Sudden Column Removal Scenario Research Articles

Force Transfer Mechanism and Component-Based Model of Cast-Steel-Stiffened Circular-Tube-Column Frames for Progressive Collapse Analysis

In this paper, the system response, stress redistribution, failure mode, and catenary effect of steel frames with circular tube columns and cast steel stiffener (CSS) joints under a sudden column removal scenario were revealed. Based on this force transfer mechanism analysis, a practical and computationally efficient component-based model considering catenary effects and CSS joint details with a series of springs was established and validated by a detailed solid-element method. By using this component-based model, the proper dynamic response increase factor of the CSS joint frames was investigated. The results show that the great overall stiffness and strength of the CSS limit the deformation of the column front shell. Therefore, the CSS joint frames have superior performance for progressive collapse prevention than the frames using welded joints without stiffeners. In addition, the component-based model is validated to be effective and the dynamic response increase factor of the frames with circular tube columns and CSS joints is smaller than 2.0.

Dynamic experiments on post-tensioned beam-column substructures following the sudden removal of a single interior column

Most experimental investigations about post-tensioned (PT) substructures have been conducted statically, neglecting the dynamic characteristic of progressive collapse. Dynamic performances of PT frame structures against progressive collapse are imperative to study under the sudden column removal scenario, which can reflect the actual progressive collapse more convincingly. This paper presents experimental programs on six half-scaled beam-column substructures, which were tested to evaluate dynamic responses after the sudden removal of a single interior column. During the tests, extensive instruments were installed in prescribed locations to record various dynamic responses such as displacements, loads, strains, and crack patterns. By comparison, the influences of post-tensioned strands (PTS) on the structural mechanisms of reinforced concrete (RC) frames against collapse were demonstrated. The findings cover the span–depth ratio of beam, bonded form of bonded post-tensioned strands (BPTS), and unbonded form of unbonded post-tensioned strands (UPTS). Experimental results highlight that the initial stiffness of RC substructures can be significantly enhanced by the PTS. Resistant mechanisms are mobilized to resist progressive collapse, such as compressive arch action and catenary action. The catenary action develops to resist progressive collapse if a larger span–depth ratio is applied in the design. Moreover, both UPTS and BPTS can increase the damping ratio of the corresponding RC, and the damping ratio of the PT specimen can reach up to 217.23% of that of the corresponding RC. And also, the proposed analytical model and theoretical equations can be well verified by the experimental results.

Dynamic response of RC beam-slab substructures following instantaneous removal of columns

High fidelity solid-element-based numerical modeling is employed in this paper to study the dynamic response of reinforced concrete (RC) beam-slab substructures following instantaneous removal of columns. After validation of the numerical model against experimental results, incremental dynamic analysis is conducted to obtain the dynamic structural resistance to progressive collapse. The numerical results for development of internal forces and distribution of stress and strain are used to illustrate the load redistribution and load transfer mechanisms of RC beam-slab substructures subjected to sudden loss of columns. The numerical model is further employed to explore parameters affecting the dynamic response and structural resistance of beam-slab substructures under sudden column removal scenario. The parameters studied include damping ratio, slab thickness, location of removed columns, multi-column removal sequence and interval. The numerical result shows that the dynamic progressive collapse resistance of the beam-slab substructure is much smaller than the quasi-static test result due to a dynamic increase factor (DIF) of 1.14. Moreover, a minimum slab thickness of 1/45 of span length is found vital for the improvement of progressive collapse resistance of RC beam-slab substructures through developing compressive membrane action (CMA) and tensile membrane action (TMA) as well as enhancing the development of compressive arch action (CAA) and tensile centenary action (TCA) of beams. When the damping ratio is smaller than 5%, the increase of damping ratio can significantly benefit the structural resistance against progressive collapse by producing smaller deflection and milder vibration. The additional loss of the corner column besides the penultimate perimeter column is found to form the most hazardous situation among the double-column removal scenarios. In contrast to the location of removed columns, the column removal sequence and interval tend to little affect the maximum deflection developed and consequently the progressive collapse resistance of substructures.

