Collapse Behavior Research Articles

Numerical investigations of seismic responses of non-isolated and isolated double-layer cylindrical reticulated shells with substructure

The seismic performance of the spatial double-layer cylindrical reticulated shell was numerically simulated using the finite element program ABAQUS, based on the data obtained from the shaking table test. And the simulated natural frequency, acceleration response, and stress response of the model are compared with the test data. The results show that the numerical analysis of spatial double-layer cylindrical reticulated shells considering lower support can accurately simulate the test results. Due to the significant impact of model vibration and other flaws on the structural reaction and the data collecting system, the precision of the test under small-seismic conditions is lower than that under large-seismic conditions. Consequently, a numerical simulation is employed to study the collapse performance of the test model. The results show that the numerical simulation can accurately investigate the failure and collapse behavior of the structure. Additionally, a numerical simulation is conducted on the shaking table test of a spatial double-layer reticulated shell structure incorporating the new three-dimensional isolation bearing. The numerical simulation results are in good agreement with the test results. However, due to the complex mechanical properties of the new three-dimensional isolation bearing, the simulation accuracy of the isolation model is less than that of the non-isolation model. Finally, the numerical simulation results show that the isolation bearing can significantly improve the seismic performance of the structure and greatly increase the safety of this kind of structure by changing the first three modes of the structure and avoiding the predominant period. The analysis conclusion of this paper will provide a good reference for the seismic isolation research and engineering practice of spatial double-layer cylindrical reticulated shell structure.

Effect of infill walls on progressive collapse behavior of self-centering precast concrete frame

To study the effect of infill walls on the progressive collapse resisting-performance of self-centering precast concrete (PC) frame structures, three 1/2 scaled, two-span and two-story self-centering PC frame specimens with and without infill walls were tested under quasi-static pushdown loading regime. The test results showed that the failure modes of self-centering PC frames were governed by concrete cracking and local spalling at the beam ends under progressive collapse scenario. Compared with self-centering bare frame, the presence of infill walls provided additional load path, thereby reducing the concrete damage at the beam ends to some extent. The full infill walls with lower strength could still increase the initial stiffness and peak resistance of self-centering bare frame to 2.47 times and 1.33 times, while the infill walls with 20% opening ratio could increase to 2.21 times and 1.19 times, respectively. Nevertheless, the infill walls also reduced the self-centering capacity of the structures. Numerical analyses further indicated that the magnitude of prestress force of steel strands between beams and columns, the strength of bed joints as well as the width of infill walls had a great effect on the progressive collapse of self-centering infilled frames. Finally, based on numerical results, a reduction factor formula was proposed to quickly estimate the structural resistance of self-centering infilled frames with different opening ratios.

Evaluating influences of deposition direction and state-dependence on large deformation processes of granular column collapse

This paper examines the impacts of deposition direction and density of granular soils on their large deformation behavior encapsulated by column collapse processes. We combine a critical state-based, anisotropic constitutive model for sand and material point method (MPM). The constitutive model includes state- and fabric-dependent dilatancy and hardening, thus accounting for the effects of density and deposition direction on the mechanical behavior of soils. The MPM model is first validated against experimental results. We then investigate the fundamental connections between local constitutive properties of soils (e.g., friction and dilation) and global column collapse response. Based on these correlations, this work further studies how material density and deposition direction influence collapse behavior, including run-out distance, residual height, and slope angle of the static region. Results indicate that run-out distance is relatively insensitive to initial soil density but can be significantly altered by the deposition direction of soils. Peak run-out distance is observed as the deposition direction is aligned with sliding band formed within the granular column. Moreover, a higher density or a smaller inclination of deposit direction leads to a greater residual height and a steeper slope of the static region. The mechanisms of above effects from soil properties perspectives are discussed.

