Residual Inter-storey Drift Research Articles

Displacement-based design procedure for the seismic retrofit of existing buildings with self-centering dissipative braces

Existing framed buildings, especially those designed according to outdated seismic codes, often offer inadequate seismic protection levels due to material degradation, low amount of reinforcement and poor construction details. Among the possible retrofit strategies, elasto-plastic dissipative braces (EPDBs) can be installed to provide supplemental stiffness and energy dissipation in the main resisting frame. Since they are based on the plastic deformation of sacrificial steel components, EPDBs are inherently affected by scarce recentering capability, i.e., presence of residual deformation at the end of the mainshock that could impair their effectiveness for aftershock events. As demonstrated in recent seismic sequences, there might be not enough time to restore (e.g., though hydraulic actuators and a reaction frame) the undeformed configuration of the structure before a subsequent shock. This issue can be overcome through self-centering dissipative braces (SCDBs), i.e., braces equipped with dampers characterized by a “flag-shaped” hysteretic behavior, which inherently facilitates the immediate re-centering of the frame. Despite this evident benefit, there is still lack of practical design procedures for the seismic retrofit of buildings through SCDBs. To fill this gap, a direct displacement-based design procedure for SCDBs tailored to building frames is here conceived and illustrated. The proposed method aims at achieving simultaneously two performance requirements: (i) a target maximum roof displacement under the ultimate-limit-state seismic event; (ii) the absence of significant residual inter-storey drifts at the end of the shaking. The implementation of the procedure is described by two applications to a steel and to a reinforced concrete case-study building. Nonlinear time-history analyses are carried out to prove the effectiveness of the proposed method, along with a comparison of the seismic performance offered by SCDBs versus traditional EPDBs implemented in the same case-study buildings.

Seismic strengthening of isolated RC framed structures through orthogonal steel exoskeleton: Bidirectional non-linear analyses

The catastrophic effects of recent earthquakes around the world have highlighted the vulnerability of civil buildings; in Europe, most of the existing buildings were built after World War II and since they have largely exceeded their useful life, are characterized by a high vulnerability linked both to the durability of the materials and to the lack of seismic provisions in design. The current trend in constructional field is to design interventions aimed at the seismic and energy improvement of these structures jointly, in order to achieve a sustainable and integrated retrofit intervention. To this aim, the use of 2D orthogonal steel exoskeletons for the seismic strengthening represents a suitable solution, providing at the same time an enhancement in thermal insulation, through a ‘double-skin’ solution. Due to the growing interest in the design of steel exoskeleton interventions, a detailed dynamic characterization of this external strengthening solution is needed. In this framework, the present work, aims to investigate the effectiveness of the investigated strengthening solution by means of bi-directional non-linear dynamic analyses. Extensive numerical analysis was carried out. The selected case-study is an Italian existing pre-1980 s RC frame building located in Mugnano di Napoli (NA, Italy), which is a medium-high seismic hazard site in Italy (peak ground acceleration equal to 0.156 g). Two alternative strengthening solutions were numerically investigated by means of non-linear time-history and incremental dynamic analyses performed applying fifteen bidirectional ground motions on three-dimensional numerical models. The results of the dynamic non-linear analyses allow to quantify more appropriate performance indicators, both in terms of expected demand and overall collapse capacity, useful for the development of optimization strategy and design of exoskeleton system. The results highlighted that both the investigated strengthening scenarios allow to increase the stiffness of the existing building and allow it to meet the current code safety requirements reducing also the residual inter-storey drift. The obtained results are not strictly related to the investigated case study, but can be extended to all the structures retrofitted that follows the presented design procedure.

Wind hazard on earthquake damaged buildings

AbstractThis study proposes a holistic approach to multihazard performance‐based assessment of a tall steel building, partially damaged by earthquake, and then subjected to wind. The case study is a 16‐storey LD‐CBF building in Montreal, designed in accordance with the Canadian code and steel standard. Advanced numerical models are developed in OpenSees; hence, they account for material nonlinearity including low‐cycle fatigue to simulate brace fracture. Wind histories are generated from wind tunnel data. The sequence of analyses is: (i) design the LD‐CBF building to respond to code‐based earthquake (2475 years return period) and verify the LD‐CBF members to design wind load (1‐in‐500 years), as well as, the interstorey drift under the service wind (1‐in‐10 years); (ii) apply the 60 min. wind load history on earthquake damaged building; (iii) assess the building response in terms of interstorey drift and residual interstorey drift, and (iv) compare the results of the case study under (1) earthquake on intact building, (2) wind on intact building, and (3) wind on earthquake damaged building. The findings are significant and allow the realistic representation of the effects of multiple hazards on steel buildings. In summary, the consequent hazard on building safety has a detrimental effect.

