Pushdown Analysis Research Articles

Progressive collapse capacity of a gravity-load designed RC building partially collapsed during structural retrofitting

The problem of progressive collapse has been a major topic in structural forensic engineering since its inception, but it has recently received a growing interest. In the last two decades, the occurrence of extreme events and their catastrophic impact on the built environment and people has promoted several research programmes and guidelines for structural design and assessment, spotlighting the importance of back-analysis and numerical prediction of progressive collapse phenomena. This paper presents a numerical study aimed at investigating the ability of existing reinforced concrete structures to prevent progressive collapse during structural retrofitting. The progressive collapse capacity of a real, reinforced concrete framed building constructed in the 1950s and partially collapsed in 2001 is discussed in relation to a couple of structural retrofitting operations that were found to be the primary causes of the accident. Existing information from past forensic investigations was integrated with a simulated design procedure to develop the capacity model of the structure, according to design codes and practice rules used at the time of construction. Nonlinear pushdown analysis with displacement control was carried out both in intact conditions and during retrofitting operations. In addition to global capacity models of the structure, the use of partial capacity models representing the building corner under retrofitting was evaluated, highlighting a very high computational efficiency of those simplified models. Analysis results also indicate that the load contribution from infill walls can significantly influence the progressive collapse resistance, particularly in relation to retrofitting works involving the corner of the building plan as actually happened. Retrofitting interventions on the real building included the concrete cover removal from ten ground-floor columns and soil excavation around column bases. The removal of concrete cover from single and multiple ground-floor columns together with the loss of supports due to soil excavation around column bases was found to significantly affect the collapse capacity of the structure. The major impact of retrofitting operations in terms of location and extent provides a simulation-based proof of the progressive collapse suffered by the case-study building, evidencing that soil excavation around more than three columns was able to produce the accident.

Investigation of snow-induced collapse in Bozüyük market

Heavy snowfall and frost are common phenomena in some areas of Turkey. Since it is an active seismic region, most engineering efforts focus on the impact of seismic loads. Meanwhile, the evaluation of structural and non-structural damages caused by snow loads are less of a concern. Depending on region geographical characteristics, snow is considered one of the most critical loads, especially in the case of large spans industrial structures, sport facilities and malls. This study investigates the snow induced failure of Bozüyük Market in Turkey. An evaluation of the attributed reasons behind the reported collapse is provided. To investigate the critical regions of the structural systems, a finite element model has been generated, linear and nonlinear static push-down analysis are carried out for the collapsed portion of the structure of interest. The snow load calculations are compared in regard to national standards TS 498 and TS EN 1991–1-3. It has been found that the construction defects were the primary reason behind the partially failure of the investigated roof. The paper highlights the urgent need to upgrade the national standards regarding snow loads to go along with the changes in snowfall density and frequency due to accelerated climate change.

Collapse capacity of modular steel buildings subject to module loss scenarios: The role of inter-module connections

In modular buildings made of volumetric units, robust structural action may be established by considering various scenarios for localisation of damage, corresponding to loss of supports at the ground floor, such as notional removal of ground floor modules. This paper studies the role of inter-module connections in resisting capacity of modular steel buildings against gravity-induced progressive collapse scenarios, through removing individual or combinations of entire modules at the ground floor. For this purpose, some typical modular buildings are modelled using the macro-model based finite element method. In order to investigate the role of inter-modular connections solely and separate from the effects of other elements, the modules are assumed volumetric rigid bodies, connected through horizontal and vertical interconnections, which are modelled employing translational axial and shear nonlinear springs. Different module loss scenarios are instantaneously imposed to the building models, and their nonlinear dynamic response is monitored in the context of alternate path method analysis. Then the ultimate collapse capacity of the modular buildings along with the collapse mechanism and failure modes are determined through the nonlinear static pushdown analysis. It is shown that the modular buildings possess considerable collapse resisting capacity and are able to offer high level of robustness compared to their conventional counterparts.

Finite element analysis of alternative load paths in a platform-framed CLT building

Multi-storey cross-laminated timber (CLT) buildings are a comparatively recent construction type. Knowledge concerning the performance of CLT buildings regarding the prevention of disproportionate collapse after unforeseeable events (e.g. accidents or acts of terrorism) is not as refined as that for concrete and steel buildings. In particular, alternative load paths (ALPs) after the removal of a wall panel in platform-framed variants have not yet been studied in detail. The goal of this work was therefore to study ALPs in CLT buildings. An eight-storey bay of an existing building was evaluated by conducting a non-linear static pushdown analysis in a finite element analysis on three representative storeys. The analyses accounted for single fastener behaviour, timber crushing, friction, brittle failure and large deformations. The force–deformation behaviours elicited under the pushdown analyses were subsequently inserted in a simplified dynamic model to evaluate the transient response of the entire bay. Four ALPs were identified in this case – shear resistance in the floor panels, arching action of the walls, catenary action in the floor panels and hanging action from the roof. The dynamic analysis did not show a collapse, unless the inter-compartment stiffness was significantly reduced. The resistance mechanisms are described in this paper, which may provide information for improved building design.