Scenarij postupnog rušenja čeličnih konstrukcija s nepravilnostima po visini

Sudden removal of load-bearing elements such as columns in engineering structures, and lack of sufficient capacity to withstand the overload caused by removal of these elements can cause damage and Progressive Collapse (PC) in structures. Therefore, the effect of sudden column removal and structural capacity against PC scenarios in medium and high-rise buildings is investigated in this study. The irregularity in height has a great influence on lateral behaviour of structures and it affects the design of cross-sections. Various sudden column removal scenarios are investigated in this research for steel structures with and without irregularity in height. To assess the effects of sudden column removal, the Alternate load Path Method (APM) and Nonlinear Dynamic Analysis (NDA) are utilized. In addition, a Nonlinear Static Analysis (NSA) is performed to investigate the capacity of structures against the PC phenomenon. Using OpenSees software, 10-, 15- and 20-storey structures with three distinct irregularity types are analysed during four different column removal scenarios. The results are presented in the form of static and dynamic nonlinear curves. The results indicate that making geometric irregularity in height in the sudden column removal scenario can cause the reduction of capacity and growth of the structural response in comparison to the structure with regularity in height. Moreover, the capacity of structures increases and the dynamic response declines by increasing the number of elements in the structures.

Performance Assessment of an Energy–Based Approximation Method for the Dynamic Capacity of RC Frames Subjected to Sudden Column Removal Scenarios

The alternative load path method is widely used to assess the progressive collapse performance of reinforced concrete structures. As an alternative to an accurate non–linear dynamic analysis, an energy–based method (EBM) can also be adopted to approximately calculate the dynamic load–bearing capacity curve or the dynamic resistance based on a static capacity curve. However, dynamic effects cannot be explicitly taken into account in the EBM. The model uncertainty associated with the use of the EBM for evaluating the dynamic ultimate capacity of structural frames has not yet been quantified. Knowledge of this model uncertainty is however necessary when applying EBM as part of reliability calculations, for example, in relation to structural robustness quantification. Hence, this article focuses on the evaluation of the performance of the EBM and the quantification of its model uncertainty in the context of reliability–based assessments of progressive or disproportionate collapse. The influences of damping effects and different column removal scenarios are investigated. As a result, it is found that damping effects have a limited influence on the performance of the EBM. In the case of an external column removal scenario, the performance of the EBM is lower as the response is not a single deformation mode according to the results in the frequency domain. However, a good performance is found in the case of an internal column removal scenario in which the assumption of a single deformation mode is found to be sufficiently adequate. Probabilistic models for the model uncertainties related to the use of the EBM compared to direct dynamic analyses are proposed in relation to both the resistances and the associated displacements. Overall, the EBM shows to be an adequate approximation, resulting in a small bias and small standard deviation for its associated model uncertainty.

Influence of imperfections on the progressive collapse of steel moment resisting frames

The performance of steel moment resisting frames with sway imperfections is numerically studied in this paper, under various sudden column removal scenarios. The response of 2D frames with varying values of sway imperfection is comparatively examined against respective perfect frames, under both nonlinear static and time history analyses. In this context, the study also investigates the role of frame design, working with two groups of alternatively designed frames: the first one governed by earthquake loading and the second governed by wind loading. Furthermore, some additional variables to the study are introduced. These are the number of frame storeys, the location of the removed column and the duration of the column removal. The obtained results reveal that the imperfect frames, depending on the location of the removed column, can deteriorate in terms of ductility, reaching increased column demands, compared to the perfect ones.

Quantification of model uncertainties of the energy-based method for dynamic column removal scenarios

