Bi-directional Ground Motions Research Articles

Multihazard resilience and economic loss evaluation method for cable-stayed bridges under the combined effects of scour and earthquakes

Cable-stayed bridges (CSBs) commonly experience scour-induced foundation issues during their service life, impacting both structural seismic resilience and economic losses. Nonetheless, these aspects remain inadequately addressed in existing seismic codes. This paper presents a comprehensive probabilistic multihazard fragility, resilience, and economic loss evaluation method for CSBs influenced by scour and earthquakes. Numerical models with various scour depths considering epistemic uncertainties in loads, structural properties, and soil conditions are first established using the Latin-hypercube sampling (LHS) method. Incremental dynamic analyses (IDAs) are then conducted on these models in cases with near-fault and far-field bidirectional ground motions, yielding probabilistic multihazard demand models and component- and system-level multihazard fragility surfaces for diverse limit states. Subsequently, resilience and economic losses are comparatively evaluated by integrating damage probabilities with corresponding uncertain functional recovery functions. Eventually, a rapid bridge traffic capacity evaluation method based on the critical traffic capacity surface concept is devised to effectively assess CSB open patterns under various peak ground accelerations (PGAs), scour depths, and repair times. The numerical results show apparent shifts in the nonmonotonic seismic fragility, resilience, and economic loss of the case CSB due to scour effects, with the rates of change reaching 31.4 %, 34 %, and 24.8 %, respectively, associated with a critical scour depth of 12 m at IM = 0.8 g. The developed analysis framework provides a reference for the life-cycle design and maintenance of CSBs affected by multihazard scour and earthquakes.

Multidimensional Seismic Response Analysis of Large-Scale Steel-Reinforced Concrete Frame-Bent Structures in CAP1400 Nuclear Power Plant

Irregularity in the plane layout of a building structure and the vertical discontinuity of lateral resistance components could lead to torsion and result in the brittle failure of a structure. According to the characteristics of the conventional island main building of nuclear power plants, this paper focuses on the conventional island main building of the CAP1400 nuclear power plant (NPP) in Shidaowan as the research object. A prototype structure model of the main building was developed using ABAQUS software. The seismic response of the structure under multidimensional ground motion was studied by inputting the X-direction and Y-direction translational and torsional components of ground motion in ABAQUS. The results demonstrate that the overall transverse displacement of the structure under bidirectional ground motion was significantly higher than that under unidirectional earthquakes, which was about 20%. Under a multidimensional frequent earthquake, the transverse displacement of the structure increased by about 13% on average compared with that under a bidirectional earthquake; the longitudinal increase was the largest, at about 28%. Finally, the lateral displacement of each layer of the steel-reinforced concrete (SRC) frame-bent main building structure with few walls proposed in this article decreased by an average of about 17% compared to the traditional SRC frame-bent main building structure. The longitudinal displacement was reduced by about 14% compared to the traditional SRC frame-bent main building structure.

Retracted: Hysteretic Energy Demand under Superposition of Bidirectional Ground Motions

Retracted: Hysteretic Energy Demand under Superposition of Bidirectional Ground Motions

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.

Seismic fragility analysis of underground structures subjected to bi-directional ground motions based on the damage weight coefficients of components

The seismic resilience of underground structures is generally based on the results of the seismic fragility analysis and the damage of all the structural components comprehensively. Whereas, the seismic behavior of underground structures is greatly influenced by the vertical ground motions. Therefore, this paper proposed a new method to study the seismic fragility of underground structures subjected to both horizontal and vertical ground motions, and by considering the damage weight coefficients of the structural components to the overall structure. Pushover/pseudo-gravity analyses were conducted to determine the demand measures and seismic performance levels of all the structural components. Then the intensity measures of earthquakes were determined and the seismic fragility curves of structural components were built by combining the seismic performance levels of structural components and the 3D incremental dynamic analyses on the underground structures. Meanwhile, according to the damage probability of each structural component, the damage weight coefficients of components to the damage of the overall structures were calculated. After that, the seismic fragility surfaces of the underground structures were built and the seismic fragility of the structures was discussed. The method developed in this study could not only be used to evaluate the damage probability of underground structures caused by the vertical ground motions, but also to evaluate the damage probability and post-earthquake repairability of the components.