Impact modelling for progressive collapse assessment of selective rack systems

Storage rack structures are pre-engineered light weight steel structures with standard details which can be quickly assembled because all building components arrive on site pre-fabricated in line with the agreed design. Since they are made using thin-walled perforated steel sections, mostly cold-formed, with mechanical joints, generally partial-strength, semi-rigid, and with a low structural redundancy, these structures are vulnerable to any action capable to induce a local damage of a member or connection. When heavily loaded, the local damage may spread progressively, generating an overall collapse or disproportional damages. Difficulties in predicting the structural behavior of storage pallet racks are amplified by the specific geometry of the structural components: members made by high slenderness thin-walled and open-section profiles (hence prone to global, local and distortional buckling problems), flexible beam-to-upright and baseplate connections with a non-linear behavior. Due to their peculiarities, additional modelling and design rules are required for these non-traditional steel structures and reference cannot be made to usual structural design recommendations and standards. In case of Selective Pallet Rack (SPR) structures, except for the earthquakes, collision of forklift trucks or other moving equipment with front upright is considered as one of the most frequent causes of local failure, with potential to develop into a progressive collapse. In the study, the robustness of SPR structures under accidental loading situations involving collision with forklift truck is assessed using both notional upright removal and explicit forklift impact approaches. Structural configurations are varied to consider different connection properties (upright base and beam-to-upright) and brace arrangements (spine bracing, top plan bracing). SPR structures are susceptible to global failure, especially if the spine bracing is in just a few spans and the rigidity of connections is low. The explicit modelling of the forklift impact provides the most accurate results, as the effects associated with the forklift impact are not properly captured when the response is evaluated using the dynamic analysis and notional upright removal approach. Non-linear static pushdown analysis can provide satisfactory results at the least computational effort, but the dynamic increase factors may require corrections.

Probabilistic assessment of failure time in steel frame subjected to fire load under progressive collapses scenario

Consecutive loads can pose a serious threat to the safety of structures. The sudden removal of load-bearing elements such as columns is one of the causes of the progressive collapse in the structures. The local collapse caused by the sudden removal of the column could affect the response of the structure in the consecutive loads. The fire load is one of the loads that threatens the safety of the structure over the lifetime of the structure. The time a structure can resist the fire load is one of the main factors in the safety of structures against thermal loads. The local damage involved in the structure, including the sudden removal of the load-bearing elements, can affect the stability of the structures against the fire load as two successive events. This research aims to calculate the stability time of the steel frame during the consecutive loading from the sudden removal of column and the subsequent fire. Once designed, the 7-story steel frame is mechanically-thermally modeled and is subjected to the sudden removal of columns in different positions. The static and dynamic pushdown analysis is used to evaluate the structure response in the scenarios of sudden removal of the column. Different modes of thermal load are defined and applied to the structure in the positions of the removed column. Finally, the probability of structural failure is calculated under the fire load after the sudden removal of the column and presented at different times. The results show that the sudden removal of the column will have a great effect on the failure time of the structure and will increase the failure probability of the structure and reduce the failure and collapse time of the structure. Finally, the robustness index is also presented based on the probability of collapse time.

A non-iterative progressive collapse design method for RC structures based on virtual thermal pushdown analysis

Disproportionate progressive collapse is a structural failure mode with low probability and high consequences. Due to this nature, progressive collapse design is usually treated as a secondary design; namely, a design check after the design for primary loadings. Various design procedures have been recommended, notably the alternate load path method through nonlinear pushdown analyses. However, most of these design procedures are iterative by nature to satisfy the design acceptable criteria. To improve the design efficiency, this study presented an innovative design technique that allows to directly determine the proper amount of reinforcement in beams and slabs of a reinforced concrete (RC) structure in order to withstand the gravitational loads under column removal scenarios. Inspired from fire-induced progressive collapse research, the proposed method employs a virtual thermal pushdown analysis, in which the temperature increase affects only the strength of reinforced steel. With carefully developed strength-temperature relationships of the rebars, the virtual thermal analysis produces a displacement-temperature curve that represents the genuine nonlinear relationship between the amount of reinforcement and structural performance (often represented by vertical displacement). This curve is then used to directly determine the amount of reinforcement at the prescribed performance target. Two beam-column sub-assemblage examples and the Alfred P. Murrah Federal Building were analyzed and redesigned to demonstrate the effectiveness of the proposed method. All three examples showed that the proposal virtual thermal pushdown method can accurately determine the appropriate amount of reinforcements to meet the performance target.