The Alternative Load Path (ALP) method is widely used to assess progressive collapse resistance of reinforced concrete (RC) structures by notional removal of one or more load-bearing elements. In general, a nonlinear time history analysis (NTHA) is needed to perform such an analysis if dynamic effects are explicitly taken into account. To avoid cumbersome nonlinear dynamic analyses, the energy-based method (EBM) is a promising technique to predict the maximum dynamic responses of a structural system. In this article, the accuracy and precision of the EBM is evaluated based on a validated finite element model of a tested RC slab subjected to a sudden column removal scenario, in particular in relation to the investigation of tensile membrane action (TMA). Influences of dynamic effects are evaluated, i.e. in relation to strain rate effects, damping, and the time duration of support removals. Strain rate effects are observed to have only slight influences on the dynamic responses. The strain rate dependency of reinforcement is found to have a more significant influence on the responses in TMA stage, although also to a limited extent. The magnitude of the load has a significant influence on the dynamic response, as do increasing damping ratios due to the corresponding significant energy dissipation. Finally, the dynamic response reduces with increasing time duration of the column removal. Based on the results of the stochastic analyses, the EBM is observed to perform well based on a comparison with the results of NTHA in both flexural and TMA stages. Furthermore, in relation to the analyzed case studies on reinforced concrete slabs, the model uncertainty of the responses obtained through the EBM compared with the NTHA is found to be represented well by a lognormal distribution with mean of 0.95 and a standard deviation of 0.20, for evaluating the loads of first rupture of reinforcement. Furthermore, a lognormal distribution with mean 0.96 and standard deviation 0.13 is found appropriate to represent the model uncertainty on ultimate load-bearing capacity predictions. Model uncertainties are also obtained with respect to the model predictions for displacements at the moment of the first rupture of reinforcement, displacements at the ultimate load-bearing capacities, and both loads and displacements at second load peaks.

Experimental dynamic collapse response of post-and-beam mass timber frames under a sudden column removal scenario

In this study, an experimental program was carried out to investigate the dynamic behaviour of post-and-beam mass timber frames, manufactured from LVL structural products, under a sudden column removal scenario. Twenty-five free-fall and two additional static tests were performed on scaled-down frames assembled with three beam-to-column connection types, referred to as “Double-beam”, “Megant type” and “T-section”, currently used in mass timber buildings. The structural responses, failure modes and dynamic increase factors (DIF) are presented and discussed. For frames assembled with connections exhibiting a brittle failure in the timber, the cracks were found to develop earlier in dynamic tests than in static tests, resulting in large experimental DIF values over 2.0. However, for connections displaying ductile failure modes, the design DIF value of 1.5 proposed in the literature was found to be reasonable. Pseudo-static responses were calculated and found to be inconsistent in predicting the dynamic responses. This paper presents an essential understanding of the dynamic behaviour of post-and-beam mass timber frames and lay the foundation for future further studies aiming at investigating the dynamic responses of the entire post-and-beam mass timber buildings with, e.g. cross laminated timber (CLT) floors.

Nonlinear Dynamic Response of a Precast Concrete Building to Sudden Column Removal

Robustness of reinforced concrete (RC) structures is an ongoing challenging research topic in the engineering community. During an extreme event, the loss of vertical load-bearing elements can activate large-deformation resisting mechanisms such as membrane and catenary actions in beams and floor slabs of cast-in-situ RC buildings to resist gravity loads. However, few studies have been conducted for precast concrete (PC) buildings, especially focused on the capacity of such structures to withstand column loss scenarios, which mainly relies on connection strength. Additional resistance resource and alternate load paths could be reached via tying systems. In this paper, the progressive collapse resistance of a PC frame building is analyzed by means of nonlinear dynamic finite element analyses focusing on the fundamental roles played by beam-to-column connection strength and tying reinforcement. A simplified modelling approach is illustrated in order to investigate the response of such a structural typology to a number of sudden column-removal scenarios. The relative simplicity of the modelling technique is considered useful for engineering practice, providing new input for further research in this field.

Progressive Collapse Resistance of Bolted Extended End-Plate Moment Connections

When a progressive collapse occurs due to sudden column removal, the moment connections must have adequate strength and be able to bridge over the damaged element. The present study comprehensively investigates the behavior of eight different types of extended end-plate beam-to-column connections against progressive collapse. The proper finite element models have been extended to assess the behavior of these bolted connections under a sudden column removal scenario. Specimens were checked by nonlinear analysis method. The fracture modes, Von-Mises stresses, vertical load–displacement and load factor–displacement curves, load transferal mechanisms, and other analytical results comparative were reported in detail and discussed for various investigated beam-to-column connections. The analysis results revealed that the overall failure of the samples occurred in the connection region under the catenary action mode at large displacements. Also, the results were verified with available experimental data. Among all investigated connections, the highest stresses could be applied to the sixteen-bolt stiffened connection, and this sample had the most excellent behavior. In the design of buildings exposed to unusual loads due to progressive collapse, the significant axial force created in the connections should be considered in the design stages of these elements. Also, it is recommended that at least three rows of bolts are embedded in the bottom area of end-plate connections when the structure is at the risk of progressive collapse.