Experimental response of HPFL-BSP strengthened RC sub-assemblages subject to corner column removal

Few existing buildings have been constructed in accordance with progressive collapse codes, resulting in poor progressive collapse behavior. Previous studies indicated that reinforced concrete (RC) structures with one lost corner column are more susceptible to progressive collapse than structures that lose a middle or edge column. To mitigate the likelihood of progressive collapse of RC structures subjected to corner column loss, we adopted a novel strengthening scheme (high-performance ferrocement laminate and bonded steel plates) to improve the progressive collapse behavior. Three one-third-scale RC sub-assemblages were constructed and tested to investigate the effectiveness of this strengthening method: control sub-assemblage, beam-strengthened sub-assemblage, and slab-strengthened sub-assemblage. The results demonstrate that beam and slab strengthening schemes can improve the static load-carrying capacity, dynamic resistance, energy dissipation, and ductility of the sub-assemblage. Moreover, the slab-strengthening scheme altered the failure modes of the beams and slabs, significantly increasing the ductility of the sub-assemblage. Consequently, the slab-strengthening scheme exhibited superior performance to the beam-strengthening scheme. Based on the energy conservation theory, the ultimate point of the sub-assemblages with a lost corner column was redefined. Furthermore, theoretical models were proposed and validated to predict the yield, peak, and ultimate loads.

Collapse behavior and mechanical response of the cobble stratum during the shield driving

The cobble stratum is prone to collapse during the shield driving. It is important to understand the collapse behavior of cobble stratum for construction safety of the tunnel. Taking Tsinghuayuan Tunnel in Beijing as the background, a test of shield tunnelling in the cobble stratum is performed using the model shield with the diameter of 280 mm. A total of 5 collapse pits occur on the ground surface during the test process. The settlements at the surface and subsurface are measured to analyze the collapse process of the cobble stratum, as well as the earth pressure in the region above the tunnel crown. The quadratic partial derivative of the settlement and earth pressure are used to judge the collapse moment of the soil. The test results show that the collapse of the cobble stratum develops with a uniform speed from the bottom to up with the shield advancing, and that the collapse region extends to the surface after the cutter head passes through the center of the collapse pit 0.5D ∼ 1.0D. Meanwhile, the final earth pressure is much smaller than its initial value only in the region above the tunnel crown, indicating the collapse region concentrating in the position directly above the crown in the cross-section. In addition, the shape of surface settlement trough changes significantly with the collapse development. Development curves of two characterization physical quantities of the surface settlement trough, i.e., the maximum settlement and width coefficient, are respectively close to the “S” shape and the inverse “S” shape.

Magnetic multi-fabrics as tools for understanding ignimbrite emplacement processes: An example from late-Variscan Tharandter Wald Caldera, Bohemian Massif

Felsic collapse calderas pose a hazard to our society, thus detailed knowledge of collapse mechanisms and behavior of eruptive products could help us to better understand the active calderas. We present a model of the eruption and collapse of Late Carboniferous Tharandter Wald Caldera (Variscan Bohemian Massif) based on field mapping and a magnetic multi-fabric approach. We investigate intra-caldera rhyolitic ignimbrites using a combination of conventional in-phase and relatively new out-of-phase anisotropy of magnetic susceptibility, along with the anisotropy of anhysteretic remanent magnetization. A two-stage caldera evolution model is proposed. (1) The high-energetic and high-temperature ignimbrites filled the paleo-valleys to form a thick ignimbrite sheet with welded to rheomorphosed central portion. Concurrently, eruptions emptied the source magma chamber triggering the piston caldera collapse. (2) The subsidence caused a monoclinal ductile bending of the still-hot and ignimbrite sheet around the caldera rim towards its center. Caldera activity was terminated by the emplacement of subvolcanic ring and radial dikes associated with hydrothermal activity. The latter likely induced abundant magneto-mineralogical alteration and formed composite fabrics. Hence, the application of the multi-fabric approach may serve as a useful tool to extrapolate reliable geodynamic proxies from the magnetic fabric of old, eroded, or altered caldera ignimbrites.

Experimental and numerical study on fire-induced collapse of double-span steel portal frames

This paper introduces experimental and numerical investigations on the fire-induced collapse behavior of double-span steel portal frames. A natural fire test was conducted on a 16 m × 6 m portal frame, and a localized collapse occurred. Thermal and displacement responses of the test frame were measured and analyzed. It was found that the steel members inside the fire compartment experienced similar temperature-time curves, which reached 1000 °C in 15 min. The heated column experienced upward expansion and downward contraction, while the side columns were pushed outside and pulled inside during the fire test. The measuring accuracy and practicability of the thermocouple, microwave radar, inclinometer, and linear variable differential transformer (LDVT) in real fire measurements were compared and evaluated. Numerical models were established in FDS and ABAQUS to simulate the thermal and structural response of the test frame and validated against experimental results, respectively. Parametric analysis was conducted on the validated numerical models with various combinations of heating conditions, heating rates, load ratios, and base stiffness. The collapse temperature of the burning frame was 1.2 and 1.1 times the temperature when the displacements of the heated side column reached their peak values along the span and height directions, respectively.

