Pushdown Analyses Research Articles

Determination of dynamic collapse limit states using the energy-based method for multi-story RC frames subjected to column removal scenarios

The Alternative Load Path method is widely adopted to perform progressive collapse analyses for reinforced concrete (RC) frame structures subjected to column removal scenarios. Considering that the progressive collapses are usually dynamic phenomena, nonlinear dynamic analyses can yield the most accurate results. However, the associated computational cost is high. Alternatively, the energy-based method (EBM) can be employed to efficiently calculate the maximum dynamic responses. Unfortunately, collapse or dynamic limit states (DLS) cannot be directly determined when the EBM is adopted for the progressive collapse analyses, because it is essentially a quasi-static approach. To tackle this issue, in this paper an EBM-Intersection Point-based (EBM-IP-based) method is proposed to effectively determine the DLS. The method is considering that the dynamic instability will occur once the dynamic capacity curve exceeds the corresponding static capacity curve. Hence, it is possible to determine the DLS by making a correction on the intersection point of the aforementioned two curves without performing nonlinear dynamic time-history analyses. Compared with the other energy components, the kinetic energy at the moment of the peak displacement response is relatively small and the effectiveness of the EBM is verified. Through both static pushdown analyses and incremental dynamic analyses for 48 column removal scenarios of six different multi-story RC frames, the effectiveness of the proposed EBM-IP-based method is verified and the associated coefficients are calibrated. Statistical information and (joint) probabilistic density functions (PDF) of the coefficients are identified. Further, stochastic analyses are carried out in order to quantify the model uncertainties when adopting the EBM-IP-based method. On the basis of all the calculation results, a Gumbel distribution is adopted to capture the PDF of the model uncertainty in relation to displacements, while a lognormal distribution is adopted to fit the PDF of the model uncertainty in terms of resistances. Moreover, a multi-variate Gaussian distribution model with two components is employed to fit the joint PDF.

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.

Impact of seismic retrofitting on progressive collapse resistance of RC frame structures

Most of the existing buildings in seismic prone regions have been built before the publication of modern design provisions against earthquakes, resulting in the need for structural retrofitting. Furthermore, some of those buildings are also subjected to additional hazards that may be either triggered by earthquakes (e.g., landslides, soil liquefaction, tsunamis) or associated with other natural or anthropogenic events, such as floods, vehicle collision, blast, and fire. A multi-hazard performance assessment of building structures is thus of paramount importance to implement integrated retrofit strategies, which otherwise would not be economically sustainable if oriented to structural risk mitigation against a single hazard. While retrofit strategies to improve the seismic performance of reinforced concrete (RC) structures have been widely investigated, structural retrofitting against progressive collapse has received very little attention. Within this context, the present paper illustrates a numerical investigation on the influence of seismic retrofitting on structural robustness of a four-storey, five-bay, RC frame building designed only to gravity loads. Seismic performance and structural robustness were respectively evaluated in OpenSees through pushover and pushdown analyses of a fibre-based finite element model. Structural robustness was evaluated under two relevant column-removal scenarios, i.e., the sudden loss of a central and a corner column, whereas earthquake resistance was assessed according to the N2 method, evidencing the need for seismic retrofitting. A retrofit measure based on carbon fibre reinforced polymers was then considered to avoid premature brittle failures. Analysis results show that this retrofit strategy was able to increase both seismic safety and structural robustness. Subsequently, a parametric analysis was carried out in order to evaluate the impact of beam span length and shear strength of the retrofitting system.

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.

Optimal EDPs for Post-Earthquake Damage Assessment of Extended Pile-Shaft–Supported Bridges Subjected to Transverse Spreading

During earthquakes, extended pile-shaft–supported bridges in laterally spreading ground can undergo inelastic deformations, especially in their embedded portions. Following earthquakes, it is critical to assess damage to these difficult-to-inspect portions and determine whether vehicles can safely pass bridges. This paper aims to identify optimal aboveground engineering demand parameters (EDPs) that are readily measurable after earthquakes and have high-quality probabilistic associations with post-earthquake load-carrying capacity of bridges as well as underground difficult-to-inspect EDPs. For this purpose, an experimentally validated bridge-soil-foundation model considering liquefaction-induced lateral spreading is adopted and subjected to ground-motion time histories in the transverse direction. Subsequently, pushdown analyses are performed to assess the post-earthquake vertical load-carrying capacity of bridges. Metrics such as efficiency, practicality, and measurability are established and examined for EDPs. Results show that residual column drift ratio is the optimal EDP for load-carrying capacity assessments, whereas maximum column drift ratio best predicts pile demands. Furthermore, developed probabilistic relationships between residual and maximum column drift ratios will assist in preliminary post-earthquake evaluation of bridges for damage assessment and posting decisions.