A modal pushdown procedure for progressive collapse analysis of steel frame structures

A modal pushdown analysis procedure is developed for progressive collapse assessment of multi-storey steel frame buildings under sudden removal of a column due to catastrophic events. Since the first vertical bending mode generally dominates the behaviour of the structure after column removal, the global response is assumed entirely in this mode shape while no contribution is considered from other modes. Thus, the target displacement of the column-removed point is estimated from the nonlinear response–history analysis of a modal inelastic single degree-of-freedom (SDOF) system under a rectangular pulse force that simulates the abrupt column removal. The properties of this SDOF system are calculated from the nonlinear static (pushdown) analysis of the damaged structure using the modal properties of the first bending mode shape. A two-step pushdown analysis procedure is developed to estimate the inelastic response of the structure and the dynamic amplification factor (DIF) to use when conducting the nonlinear static analysis. The accuracy of the proposed procedure is estimated and compared to other formulations in the literature. For this reason, a series of three-dimensional steel frame buildings with varying number of spans and storeys have been considered in the analysis. Different loading levels and column removal scenarios are investigated. The study results show that the modal pushdown procedure gives accurate solution, accounting for both real plastic deformation demand and catenary stiffening action in steel beams.

Progressive collapse performance analysis of precast reinforced concrete structures

SummaryIn this paper, the progressive collapse performance analysis of precast reinforced concrete (RC) structures is performed. A numerical simulation framework for precast RC structures is developed on the basis of the OpenSEES software, where the fiber frame element is used for beam and column type members and Joint2D element is used for the beam‐to‐column connections. The conjugated material models are then introduced, and a min–max failure criterion is imposed on the original models to reflect the steel fracture and concrete crushing when the structure is undergoing progressive collapse. In addition, to overcome the computational difficulties arisen from progressive collapse behavior, two enhanced nonlinear solutions , that is, the consistent quasi‐Newton algorithm and the explicit KR‐α algorithm, are employed, respectively, for static and dynamic analysis. A 10‐storey prototype precast RC structures is designed to verify the developed numerical framework, and the progressive collapse resisting mechanism of the structures is investigated through both static pushdown analysis and dynamic column‐removal analysis. Finally, influences of some typical parameters in precast RC structures on their progressive collapse performance are studied.

Influence of masonry infills on the progressive collapse resistance of reinforced concrete framed buildings

Despite the increasing interest in progressive collapse-resistant design and analysis of reinforced concrete buildings that was triggered by accidental and man-made extreme events occurred over the last couple of decades, only few studies, especially numerical ones, have been carried out so far on the role of masonry infill walls. Just like in the case of first earthquake engineering applications, infills are usually considered as non-structural or architectural elements and, hence, their resistance is commonly ignored, given also that current design guidelines do not provide specific indications concerning this point. Although such an assumption leads to an ease in both design and assessment of structures, it may also give rise to misleading and overly conservative results, as the presence of masonry infills may result in extra vertical resistance.Thus, this paper presents the outcomes of a large number of progressive collapse simulations aimed at quantifying the effects of infill walls on the vertical load-carrying capacity of reinforced concrete frames for different levels of damage, thus allowing evaluation of the interaction between these structural elements and the surrounding frame for different regimes/stages of the response. To this end, a macro-model concept was first developed and its effectiveness was then evaluated by comparing numerical results to experimental data from a past test on a one-third scaled planar structure featuring full-height infill walls. After validation, the proposed model was used to predict behavioural changes in the response of infilled reinforced concrete structures as a consequence of parametric variations in the geometry of the selected prototypes. Counterpart bare frames were also analysed in order to present a twofold comparison, in terms of resistance and dissipated energy. Finally, the manuscript describes the results of a further set of analyses, in which uncertainties in the mechanical properties of the masonry infills were modelled and propagated through fibre modelling and pushdown analysis techniques.

