Alternate Load Path Method Research Articles

Blast-Induced Progressive Collapse Analysis: Accounting for Initial Conditions and Damage

The paper presents the progressive collapse analysis of structures, focusing on the impact of the initial conditions (particularly initial velocity) and the damage. It proposes a method that calculates the residual axial load capacity and damage of columns based on their strain profile and considers the effects of multiple blast locations. The methodology involves the conventional design of a three-story moment-resisting frame, selecting blast parameters, calculating blast pressures, and performing structural and progressive collapse analyses. The findings reveal that the Alternate Load Path Method (APM) overestimates the capacity compared to a benchmark blast–structure interaction analysis, especially when unsuitable initial conditions and damage properties are used. To address this limitation, the paper concludes the recommendations for incorporating appropriate initial conditions and damage considerations for a relatively accurate progressive collapse analysis.

Numerical predictions of progressive collapse in reinforced concrete beam-column sub-assemblages: A focus on 3D multiscale modeling

The progressive collapse of reinforced concrete (RC) beam-column sub-assemblage under catenary action (CA) using the alternate load path method to evaluate structures' robustness has raised much attention in the past decade, both in experimental tests and finite element (FE) simulations. However, a comprehensive multiscale method within concrete to assess structural robustness against progressive collapse, explicitly surrounding concrete matrix under CA, is generally lacking and has not been thoroughly explored in the relevant literature. This study aims to develop an FE macromodel to reliably simulate the progressive collapse resistance of seismic and non-seismic RC beam-column sub-assemblages. The proposed macroscale FE models are extensively validated by experimental results dominated by the CA and excessive deformation of RC beam-column sub-assemblages. Then, the macroscale FE model is further partitioned at the critical region with high-stress concentration to establish a sub-model and elucidate the underlying mesoscopic mechanism to motivate the CA by performing sub-modeling analysis. A 150 mm × 150 mm × 150 mm mesoscale heterogeneous model is established to be composed of aggregates, interfacial transition zone (ITZ), pores, and mortar by 3D voxel and Voronoi-based methods. The numerical predictions of the three macroscale models demonstrate good agreement of the overall deformation and load resistance trends with experimental results at both structural and sectional levels, but an overestimation of the load resistance peak is observed when concrete is crushed. Compared to the macroscale models, the sub-modeling analysis provides a more in-depth understanding of localized phenomena such as cracks and fractures. The 3D mesoscale model is further investigated with different aggregate volume fractions following the Fuller gradation. It is found that aggregates and ITZ (higher porosity, lower elastic modulus, and lower tensile strength compared to the bulk mortar) are more prone to concrete failure mechanisms without considering the role of reinforcement leading to the CA at the mesoscale, maintaining the concrete properties of the three macroscale models. In terms of the material constitutive model, the concrete damage plasticity model, and cohesive elements for mortar and ITZ, respectively, under uniaxial compression and tension behavior, the importance of interface bonding in CA of the surrounding concrete matrix is underlined. Additionally, the established mesoscale modeling method facilitates comprehension of the responses exhibited by macroscale RC sub-assemblies, ultimately shedding light on fracture initiation and propagation mechanisms.

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.

Evaluation of progressive collapse resistance performance of steel OMF with WCPF connections

A welded cover plated flange (WCPF) connection, which is a pre-qualified connection detail improving a weak weld access hole and the ductility of a welded unreinforced flange-bolted web (WUF-B) connection, has a simple and efficient advantage in construction. In this study, a new modelling approach of the WCPF connection by employing 1-D element was proposed for the evaluation of progressive collapse resistance capacity performance. The model was developed by substituting the average width of trapezoidal shapes of cover plates welded to the top and bottom flanges and by assessing the equivalent flange thickness based on the moment of inertia. The proposed model was verified through comparisons with experimental and 3-D numerical results, showing discrepancy within 5.7%. To evaluate the performance of the WCPF connection, a prototype structure was adopted from the previous study for the appraisal of the WUF-B and reduced beam section (RBS) connections. The alternative load path method was performed using an energy-based approximate analysis considering the dynamic effect of sudden column loss. The performance of the structure was evaluated in terms of structural robustness and sensitivity. Furthermore, the results were compared to those of the structures with the WUF-B and RBS connections analyzed in the previous study. The structure with the WCPF connections showed 33% more improved structural robustness and 11% less sensitivity to progressive collapse when one column was removed. In a two-column removal scenario, only the structure with WCPF connections indicated to have proper progressive collapse resistance capacity. The WCPF connection was deemed more reliable than WUF-B and RBS ones.