Design and analysis of buckling-induced honeycombs with tailorable out-of-plane crushing performance

Novel honeycombs with buckling-induced features and tailorable properties have been designed and fabricated using the fused deposition modeling (FDM) method. Quasi-static out-of-plane compression tests were carried out to investigate the topological dependence of the crushing behavior of the buckling-induced honeycombs (BIHs). The results demonstrated that the crushing performance of BIHs can be artificially controlled by altering their shape parameters. In particular, the initial peak force (IPF) and the undulation of the mechanical response of BIH can be effectively reduced by increasing the layer number or arranging the asymmetric layers. A finite element model validated against experimental results was also utilized to reveal the underlying deformation mechanism and study the corresponding displacement-crushing force responses for BIHs with different topological parameters. It was uncovered that the buckling-induced mechanism is beneficial for tuning the stiffness and mitigating local buckling resistance through the pre-determined collapse behavior of cell walls. Further, a multi-objective optimization process of BIH was performed to seek the optimal design solution for energy-absorbing structures in specific scenarios. The findings of this study provide a theoretical basis for the development of new ideas and optimization solutions for the design of lightweight and performance-tailored energy-absorbing structures.

An improved convected particle domain interpolation material point method for large deformation geotechnical problems

AbstractA novel material point method called the improved convected particle domain interpolation (ICPDI) is proposed in this paper to simulate large‐deformation problems in geotechnical engineering. The ICPDI framework is based on the existing convected particle domain interpolation (CPDI) and employs an adaptive orthogonal improved interpolating moving least square (AOIIMLS) shape functions. The AOIIMLS shape functions prevent computational instability problems caused by singular or ill‐conditioned matrices through avoiding the direct solving of inverse matrices. Additionally, ICPDI adopts the velocity gradient to calculate the velocity field in particle domains and reduces cell‐crossing errors by using AOIIMLS shape functions. To reconstruct the velocity function in the background grid, the velocities of the material points and four related corner points are employed through AOIIMLS shape functions. The bar axis‐aligned vibration, ring radial expansion, slope elasto‐plastic slumping, and post‐failure tunnel collapse behavior examples are used to verify the accuracy and effectiveness of ICPDI by comparing the results with other numerical methods and experiments. Numerical simulation results show that ICPDI outperforms the material point method (MPM) and CPDI in terms of computational accuracy and convergence while reducing cell‐crossing errors. Consequently, this study demonstrates the capability of ICPDI in simulations of large‐deformation geotechnical problems.

Research on the collapse characteristics of single cavitation bubble near solid particle by the VOF method

In this paper, the collapse behavior of a single cavitation bubble at different distances near a solid particle of typical scales is numerically simulated and researched with the volume of fluid (VOF) method. Based on the key parameters analysis of the pressure field, velocity vector, collapse time the tendency of cavitation bubble collapse characteristics at different distances during the change of particle size is studied with the variable of the distance and relative size between the particle and the cavitation bubble. The dimensionless distance parameter ‘γ’ is specifically presented in the simulation process, the cavitation bubble collapse impact is largely directed to the particle when 3>γ > 2, while the wall hardly affects the interaction between the cavitation bubble and the solid particle as γ > 3. The results illustrate that as the solid particle and wall exist, the distance and particle size affect both the peak collapse pressure and the collapse jet velocity of the cavitation bubble, and the influence of solid wall on the cavitation bubble at the same distance is much greater than that of solid particles. When the particle size increases, the particle gradually affects the cavitation bubble in a way similar to the wall. While as the distance decreases or the particle size increases, the influence of particle and wall on the evolution process of the cavitation bubble expands, meanwhile, the collapse pressure and collapse jet velocity of the cavitation bubble are promoted with the optimized distance and particle size, which brings marvelous cavitation effect. The numerical methods and conclusions of this paper provide a valuable reference for cavitation applications of sand-containing fluids.