Shaking table tests of sliding‐prone blocks subjected to unidirectional and bidirectional ground and floor motions

AbstractFreestanding museum collections with low friction coefficients and high aspect ratios may be damaged due to excessive sliding displacements during earthquakes. However, several key issues have not been adequately addressed, such as the friction and sliding behavior of museum collections under actual conditions. Unidirectional and bidirectional shaking table tests were conducted to determine the maximum sliding displacements (MSDs) of a freestanding glass block on sandpaper, which had the lowest friction coefficient among forty‐two contact interfaces in slow‐pull tests. Fourteen far‐field and fourteen near‐fault pulse‐like ground motion records were applied with peak ground accelerations (PGAs) of the major components scaled from 0.05 to 0.6 g. Shaking table tests of a full‐scale three‐story reinforced concrete frame structure containing glass blocks were carried out. Seismic fragility curves corresponding to the sliding failure of the glass block were generated based on the experimental results considering the friction coefficient uncertainty. The results show that the influence of the bidirectional interaction on the MSD is more significant for near‐fault pulse‐like ground motions than far‐field ground motions. For a specific ground motion record, the sliding displacement of the glass block may not increase with the increase of the PGA or peak floor acceleration due to the friction coefficient uncertainty, but this has a negligible influence on the fragility. A clearance around sliding‐prone museum collections with friction coefficients larger than 0.20 is recommended to ensure that the probability of exceedance is lower than 5%.

Ductility-related seismic modification factor for CLT shear-wall and glulam moment-resisting frame dual system

The cross-laminated timber (CLT) shear-wall and glulam moment-resisting frame (CLTW–GMRF) dual system is a recently completed research prepared for the British Columbia (BC) Forestry Innovation Investment Ltd. With the introduction of new structural systems, the need to update existing building code becomes evident. Accordingly, this study evaluates the ductility-related force modification factor ( Rd) of the CLTW–GMRF system for the National Building Code of Canada, utilizing the FEMA P-695 procedure. In two performance groups, 16 archetype buildings are designed considering different building storey heights, CLT shear-wall locations, and wall-frame moment proportions. Numerical model of the systems is developed in OpenSees and incremental dynamic analyses are conducted using 30 bi-directional ground motion records that represent the seismicity of Vancouver, BC, Canada. Collapse margin ratios are calculated to assess the adequacy of the trial Rd factors. The research determined that with an over-strength factor of 1.5, an Rd of 3 is found to be acceptable for the system.

Experimental and numerical investigations on adaptive stiffness double friction pendulum systems for seismic protection of bridges

This study examines the design, development, and characterization of double friction pendulum systems with variable sliding surface geometry. The proposed isolator has a spherical surface with a small radius within an inner sliding range while different geometric functions are used to describe the sliding surface in the outer range. As a result of variable curvature used as sliding surface, the isolators exhibit an adaptive stiffness behavior with increasing displacement amplitude. First, the analytical equations that describe the characteristics of the proposed isolators were derived. Then, a large-scale prototype adaptive isolator that employs a logarithmic function for the sliding surface geometry in the outer range was fabricated. The response of the prototype isolator was characterized under increasing amplitude reversible cyclic loads considering two different levels of vertical isolator loads. A high-fidelity finite element model was developed to capture the response of the prototype isolator. The results obtained from the experimental tests and numerical simulations were used to verify the analytical equations derived for the proposed isolators. Next, a typical multi-span bridge structure was modeled with adaptive stiffness isolators and its response under bi-directional ground motions records were analyzed. In contrast to a conventional double friction pendulum bearing, the suggested isolators yield significantly reduced base shear forces while exhibiting greater isolator displacements. However, the proposed isolators retain the capability to effectively curtail excessive displacements, ensuring the prevention of collapse.

