Pushdown Analysis Research Articles

Backtesting the iconic Polyfytos balanced-cantilever bridge to enhance condition assessment

This paper introduces a comprehensive framework for reliable damage assessment and decision-making for bridge intervention planning. By utilizing historical data and 3D-UAV photogrammetry, a detailed 3D numerical model is created, incorporating advanced modeling and scenario-based approaches. The methodology is applied to the Polyfytos bridge in Greece, which faces significant vertical deck deflections that disrupt traffic and impact local communities. This approach offers a reliable, cost-effective, and efficient process, allowing stakeholders to make informed decisions with minimal physical interaction with the bridge. The integration of advanced modeling with in-situ measurements and expert judgment is emphasized. For the Polyfytos bridge, the framework helps prioritize retrofits and assess the deck’s remaining strength under various loads, providing estimates of its overstrength. This aids in evaluating the bridge’s ability to handle additional vertical loads through pushdown analysis. Overall, the framework is valuable for rapid infrastructure assessment, identifying damage patterns, severity, and the urgency of interventions related to structural strength.

Assessment of Different Methods for Enhancing Progressive Collapse Resistance of Irregular Reinforced Concrete Buildings Using Pushdown Analysis

Ensuring structures meet rigorous structural requirements is paramount in mitigating progressive collapse risk. In this comprehensive investigation, we scrutinize the impact of four distinct mitigation techniques on the propensity for progressive collapse in a six-story building featuring irregular structural attributes. The study adheres to the concrete building construction code ACI 318-14 and evaluates methods that include: (a) reinforcing the reinforced concrete (RC) slab with high-performance fiber-reinforced cementitious composites (HPFRCCs), (b) enhancing the RC slab with carbon fiber-reinforced polymers (CFRPs), (c) incorporating steel plate shear wall (SPSW) within specific columns, and (d) introducing an innovative approach named as the steel belt strip (SBS). In the context of 10 independent column loss scenarios conducted on the first floor, the nonlinear dynamic analysis reveals that HPFRCC effectively reduces vertical displacement under the removed column by up to 99.89% in certain scenarios. Meanwhile, the use of CFRP layers leads to reductions of up to 95% in vertical displacement, but with variations in effectiveness across scenarios. Notably, the SBS technique demonstrates remarkable potential by reducing vertical displacement by 97%, 89%, and 25.9% in different scenarios. This reduction, in conjunction with the mitigation of axial load on adjacent columns, makes the SBS a standout performer. Moreover, pushdown analysis indicates that, with the employment of these mitigation methods, the maximum loading factor can be increased up to 2.14 times in specific scenarios, significantly enhancing the structure’s resistance to progressive collapse. This pioneering research not only bolsters the resilience of irregular RC buildings but also holds profound implications for industry standards, risk assessment, and construction technology innovation.

Progressive Collapse Resistance Assessment of a Multi-Column Frame Tube Structure with an Assembled Truss Beam Composite Floor under Different Column Removal Conditions

To estimate the progressive collapse resistance capacity of a multi-column frame tube structure with an assembled truss beam composite floor (ATBCF), pushdown analysis and nonlinear dynamic analysis are conducted for such a structure using the alternate load path (ALP) method. The bearing capacities of the remaining structures under three different work conditions, which are the side middle column removal, the edge middle column removal, and the corner column removal, are individually studied, and the collapse mechanism of the remaining structures is analyzed based on the aspects of the internal force redistribution and the failure mode of the second defense line. Simultaneously, the influence of the column failure time on the dynamic response of the remaining structure and the dynamic amplification coefficient is discussed. The results indicate that the residual bearing capacity of the remaining structure following the bottom corner column removal is higher than that of the one following the side or edge middle column removal, while the latter has a stronger plastic deformation capacity. When the ALP method is adopted to operate the progressive collapse analysis, it is reasonable to take the column failure time as 0.1 times the period of the first-order vertical vibration mode of the remaining structure, and it is suitable to set the dynamic amplification coefficient as 2.0, which is the ratio of the maximum dynamic displacement to the static displacement of the remaining structure under the transient loading condition.

