Collapse Analysis Research Articles

Progressive Collapse Analysis of Single-Layer Latticed Domes With Fabricated Joints

Progressive collapse accidents of single-layer latticed domes seriously threaten public safety. The progressive collapse-resisting capacity (PCRC) is gradually becoming an essential requirement in the design of spatial structures. Currently, the joint system used in spatial structures can be divided into two categories: welded joints and fabricated joints. The semi-rigidity of fabricated joints may have a significant influence on the PCRC of single- layer latticed domes. In this study, the PCRCs of single-layer fabricated latticed domes with identical span and rise-to-span ratio are evaluated based on the critical progressive collapse load (CPCL). The collapse mechanism of single-layer latticed domes with different grid forms is revealed by progressive analysis. In addition, the effects of joint rigidity, grid form and type of initial failure are further evaluated. The results indicate that the collapse mechanism of single-layer latticed domes includes the radial propagation type and the circumferential propagation type. The latticed domes with quadrilateral grids have much lower PCRC than those with triangular grids. The CPCLs of weld-jointed latticed domes are 5% to 22% higher than those of the fabricated latticed domes with the same grid form. The above influence should be fully considered in the progressive collapse-resisting design of latticed domes with fabricated joints.

Anti-collapse mechanism and reinforcement methods of composite frame with CFST columns and infill walls

Masonry infill walls serve as building partitions and are generally considered non-structural components. Their weights are considered in progressive collapse analysis, but the resistance of the infill walls is normally ignored in design standards. Based on the reasonable selection of constitutive models, a refined finite element (FE) model for the collapse resistance of concrete-filled steel tubular (CFST) composite frame with infill walls was established by ABAQUS/Explicit. Cohesive elements were inserted between different masonry blocks to simulate the mortar joints. The collapse resistance contribution and reinforcement methods analysis of the CFST frame with infill walls were carried out based on the validated FE models. Results show that the infill walls significantly contribute to resisting vertical load in the initial loading stage, with a maximum contribution of 55.3%. The infill walls, which are treated as the equivalent compressive struts, change the load-resisting path and effectively improve the load redistribution ability of the frame. The V-type oblique arrangement of tie rebars has better tie effect and collapse resistance of the frame than other arrangements. After pasting the CFRP sheet and spraying the ECC material to reinforce infill walls, the peak load can be increased by 25.1% and 22.9% respectively, and the ultimate load can be increased by 96.2% and 74.5% respectively. X-type pasting the CFRP sheet reinforcement has a better collapse resistance than others. Furthermore, based on the simplification of the infill walls as the diagonal struts, the simplified calculation formulas of anti-collapse capacity of CFST frame with infill walls were studied.

Progressive collapse analysis of seismically designed braced and unbraced steel frame structures

Progressive collapse analysis of seismically designed braced and unbraced steel frame structures

Collapse scale estimation of a steel-framed building under large-scale fire spread using key element index

In this study, the collapse behavior of a steel-framed building induced by the spread of a large-scale fire was analyzed using the ASI-Gauss code, and the collapse scales of buildings were estimated using a key element index. The results of the fire-induced collapse analyses indicated that the collapse scales were highly dependent on the fire range and location. The collapse scales tended to increase when the fire range widened on the lower floors. Moreover, there was a greater increase in scale when fire occurred in the peripheral area of the building, compared to when the fire occurred in the inner area. Based on the numerical results, the collapse scales of a building were examined using the relationships between the integrated values of the key element index (KI), a parameter that indicates the contribution of columns to the overall strength of a building, and the sum of the heights of the remains. It was confirmed that the collapse scales were larger when the integrated value of KI of the columns in the spreading range of the fire reached a specific threshold, indicating that the collapse scales of buildings can be estimated by accumulating the KI of damaged columns.

Currency Crisis or Overproduction? A Marxian Analysis of the Exchange Rate Peg Collapse in Brazil

We revisit the recent past of the Brazilian economy in an attempt to present an alternative characterization of the nature of the late 1990s crisis. The theoretical basis of this analysis is Marxian political economy. This choice is justified by the contraposition between the Marxian theory of overproduction cyclical crisis and the most popular currency crisis theories, revealing that while the latter focus on the phenomenon’s appearance, the former analyzes it in depth. The analysis of capital accumulation during Brazil’s Real Plan shows that the examined crisis can be characterized as another manifestation of the aforementioned phenomenon: the overproduction cyclical crisis. JEL Classification: B51, E32, N16