Bi-directional semi-active tuned mass damper for torsional asymmetric structural seismic response control

Tuned mass damper (TMD) is a popular vibration absorber. To improve the seismic protection performance of a bi-directional passive TMD, a bi-directional semi-active TMD (BSTMD) with adaptive stiffness, variable mass and semi-active damping is proposed in this study. The BSTMD can adapt to structural X- and Y-directional instantaneous frequencies at the same time under bi-directional ground motions, which are identified through wavelet transform (WT), and the instantaneous angle of a diamond spring device is adjusted according to the instantaneous frequency ratio of two directions, which means that the stiffness ratio of two directions is retuned first. Then, the mass is retuned to match the exact instantaneous frequency. At last, the semi-active damping is realized according to an extended output signals-based control algorithm. A two-directional asymmetric torsional benchmark model is proposed as a case study. For comparison, two optimal passive TMDs implemented in X and Y directions separately and two unidirectional STMDs with variable stiffness and damping implemented in X and Y directions separately are investigated as well. Numerical results show that under bi-directional earthquake excitations in the benchmark problem, the two optimal passive TMDs have a good control effect. Two unidirectional STMDs have the best aseismic mitigation effect generally, in both lateral and torsional dynamic responses; while the BSTMD has a comparable control effect with less electromechanical devices, and can reduce the stroke of unidirectional STMD to a great degree. Though the BSTMD is aimed at X- and Y- directional dynamic responses, it can control torsional responses effectively as well, and when the eccentricity is enlarged to double, it remains effective for seismic mitigation.

An algorithm for spectrally matching bi-directional ground motions to a target RotD100 spectrum while maintaining the radial spectral acceleration pattern

An integrated algorithm to spectrally match two seed-recorded horizontal bi-directional ground motion components to a maximum-direction response spectrum (RotD100) while maintaining the radial spectral acceleration pattern (RadSAP) at target natural periods is presented. The algorithm is based on the complex-discrete-Fourier-transform (CDFT) and iterative manipulation of the seed-recorded bi-directional ground motions. Initially, a population of candidate bi-directional ground motion pairs is generated, and the candidate resulting in the minimum error in RadSAP is picked. Subsequently, the CDFT coefficients of the picked bi-directional ground motion near the target natural periods are rotated to modify the orientation angle, which contributes to the modification of RadSAP. Then, a double iterative method is introduced to modify the bi-directional ground motion after CDFT coefficients rotation to be spectral and envelope shape compatible in the frequency and time domain. In order to show the effectiveness of the proposed algorithm, two target response spectra are determined following the current ASCE/SEI 7-16 and CJJ 166-2011 specifications, and 10 bi-directional ground motions are selected based on the resemblance in response spectrum for each target spectrum. It is shown that with the proposed algorithm, the RotD100 response spectra estimated from the modified bi-directional ground motions closely match the smooth target RotD100 response spectrum, and the RadSAPs at these target natural periods show an improved match with the seed-recorded bi-directional ground motions than the previous version method. Furthermore, the waveforms of the results obtained using the proposed method are similar to that of the scaled seed records in terms of acceleration, velocity, and displacement. Thus, the generated bi-directional ground motions can be used for future seismic risk assessment of buildings considering the directionality effects.

Comprehensive evaluation of target spectra for selecting bidirectional ground motions in nonlinear response history analysis of frame buildings at far‐field sites

AbstractAn ensemble of bidirectional ground motions (GMs) is required as input for nonlinear response history analysis (RHA) of complex 3D structures. In building codes, an ensemble of GMs is often developed from a given design spectrum, or target spectrum. In the research literature, several target spectra have been proposed for such intensity‐based assessments. The present study aims to comprehensively evaluate different options for developing target spectra to select bidirectional GMs as inputs to nonlinear RHAs of 3D structural systems. To achieve this goal, we conducted both intensity‐based and risk‐based assessments of 49 multistory buildings with varying dynamic characteristics, heights, and plan shapes. The results from performing 11,074 bidirectional nonlinear RHAs and deriving the seismic demand hazard suggest that the Conditional Mean Spectrum‐Uniform Hazard Spectrum (CMS‐UHS) Composite Spectrum appears to be the most promising alternative. With less computational effort than use of multiple CMS, the Composite Spectrum tends to accurately estimate story drift ratios (average overestimation of 4%) and floor accelerations (average overestimation of 3%). Moreover, the relative ranking between the various target spectra options remains largely independent of the building type, height, and plan shape. However, the precision in estimates of demand tends to decrease for buildings with increasing complexity (e.g., more realistic, or taller, or more asymmetrical in plan).

