) is developed. Trilinear force–deformation relationship of the dual RC-BRBF system was approximated as the bilinear capacity curve to derive the yield displacement. The design base shear was determined based on the energy balance equation which accounted for the energy dissipation capacity quantified by Large Takeda model. Plastic design procedure were presented to derive the section internal forces. The proposed methodology was verified through a 5- and 10-story RC frame structures with chevron-configured BRBs. Numerical model was established and validated to assess the seismic performance through nonlinear static pushover analysis and time history analyses using FEMA P695 recommended ground motions. The analytical results show both RC-BRBFs can achieve the intended performance levels in terms of capacity curves, yield mechanism, story drift ratio distribution, residual drift, maximum ductility and cumulative ductility demands. Furthermore, the developed design procedure can be easily extended to other BRB configurated dual structural systems to achieve the desired seismic performance.

Experimental Investigation of the Hysteretic Performance of Dual-Tube Self-Centering Buckling-Restrained Braces with Composite Tendons

AbstractThis paper presents the results of experimental testing a novel dual-tube self-centering buckling-restrained brace (SC-BRB) with pretensioned basalt fiber-reinforced polymer (BFRP) composite tendons. Cyclic tensile experiments are first conducted on two sets of BFRP tendons with different diameters. The results confirm that the BFRP tendons have a stable cyclic elastic modulus and sufficient elongation capacity, making them suitable for use as the self-centering tendons in SC-BRBs. Quasi-static experiments are performed using two dual-tube SC-BRB specimens with different core plate areas. Before the failure of the self-centering system, both specimens stably exhibit the expected flag-shaped hysteresis response, with a relatively small residual deformation. The internal forces in the BFRP tendons and the gaps between the tubes and the end plates are measured to validate the performance of the self-centering system. Both specimens meet the requirements for ultimate ductility and cumulative ductility...

Experimental Study of Hysteretic Steel Damper for Energy Dissipation Capacity

This study aims to evaluate energy absorption capacity of hysteretic steel damper for earthquake protection of structures. These types of steel dampers are fabricated from mild steel plate with different geometrical shapes on the side part, namely, straight, concave, and convex shapes. The performance of the proposed device was verified experimentally by a series of tests under increasing in-plane cyclic load. The overall test results indicated that the proposed steel dampers have similar hysteretic curves, but the specimen with convex-shaped side not only showed stable hysteretic behavior but also showed excellent energy dissipation capabilities and ductility factor. Furthermore, the load-deformation relation of these steel dampers can be decomposed into three parts, namely, skeleton curve, Bauschinger part, and elastic unloading part. The skeleton curve is commonly used to obtain the main parameters, which describe the behavior of steel damper, namely, yield strength, elastic stiffness, and postyield stiffness ratio. Moreover, the effective stiffness, effective damping ratio, cumulative plastic strain energy, and cumulative ductility factor were also derived from the results. Finally, an approximation trilinear hysteretic model was developed based on skeleton curve obtained from experimental results.

Experimental Verification of Spliced Buckling Restrained Braces

A critical facility constructed in the 1980s was housed in a building whose original seismic force-resisting system included chevron-braced frames and pre-Northridge earthquake moment frames. In the mid-1990s, a code-based seismic retrofit was designed. This phased retrofit was only partially completed. A more recent seismic evaluation of the building in its partially retrofitted condition revealed major structural deficiencies. Another retrofit was designed using field-spliced buckling restrained braces (BRBs) that allowed the building to remain operational during construction. The paper summarizes the analyses performed for the seismic retrofit and the development, prototype testing and erection of the spliced BRBs. The project testing protocol was compared with current AISC Seismic Provisions' testing protocol for BRBs (AISC 341-10), which shows that if properly detailed and fabricated, BRBs used for this retrofit project can have peak and cumulative ductility well in excess of the current AISC testing criteria.

A new modular buckling restrained brace for seismic resistant buildings

This paper proposes an innovative BRB as a new energy dissipation device for earthquake resistant buildings. Its steel yielding core is modular, and this very design enables the yielding force and plastic deformation to be adjusted according to building requirements. Based on connecting several Seriated Modules, which are comprised of any constant number of Shear Basic Dissipation Units, deformation is proportional to the number of Seriated Modules and force to the number of Shear Basic Dissipation Units (on the Seriated Modules). Assembling the brace consists of sliding the greased yielding core into the restraining unit and coupling it with pins, thus providing easy inspection or replacement of the dissipation unit if required. Fully-scaled prototypes have been tested under reversal cyclic displacements and the hysteretic response has been proved stable and with a high cumulative ductility. The main parameters are the yielding force and the yielding displacement; which can be predicted with simple expressions. A methodology to design a restraining unit able to tackle of buckling by taking into account the initial sway deformation and the functional gap between the yielding core and the restraining unit is proposed. The hysteretic behavior has been simulated with conventional FEM software.

Evaluation of Ductility and Load Carrying Capacity in RC Beam-Column in Exterior Joints Enhanced with FRP

One of the techniques of strengthening of the reinforced concrete (RC) structural members is through confinement with a composite enclosure. This external confinement of concrete by high strength fiber reinforced polymer (FRP) composite can significantly enhance the strength and ductility and will result in large energy absorption capacity of structural members. An experimental investigation of the behavior of retrofitted FRP wrapped exterior beam-column joints under seismic conditions is presented. Also, the experimental study on exterior beam-column joint of a multistory reinforced concrete building under the seismic has been analyzed using ANSYS software. Two specimens were cast and tested to failure during the present investigation. One is Control specimen test up to 70% of the ultimate load (without FRP), and another specimen test up to 70% of the ultimate Load (with one layer of FRP). The results show about 18% has been obtained by retrofitting with FRP sheets in load carrying capacity. Also an increase about 54% has been obtained by retrofitting with FRP sheets in cumulative ductility.