Modeling the Effect of RC Column Failure over the Frames

The locally or entirely collapse of a structure triggered by failure of one or a couple elements can be considered as progressive collapse. New load distribution and additional loads may be created for the remaining elements of the frame. To accurately understand the progressive collapse mechanism, it is needed to accurate estimation of load distribution after failure of an element. The removal of a column and pushdown analysis is a widely used approach to evaluate the progressive collapse mechanism. However, in this study, effect of removal of three different columns on the frame are studied under two conditions; a) removal of column and pushdown analysis, b) loss on the axial capacity of column under cyclic loading. To axial capacity loss of reinforced concrete column, author’s previously developed axial capacity model is employed. A 2D three-story five-bay benchmark frame is analyzed under pushdown and quasi-static cyclic loading. Distribution of loads after failure of a column is investigated under six different scenarios.

Progressive collapse analysis and retrofit of a steel-RC building considering catenary effect

Despite their low probability of occurrence, the consequences of abnormal loads may be very important, both in economic terms and in terms of human lives. This has stimulated the development of strengthening and retrofitting techniques to mitigate the risk of progressive collapse of buildings. However, their application to real-scale buildings is still lacking. This paper describes the progressive collapse analysis and retrofit of a steel-reinforced concrete hospital building. The progressive collapse performance under different column removal scenarios is investigated using both nonlinear static and dynamic analyses. A two-step pushdown analysis procedure is developed to estimate the dynamic amplification factor (DIF) to partially compensate for the dynamic effects. The results have revealed the vulnerability of the building due to the low tensile axial resistance of the beam-to-column connections. Both the hypothesis of DIF = 2 and the almost inversely proportional relationship between DIF and vertical deflection have proven to be ineffective due to the catenary effect. A retrofit solution is proposed based on an outrigger-belt truss system on the rooftop level. The results show the effectiveness of the retrofit strategy. The displacement dynamic response of the retrofitted structure is significantly reduced if compared to the original structure since it goes from about 20 cm to less than 1 cm. However, the tensile strength of column-to-column connections of the top three floors is inadequate and should be increased. To this aim, a strengthening intervention is developed to increase the tensile strength from 565 kN to 965 kN, thus allowing the tensile axial forces caused by the column removed to be resisted.

Non-Linear Analysis of R.C. and P.R.C. Girder Bridges

In professional practice, the design and verification of Reinforced Concrete (RC) and Prestressed Reinforced Concrete (PRC) structures are performed using a simplified calculation provided by the Eurocodes that limits resistance but that also includes a certain level of structural safety. Some aspects that directly affect the simplified methods involve the use of linear constitutive laws of materials. The use of non-linear laws is evident in the exploitation of reservoirs of strength and deformations of plastic materials in the Ultimate Limit State. The purpose of this research is to evaluate the increase in resistance to bending actions during the plasticization of the beam of existing bridges to support the decision-making process of the engineer in the assessment of existing structures. To achieve this, two codes (MEG Ductility, MEG Fiber Sections) were developed to provide the moment–curvature diagram of RC and PRC sections using non-linear bonds, and in this paper, the study of RC sections is reported. Furthermore, through a push-down analysis, two RC and PRC viaducts have been analyzed using the moment–curvature characteristics obtained from the realized codes and by varying the non-linear constitutive bonds. The results of this study provide valuable insights into the behavior of RC structures under bending actions and demonstrate the importance of considering non-linear material laws for accurate structural assessments. The findings contribute to the enhancement of the decision-making process of engineers when dealing with existing infrastructures.