Performance-based wind and earthquake design framework for tall steel buildings with ductile detailing

According to the Canadian building code, wind design relies on prescriptive static methods, which lead to a conservative design. In consequence, in moderate seismic regions where both winds and earthquakes are critical, the size of ductile members resulting from seismic design, and especially those of bottom floors, may not accommodate the elastic wind demand and larger member sizes are required. In general, this is the case of rectangular buildings, where in the direction perpendicular to the largest building dimension, the base shear due to elastic wind demand is critical, while in the orthogonal direction the seismic demand governs. Hence, in one direction, the allowable base shear increases above the seismic demand, which results in reduced energy dissipation and amplification of torsion. To mitigate the incoherence in the current building code, a refined code-based multi-hazard design approach, targeting performance of tall steel buildings in Eastern Canada, is proposed. Thus, accounting for the building’s overstrength and allowing limited controlled inelasticity under high-intensity wind, a wind-related reduction factor RW is proposed to reduce the design wind load. The method is implemented for the design of two identical 15-storey steel braced frame buildings, but of different occupancy, hospital and office, respectively. Nonlinear response history analyses are performed to verify the member sections of steel braced frames, while the parameters investigated are the interstorey drift, residual interstorey drift and floor acceleration. Then, seismic and wind incremental dynamic analyses provide insight into the multi-hazard dynamic response of buildings subjected to ground motions and winds of increasing intensity. The fragility concept is used to quantify the performance of studied buildings designed with RW = 2 versus the building designed with RW = 1. Comfort criteria, as well as, the drift acceptance criteria, commonly considered in research and practice, are used to verify the effectiveness of the proposed method. The nonlinear response of the studied buildings at the design level and beyond shows that using RW = 2 for wind design does not change the response at design level, but slightly decreases the collapse capacity within the acceptable range.

Mechanical model and seismic performance of frames with a self-centring connection

The desired structural performance of a novel self-centring pinned beam–column connection with friction dampers (SC-PC-FD) has been reported. An accurate mechanical model of the SC-PC-FD connection is required for easy modelling of frames with these connections using common commercial structural analysis and design software. This paper presents a simple mechanical model for a SC-PC-FD connection. The accuracy of the model was verified using results from experimental and numerical studies on two-strand and four-strand SC-PC-FD connections. Moreover, the seismic performance of frames with SC-PC-FD connections was evaluated using incremental dynamic analysis and compared with that of moment-resisting frames. For this purpose, one-, three- and five-storey building models with moment connections and SC-PC-FD connections were designed. The two-dimensional frames were subjected to far-field, pulse near-field and no-pulse near-field earthquake records and the collapse margin ratios (CMRs) and fragility curves of the models were obtained. The developed component-based mechanical model accurately predicted the monotonic and cyclic behaviour of the SC-PC-FD connection. With the novel SC-PC-FD system, the maximum residual interstorey drift ratio and the number of developed plastic hinges at the main members of the self-centring models were reduced significantly, while the CMRs were increased.

Self-centring hybrid-steel-frames employing energy dissipation sequences: Insights and inelastic seismic demand model

This paper explored the seismic behaviour of self-centring hybrid-steel-frame (SC-HSF) employing energy dissipation sequences and the corresponding inelastic seismic demand model. The SC-HSF employing energy dissipation sequences was composed of the self-centring main frame (SCMF) and energy dissipation bays (EDBs). Two prototype structures were designed and developed using modelling techniques validated by experimental data. Nonlinear cyclic pushover analyses and nonlinear dynamic analyses were conducted to examine the seismic behaviour of the prototype structures. The seismic response of prototype structures including peak interstorey drifts and post-earthquake residual interstorey drifts were examined in detail. After verifying the promise of the SC-HSF structures, the energy factor for quantifying the inelastic seismic demand was developed by nonlinear spectral analyses based on the equivalent single-degree-of-freedom (SDOF) systems assigned with the structural hysteretic model. The effects of the structural hysteretic parameters on the mean and probabilistic features of the energy factors were discussed in detail. In addition, the lognormal distribution was selected to develop a probabilistic spectral seismic demand model based on a comparative study, and the prediction equations were developed to simulate the probabilistic features of the energy factors. Finally, the probabilistic spectral seismic demand model was used for evaluating the behaviour of the prototype structures, and the sufficiency of the model was justified.