Experimental study on rocking blocks subjected to bidirectional ground and floor motions via shaking table tests

AbstractTo provide an insight for reliable seismic risk assessment of small building contents, the rocking response of freestanding wooden blocks subjected to 11 bidirectional horizontal ground motion records scaled to various intensity levels is investigated via shaking table tests. Three prisms and three cylinders with slenderness ratios of 2, 3 and 4, and three prisms having the same slenderness ratio of 3 but different size parameters of 158 mm, 237 mm and 316 mm, are considered. The peak ground acceleration statistics corresponding to rocking and overturning of the blocks are obtained. Shaking table tests to investigate the rocking response of the prisms located on different floors of a full‐scale three‐story reinforced concrete frame structure were also conducted. Experimental fragility curves corresponding to rocking and overturning occurrence of the blocks are finally generated. The experimental results highlight that the minimum rocking accelerations are different for the prisms with the same slenderness ratio but different sizes. Moreover, compared with the prism on the ground, the prism on the top floor has significantly higher rocking demand, while the prism on the second floor may have lower rocking demand. Furthermore, the cylinder has higher rocking and overturning fragility than the prism with the same height and width. The rocking and overturning fragility increases as the block becomes slenderer or smaller. The proposed critical rocking acceleration under bidirectional seismic excitation in real conditions is a half of the theoretical one under unidirectional excitation.

Development of a bidirectional rocking isolation bearing system (Bi‐RIBS) to control excessive seismic response of bridge structures

AbstractA bidirectional rocking isolation bearing system (Bi‐RIBS) is proposed to provide seismic protection for bridge structures. By using the 3‐D rocking motion of the Bi‐RIBS, this system acts as a mechanical fuse to limit the maximum force transmitted to the bridge piers and as a restoring component to control an excessive girder response. Possible applications in bridge structures were discussed. A simple analytical model was established to characterize the dynamics of an example bridge featuring such a Bi‐RIBS. A series of dynamic analyses were performed by using the proposed model to investigate the effects of several factors on controlling the seismic responses of the bridge, for example, the design parameters of Bi‐RIBS including inclined angle and size, the damping property at the support interface, and the mass ratio. The peak ground accelerations of the bidirectional ground motion record were scaled to various levels to evaluate the maximum performance indices of the bridge structure and the response control effectiveness of the Bi‐RIBS compared to the uncontrolled counterparts. The simulation results demonstrated that the proposed Bi‐RIBS could effectively control the maximum pier displacement while keeping the bearing from overturning if suitable parameters were selected. In particular, the control effectiveness on the maximum pier response becomes more significant as the seismic intensity increases, due to its distinctive negative stiffness property.

Improved simpler R/C hysteresis model considering biaxial interaction

From practical point of view, it is evident that the seismic wave acted on structures through two mutually orthogonal components which have significant combined effect on inelastic demands of the structure. Usually a smaller amount of ground motion generally applied in only one direction than the other and in most of the cases the studies considered only limited inelasticity. Therefore, further research is needed that considers ground motion in both horizontal directions with corresponding bi-directional intensities. Study shows, the combined effects cause significant amount of degradation of strength and stiffness which in turn cause early yielding of R/C(Reinforced Concrete) structural member. Conventional uni-axial model does not consider this type of bi-directional interaction. Some existing simpler bi-axial hysteresis model which can capture biaxial interaction shows satisfactory results, but still the deviation from experimental results are very prominent. On the other hand, some existing sophisticated bi-axial hysteresis model shows better accuracy in predicting response of R/C structural elements but these types of models require large number of calibrated test results which makes them case-specific. In this backdrop, by using principle of yield surface, this study aims to incorporate bi-directional interaction over a simpler hysteresis model which primarily able to capture uni-directional loading effects. Detailed computational scheme of the enhanced simpler uni-axial hysteresis model and extension of the model to capture bi-directional interaction with its performance in prediction of inelastic cyclic behaviour of R/C structural members are presented in this paper. From the performance point of view, it is clearly visible that the proposed simple bi-axial hysteresis model can predict experimental load–displacement curves of R/C structural members under bi-directional reversible loading with acceptable accuracy. The requirement of limited number of input parameters for the present proposed bi-axial hysteresis model make it more convenient to assess the progressive seismic damage under bi-directional ground motion.