Empirical formula to assess ultimate strength of side shell on passenger ship under combined axial and shear load based on experimental and numerical analysis

This study proposes an empirical formulation to assess the ultimate strength of side shells on passenger ships subjected to combined effects of axial compression and shear loads. The deteriorating effects of large openings and strengthening effects of stiffener reinforcements were considered in the proposed formulation for a wider range of applications. To verify accuracy of the empirical formula, an experimental test was first conducted to inspect the collapse behaviour and influential parameters of the side shell. More than 5000 side-shell scenarios were subsequently adopted as the input dataset based on the experimentally validated nonlinear finite element method. A simplified polynomial shape was proposed for the empirical formula by comparing various generation sets of the four-parameter-based formulations. A reliable solution to the proposed empirical formula was obtained with respect to a high determination coefficient compared to the numerical results. The developed empirical formula can be considered as applicable and beneficial for practical structural design work of side shells with large openings in modern passenger ships.

Progressive Collapse Analysis of Reinforced Concrete Multistoried Frame Structure

Abstract: The objective of this project is to analyze the progressive collapse behavior of 10 story reinforced concrete frame structures by removing column suddenly from different locations, as per the GSA guidelines. To achieve this, a structural model of the building has been developed in ETABS version 18.1.1 and loads are applied as per GSA guidelines. The design and detailing of the structure are done in accordance with IS codes, using the special moment-resistant frame linear static analysis method. In accordance with GSA guidelines, three-column removal scenarios have been studied on the ground floor, including the removal of a Corner column, Middle column of longer and Middle column of shorter side. The Demand/Capacity ratios (DCR) for each member have been calculated using the linear static analysis method. Members with a DCR ratio greater than 2 are expected to fail in a similar column removal case. Past studies have revealed that shear in a beam and columns are not crucial in progressive collapse. However, the linear static analysis method has demonstrated that beams are prone to fail in flexure.

Out of-plane failure analysis of masonry walls subjected to hydrostatic and hydrodynamic loads induced by flash floods

Damage surveys from past flash flood events show that the combined hydrodynamic impulsive loading and the subsequent hydrostatic loading due to rising water levels caused the failure of masonry walls/buildings. However, limited studies have been conducted to understand the responses of masonry walls to these loading states. To bridge this knowledge gap, an explicit 3D shell element based finite element modelling method that incorporates a homogenised anisotropic masonry material model was developed and applied to analyse the out-of-plane collapse behaviour of masonry walls under flash flooding conditions. The developed modelling method was validated with an available experimental study of masonry wall subjected to hydrostatic loading conditions. It was then extended to comprehend the behaviour of masonry walls under hydrodynamic impulsive water pressures. Results reveal that the effect of hydrodynamic impulsive loading generated by the first hit of the flash flood water is significant in reducing the stiffness of the masonry. This reduction in stiffness can result in an early collapse of the wall, even with a gradual rise of hydrostatic water level. This study has also evaluated the behaviour and damage patterns of masonry walls with two different slenderness ratios (single brick/24.5 and double brick/11.7) under flash flooding and prescribed the maximum percentage of surface area of inundation that the walls can resist. The importance of considering hydrodynamic impulsive loading in designing masonry buildings vulnerable to flash flooding and the capability of the modelling technique developed in this research for evaluating their vulnerability under these flooding scenarios are highlighted.

Volume change behavior of compacted loess under drying/wetting and freezing/thawing cycles

The long-term drying/wetting (D/W) and freezing/thawing (F/T) cycles damage the structure of the roadbed soil in loess areas, leading to a series of engineering geological disasters, such as roadbed collapse and cracking. In this study, a series of field monitoring was carried out on the Jihe Expressway, which was built on the Loess Plateau in China. It shows that drying/wetting (D/W) and freezing/thawing (F/T) cycles are important factors leading to periodic settlement and heave of loess roadbeds. A new temperature-controlled unsaturated soil triaxial apparatus was developed to explore the deformation mechanism of compacted loess under D/W and F/T cycles. The results of laboratory tests indicate that, in the isotropic stress state, both D/W and F/T cycles can reduce the void ratio and increase the volume deformation of compacted loess. In the D/W cycle, the soil samples show the collapse behavior, but the deformation of heavily over-consolidated samples is relatively less compared with lightly over-consolidated samples. On the other hand, repeated F/T cycles lead to fluctuating changes in the volume of compacted loess. Increasing the dry density can effectively reduce the deformation caused by F/T cycles. Moreover, the combination of the D/W and F/T cycles may further enhance the volume changes of the compacted loess. As the number of D/W and F/T cycles increases, the compressibility and irrecoverable deformation of the compacted loess increases, leading to a deterioration of its engineering properties.