Performance‐based assessment of seismic‐resilient steel moment resisting frames equipped with innovative column base connections

AbstractLow‐damage and self‐centring column base connections have been proposed in the last two decades as innovative solutions able to provide the seismic resilience in Moment Resisting Frames (MRFs). Although many works have demonstrated the benefits deriving from the adoption of these systems, only a few research studies investigated the significant parameters influencing their self‐centring capability. This paper investigates the influence of the frame layout (i.e., storeys and bays number) on the seismic performance of perimeter MRFs equipped with damage‐free self‐centring column bases previously studied by the authors. Nine case‐study perimeter steel MRFs are designed and modelled in OpenSees. Incremental Dynamic Analyses are performed monitoring both global and storey‐level Engineering Demand Parameters, including peak and residual interstorey drifts. Fragility curves are subsequently used to evaluate the self‐centring capability of the structures. The present study provides insights on the use of the adopted connections for the residual drift reduction of MRFs and defines the boundaries of the investigated parameters for their application. Results highlight that the self‐centring behaviour is particularly sensitive to the number of storeys and tends to reduce with the increasing height of MRFs equipped with the proposed connections.

Replaceability evaluation method of shear link for RCS hybrid frame

A reinforced concrete column and steel beam (RCS) hybrid frame structure with replaceable members was proposed in this paper. Non-linear pushover analyses were conducted to investigate the overall mechanical performance of the proposed structural system. Based on the residual deformation of replaceable links after an earthquake, a method for evaluating the replaceability of members of the RCS hybrid frame was proposed. The acceptable residual inter-storey drift and residual rotation drift at the end of the link were adopted as the two indices in this method. Numerical models and full-scale experiments were performed to systematically investigate the stress and deformation of the entire section of the replaceable steel links. The residual deformation was shown to increase with an increase in the inter-storey drift (θ) and decrease with an increase in the length ratio. Then the control values of the acceptable residual deformation indices were determined through a statistical analysis of the residual deformation of links with different length ratios and link-column connection modes: when the residual inter-storey drift was less than 0.0048 rad and the residual rotation drift at the end of the links was less than 0.0074 rad, the link could be easily replaced. These findings can provide reference for similar structural designs.

Performance-based assessment of seismic-resilient steel moment resisting frames equipped with innovative column base connections

Many recent research studies have focused on developing innovative seismic-resilient structural systems to reduce repair costs and downtime in the aftermath of an earthquake. In this regard, dealing with steel Moment Resisting Frames (MRFs), recent research works have demonstrated the benefit deriving from the adoption of both low-damage and self-centring column base connections, both in terms of damage and residual drifts reduction. Although several technologies have been developed in this direction, only a few research studies investigated the significant parameters influencing the self-centring capability of these systems. Within this framework, the present study investigates the influence of the frame layout (i.e., storeys and bays number) on the seismic performance, including the self-centring behaviour, of perimeter MRFs equipped with damage-free self-centring column bases previously studied by the authors. Nine case-study perimeter steel MRFs are designed and modelled in OpenSees. Incremental Dynamic Analyses are performed with a set of 30 ground motion records while monitoring both global and storey-level engineering demand parameters, including peak and residual interstorey drifts. Fragility curves are successively used to evaluate the self-centring capability of the structures. The present study provides insights on the use of the adopted connections for the residual drift reduction of MRFs and defines the boundaries of the investigated parameters for their application. Results highlight that the self-centring behaviour is particularly sensitive to the number of storeys and tends to reduce with the increasing height of MRFs equipped with the proposed connections.