Static and Dynamic Responses of Reinforced Concrete Structures under Sudden Column Removal Scenario Subjected to Distributed Loading

In this paper, static and dynamic experiments on reinforced concrete beam-column frames under single-column-removal scenario applying a multipoint loading method were conducted. One of the objectives was to investigate structural behavior compared with the single-point loading method, which has been popularly used in previous studies. By equally applying point loads at four locations of the double-span beam structure, the test setup successfully simulated the uniformly distributed loading condition, which is generally applicable for gravity loads in practice. Compared with the previously conducted static tests based on concentrated loading method, structural response from the static tests under multipoint loading condition differed not only on load-bearing capacity but also on failure sequence and displacement profile. On the basis of the test results, the analytical relationship between behaviors of the two loading methods was developed and verified. Compared with the static tests, the dynamic tests highlighted dynamic effects created by the column loss event and confirmed the structural behavior and failure modes observed in the static environment. The dynamic tests also verified the correctness and conservatism of the dynamic assessment framework using a previously proposed energy-based approach. Most important, both the static and the dynamic tests of structures under distributed loads showed less development of catenary action against progressive collapse compared with concentrated loading tests.

Impact of two columns missing on dynamic response of RC flat slab structures

Sudden removal of columns caused by unexpected extreme loading may increase the bending moment and shear force at surrounding column-slab connections significantly, which may trigger punching shear failure at these connections and lead to progressive collapse of entire reinforced concrete (RC) flat slab structures. To quantify the dynamic load redistribution of flat slab structures subjected to different extents of initial local damage (one-column or two-column removal), two multi-panel RC flat slab substructures were tested subjected to simulated sudden column removal scenarios. These two specimens have identical dimensions and reinforcement details. One of the substructures suffered a loss of an interior column scenario while another one was subjected to a two columns (one interior column and one edge column) missing scenario. The dynamic response, deformation shape, failure mode, and local strain gauge results are presented. It is found that although both specimens had exceeded their yield load capacity, no collapse occurred as considerable compressive membrane action developed in the RC slab to help redistribute the loads. With the drop panels, no punching shear failure was observed in the slab-column connections after removal of the column. To further study the progressive collapse robustness of flat slab structures, finite element (FE) models were validated and parametric studies were carried out. Numerical analysis indicated that the axial force initial carried by the lost columns may amplify up by 1.25 times before redistribution into surrounding columns. Moreover, the dynamic ultimate load capacity of Specimens S1 and S2 are as large as 1.92 and 1.18 times of their design service load, respectively.

Experimental study on progressive collapse resistance of steel frames under a sudden column removal scenario

A comprehensive experimental apparatus for the progressive collapse testing of steel frames has been developed. The apparatus is suited for the testing of planar steel frames to study the load transfer process and the progressive collapse resistance of steel structures under a column removal scenario. In order to simulate a sudden removal of a middle column at the ground storey of the frames, a removable column unit has been designed to allow for an instantaneous knock-out by a pendulum hammer during the test. To avoid the out-of-plane instability of the planar steel frames, an out-of-plane restraining system has been designed and integrated into the test apparatus. Weights simulating the desired gravity loads were attached to the test frame through holding baskets, which were designed to minimize unwanted shaking and ensure that the suspended baskets moved together with the deformed steel frames during the tests. Experimental results showed that the column removal mechanism in the test apparatus was effective. Using this apparatus, the dynamic behaviour of three planer steel frames under a column removal scenario was investigated. Based on the measured deformations and strains, the dynamic response, collapse modes, load transfer path of the steel frames after the removal of the middle bottom column are studied.