Tests and analysis of RC building, with or without masonry infills, for instant column loss

Abrupt loss of a ground story column was experimentally simulated on a 0.8:1-scaled model of a 2 × 3 bay, two-story concrete building with masonry infills along the perimeter of the second story. Three cases were investigated in the infilled building: loss of a column at a corner of the building, inside the plan area or at the perimeter; loss of the perimeter column was also studied with the infills removed and the weight on the model structure increased, to simulate a third story. In general, there was almost no visible damage after each test, neither in the concrete structure nor in the infills. Residual diagonal cracks were visible at the bottom face of slabs, starting from the removed interior column, and especially from the removed exterior column in the repeat test without infills; after the additional load on the floors had been removed, these cracks were not visible anymore. The excellent performance even without the infills is due to the continuity of the bottom bars of beams through the beam/column joints and to the placement of two-way top and bottom reinforcement throughout the slabs, continuous across the supports on beams. During the quasi-stationary free vibration stage that followed column removal, the accelerations measured on the slabs adjacent to the column being removed exceeded only marginally the acceleration of gravity upwards and downwards. This confirms that it is good practice to place two-way top reinforcement in slabs, as well as to use a magnification factor of 2 on the gravity loads of these slabs in pushdown analyses performed to investigate loss of column incidents. Numerical simulation of the tests was successful as far as the prediction of the residual deflections and the decay of vertical vibrations are concerned, but could not capture the high frequency features of the transient vibration.

Estimating the cross-sectional area of inverted-V braces required for mitigating the progressive collapse of Steel Intermediate Moment Resisting Frames

The use of inverted-V braces is one of the retrofitting strategies engineers employ to mitigate progressive collapse in steel intermediate moment-resisting frames (SIMFs). However, the required cross-sectional area of the bracing member is not only dependent on the structural configurations but also on the seismicity of the region. In this study, a new equation is proposed to estimate the cross-sectional area of inverted-V braces required to mitigate failure progression in SIMFs that are subject to abrupt loss of an exterior column in the first storey. In the proposed equation, the area of beam element in the affected span and the seismicity of the region are considered. For this purpose, six SIMF buildings are designed, considering variation in the seismic base shear and the number of storeys. Then, the structural response of these SIMFs when subjected to an exterior column loss is studied. Using dynamic pushdown analyses, failure load factors of these frames are determined. Then, inverted-V braces of five different sizes are added to the studied frames. Results provide a mathematical correlation between the base shear coefficients, the size of structural elements and the associated retrofitting effect. This approximate equation is then validated by analysing two extra case study structures.

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.

Finding Critical Element in the Progressive Collapse of RC Structures Using Sensitivity Analysis

Failure of some elements in the structure can play triggering role for beginning of collapse progression. The critical element is the structural element that when it fails, leads to progressive collapse. To find the critical element of the structure, sensitivity analysis should be done. But there are not specific structural criteria for using in sensitivity analysis. In this paper following GSA, UFC 4-023-03 and ASCE guidelines, sensitivity analysis has been modified and applied to find the critical element of a major number of reinforced concrete structures. 1080 3D nonlinear pushdown analyses were done and the results showed that the place of the critical elements differs in different stories and different plan shapes of high rise structures. In the structures with high aspect ratio in height, the critical element of the whole structure is located in the story of 2/3 height of the structure. When the aspect ratio of the structure in plan increases, sensitivity of the columns in the long dimension of the structure become closer to each other.

Developing a plastic hinge model for reinforced concrete beams prone to progressive collapse

It is known that building structures would undergo nonlinearity during progressive collapse. Given this, modelling the nonlinear behaviour of structural members is critical for assessing their resistance. The objective of this study is to develop the nonlinear modelling parameters of reinforced concrete (RC) beams for the progressive collapse analysis. To achieve this, three types of RC moment-resisting buildings located in high, moderate, and low seismic zones in Canada are designed. Nonlinear pushdown analyses are then conducted on 27 three-dimensional finite element models using ABAQUS to examine the case that one column on the ground level is removed. Based on the analysis results, an idealized moment-rotation curve for modelling the plastic hinge in beams with different ductility is proposed. In comparison with the 2013 GSA modelling parameters, smaller chord rotations are observed from the detailed finite element analysis.