Mainshock‐aftershock state‐dependent fragility curves: A case of wood‐frame houses in British Columbia, Canada

SummaryDuring a mainshock‐aftershock (MSAS) sequence, there is no time to retrofit structures that are damaged by a mainshock; therefore, aftershocks could cause additional damage. This study proposes a new approach to develop state‐dependent fragility curves using real MSAS records. Specifically, structural responses before and after each event of MSAS sequences are used to obtain statistical relationships among the engineering demand parameter prior to the seismic event (pre‐EDP), the intensity measure of the seismic event (IM), and the engineering demand parameter after the seismic event (post‐EDP). The developed fragility curves account for damage accumulation, providing the exceeding probability of damage state (DS) given the IM of the event and the DS of the structure prior to the seismic excitation. The UBC‐SAWS model, which was developed for wood‐frame houses in British Columbia, Canada, is considered as a case study application. Results indicate that for the examined structural typology, state‐dependent fragility curves based on residual interstorey drift ratio (pre‐EDP), peak ground velocity (IM), and maximum inter‐storey drift ratio (post‐EDP) are the best choice to characterise the cumulative damage effect. An illustration of the developed fragility curves is provided by considering a hypothetical MSAS scenario of a Mw 9.0 Cascadia mainshock triggering a Mw 6.0 crustal event in the Leech River fault, affecting wooden houses in Victoria, Canada. The MSAS scenario increases Yellow tags (restricted access) by 12.3% and Red tags (no access) by 4.8%.

Comparison of different distributions of viscous damper properties in asymmetric-plan frames

In this article, one of the procedures to design viscous dampers proposed in literature is applied to 3D asymmetric-plan buildings, considering different distributions for the damping coefficients, which are assumed to be proportional to specific structural or response parameters. The main purpose was to investigate the effectiveness of different vertical and in-plan distributions of the damping coefficients of nonlinear viscous dampers for the seismic retrofit of existing buildings. For comparison purposes, all the distributions were applied utilizing both a simplified and an extended method for the 3D structures, where the simplified method takes into account only the translation in the seismic direction, and the extended method considers the translations along the two orthogonal directions together with the floor rotations. The proposed distributions were then applied to a typical case study involving an asymmetric-plan six-storey RC building. The effectiveness of the different distributions was examined through time-history analyses, assuming nonlinear behaviour for both the viscous dampers and the structural elements. The results of the nonlinear dynamic analyses were examined in terms of maximum and residual inter-storey drifts, peak floor accelerations and maximum damper forces.

Seismic drift response of seesaw-braced and buckling-restrained braced steel structures: A comparison study

A numerical comparison study of the interstorey and the residual interstorey seismic drifts of steel structures equipped with the seesaw system and buckling-restrained braces is carried out. This investigation involves inelastic time-history seismic analyses of 2-, 5- and 8-storey 3-D steel structures, with specific orientation of columns and configuration of braces, for the design basis earthquake. The effects of soil-structure interaction and seismic incident angle are also considered in these analyses. Comparison of the seismic drift responses experienced by the seesaw-braced and the buckling-restrained braced steel structures, reveals different peak interstorey drift values but in many cases similar drift concentration along the height of the structures. Furthermore, the seesaw-braced steel structures exhibit, in general, larger peak residual drifts than buckling-restrained braced steel structures.

Seismic response of low-rise 3-D steel structures equipped with the seesaw system

The efficiency of the seesaw system when applied to low-rise 3-D steel structures is presented in this paper. This efficiency is judged by several seismic response results coming from inelastic seismic time-history analyses of 2-, 5- and 8-storey steel structures. These response results involve height wise distributions for peak interstorey drift ratios (IDR), peak residual interstorey drift ratios (RIDR) and plastic hinge formations in frame elements as well as peak forces to spiral strand ropes and viscous dampers of the seesaw system. For the foundation of the steel structures, different soil types are considered in order to assess the effects of soil-structure interaction (SSI). The seismic incident angle is also taken into account. From the results presented it is concluded that the seesaw system, essentially working always in tension, constitutes a bracing solution that can be potentially proposed by seismic codes as an alternative seismic force resisting system for low-rise steel structures.

Seismic Response of Steel Structures Equipped with the Seesaw System

ABSTRACTThis work provides seismic response results from non‐linear seismic analyses of low‐rise 3‐D steel structures equipped with the seesaw system. In particular, seismic response results involving height wise distributions for peak interstorey drift ratios (IDR) and peak residual interstorey drift ratios (RIDR) as well as plastic hinge formations are obtained for 2‐ and 8‐storey fixed‐base steel structures. Additionally, soil‐structure interaction is considered for these steel structures and its effect in the aforementioned seismic response results is discussed. It is concluded that the seesaw system constitutes an attractive solution for low‐rise 3‐D steel structures as buckling problems associated with common steel braces are eliminated and their damping capacity increases considerably.