Ultimate strength assessment of rectangular plates subjected to in-plane compression using a statistical model of welding initial deflection

Stiffened panels in steel ships and offshore structures are usually fabricated by fillet welding to attach stiffeners to a plating. Thermal contraction due to the welding causes angular distortion of the plate along the stiffeners, and the plate initially deflects. This welding initial deflection significantly affects the ultimate strength and collapse behavior of the stiffened panels, and it is one of the important uncertainty factors in ultimate strength assessment. This study proposes a methodology to quantify the uncertainty of the ultimate strength of rectangular plates due to the welding initial deflection. This paper has twofold. One is the development of a statistical model of the initial deflection shape based on measured data in past studies. Bayesian statistics is adopted since it can consider uncertainty accompanied by the insufficient number of measured data. A regression model of the initial deflection is selected as the best model from several candidate models based on an information criterion. The other is the assessment of probability distributions of the ultimate strength of simply supported rectangular plates. The probabilistic distributions of the ultimate strength are calculated by Monte Carlo simulation using a nonlinear finite element method. Initial deflection samples are generated from the developed statistical model and applied to finite element models of the rectangular plates. The analysis result indicates that the probability distribution of the ultimate strength depends on the collapse mode which is changed by the initial deflection shape. As a usage example of the proposed methodology, existing formulas of the ultimate strength are evaluated and adjusted to give safe side estimations for design.

Unsteady cavitation dynamics and pressure statistical analysis of a hydrofoil using the compressible cavitation model

A compressible cavitation model is developed in this paper, in which the bubble wall velocity is obtained by solving the compressible Rayleigh–Plesset (R–P) equation. Additionally, vapor compressibility is also included during evaporation/condensation to correct the phase change rate. The predicted results around a National Advisory Committee for Aeronautics (NACA) 66 (mod) hydrofoil are compared with the available experimental data, and a satisfied agreement is obtained. By (mod), we mean the NACA 66 hydrofoil modified by Brockett [“Minimum pressure envelopes for modified NACA-66 sections with NACA a = 0.8 camber and BuShips type I and type II sections,” Technical Report No. 1780 (David Taylor Model Basin Washington DC Hydromechanics Lab, 1966)] and Valentine [“The effect of nose radius on the cavitation-inception characteristics of two-dimensional hydrofoils,” Technical Report No. 3813 (Naval Ship Research and Development Center, 1974)]. Several crucial flow properties, e.g., fluid compressibility, cavitation evolution features, and pressure statistical characteristics, are studied in detail. The results suggest that the developed compressible cavitation model is better suited for predicting the collapse behavior of cavitation. Moreover, our work captures the liquid re-entrant jet and bubbly shock waves well and reveals that these two mechanisms jointly dominate the cavity shedding dynamics. Shock-induced pressure pulses play a more important role in flow features, with a maximum amplitude exceeding 200 kPa, significantly larger than the pressure pulse caused by liquid re-entrant jets. Finally, the statistical analysis indicates that the pulsating pressure presents non-Gaussian nature with positive skewness, and shock waves exhibit high-frequency and high-energy characteristics.

Experimental and Numerical Study on Progressive Collapse of the Midcolumn in a Glulam Timber Frame Exposed to Fire

This paper presents experimental and numerical investigations on the progressive collapse behavior of a two-story glulam frame when the middle column is exposed to ISO834 standard fire. The stress characteristics, temperature distributions, and deformation relationship curves of the bottom middle column after a fire are obtained. The collapse resistance performance and the mechanism of the glulam structure under local fire are studied in combination with the failure mode of the frame. The experimental results show that the failure time of the middle column in fire is 16.8 min, and the time to determine the progressive collapse of the structure is 17.17 min when the rotation angle exceeds the limit. The structure can remain stable for some time after the failure of the fire column, but as the fire continues to spread, the structure will collapse further. In addition, a temperature-field analysis model with the grid element type of DC3D8 and a structural field analysis model with the grid element type of C3D8R was established by using ABAQUS software under the experimental conditions. The numerical simulation is carried out by means of thermal–mechanical sequential coupling. The numerical simulation results show that the temperature of the beam end rose to more than 300 °C in about 15 min although it was not directly exposed to fire. The temperature of the whole connector at the pillar foot in the bottom column reached more than 700 °C when the fire time reached 60 min. The numerical simulation results agree well with the experimental results. The analysis results show that, in the failure process of the fire column, the junction of beam ends begins to produce stretching force to form a catenary effect. As the fire time increases, the catenary effect eventually fails. The stretching force at the beam end rapidly decreases and withdraws from the work, causing the progressive collapse of the frame.