Scheme for beam progressive collapse mitigation

Latest recommendations have made provisions to improve structure resistance to progressive collapse in the event of interior support collapse. This paper defines a mitigating scheme to repel progressive collapse in reinforced concrete beams due to damaged interior supporting member by providing a new path to transfer the loads to other supporting members. The mitigating scheme suggests the use of unbounded unstressed externally installed fibre reinforced plastic cables with straight profile and three deviators. An open source finite element package for structural analysis (ZEUS-NL) using the fibre element approach is adopted to numerically model the mitigated beam. The proposed numerical model evaluates the progressive collapse of such beams using a push-down analysis to simulate column removal. It assumes that the anchorage and deviator locations of the external cables act as rigid arms that connect the external cables to the beam. The numerical results demonstrate that the defined mitigating scheme increases the beam resistance to progressive collapse due to interior column failure.

Dynamic increase factor for progressive collapse analysis of semi-rigid steel frames

An empirical and efficient method is presented for calculating the dynamic increase factor to amplify the applied loads on the affected bays of a steel frame structure with semi-rigid connections. The nonlinear static alternate path analysis is used to evaluate the dynamic responses. First, the polynomial models of the extended end plate and the top and seat connection are modified, and the proposed polynomial model of the flush end plate connection shows good agreement as compared with experimental results. Next, a beam model with nonlinear spring elements and plastic hinges is utilized to incorporate the combined effect of connection flexibility and material nonlinearity. A new step-by-step analysis procedure is established to obtain quickly the dynamic increase factor based on a combination of the pushdown analysis and nonlinear dynamic analysis. Finally, the modified dynamic increase factor equation, defined as a function of the maximum ratio value of energy demand to energy capacity of an affected beam, is derived by curve fitting data points generated by the different analysis cases with different column removal scenarios and five types of semi-rigid connections.

Scheme for beam progressive collapse mitigation

Latest recommendations have made provisions to improve structure resistance to progressive collapse in the event of interior support collapse. This paper defines a mitigating scheme to repel progressive collapse in reinforced concrete beams due to damaged interior supporting member by providing a new path to transfer the loads to other supporting members. The mitigating scheme suggests the use of unbounded unstressed externally installed fibre reinforced plastic cables with straight profile and three deviators. An open source finite element package for structural analysis (ZEUS-NL) using the fibre element approach is adopted to numerically model the mitigated beam. The proposed numerical model evaluates the progressive collapse of such beams using a push-down analysis to simulate column removal. It assumes that the anchorage and deviator locations of the external cables act as rigid arms that connect the external cables to the beam. The numerical results demonstrate that the defined mitigating scheme increases the beam resistance to progressive collapse due to interior column failure.

Progressive collapse fragility models of European reinforced concrete framed buildings based on pushdown analysis

Structural safety for extreme loads that may cause local damage to single primary components or even the progressive collapse of the structure has been probabilistically assessed in a few studies, hence neglecting uncertainties in loads and system capacity. As such, this paper moves from a deterministic to a probabilistic framework, proposing new progressive collapse fragility models based on pushdown analysis of low-rise, reinforced concrete framed bare structures. Two building classes representative of structures designed for either gravity loads or earthquake resistance in accordance with current European codes were investigated. Monte Carlo simulation was used to generate random realizations of 2D and 3D structural models. Fiber-based finite element models were developed within an open source platform. The primary output consisted of fragility functions for each damage state of interest, given the loss of corner column at the ground floor. The fragility models were compared to those derived through incremental dynamic analysis (IDA) to assess the inaccuracy of progressive collapse fragility functions derived through pushdown analysis. Load capacity predictions provided by those analysis methods were used to develop regression models for a quick estimation of dynamic amplification factor at a given displacement/drift level. The analysis results show a significant influence of both seismic design and secondary beams on robustness of the case-study building classes.

Proposal of a probabilistic assessment of structural collapse concomitantly subject to earthquake and gas explosion

In recent decades, many public buildings, located in seismic-prone residential areas, had to grapple with abnormal loads against which the structures were unguarded. In this piece of research, an ordinary three dimensional reinforced concrete building is selected as case study. The building is located in an earthquake-prone region; however, it is designed according to seismic building codes. Yet, it is not shielded against abnormal loads, such as blasts. It is assumed that the building suffers a blast load, due to mechanical/thermal installation failure during or after intense seismic oscillations. These two critical incidents are regarded codependent and compatible. So the researchers developed scenarios and tried to assess different probabilities for each scenario and carried out an analysis to ensure if progressive collapse had set in or not. In the first step, two analysis models were used for each scenario; a non-linear dynamic time history analysis and a blast local dynamic analysis. In the second step, having the structural destructions of the first step in view, a pushdown analysis was carried out to determine the severity of progressive collapse and assess building robustness. Finally, the annual probability of structural collapse under simultaneous earthquake and blast loads was estimated and offered.