Shaking table test of a 10‐story self‐centering tube building

AbstractThe severe damage of conventionally designed buildings and consequent socioeconomic impacts after major seismic events have spurred the development of self‐centering systems with high seismic resilience. Post‐tensioned (PT) walls with rocking interfaces allowed to open and close and unbonded PT bars that provide most of the re‐centering ability have been developed extensively as a promising self‐centering technology. Aiming at providing essential insights into the seismic performance of self‐centering tube systems, a 1/6‐scale ten‐story self‐centering tube building was designed, constructed, and tested on a shaking table subjected to a series of unidirectional and bidirectional ground motions with increasing intensities. The test building consisted of a self‐centering tube that included four PT walls and provided the primary lateral force resistance in both directions, a perimeter rocking frame that was designed mainly to carry gravity loads, and particular connections with slots to accommodate the potential displacement incompatibility among the PT walls and surrounding components. The experimental results indicated the excellent seismic performance of the test building that had reliable structural integrity and experienced only confined damage even when subjected to extremely high intensities. The building also exhibited satisfactory re‐centering ability with minimal residual deformations at the conclusion of testing. It was demonstrated that the self‐centering tube system is a desirable low‐damage alternative to traditional tube systems in earthquake‐prone regions. The benchmark data from this test provided unique suggestions and support for further research on the design methods, numerical modeling, and experimental testing of self‐centering tube systems.

Loss Assessment of Non-Ductile RC Buildings Accounting for Bidirectional Ground Motion

The ongoing seismic events in the world highlight the significant vulnerability of the existing building stock. In particular, in Italy, several structures have been designed without seismic criteria and showed significant damage after recent earthquakes, causing many casualties and great economic losses. Earthquake impact assessment has become one of the most investigated topics by several research groups and within national and international projects. In Italy, for example, the National Department of Civil Protection has allocated several economic funds within the ReLUIS project to define methodologies able to support the decision-making process for seismic prevention activities and risk reduction.This work aims to assess economic losses using the methodology proposed by FEMA-P58, according to the Performance-Based Earthquake Engineering method, evaluating the influence of bi-directional ground motion on loss estimates. The analyzed case study is a three-dimensional nonlinear frame characterized by one weak and one strong seismic directions and modeled using OpenSees software. The model considers the joint deformability and the flexural and shear damaging behavior of beams and columns. Thirty time-history analyses were performed considering bi-directional ground motions applied in the two main directions of the building and applying the higher spectral acceleration firstly in the weaker direction and then in the stronger one. Eight increasing hazard levels were selected for the nonlinear time-history analyses, and the corresponding structural analysis results, in terms of interstory drift ratio and peak floor acceleration, were implemented for the loss assessment. The results of the loss assessment are then discussed in terms of expected annual loss and loss hazard curve.