Способы расчета несущих конструкций на устойчивость к прогрессирующему разрушению

Introduction. Calculation methods and current normative documents used in the calculation of buildings for resistance to progressive collapse are considered. The key methods of analysis are listed and fundamenta.rules of each of them are stated. The advantages and disadvantages of these methods are analyzed. Materials and methods. The calculations of stability to progressive collapse have been carried out for a multi-span flat frame at the failure of the middle post of the ground floor. The software complex LIRA-SAPR 2021 R1.2 was used to perform calculations. The task was solved by several methods: the static calculation, quasi-static calculation and dynamic calculation. The nonlinear functioning of construction and material was considered by step-methods with using the flow curve from SP 16.13330.2017. Quasistatic calculation was performed in two variants: pulldown and pushdown analysis. The dynamic calculation was carried out by direct integration of the equations of motion using the module “Dynamics in Time”. Two variants with different element elimination time were considered. Results. The results are analyzed and summarized in Table 2. The static calculation yields force and displacement values that are clearly underestimated as compared to other methods. Forces and displacements obtained by quasistatic analysis are greater than those obtained by dynamic analysis. The results obtained in the pulldown and pushdown analyses are close in value. Conclusions. Quasistatic calculations give higher forces and displacements than dynamic calculations. The results of pushdown analysis correlate better with the results of calculations in the dynamic formulation. In order to determine forces more accurately when using quasi-static calculation, a justification of the dynamical coefficient is necessary.

Progressive collapse resistance and uncertainty analysis of post-tensioned steel frames

Post-tensioned (PT) steel frames with prestressed strands and replaceable energy dissipation angles demonstrate enhanced resilience during earthquakes compared to traditional steel frames. This study aimed to investigate the collapse resistance of PT steel frames in the different column removal scenarios. A macro model of a typical PT connection was developed using OpenSeesPy, a python library for the OpenSees finite element software framework. The model was validated by experimental results and applied to a six-story, four-bay office building. The collapse resistance mechanism of the building was analyzed in detail through a static pushdown nonlinear analysis, considering the edge column and middle column removal scenarios on the ground floor. A probabilistic analysis was conducted, incorporating uncertainty modeling and sensitivity analysis, to determine the effect of parameters on the collapse resistance of the structure. The collapse fragility functions corresponding to different structural performance levels were developed by the Latin hypercube sampling method with random pushdown analysis under the edge column removal and middle column removal scenarios, respectively. The uncertainty analysis results indicated that the PT steel frame investigated in this work has good collapse resistance.

Evaluation of the Failure Probability of a 2D RC Frame Subjected to Column Loss

Abstract: This study regards the evaluation of the failure probability of a symmetrical 2D reinforced concrete frame composed of 4 spans and 5 floors, in case of an accidental event which causes the central base column loss. The frame is an internal one of a typical building designed in a highly seismic area, characterised by a high ductility class. The frame is modelled in the non-linear finite elements software Atena 2D, accounting for both geometrical and material non-linearities. The uncertainties relevant to the problem are included by sampling both material and action variables, adopting the Latin Hypercube Sampling technique. To compute the failure probability associated to the accidental scenario, two sets of analyses are considered: the first set to compute the capacity of the structure against the column removal by means of displacement-controlled pushdown analysis; the second set to evaluate the demand in terms of external loads, properly combined within the accidental combination according to the codes. The external load is then amplified in order to include the dynamic effects characterising a scenario of a structural member loss. Finally, the probability of the demand exceeding the capacity is evaluated.

Progressive collapse mechanisms of multi-story steel-framed modular structures under module removal scenarios

Due to different assembly requirements and novel integration strategies, the modular structures may have undesirable loading mechanisms and distinct structural behaviors. However, there are limited data on the progressive collapse performances of modular structures, which impedes their industrial applications. This study numerically investigates the structural robustness of multi-story steel-framed modular structures against progressive collapse by using pushdown analysis. A six-story structure with five modules per floor is designed and established. The applied load, failure process and load redistribution mechanisms are studied under module removal scenarios. Parametric analyses are also conducted to investigate influences of cross-sectional dimensions of frame members, number of stories and bays, arrangements of bracings, and module removal scenarios on the robustness of the modular structures. The results show that the prototype modular structure designed with Hong Kong design code can withstand collapse under module removal scenarios. The load redistribution mechanisms among columns are significantly influenced by the overturning action and bracing effects. The ceiling beam in the lower module and the floor beam in the upper module form a double beam system. The column section, beam section, arrangement of bracings and number of stories significantly influence the robustness of the modular structure. Finally, a design method based on buckling load equation for columns is proposed to estimate the progressive collapse resisting capacity of modular structures with good accuracy and efficiency.