06.03: Dynamic increase factor for nonlinear static alternate path analysis of steel moment‐resisting frames against progressive collapse

ABSTRACTThe paper investigates the dynamic increase factor to be assumed in the nonlinear pushdown analysis of seismically designed steel moment‐resisting frames as a consequence of sudden column removal. The influence of the fundamental parameters, as well as the effect of various design variables, such as the number of stories, the number of bays, the location of the removed column and the level of seismic design load were investigated. The dynamic increase factor was estimated by direct comparison of static analysis with full nonlinear dynamic analysis. Eventually, the values obtained were expressed as a function of the vertical displacement at the location of the removed column and then compared with the GSA formulation based on the ductility factor.

Progressive collapse of steel moment-resisting frame subjected to loss of interior column: Experimental tests

A static push-down analysis is conducted experimentally using a 1/3 scale one-story bare steel moment frame substructure in this study. The objectives of this test include: (1) investigating the behavior of bare steel moment frame under column loss scenario; (2) validating the computational models developed for the purpose of investigating progressive collapse of steel frame structures. The contributions of collapse resisting mechanisms including flexural action and catenary action to the robustness of the system as the increase of the vertical displacement of the center column are quantified. The test results reveal that flexural action plays an important role in resisting progressive collapse along the entire loading process. However, the catenary action becomes the primary collapse resisting mechanism in the final stage of loading. Dynamic responses of the test specimen are estimated using energy-based method. It is shown the test specimen behaves elastically subjected to sudden loss of the center column and therefore progressive collapse will not occur. The dynamic increase factor is also estimated on the basis of the testing results. The analysis results suggest that catenary action has a great impact on the value of the dynamic increase factor under large deformation conditions.

INCREASING ROBUSTNESS OF REINFORCED CONCRETE STRUCTURES UNDER COLUMN LOSS SCENARIO

This paper presents a simple technique to enhance robustness of reinforced concrete (RC) plane frames to progressive collapse under column loss scenario. The response of the enhanced/mitigated RC frames is analyzed using fiber force-based finite element analysis and applying displacement-controlled nonlinear static pushdown at the location of failed column. The technique involves addition of external unbounded steel cables to the continuous beam in each floor at anchorage and deviator locations. The cables transfer the loads above the failed column to the anchorages and deviators that are assumed to perform as rigid arms, which in turn redistribute the loads to adjacent columns. The numerical model computes the frame progressive collapse robustness using push-down analysis to simulate a column elimination and estimate the effects of cable catenary action on the frame. Two-dimensional RC frame of six stories and four bays was adopted in the study. The numerical results demonstrate the prospect of increasing robustness of RC frames to progressive collapse using presented technique.

Robustness Assessment of Steel Moment Resisting Frames

Nowadays, many buildings with steel Moment Resisting Frames (MRF) are built in seismic zones when seismic codes are at its early stages of development, and as such, these structures are often designed solely to resist lateral wind loads without providing an overall ductile mechanism. On the other hand, current seismic design criteria based on hierarchy of resistance allow enhancing the structural ductility and controlling the structural plastic behaviour. Therefore, seismic design criteria might also be beneficial to improve the structural robustness. In order to investigate this issue for steel MRF, a parametric study based on pushdown analysis and on the Energy Balance Method is described and discussed in the present paper. With this regard, the following cases are examined: (i) MRF not designed for seismic actions and (ii) MRF designed for seismic actions. The investigated parameters are (i) the number of storeys, (ii) the interstorey height, (iii) the span length, (iv) the building plan layout and (v) the column loss scenario. Results show that the low-rise and long span structures are the most prone to progressive collapse and that the elements in the directly affected zone of the wind designed 8 storey structures respond in the elastic range. Structures designed according to the capacity design principles were found to be less robust than wind designed structures that are characterized by strong beams and weak columns. The number of elements above the removed column and size of beam cross section were found to be key parameters in arresting progressive collapse.

Modeling progressive collapse of 2D reinforced concrete frames subject to column removal scenario

In this study, a new modeling procedure for progressive collapse analysis of 2D reinforced concrete (RC) frames subject to single or multiple column removal scenario is proposed. Different from traditional pushdown analysis, the proposed method incorporates the effects of service loads before column removal into the analysis. To trace the collapse sequence of the structure, a member removal algorithm based on combined actions of flexural/shear/axial failures is employed. For detecting substructure collapse mechanisms, a specially designed searching algorithm is developed. Furthermore, the locations and magnitudes of collapse impacts are respectively determined by rigid-body kinematics and energy principle with both inelastic and oblique impact effects considered. Numerical examples with different loading and column removal scenarios are given to validate the suggested damage assessment procedure, the member failures identification procedure and the collapse searching algorithms as well as to demonstrate the effectiveness of the proposed modeling approach.