Modified plasticity constitutive model for extruded aluminum alloys

Aluminum alloys have been increasingly used in a wide range of construction applications, especially in important public buildings. A plasticity constitutive model that can accurately describe the elastoplastic behavior of aluminum alloys under complicated stress states is of great importance in precisely simulating aluminum alloy structures under complicated working conditions. Also, a precise plasticity model serves as the foundation for studying the ductile fracture of metals, and is therefore crucial for structural analysis involving large deformation, such as progressive collapse analysis. The classic J2 plasticity model based on the von Mises yield criterion is the most commonly utilized model for ductile metal materials. However, it ignores the effect of stress state on metal plasticity behavior, making it inapplicable to aluminum alloy materials under various complicated stress states. This study experimentally demonstrated that stress triaxiality and Lode angle have a noticeable effect on the plasticity behavior of extruded aluminum alloys (6061-T6, 6082-T6, and 6063-T5). Accordingly, a plasticity constitutive model suitable for extruded aluminum alloys under complicated stress states was proposed and validated, including a full-range hardening law and a new yield criterion. In addition, the parameter calibration method for this new model was detailed. Finally, comparisons between the experimental and numerical results proved the high accuracy of the proposed model in predicting the actual response of a structural extruded aluminum alloy under complicated stress states. Compared with previous studies, the proposed model can not only consider the effects of stress triaxiality and Lode angle, but it can also provide a more reasonable description of yield surface under considerably high or low stress triaxiality.

Progressive collapse analysis of precast reinforced concrete beam-column assemblies with different dry connections

Beam-column joints using dry connections usually experience severe damage under large deformations, causing precast concrete (PC) frames with dry connections to become highly vulnerable to progressive collapse. Hence, this study conducted a static pushdown test adopting uniformly distributed loading on four PC beam-column assemblies using dry connections and one reinforced concrete (RC) substructure to investigate the collapse-resisting behavior under the middle-column removal scenario. The tested dry connections included top-and-seat angle connection (TA), strengthened top-seat angle connection (STA), and two refined connections with unbonded post-tensioning tendons (UPTA and UPSTA, respectively). Results showed that compared with specimen RC, the resistance of specimen TA at the beam flexural and compressive arch action (B-CAA) and catenary action (CA) stages dropped by 41% and 27%, respectively, due to the buckling of steel angles and endplates (B-CAA) and the fracture of steel angles and bolts (CA). Specimen STA had a 7% greater resistance of B-CAA because of the strengthened steel angles. However, the ductility decreased, with the displacement of rebar fracture decreasing by 37%, leading to a 30% resistance reduction of CA. The unbonded post-tensioning tendons dramatically improved the structural integrity, contributing to 52% and 97% increase in the resistance of the CA of UPTA and UPSTA, respectively. Further numerical analyses indicated that the restraint gaps reduced the initial stiffness of the collapse responses, and a good rebars welding anchorage condition could remarkably improve the resistance in the B-CAA and CA stages. An improved joint was proposed based on UPTA and rebar welding anchorage to improve deformation capacity while retaining reasonable collapse resistance. Finally, the resistance contributions from different mechanisms and components were identified through a developed calculation procedure.

Inertial effects in just-saturated axisymmetric column collapses

This work introduces a scaling analysis of sub-aerial axisymmetric column collapses of glass beads and Newtonian glycerol-water solutions mimicking some of the behaviours of debris flows. The beads were in a size range where their inertia partly decouples their collapse behaviour from the water column. Experiments explored a range of viscous, surface tension and particle inertia effects through systematic variation of particle size and fluid viscosity. Crucially a geotechnical centrifuge was used to access elevated effective gravitational accelerations driving the collapse, allowing field-scale viscous and surface tension effects to be replicated. Temporal pore pressure and run out front position evolution data was extracted using a pressure transducer and high speed imaging, respectively. A least-squares fitted scale analysis demonstrated that all characteristic dimensionless quantities of the acceleration phase could be described as a function of the column-scale Bond number text{ Bo }, the Capillary number text{ Ca }, the system size r^*, and the grain-fluid density ratio rho ^*. This analysis demonstrated that collapses as characterised by pore pressure evolution and front positions were controlled by the ratio of text{ Bo}/text{Ca}. This indicates that grain-scale surface tension effects are negligible in such inertial column collapses where they may dominate laboratory-scale granular-fluid flow behaviour where geometric similarity between grain and system size is preserved.Graphical abstract

Progressive collapse and soil stress analyses of Manupali steel truss bridge in Lantapan, Bukidnon under hydraulic and traffic threats