Evaluation of progressive collapse behavior in reinforced concrete buildings

Progressive collapse is a catastrophic chain reaction of failure of a structure that is caused due to loss of vertical load bearing element of the structure, resulting damage of a part of the structure or entire structure. In our research work 10 storey regular Reinforced Concrete framed structure is considered and is seismically designed with IS 1893:2016 in SAP2000 version 20 modeling. The different column removal scenarios both in plan and elevation suggested by guidelines were examined by alternate load path method using nonlinear staged construction available in the software and then identify the potential of the structure to withstand progressive collapse. Numerical results were compared by analyzing columns and beams separately by calculating demand capacity ratios and the requirement of percentage of steel for failed structural elements are predicted both in flexure and shear stresses. Our objective is to provide clear conceptual step-by-step descriptions of various procedures for progressive collapse analysis 3D (three-dimensional) Finite Element Methods (FEM) and non-linear static push-down analysis in SAP2000 software was used to assess the progressive collapse potential of a typical gravity-load designed mid-rise reinforced concrete building with open ground floor. The beam is actually designed to resist the shear force up to 39.84 kN. So in order to resist the shear failure we need to provide enough vertical reinforcement. The failed structural elements were re-designed to resist progressive collapse in order to satisfy the acceptance criteria recommended by the guidelines. It’s showed that the incorporation of perimeter beams in buildings improved the progressive collapse resistance as it reduces joint displacement and chord rotation at column removal locations by providing sufficient stiffness and load paths for increased gravity loads. The study results can be used to develop and calibrate the nonlinear numerical model for analyzing high-rise building progressive collapse behavior and can help provide information that may improve new and existing reinforced concrete core-wall building robustness against progressive collapse.

Investigation on progressive collapse resistance of prestressed concrete frames with infilled walls

The finite element numerical model of prestressed concrete frames with infilled walls (IW-PC frame) is established to investigate the progressive collapse resistance under the failure of middle column. The simulation of infilled walls adopts the equivalent three-strut diagonal bracing model. The method of node coupling is adopted in the simulation of prestressed tendons Then the pushdown analysis of the structure is carried out. Meanwhile, the effects of the parameters of infilled walls and prestressed tendons on the compression arch action and catenary action are studied. The results show that the infilled walls greatly improve the anti-collapse bearing capacity of IW-PC frame. They enable beams to reach peak loads in advance, and transform the axial force of beam and prestressed tendons in advance. It is more conducive to make the prestressed tendons fully stressed, so that the structure can enter the catenary action in advance, thereby improving the bearing capacity.

Reliability analysis of reinforced concrete structure against progressive collapse

New reliability computation framework is proposed based on polynomial chaos expansion method and used to investigate the reliability of four typical configurations of reinforced concrete (RC) frame structures under progressive collapse. The analytical model of considered structures was generated using displacement-based fiber elements to simulate frame structural components and an appropriate macro model to simulate masonry infills and subjected to pushdown analysis to assess the anti-collapse capacity of the structures. The reliability and failure mode of frame structures under different column-loss scenario are obtained from the analyses. Finally, based on PCE-based computation, sensitivity analyses are conducted. The effect of uncertain parameter on the progressive collapse resistance of RC frames are discussed. Results shows the failure probabilities of RC frame structure range from 0.0162 to 0.1373. The reliability of frame structures under side column-loss scenario is lower than the other conditions.

Evaluation of the Progressive Collapse of the Reinforced Concrete Frames Considering the Soil–Structure Interaction: Parametric Study Based on the Sensitivity Index