Analysis of robustness of steel frames against progressive collapse

A finite element (FE) modelling study on the progressive collapse of steel frames under a sudden column removal scenario is presented. The FE models were developed with refined shell elements using the general purpose FE software package ABAQUS. The FE models were first validated by comparing the predicted responses with the measured results from an experimental study on the progressive collapse of three steel frame specimens. A new bearing capacity-based index was introduced to quantify the robustness of the steel frames. The robustness index takes into account the dynamic effects and the plastic internal force redistribution. By incorporating the experimental results and the numerical simulations, the dynamic amplification factor in the progressive collapse of the steel frames was assessed. The validated FE models were further applied to identify the collapse modes of planar steel frames and evaluate the influences of a range of mechanical and geometrical parameters on the progressive collapse and the robustness. The results showed that, for a column-instability induced progressive collapse mode, the influences of the damping is larger than the influences of the strain rate of material on the robustness. However, for the connection-failure induced progressive collapse mode, the influences of the strain rate is larger than the damping. The type of the steel frame (e.g. weak-beam strong-column or vice versa) and the location of the column removal were both found to play an important role in influencing the critical load and the robustness of steel frames.

Influence of modelling strategies on uncertainty propagation in the alternate path mechanism of reinforced concrete framed structures

Reliable performance-based evaluation of structures subjected to extreme loading scenarios, which is a function of structural response uncertainty characterization is a vital question. This paper aims to study the major sources of uncertainty in the alternate path response quantities of reinforced concrete framed structures subjected to sudden column removal scenarios. Using global variance-based sensitivity analysis, influence of nonlinear modelling approaches on uncertainty propagation is studied. Sensitivity of structural response quantities to the input uncertainties using plastic analysis with lumped plastic hinges found to be quite distinct compared with those of obtained using fibre-based modelling approaches, where axial–flexural deformation interaction, and in turn, compressive arching action is taken into account. Moreover, uncertainty propagation at different load levels is investigated using nonlinear incremental dynamic analysis (NIDA). Results obtained from displacement-based element (DBE) formulation, and force-based element (FBE) formulation were in good agreement at low to moderate load factors, where use of DBE formulation found to be computationally more efficient. However, at high load factors, where the structure is prone to progressive collapse, FBE formulation provides more reliable solution as the DBE formulation underestimates local response quantities, and in turn, underestimates the probability of failure. Finally, as uncertainty evaluation using fibre-based modelling approaches is computationally expensive, a substructure technique is applied, and influence of structural idealization on uncertainty propagation in structural response quantities is investigated. Results show that structural idealization is an efficient technique for reducing computational costs in terms of probabilistic analysis, especially when hundreds or thousands of simulations are needed to be performed.

Dynamic analyses of bolted-angle steel joints against progressive collapse based on component-based model

Some design methods have been proposed to prevent progressive collapse of building structures. Alternate Path (AP) Method is the most effective and popular one among them. Based on component-based joint models, this paper takes AP Method to study the dynamic performance of two-dimensional (2D) bolted-angle steel joints under a sudden column removal scenario. The comparison between the quasi-static and dynamic responses of the component-based models simulated by finite element software and the experimental test results shows that the component-based models are reliable. After that, based on the validated component-based models, parametric study was conducted in order to study the dynamic responses of bolted-angle steel joints subjected to different levels of sudden gravity loads. These 2D steel joints employ two types of beam–column connections, including web cleat connections and top and seat with web angle connections. Dynamic increased factors (DIFs) are obtained by comparing the acquired dynamic responses with the corresponding nonlinear static responses of the bolted-angle steel joints. Finally, DIFs calculated in this study are compared with the regulations of Department of Defense (DoD) in United States and a simplified energy balance method. As a conclusion, it is found that the numerical results in this study are in good agreement with the energy balance method.

Dynamic Performance of Flush End-Plate Beam-Column Connections and Design Applications in Progressive Collapse

An experimental program was conducted in this study to investigate the dynamic behavior of flush end plate steel beam-column cruciform connections following instantaneous removal of a central supporting column. The dynamic tests were performed by using a quick-release mechanism to simulate sudden column-removal scenarios. In the test program, the geometries of the flush end-plate connections remained unchanged but subjected to five different magnitudes of uniformly distributed load. Another five quasi-static tests were also carried out for comparison with the dynamic response and investigation of the dynamic increase factors (DIF). Test results showed that the release-time durations of the column support force were approximately 30 ms for all five dynamic tests. For the same initial applied dead loads, the maximum dynamic displacement was significantly increased compared to the corresponding quasi-static displacement. In order to observe the full dynamic performance of the tested connection until final failure, a general-purpose finite-element software was used to conduct the three-dimensional numerical simulations. Comparison results showed that the numerical model could accurately simulate the monotonic quasi-static test results and the dynamic test results under sudden column removal. Subsequently, a series of parametric studies was conducted to investigate the connection behavior considering the load-release time, different loading methods, and the magnitude of uniform distributed load. By comparing the full dynamic response of the flush end-plate connection with its corresponding quasi-static response, both the displacement-based DIF and force-based DIF could be respectively determined. The paper also addresses which DIF is more appropriate for the design of structures to resist progressive collapse.