Bridges designed to comply with current design codes may not provide enough strength to arrest a possible local failure following an abnormal event, thus leading to a progressive collapse. One may employ different approaches that vary according to linearity and dynamicity to analyze the potential of a structure to progressive collapse. Together with a prior risk assessment, this study analyzed the susceptibility of the Manupali steel truss bridge to progressive collapse using an adapted nonlinear static approach and assessed the bridge’s pile foundation capacity concerning changes in the imposed stresses caused by the dynamic effects of progressive collapse. Using P-Delta analysis in STAAD.Pro CONNECT Edition V22, this study determined that under its self-weight, the Manupali steel truss bridge is susceptible to progressive collapse, i.e., it is fracture critical. Nonetheless, being such does not mean the bridge is inherently unsafe, only that it lacks redundancy in the design. Furthermore, this study found that a collapse does not significantly detrimentally affect the foundation system except when the dynamic effect is so tremendous. With the results, this study recommends that the design of bridges should consider abnormal load cases to mitigate progressive collapse.

Progressive collapse assessment of Osmangazi Suspension Bridge due to sudden hanger breakage under different loading conditions

The design life of suspension bridges can expire in a shorter time than the estimated time due to many factors such as strong winds, earthquakes, heavy tonnage vehicle loads, vehicle crashes etc. Small cracks/damages that may occur due to corrosion and fatigue effects, especially in steel elements, may increase over time and cause sudden breakages. It has been seen in the past years that hangers, which are one of the slender structural elements, can break with the tearing of the plates, especially at the hanger-deck connection points. The creation of various damage/accident scenarios during the design of these structures, which are of high importance in terms of both the country's economy and life safety, will enable quick decision-making during possible events. For this purpose, scenarios for different loading condition and different number of hanger breakage situations were created for the Osmangazi Suspension Bridge with a main span of 1550 m, which was put into service in Turkey in 2016, and progressive collapse analyses were made. The analyses, which was started by removing only one hanger, taking into account the dead load and dead load + vehicle load of the bridge, continued until the bridge collapsed. After each removed hanger, the internal force and displacement values of the hangers, cables, deck and towers of the bridge were obtained and compared with each other. The results obtained show that large force and displacement values occur in the field where the hanger is breakage, but the other parts of the bridge are not affected by this event. As the number of hangers breakage increases, the tensile strength of the hanger immediately adjacent to the hanger breakage may exceed the ultimate tensile force that the hanger can bear. This situation causes the hanger to start to break automatically and the bridge to collapse.

Progressive Collapse Analysis by Comparing Intermediate Moment Resisting Frames and Dual Systems with Buckling Restrained Braces

Progressive collapse is the term used to describe the phenomena where localised damage to a key structural element causes the entire or a portion of the structural element to fail. The progressive collapse potential of steel dual systems with buckling restrained bracing was assessed and compared in the current study with that of the more traditional intermediate moment resisting frames. Utilising the alternate path approach, the study was carried out 5- in storey frames. The crucial columns and nearby braces, if existent, were instantaneously removed following GSA rules, and the structure's capacity to properly absorb member loss was examined. ETABS software was used to model, analyze and perform non-linear dynamic analysis using El Centro data on the structures. The results showed that the dual systems showed better progressive collapse capacity when compared to the intermediate moment resisting frames.

Late mechanical properties and energy evolution mechanism of cemented tailings backfill under early damage

Cemented tailings backfill (CTB) is a composite material prepared using cement, tailings and water. During early mining operation, CTB is inevitably subject to failure and damage caused by human or equipment crushing. However, the current literature is silent on the condition of the CTB after early damage. In this study, an analysis method of mechanical properties and failure models of early damaged CTB based on energy evolution was proposed which provided new ideas to reduce the failure and collapse analysis of CTB in mines. The results show that the early damage had significant effects on the late mechanical properties, energy evolution, failure model and microstructure of the CTB. Moderate early damage improved the later loading capacity of CTB. The UCS increased and then decreased in the late CTB at damage ages 3 d and 7 d, whereas it continued to decrease at ages of 14 d and 21 d. The early damage input energy was divided into releasable elastic deformation energy dominated by compression intensive deformation and plastic deformation energy dominated by damage deformation. The total energy after maintenance of the damaged CTB was the sum of the undamaged CTB energy and the early elastic deformation energy and then removed the plastic deformation energy. The late CTB failure model was from shear damage to tensile damage and then to mixed tensile-shear damage, which showed a certain damage effect. Combined with the economic benefits and the late mechanical properties of the damaged CTB, the CTB with a damage age of 7 d was more advantageous.