Seismic performance assessment of conventional CLT shear wall structures and post-tensioned CLT shear wall structures

This paper presents the performance-based seismic assessment framework on conventional CLT shear wall structures (C-CLTStrs) and post-tensioned CLT shear wall structures (PT-CLTStrs). Numerical models of both the conventional CLT shear walls and the PT CLT shear walls were developed and calibrated with experimental results. A direct displacement-based design (DDD) procedure was then developed and demonstrated by the design examples of one 8-storey C-CLTStr and a set of 8-, 12-, and 16-storey PT-CLTStrs. Corresponding simplified structural models were developed. A series of pushover and time-history dynamic analysis was conducted afterwards to calibrate the calculated structural performance objectives with the design targets of the DDD procedure. Finally, using 50 mainshock (MS) and 50 mainshock-aftershock (MSAS) earthquake records, probability seismic demanding analysis (PSDA) were conducted to evaluate two engineering demanding parameters of the structures, namely the maximum inter-storey drift (MaxISDR) and the residual inter-storey drift (ResISDR). The MaxISDR limit states of the PT-CLTStrs are recommended at 0.7%, 1.4%, and 2.2% for the immediate occupancy (IO), life safety (LS), and collapse prevention (CP) hazard levels, respectively. The MaxISDR of the PT-CLTStrs is almost twice that of the C-CLTStrs, while the ResISDR is at most 50% of that of the C-CLTStrs. The damage probability of the 8-storey PT-CLTStr indicated by ResISDR is not significantly sensitive to the consideration of aftershocks seismic input, whereas, when aftershocks are considered, up to a 7.0% difference under the LS hazard level is caused in the damage probability of the 8-storey C-CLTStr indicated by ResISDR.

Use of energy-dissipative rocking columns to enhance seismic performance of buckling-restrained braced frames

Buckling-Restrained Braced steel frames (BRBFs) exhibit well-controlled seismic behavior due to their excellent lateral load resisting capacity and energy dissipation capacity. However, they always suffer from concentration of inter-storey drifts and excessive residual deformations in weak/soft stories under strong earthquakes. A novel system of Energy-Dissipative Rocking Column (EDRC) is proposed in this paper to improve the seismic performance of multi-storey BRBFs. It consists of dual hinge supported steel column branches and replaceable steel strip dampers between them. Nonlinear time historey analyses are conducted on a six-storey prototype BRBFs with EDRCs to investigate the effectiveness of EDRCs on improving the seismic performance of BRBFs under different levels of earthquakes. It is found that the EDRC can not only mitigate the maximum and residual inter-storey drifts, but facilitate more uniform distribution of inter-storey drifts. A rational range of EDRC stiffness ratio less than 0.2 is recommended for the seismic design of BRBFs with EDRCs.

Geosynthetic-reinforced cushioned piles with controlled rocking for seismic safeguarding

In this study, a cushioned pile foundation reinforced with geosynthetics is proposed to protect buildings and foundations from seismic energy. This composite foundation utilises piles to control foundation settlement while the geosynthetic-reinforced cushion modifies the dynamic structural characteristics and the load transfer mechanism. The seismic performance of this proposed foundation system is evaluated numerically using FLAC3D software. A fully coupled nonlinear dynamic analysis was conducted in the time domain. The variation of shear modulus corresponding to shear strains in the soil is used to simulate the dynamic behaviour of the soil, while the influence of the plasticity index is also captured. The soil-geosynthetic interface utilises the Mohr-Coulomb failure criterion to capture possible sliding and pull-out of the reinforcement layers. 3D numerical predictions of the tensile forces mobilised in the geosynthetic layers, the shear forces, the lateral deformations and maximum and residual inter-storey drifts in the building are presented and discussed in this paper, as well as how the shear forces and bending moments develop in the piles, and the lateral pile displacements. The results indicate that the proposed geosynthetic-reinforced cushioned pile foundation can provide design engineers with an alternative solution for safeguarding buildings constructed on soft soils in earthquake-prone regions.