Investigations of nonlinear dynamic performance of top-and-seat with web angle connections subjected to sudden column removal

It is well known that progressive collapse is a complicated dynamic process with geometry and material nonlinearities. Sudden column removal scenario is a simple yet effective method for analysis and design of structures to mitigate progressive collapse. The main objective of this study is to investigate the dynamic performance of top-and-seat with web angle (TSWA) steel beam–column connections under progressive collapse condition. This type of connection represents typical bolted cleat connections with excellent ductility. Each specimen consisted of two adjoining beams pinned at the far ends and connected to a middle column stub. Five dynamic tests for the TSWA connections subjected to sudden removal of the middle columns were conducted in Nanyang Technological University. Another five corresponding static tests were also carried out for comparison with the dynamic behaviour. Test results showed that the release-time durations of the column support force were around 30ms for all the five dynamic tests. Transient dynamic responses with free vibrations were observed for the connections following instantaneous removal of the middle columns. The maximum dynamic displacement was significantly increased compared to the static connection response. In addition, numerical simulations were also conducted using the general-purpose finite element software ABAQUS. The three-dimensional finite element model was validated by comparing the simulation results against the test data. Parametric studies were carried out to investigate the full dynamic connection performance and its structural resistance under push-down analysis to simulate progressive collapse. By comparing the full dynamic response with its corresponding quasi-static response, both the displacement-based dynamic increase factor (DIF) and force-based DIF were investigated, respectively. The paper ends with some discussions on practical applications of displacement-based DIF and force-based DIF.

Component-based steel beam–column connections modelling for dynamic progressive collapse analysis

A component-based model is developed to predict the dynamic response of bolted-angle connections, such as web cleat connections and top and seat with web angle (TSWA) connections subjected to sudden column removal scenario. This model considers the behaviour of bolted-angles under large tension forces. A failure criterion determined from the test results is introduced into the model for the bolted-angle component to predict the connection resistance. The hysterical behaviour of each component under cyclic loads is also included for ensuring dynamic analysis. The proposed component-based connection models with detailed springs as well as their constitutive laws are implemented within a self-developed finite element programme FEMDYA to validate the model against both static and dynamic test results. A comparison study showed the capabilities of the component-based model in predicting the connection performance. Based on the failure criterion of the connection component, an accurate simulation of the fracture of the connections is conducted. Subsequently, the component model is incorporated directly into two types of 4-storey steel frames to simulate catenary action developed due to the loss of support to a middle column. The analysis results indicate that a value of up to 2.9 should be used as the dynamic increase factor for structures with web cleat connections when incorporating the dynamic effects into the nonlinear static load resistances. It is also shown that the ultimate load capacity of unbraced structure is much smaller than the one in the braced frame due to horizontal movements of adjacent columns under catenary action.

Redesigning composite frames for progressive collapse

Explicit evaluation and improvement of a building's robustness require taking into account all the main resistance mechanisms, employing realistic failure criteria and obtaining quantitative results based on a suitable level of structural idealisation. The Imperial College London method has made significant progress towards establishing a soundly based analysis methodology for calculating and comparing the performance of different designs. Recent advances have facilitated the execution of extensive parametric studies that are quick to run and thus able to provide comprehensive results. These advanced tools are employed here to examine the robustness of a simplified version of the Cardington test frame and to compare its performance with that of a bare steel equivalent. Both arrangements fail to provide the necessary resistance, with the bare steel being inherently less robust. The paper introduces a step-by-step methodology to determine the most efficient and practically applicable changes, making it possible to redesign the composite frame in a way that it will be sufficiently robust to cope with any sudden column removal scenario. Comparison of the methodology with simply increasing tying capacity reveals that the latter does not have a direct and proportional effect on the frame's resistance. This leads on to consideration of how tying capacity might be used within a more informed context.