In this essay, to investigate the progressive collapse of the reinforced concrete (RC) frames, a nonlinear static pushdown analysis was performed with column removal scenarios from the first story. At first, a numerical model was simulated and verified with the experimental model in SeismoStruct software without soil–structure interaction (SSI). Afterward, the foundation, soil, and the RC frame were modeled simultaneously in FLAC software and verified with the numerical model of the SeismoStruct software. Furthermore, the effect of SSI was studied on the progressive collapse of RC frames based on the sensitivity index (SI). The sensitivity index is defined as the ratio of the residual capacity under gravity loading of the structure by removing the column to the value of the undamaged structure. The results showed that by considering SSI, the sensitivity index decreases. Then, a parametric study of the framed structures (thickness of the foundation) and substructures (soil density, soil types, soil layers, and the soil saturation conditions) was performed to evaluate the progressive collapse-resisting capacity based on the sensitivity index. The results showed that by considering SSI, with an increase in the soil density and decrease in the groundwater level, the conditions would be better for preventing progressive collapse. It was also shown that rock and silty sands (SM), compared to other studied soil types, and SM and silty sands—silty clay with low plasticity—silty sands (SM-CL/ML-SM), compared to other studied soil layers, are better for preventing progressive collapse.

Numerical investigation on progressive collapse resistance of building isolated by friction pendulum bearings

The horizontal stiffness of the isolated layer would be reduced by friction pendulum bearings (FPB) to enhance the seismic performance of the structures, which means that compressive arching action (CAA) and catenary action (CA) cannot work entirely in FPB isolated buildings, as a result, progressive collapse resistance of the isolated buildings would be reduced. In this paper, progressive collapse resistance of the buildings isolated by friction pendulum bearings was investigated through finite element (FE) analyses. The progressive collapse behaviors of reinforced concrete (RC) buildings isolated by FPB were numerically studied. The load–displacement curve of the structure, the stress–strain responses of the reinforcement, and the deformation mode of the columns based on pushdown analysis were presented and discussed. The influences of the equivalent radius, friction coefficient, axial force of FPB, and the peripheral constraints of the failed column were addressed in some detail. The analysis results indicate that the collapse resistance of the FPB isolated buildings was reduced significantly compared with fixed-based buildings. The equivalent radius, friction coefficient, and applied axial force show limited effect on the progressive collapse response of FPB isolated buildings, but peripheral constraints of the failed column have a significant influence upon the progressive collapse resistance capacity in catenary action (CA) of FPB isolated buildings.

Reliability of fully assembled precast concrete frame structures against progressive collapse

Although fully assembled precast concrete (PC) frame structures using dry connections have been widely promoted, limited studies have been carried out on anti-progressive collapse performance. This study presented a methodology to analyze and compare the reliabilities of entire structural systems between RC and fully assembled PC frame structures, which evaluates the risk and vulnerability of a structure when column failure occurs under accidental loads. First, based on the existing test results of three half-scale moment sub-structures, nonlinear finite element (FE) macro-models were established in OpenSEES software. The verified FE models were applied to three seven-story frame structures (one RC frame and two PC frames). To evaluate the progressive collapse resistance, nonlinear pushdown analysis was conducted on the frame structures using the alternate load path (ALP) approach. Combining the Nataf transformation-based point estimate method (i.e. the improved point estimate method (IPEM)) with the nonlinear analysis results, various load amplification factors (αmax) were estimated. Finally, the reliability indices of the intact and damaged frame structures were calculated using the Zhao-Ono high-order moment method (HOMM). The results revealed that the fully assembled PC frames had higher failure probability (2.1–6.6%) than the RC frame (0.2%) in a catastrophic event.

Robustness Assessment of Reinforced Concrete Frames under Progressive Collapse Hazards: Novel Risk-Based Framework

Robustness assessment is an important component for performance-based progressive collapse design. However, existing methods either do not consider the cascading failure feature of progress collapse, or fail to recognize the randomness in material, geometrical and loading parameters. This paper presents a novel robustness assessment methodology for progressive collapse design of reinforced concrete frames. The proposed methodology includes several novelties: First, it uses a new risk-based robustness index recently developed by the authors. The index quantifies the whole spectrum of risk caused by initiating hazardous events. Second, it includes a unique directional simulation technique, making probabilistic nonlinear pushdown analysis a computationally affordable task. Finally, the assessment can assist in determining if an enhancement design is warranted for such a low-probability-high-consequence event. The study examined four different frame designs to evaluate the effectiveness of seismic and progressive collapse design provisions. The Alternate Path Method (APM) was shown to improve structural robustness significantly, although achieved with considerable additional cost. Ductility designed for seismic loading was also shown to be beneficial for structural robustness against progressive collapse.