Hysteretic model for corroded reinforced concrete columns retrofitted with FRP

A hysteresis model was developed for fiber reinforced polymer (FRP)-retrofitted reinforced concrete (RC) columns with corroded reinforcing bars. The test data of 49 FRP-retrofitted corroded columns and 19 intact columns (with no corrosion or FRP wraps) under repeat-cyclic loading were collected to establish a database. A polygonal model was adopted to simulate the hysteretic behavior of FRP-retrofitted corroded columns. This was determined using backbone and cyclic parameters. For the backbone parameters, a hybrid influence factor (HIF) was introduced to incorporate the coupling effects of corrosion and FRP retrofitting. A suite of empirical equations was developed using multivariate linear regression analysis to predict the HIFs of each backbone parameter in association with the corrosion rate and important column design parameters. Moreover, an empirical relationship was developed to determine the cyclic parameters of the hysteretic model using a regression analysis. The predicted hysteretic curves were compared with the experimental results, demonstrating sufficient accuracy for both intra- and extra-database tests. Finally, the developed hysteretic model was used to establish a macro-type structural model for the FRP-retrofitted corroded RC frames. This benefitted the analysis of structural collapse under earthquakes, and the effects of the corrosion rate and FRP retrofitting schemes on the seismic collapse capacity of RC frames were examined.

Analytical approach for force-displacement behavior of deformed reinforcing bars embedded in concrete

Component-based joint model suggested by Eurocode is a simple yet efficient approach to evaluating the joint behavior of composite beam-column subassemblies. The reinforcing bars in this approach play an instrumental role, especially for progressive collapse analysis where the ultimate resistances and structural ductility of beam-column subassemblies are significantly influenced and in some extreme cases directly governed by the reinforcing bars. This paper describes an analytical approach for predicting the force-displacement characteristics of deformed reinforcing bars that are embedded in concrete blocks. In contrast to previous studies that roughly predefined the profiles of bar and bond stresses in tension, this paper utilizes an iteration method to provide a more accurate and simpler description of such non-uniform local behavior. This approach has greater flexibility to account for the variations in the embedment length of reinforcing bars, lateral restraints and failure modes. The proposed approach is verified using four groups of published reinforcing bar pull-out tests. The predicted force-displacement relationships, distributions of local slips, bond stresses, and bar stresses along the length are shown in reasonable agreement with the test results. Finally, component-based joint models are established for composite beam-column subassemblies under progressive collapse scenarios, in which the force-displacement relationships of the reinforcing bar components are determined through the proposed approach.

Analytical model for progressive collapse of RC frame structures subjected to blast loadings

An improved analytical model that enables tracing of the progressive collapse of RC frame structures under blast loading is introduced in this paper. The moment-curvature relation uniquely defined in an RC section is used for the simulation of the bending behavior, and then the constructed nonlinear moment-curvature relation is modified with the consideration of many factors such as the effects of bond-slip, axial force and catenary action, which dominantly affect the nonlinear response of RC structures. Upon the definition of the monotonic moment-curvature envelope, the hysteretic unloading and reloading paths are defined to trace the dynamic bending behavior of an RC section on the basis of the hysteretic curve of reinforcing steel. In advance, to describe the direct shear failure, the empirical direct shear stress-slip relation suggested by Krauthammer and Astarlioglu is considered in the solution procedure and implemented into the formulation with the use of non-dimensional spring element. Moreover, as was in the moment-curvature relation, the hysteretic rule in the shear stress-slip relation proposed by Krauthammer and being used in many previous researches is also adopted. Because the numerical approach based on the moment-curvature relation of RC sections will dramatically reduce the solution steps, this approach makes it possible to trace the collapse not only of RC members but also of RC structures that are comprised of many structural members and require enormous solution procedures. After verifying the reliability and accuracy of the introduced numerical model through correlation studies of the RC members and a simple frame, the collapse analyses of multi-bay and multi-story RC frames are performed to prove the possibility for the progressive collapse analysis of entire frame structures only with the use of beam elements.

Machine Learning-based Optimum Reinforced Concrete Design for Progressive Collapse

This paper investigated progressive collapse analysis of three-dimensional (3D) reinforced concrete (RC) frames that are optimized for carrying structural loads by introducing a unique simultaneous multi-column removal load path using Machine Learning. The investigation includes formulating an integrated computational framework that incorporates a self-training machine learning algorithm. This algorithm is used to train the largest machine learning models of 3D RC frames containing more than 600 optimized structures to predict the posterior based on the trained priors. The efficiency of the computational framework was shown by conducting a comprehensive study on the optimization and behavior of structures considering seismic loading, alternative load path due to progressive collapse, and second order (P–delta) effects. The results show that the proposed framework ensures that system solutions meet both structural integrity and constructability requirements of the ACI and the Unified Facilities Criteria.