Novel application of geosynthetics to reduce residual drifts of mid-rise buildings after earthquakes

Geosynthetics have been used in variety of geotechnical engineering projects, such as ground improvement, erosion control, slope stabilisation and foundation strength improvement and they have been proved to be cost and time effective in many cases. In this study, a geosynthetic reinforced composite soil (GRCS) foundation system is proposed for seismic protection of mid-rise buildings supported by a shallow foundation potentially suffering from residual structural drift or permanent foundation settlement. To evaluate the proposed GRCS, a conventional reinforced concrete moment resisting building sitting on this composite ground under the earthquake excitations of 1978 Tabas, 1994 Northridge and 1995 Kobe was numerically simulated using FLAC3D software. The effect of soil-structure interaction (SSI) was captured using direct method of analysis adopting a three-dimensional numerical model. By adopting direct calculation method, the soil deposit, the geosynthetic reinforcement, the foundation and the structure were simulated simultaneously. Inelastic behaviour of the structure was considered, while hysteretic damping algorithm was adopted representing the variation of the shear modulus and corresponding damping ratio of the soil with cyclic shear strain capturing the energy dissipation characteristics of the soil. Both material and geometry nonlinearities were taken into account at the interface between the foundation and ground surface. The results are then presented in terms of mobilised tensile force in geosynthetic layers, the response spectra at bedrock and ground surface level, the shear force developed in the superstructure, the maximum foundation rocking angle, the maximum lateral deflection, the maximum inter-storey drift, and most importantly the residual inter-storey drift and permanent foundation settlement. The results showed that the proposed GRCS could offer design engineers a rational and cost-effective alternative solution to conventional deep foundations such as pile foundations, particularly for mid-rise buildings potentially suffering from earthquake-induced residual drifts and permanent settlements.

Peak and residual responses of steel moment-resisting and braced frames under pulse-like near-fault earthquakes

This paper presents the behaviour of steel moment resisting and braced frames under pulse-like near-fault earthquakes. The key properties for characterizing near-fault ground motions with forward directivity and fling step effects are discussed, and the influence of varying brace properties on the key engineering demand parameters such as maximum inter-storey drift (MID), residual inter-storey drift (RID) and peak absolute floor acceleration (PA) is revealed. Among other findings, it is shown that the structural responses are related to spectral accelerations, PGV/PGA ratios, and the pulse period of near-fault ground motions. The moment resisting and self-centring braced frames (MRFs and SC-BRBFs) generally have comparable MID levels, while the buckling-restrained braced frames (BRBFs) tend to exhibit lower MIDs. Increasing the post-yield stiffness of the braces decreases the MID response. The SC-BRBFs generally have mean residual drifts less than 0.2% under all the considered ground motions. However, much larger RIDs are induced for the MRFs/BRBFs under the near-fault ground motions, suggesting that these structures may not be economically repairable after the earthquakes. From a non-structural performance point of view, the SC-BRBFs show much higher PA levels compared with the other structures. A good balance among the MID, RID, and PA responses can be achieved when “partial” SC-BRBs are used. To facilitate performance-based design, RID prediction models are finally proposed which enable an effective evaluation of the relationship between MID and RID.

Seismic performance of reinforced concrete frames retrofitted using external superelastic shape memory alloy bars

Pre-1970s designed and built reinforced concrete frame structures are considered unsafe when subjected to seismic loads. Insufficient anchorage of the beam reinforcement in the beam-column joints of these structures is considered a main deficiency. Newly built frame structures are seismically designed for safety, where high inelastic deformations can occur under moderate to strong earthquakes. Minimizing these inelastic deformations makes the structure repairable. One way to minimize these residual deformations is by using smart materials such as superelastic shape memory alloys (SMAs). In this paper, the seismic performance of RC frames retrofitted using external superelastic SMA bars is investigated and compared to the behaviour of a regular steel RC frame structure. Nonlinear time history analysis is performed for a six storey RC frame structure located in a high seismic region. After performing the analysis, two retrofitted frames are assumed and analyzed at the load intensities causing failure of the steel RC frame. The performance of the retrofitted frames is compared to the steel RC frame in terms of the damage level, the Maximum Inter-Storey Drift (MID) ratio, Maximum Residual Inter-Storey Drift (MRID), Maximum Roof Drift Ratio (MRDR), Residual Roof Drift Ratio (RRDR), and the earthquake intensity at collapse. Analysis results show improved seismic performance for the two retrofitted frames as compared to the original steel RC frame. This improvement was represented by lower level of damage at the same earthquake intensity; small reduction (10–15%) in the MID and MRDR values; significant reduction (50–70%) in the MRID and RRDR; and increased seismic capacity.