Finite element analysis of alternative load paths to prevent disproportionate collapse in platform-type CLT floor systems

• Non-linear model for alternative load paths in cross-laminated timber floors. • Calibration to experimental results and parameter variations. • Collapse resistance by catenary and arching action, and the platform joint itself. • Collapse resistance increases at lower storeys and decreases with longer spans. • Catenary action requires novel connections, arching action requires thick panels. Multi-storey buildings require mitigation of consequences of unexpected or accidental events, to prevent disproportionate collapse after an initial damage. Cross-laminated timber (CLT) in platform-type construction is increasingly used for multi-storey buildings, however, the collapse behaviour and alternative load paths (ALPs) are not fully understood. A 3D non-linear component-based finite element model was developed for a platform-type CLT floor system to study the ALPs after an internal wall loss, in a pushdown analysis. The model, which accounted for connection failure, timber crushing and large displacements, was calibrated to experimental results and then adapted for boundary conditions corresponding to typical residential and office buildings. Subsequently, five parameters (floor span, connection type, vertical location of the floor, tying level, horizontal wall stiffness) were varied, to study their effects on the ALPs in 80 models. The results showed that three ALPs occurred, of which catenary action was the most dominant. Collapse resistance was mainly affected by the floor span, followed by the axial strength, stiffness and ductility of the floor-to-floor connection, the weight of the level above and the floor panel thickness. This study provides an approach to model ALPs in a platform-type CLT floor system to design disproportionate collapse resistant multi-storey CLT buildings.

Progressive collapse resistance of framed buildings with partially encased composite beams

Several research contributions stemmed from the increasing interest in progressive collapse-resistant design and assessment of structures, which was driven by extreme events all around the world. Most of studies focused on the robustness of steel and reinforced concrete (RC) structures, highlighting a knowledge gap on the progressive collapse resistance of framed buildings with partially encased (PE) continuous composite beams, which are an attractive solution compared to, for instance, their cast-in-place RC counterparts.This paper presents the main outcomes of a numerical investigation that was aimed at evaluating/exploring the vertical load-carrying capacity of framed buildings with PE beams after column loss. A numerical fibre-based model was developed and successfully validated against experimental data on two full-scale composite beam specimens, indicating a high accuracy level of the models with displacement-based fibre elements. Then, a wide set of framed building structures with PE beams was generated according to Eurocodes, evaluating their progressive collapse resistance through the alternate load path method. Pushdown analysis was carried out to investigate the gravity load capacity under increasing downward displacement at the location of the removed column. Analysis results outline a huge sensitivity of progressive collapse resistance to the beam type (i.e. PE versus RC), beam depth and span length, with minor influence of longitudinal reinforcement in the case of PE beams. The peak load capacity under column loss was characterised at several limit states corresponding to increasing levels of damage, allowing the proposal of multiple regression models for progressive collapse design and assessment.

A rigid block model with no-tension elastic contacts for displacement-based assessment of historic masonry structures subjected to settlements

This paper deals with the vulnerability assessment of historic masonry structures subjected to settlements using rigid block modelling. A 2-D rigid block model with unilateral elastic contacts and finite friction is developed for the evaluation of the displacement capacity in the large displacement regime by push-down analysis. A variational formulation of the rigid block model is adopted, which relies on associative behavior for displacement rates. Under this assumption, the equation systems governing the behavior of the rigid block model can be uncoupled into two equivalent force and displacement-based problems, thus reducing computational costs. The numerical model was validated against the results of an ad-hoc experimental campaign on small scale tuff panels and against the tests on a small-scale masonry façade subjected to moving supports, from the literature. Applications of the proposed modelling approach are presented to the assessment of a full scale, monumental masonry façade. Following classic force-displacement methods that are used in the case of seismic actions, capacity curves are proposed for the damage assessment induced by settlements. Those state the relation between the base reaction at the moving supports and the displacement of a control point, which is obtained from the push-down analysis. Finally, comparisons with empirical assessment methods from the literature are presented.