Progressive collapse behaviour of composite substructure with large rectangular beam-web openings

This study explores the progressive collapse resistance of composite substructures with the fully-welded connection (FC) and fully-welded connection with rectangular web openings (FCRO). Quasi-static loading tests were conducted to analyze failure modes, internal forces, and resistance mechanisms. The effect of substructure's boundary constraints on its anti-collapse behaviour was investigated through validated numerical models. The results show that the damage mode of the FC specimen involves tensile beam flange fracture at the beam root, while the FCRO specimen experiences fracture of the rectangular web openings. The resistance development of the FCRO specimen includes bending, bending-catenary mixed, and catenary stages, whereas the FC specimen undergoes bending and bending-catenary mixed stages. In the bending-catenary mixed stage, the FCRO specimen exhibits a 69.2% higher maximum resistance and a 15.3% larger displacement compared to the FC specimen. Despite the reduction in flexural capacity, incorporating large rectangular openings in the beam web enables plastic hinge to shift outward at the beam root, promoting the effective evolution of the composite beam’s axial force. The study derived expressions for the boundary axial constraint coefficient and attenuation coefficient to the FCRO specimen. Traditional strengthening methods were found to have limited effectiveness in enhancing the collapse resistance of unreinforced composite substructures. Consequently, a novel and effective construction measure was proposed, resulting in a significant enhancement of 78% in maximum resistance and 85% in corresponding deformation of the substructure.

Innovative scheme for RC building progressive collapse prevention

Progressive collapse of reinforced concrete (RC) building due to column failure can cause human casualties and severe irreparable damage or total collapse of the building. Different methods have been presented to mitigated progressive collapse of RC buildings; however, most of them are installed externally after construction and are costly, demanding, and require manufacturing mitigating elements such as steel cables, steel devices, or composites. This study presents an innovative mitigating scheme to improve the progressive collapse resistance of such buildings. The proposed scheme applies during construction and comprises of adding short wasted leftover steel bars from the construction site with special configuration in the slab around potential failed interior column. To examine the effectiveness of the proposed scheme, three-dimensional nonlinear fiber element-based model was developed, validated, and utilized for the analysis of such buildings. The findings of the study show that the proposed scheme improved progressive collapse behavior of the building with a percentage increase in total dissipated energy up to 241.8%. The scheme is eco-efficient and cost effective as it requires minimum amount of material, saves energy required to produce new steel bars, and can serve as an effective solution to mitigate progressive collapse of RC buildings subjected to column failure.

Performance-based seismic design and vulnerability assessment of concrete frame retrofitted by metallic dampers

Concrete frame has been one of the most widely employed structural types in engineering practice and would also have widespread application in the future. However, severe failure even collapse behavior were also detected for the pure concrete frame in strong earthquakes. So it is necessary to improve the seismic performance of pure concrete frame. This paper aims to analyze the seismic performance of metallic damper retrofitted concrete frame. Three concrete frames with metallic damper were selected as the research objects. The performance-based seismic design using the equivalent energy method was employed to design the prototype buildings, in which the multi performance objectives were considered. The concrete beam and column was designed taking the additional forces caused by the metallic damper into consideration. Further, the numerical model of the concrete frame with metallic damper was developed and verified by the test results. Time-history analyses were performed under frequently-occurred, design-based and maximum considered earthquakes to validate that the seismic performance of prototype buildings complied with the design objectives. Subsequently, seismic vulnerability of three prototype buildings were evaluated in terms of non-collapse and collapse fragilities. The analytical results indicated the performance-based design method is suitable to design the concrete frame with metallic dampers and the metallic damper could significantly improve the seismic vulnerability of pure concrete frame. This paper is beneficial for the design and application of metallic damper in concrete frames.