On the Robustness of Earthquake-Resistant Moment-Resistant Frames: Influence of Innovative Beam-to-Column Joints

Background: The deformation capacity of beam-to-column connections strongly influences the robustness of earthquake-resistant Moment Resistant Frames (MRFs) when subjected to a loss-of column scenario. As a consequence, with the aim of foresee the structural response up to the failure, an accurate modelling of the ultimate behaviour of the joints is needed. Objective: In this paper, the influence of the connections on the behaviour of MRFs under a loss-of-column scenario has been analysed considering an accurate modelling of the joints. Method: In addition, in order to achieve this goal, different beam-to-column joints designed for seismic actions and tested at the Salerno University, have been modelled and introduced in a case-study structure, whose response has been evaluated by means of push-down analyses. In particular, the connections analysed and modelled are of three different types: a dog-bone connection, a partial strength Double Split Tee (DST) joint and a partial strength connection with friction dampers. Results / Conclusion: The results of pushdown analyses performed by means of SAP2000 computer software have been examined with the aim to determine the Residual Reserve Strength Ratio (RRSR) index that, combined with the energy balance method proposed by Izzudin et al. (2008), allow to assess the structural ro-bustness.

Evaluation of Structural Robustness against Column Loss: Methodology and Application to RC Frame Buildings.

A computational methodology is presented for evaluating structural robustness against column loss. The methodology is illustrated through application to reinforced concrete (RC) frame buildings, using a reduced-order modeling approach for three-dimensional RC framing systems that includes the floor slabs. Comparisons with high-fidelity finite-element model results are presented to verify the approach. Pushdown analyses of prototype buildings under column loss scenarios are performed using the reduced-order modeling approach, and an energy-based procedure is employed to account for the dynamic effects associated with sudden column loss. Results obtained using the energy-based approach are found to be in good agreement with results from direct dynamic analysis of sudden column loss. A metric for structural robustness is proposed, calculated by normalizing the ultimate capacities of the structural system under sudden column loss by the applicable service-level gravity loading and by evaluating the minimum value of this normalized ultimate capacity over all column removal scenarios. The procedure is applied to two prototype 10-story RC buildings, one employing intermediate moment frames (IMFs) and the other employing special moment frames (SMFs). The SMF building, with its more stringent seismic design and detailing, is found to have greater robustness.

Rate-Dependent Progressive Collapse Resistance of Beam-to-Column Connections with Different Seismic Details

AbstractThe seismic behaviors of different steel beam-to-column moment connections have been fully described by many researchers. Some researchers focus on their progressive collapse resistances by static and rate-independent analyses. However, the influence of strain-rate effect should not be neglected when the main column is removed instantaneously in a progressive collapse analysis. In this paper, the progressive collapse performances of typical steel moment connections with different seismic details, including the welded unreinforced flange-bolted web (WUFB), the welded cover plated flange (WCPF), and the reduced beam section (RBS) connections, are studied by numerical analyses. The rate-dependent stress–strain curves of Q345 steel were obtained from a high-speed tensile machine first. Static push-down analyses were applied to investigate the progressive collapse resistances of beam-to-column connections with different seismic details. The numerical results show that the WCPF connection has the best p...

Structural Redundancy of Prestressed Concrete Box Girder Bridges

Bridges are usually designed and evaluated on the basis of member strength and serviceability criteria; however, they are expected to have sufficient levels of reserve strength and multiple paths to resist collapse should any of their members get damaged or exceed their nominal strength capacity. The ability of a structural system to redistribute the load around damaged members is referred to as structural redundancy. To account for bridge redundancy during the design and safety evaluation process, the AASHTO load and resistance factor design and load and resistance factor rating provide a preliminary set of load modifiers or system factors, most of which were developed based on the code writer’s judgment and experience. This paper evaluated the redundancy of prestressed concrete box girder bridges under vertical loads and lateral loads. Pushover and pushdown analyses were performed by using frame and grillage models in SAP2000. The grillage models were validated by more advanced finite element models built in ABAQUS. The effects of different damage scenarios and types of connections between the box girder and columns on the structural redundancy level were investigated. On the basis of those results, a set of system factors for prestressed concrete box bridges accounting for the system redundancy is proposed. The proposed system factors can be used during the design and safety assessment of prestressed concrete box girder bridges subjected to transient lateral load and vertical vehicle load.

Progressive collapse resistance of RC beams

The current guidelines for evaluating progressive collapse potential of existing and new buildings require analyzing and evaluating the structure for the case of an instantaneous loss of a primary vertical support, such as a column. In this paper, the response of a continuous beam bridging over a lost column is evaluated. A series of beam models are developed by changing structural characteristics such as lateral load design type (ordinary vs. special frames), axial stiffness at the beam boundaries, steel yield stress, amount of integrity reinforcement at bar cut-off locations and the beam span to study their effects on the performance of the beam. The modeling technique used for the analyses of the beams has been validated by comparing experimental and analytical results of an RC beam subjected to large deformations. Push-down analyses are carried out in order to study and characterize the full range of response and compare the behavior of the beams. For each case, the behavior of the critical sections are evaluated and used to describe load transfer mechanisms. The effects of different structural characteristics on the performance of the beam to resist progressive collapse are discussed by comparing the results of the analyses.