Study on the collapse performances of fabricated single-layer spatial network structures based on discrete beam elements

Using discrete beam elements to simulate the mechanical properties of assemble joints, the collapse performances of free-form, cylindrical, and K6 spherical surface latticed shells were analyzed. The effects of grid sizes, rise-span ratios, and connection behaviors on structural collapse performances were discussed. The main conclusions were obtained: (1) By conducting an integral scaled model test of a free-form latticed shell, the accuracy of the collapse analysis model with discrete beam elements was verified. (2) Multiple collapse shapes were obtained for the latticed shells with various structural parameters. To ensure an excellent collapse-resistant capacity, the grid size should not exceed 4 m, and the rise-span ratio is suggested as 1/4 for the cylindrical latticed shells, and the grid size should not be greater than 3 m, and the rise-span ratio should not be less than 1/4 for the spherical surface latticed shell. (3) The connection behaviors of assemble joints significantly influence the structural collapse-resistant capacity. When the stiffness and bearing capacity of the assemble joint drop to 50% of the joint designed based on “strong joints and weak tubes”, the robustness index decreases rapidly. However, more than 80% of the collapse load is still reserved for the cylindrical latticed shell and approximately 60% for the spherical surface latticed shell.

Geometric imperfections in CFS structural members: Part I: A review of the basics and some modeling strategies

Unavoidable geometric imperfections complicate the load–displacement response of thin-walled cold-formed steel (CFS) structural members. While the inclusion of geometric imperfections in shell finite element (FE) collapse simulations has long been the subject of research, no consensus exits on modeling their full three-dimensional spatial pattern. This paper is the first part in a two-part series and provides a review of the basics and a summary of some efforts geared towards modeling geometric imperfections. We discuss the necessary ingredients for systematic characterization of elastic buckling mode shapes, due to their frequent use in approximating geometric imperfections, and make a conscious effort to express some of the existing geometric imperfection models through three components: imperfection shape, magnitude, and combination coefficient. Different choices and selections of these components, pertaining to either the inherent buckling behavior of the members and/or physical measurements are critically examined. The details required to develop high fidelity nonlinear FE models of CFS members seeded with geometric imperfections are presented. We then perform a comparative study of collapse analysis results obtained from adopting different imperfection modeling strategies. The noticeable variability in the load carrying capacity and the stability behavior highlights an urgent need for reliable probabilistic frameworks for this class of problems. A stochastic framework to generate samples of imperfect shell FE models from limited available data and validate the prescribed or practice-oriented geometric imperfection models is presented in a companion paper (see Part II Farzanian et al., (2023)).

Geometric imperfections in CFS structural members, Part II: Data-driven modeling and probabilistic validation

This paper is the second part in a two-part series that examines the role of geometric imperfections in load–displacement response and collapse behavior of cold-formed steel (CFS) structural members. In part I (Farzanian et al., 2023) a review of the basics and a summary of efforts geared towards modeling geometric imperfections was provided. This included the ingredients needed for systematic identification of elastic buckling mode shapes, due to their frequent use in approximating geometric imperfections, and the development of high fidelity shell finite element (FE) nonlinear collapse analysis of CFS members seeded with different geometric imperfection models. Part II is the companion to the analysis in part I that revealed a noticeable variability in the collapse behavior and load carrying capacity of CFS members as a result of adopting different imperfection modeling strategies. In this part we provide the necessary steps to build a probabilistic framework that rests on machine learning, polynomial approximation, and parametric and non-parametric statistical inference and uses imperfection data to build a consistent stochastic field model of geometric imperfections. This data-driven model is then used to generate the much needed realizations of geometric imperfections that are faithful to the underlying statistics of measured data and therefore can be seeded, directly, in nonlinear collapse analysis of CFS members. Nonlinear shell FE analysis, within a stochastic simulation framework, is finally used to (statistically) quantify the impact of geometric imperfections and to enable probabilistic validation of geometric imperfection models.

A Review Paper on Progressive Collapse Analysis of Different Shell Structure: A Critical Review

Abstract: Progressive collapse occurs when one of the structural members fails, causing other structural members to fail. This leads to the collapse of all or part of the structure. Failure of a vertical structural member is the most common cause of progressive structural collapse Explosive charges, accidents or deliberate destruction can cause the column to fail and collapse. The analysis is performed by removing the columns at different locations one by one according to General Service Administration (GSA) guidelines, and then evaluating the radius and column DCR values. The results concluded that the column removed from the center is more vulnerable to progressive collapse.