A physical model for dynamic analysis of structures equipped with variable curvature frictional isolators

During high magnitude ground motions, the internal lateral impact between inner sliders of frictional isolators and restraining rims of sliding surfaces may occur, jeopardizing the benefits of seismic isolation. In this study, a variable curvature friction isolator that exhibits a smooth-hardening behavior at large lateral displacements is evaluated as an alternative to mitigate the adverse effects of internal impacts. The geometry of the sliding surface is obtained by revolving a plane ellipse around a vertical axis. The pendular force transmitted by the isolator increases in stiffness as the device is laterally deformed. This research presents a physical model of variable curvature frictional isolators valuable for analyzing the three-dimensional dynamic response of structures equipped with variable curvature devices. The suggested physical model is capable of accounting for essential modeling features such as large deformations, P-∆ effects, sticking and sliding phases, uplift, kinematics constraints, and the lateral impact behavior. The presented force-displacement relationship of the frictional bearing with smooth-hardening behavior was validated using a Finite Element Model (FEM) under static and dynamic loads. An accurate representation of the coupling between the horizontal components of the pendular and frictional forces transmitted by the isolator is achieved by employing the physical model. The impact parameters of the physical model were calibrated to match the dynamics response of the FEM subjected to unidirectional and bidirectional ground motion inputs. Finally, a comparative example of a base-isolated three-dimensional structure is presented to show how the dynamic response is affected when variable curvature bearings form the isolation system.

Failure analysis of a U-shaped concrete-block masonry wall structure via shaking table tests

Studies on the seismic behavior of masonry fence has been limited even though those structures have a high hazard potential during earthquakes. In this study, the seismic performance of a U-shaped concrete block masonry structure, which represents typical fence walls in South Korea, is assessed. We conduct dynamic shaking table tests using incremental horizontal bidirectional ground motion, and the experimental results are analyzed in terms of visual damage inspection, natural frequency trends, hysteretic responses, and damage limit identification. Thin cracks gradually initiated at the bottom mortar joints, and finally, a severe stair-step cracks developed abruptly, leading to complete structural collapse. Considering the rapid damage progression, we suggest a novel damage limit criterion for this specimen, which is unlike to that of other ordinary masonry structures. The findings of this study can improve the understanding of the collapse process of masonry fence walls and better estimate their damage conditions.

Modification in Response of a Bridge Seismically Isolated with Lead Rubber Bearings Exposed to Low Temperature

This study investigates the response modification in a bridge seismically isolated with lead rubber bearings (LRBs), due to change of ambient temperature from 20oC to -30oC. Accordingly, a large-size LRB was tested after conditioned at corresponding temperatures and change in its hysteretic properties was noted. Use of analytical tool in modeling nonlinear response of the tested LRB was justified by comparing the experimentally and analytically obtained force-displacement curves. Then, verified analytical representation of LRB was employed in nonlinear response history analyses conducted to quantify the change in response of a representative LRB isolated bridge when subjected to bidirectional ground motion excitations at 20°C and -30°C. Analyses results are also employed to assess the use of property modification factor, , to change isolator properties in order to represent low temperature behavior. It is revealed that for the selected ground motion records, the average isolator force remains almost the same for both ambient temperatures. Moreover, using property modification factor will result in accurately estimated isolator displacements, but overestimated isolator forces, in an average sense.

The Over-Strength Coefficient of Masonry-Infilled RC Frame Structures under Bidirectional Ground Motions

The over-strength coefficient is one of the key factors for the seismic safety of a structure. For RC frames, the infill wall may improve the lateral bearing capacity, while the seismic demand increases as well, which leads to the unexpected seismic performance of an infilled RC frame in past earthquakes. Therefore, it is necessary to systematically study the over-strength effect of the infilled RC frames from the point of seismic capacity and demand. In this paper, 36 RC frame structures with/without infill walls are designed, and the corresponding finite element modelings, considering the in-plane and out-of-plane performance coupling effect of infill walls, are established to conduct incremental dynamic analyses (IDA). The seismic capacity values of over-strength coefficients are calculated, utilizing the IDA results under bidirectional ground motions. The effects of seismic precautionary intensity and number of stories on the over-strength coefficient of the RC frame with/without infill walls are discussed. The over-strength coefficient capacity value of the infilled frame is apparently higher than that of the bare frame, due to the contribution of infill walls. However, the seismic demand analysis of the over-strength coefficient shows that the capacity–demand ratio of masonry-infilled RC frame structures is greatly reduced, especially for the bottom soft-story infilled frame.