Effect of span length on progressive collapse behaviour of steel moment resisting frames

This paper presents results of an investigation into the effect of span length on progressive collapse behaviour of seismically designed steel moment resisting frames which face losing one of their columns in the first story. Towards this aim, several nonlinear static and dynamic analyses were performed for three frames designed for a high seismic zone considering various span lengths. The analysis results revealed that beams and columns of the studied frames had adequate strength to survive one column loss in the first story. However, in order to determine the residual strength of the frame, a series of nonlinear static analyses called pushdown analyses were performed. It was shown that by decreasing the span length to half, the strength of the studied frames increases 1.91 times based on the performance-based analysis perspective. Besides, results of nonlinear static analyses revealed that by increasing the applied loads, the investigated structures are more susceptible to progressive collapse when they lose an internal column.

Assessment of Progressive Collapse Capacity of Earthquake-Resistant Steel Moment Frames Using Pushdown Analysis

The study investigates the progressive collapse resisting capacity of earthquake-resistant steel moment-resisting frames subjected to column failure. The aim is to investigate whether these structures are able to resist progressive collapse after column removal, that may represent a situation where an extreme event may cause a critical column to suddenly lose its load bearing capacity. Since the response to this abnormal loading condition is most likely to be dynamic and nonlinear, both nonlinear static and nonlinear dynamic analyses are carried out. The vertical pushover analysis (also called pushdown) is applied with two different procedures. The first one is the traditional procedure generally accepted in current guidelines that increases the load incrementally to a specified level after column has been removed. The second procedure tries to reproduce the timing of progressive collapse and, for this reason, gravity loads are applied to the undamaged structure before column removal. The load-displacement relationships obtained from pushdown analyses are compared with the results of incremental nonlinear dynamic analyses. The effect of various design variables, such as number of stories, number of bays, level of seismic design load, is investigated. The results are eventually used to evaluate the dynamic amplification factor to be applied in pushdown analysis for a more accurate estimation of the collapse resistance.

Progressive collapse-resisting capacity of framed structures with infill steel panels

In this study the effect of infill steel panels on enhancing the progressive collapse resisting capacity of moment frames is evaluated, and a simple design procedure for infill steel plates is proposed to enhance the progressive collapse resisting capacity of steel moment frames. The progressive collapse potentials of model structures are evaluated by arbitrarily removing a center column and carrying out nonlinear static pushdown analyses using the nonlinear finite element analysis code ABAQUS. The performances of structures with partial or perforated infill panels are also studied. Then a preliminary design procedure for infill steel panels is proposed based on the equivalent single brace simplification of steel panels. The analysis results show that the infill steel panels, even the partial infill panels or panels with perforation, are effective in reducing the progressive collapse potential of moment frames. It is also shown that the proposed design procedure may be effective in preliminary design of infill steel panels to prevent progressive collapse of steel moment frames.

강판벽이 설치된 건물의 연쇄붕괴 저항성능

article i nfo In this study the effect of infill steel panels on enhancing the progressive collapse resisting capacity of moment frames is evaluated, and a simple design procedure for infill steel plates is proposed to enhance the progressive collapse resisting capacity of steel moment frames. The progressive collapse potentials of model structures are evaluated by arbitrarily removing a center column and carrying out nonlinear static pushdown analyses using the nonlinear finite element analysis code ABAQUS. The performances of structures with partial or perforated infill panels are also studied. Then a preliminary design procedure for infill steel panels is proposed based on the equivalent single brace simplification of steel panels. The analysis results show that the infill steel panels, even the partial infill panels or panels with perforation, are effective in reducing the progressive collapse potential of moment frames. It is also shown that the proposed design procedure may be effective in preliminary design of infill steel panels to prevent progressive collapse of steel moment frames.

Fragility analysis of steel moment frames with various seismic connections subjected to sudden loss of a column

In this study the progressive collapse potential of steel structures having WUFB, RBS, and WCPF connections was investigated considering the uncertainty in material properties such as yield strength, live load, and elastic modulus. The beam-end rotation was used as a member-level limit state for progressive collapse. Pushdown analyses of the model structure with three different connection types were carried out after removing one of the first-story columns. Fragility curves were obtained based on the probability of exceeding a given limit state for vertical displacement using the First-Order Second Moment (FOSM) method. The analysis results showed that the RBS connections showed the highest load resisting capacity against collapse due to their highly ductile behavior and that the loss of an exterior column turned out to be more vulnerable for progressive collapse than the loss of an interior column.