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

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

Alternate load path behaviour in structures with non-symmetrical design under column missing scenario

In the design and assessment of reinforced concrete (RC) structure against progressive collapse via single column removal scenario, also known as “alternate load path method”, development of secondary mechanisms, i.e. compressive arch action (CAA) and catenary action (CA) in double-span beams has been investigated and identified in many previous researches. The majority of the experimental tests are conducted on symmetrical double-span beams (identical span length and reinforcement detailing at both beam span). However, variations in details of beams adjacent to one another are not uncommon in RC building designs and constructions. Hence, a research study (as presented in this paper) with total of 5 RC frame tests are conducted to investigate the development of secondary mechanisms (CAA and CA) in a double-span beam with unsymmetrical 1) span length and 2) beam detailing. For each unsymmetrical case (span length and beam detailing), there will be 1 unsymmetrical double-span beam, and 2 symmetrical double-span beams (each representing one side of the unsymmetrical double-span beam) to serve as reference for quantifying the development of secondary mechanism in unsymmetrical double-span beams. The behaviour and development of secondary mechanisms are thoroughly analysed based on test observation, measured forces and displacements, etc.

Experimental investigation on alternate load path mechanisms in double-span beams with unsymmetrical span lengths and reinforcement ratios

In the design and assessment of reinforced concrete (RC) structures against progressive collapse via single column removal scenarios, also known as the “alternate load path (ALP) method”, the development of secondary mechanisms in double-span beams, i.e. compressive arch action (CAA) and catenary action (CA), has been thoroughly investigated and identified in many previous studies. The majority of the experimental tests were conducted on symmetrical double-span beams (identical span length and steel reinforcement ratio for both beams). However, variations in span length and reinforcement details of beams adjacent to one another are common in RC buildings due to architectural requirements. Hence, an experimental study with a total of 6 tests was conducted to investigate the development of ALP mechanisms (CAA and CA) in double-span RC frames with unsymmetrical 1) span length and/or 2) longitudinal reinforcement ratio. The 6 tests included 3 symmetrically-designed specimens that served as the baseline to facilitate comparison and quantification of the ALP development for the other 3 unsymmetrical continuous beams. The behaviour and development of ALP mechanisms in all the 6 specimens were analysed at structural level including general observations and measurements of the external forces, displacements, and strains. Last but not least, a simplified method that was initially developed based on symmetrical test data was employed to validate unsymmetrical test results, with the aim to provide a robust and simple tool for preliminary design considerations of the ALP mechanisms.

Effect of alternative load path design method on preventing progressive collapse and reducing the rehabilitation cost using FEMA-P58

The alternative load path (ALP) method is an important modern design approach to prevent progressive collapse of buildings by redesigning adjacent structural elements to provide an alternative load path in case of partial collapse. This may lead to tangible changes in the mass and stiffness of the building, which means a change in the seismic behavior of the building. This shows the fact that choosing and designing an alternative load path is not an easy task. Studying the improvement in the seismic behavior of the building, whether direct or indirect, as a result of using the ALP, is the main objective of this paper. To achieve this goal, this study examined approximately 96 models, including the study of the possibility of progressive collapse occurring, whether there is or isn't an alternative path for the loads using non-linear static and dynamic analysis, as well as evaluating the study models using various seismic evaluation methods, where both the nonlinear static pushover analysis method and the FEMA-P58 method were used and compared. The study models are divided into two sections, with and without (ALP). The study models are also categorized by building height using heights of 6, 9, 12 and 15 floors. The models were also divided based on the locations of weak points in the original design that may be susceptible to damage and lead to progressive collapse, whether they are internal, side, or corner weak columns. The findings from the examined models indicate that the efficiency of (ALP) systems is more prominent in low and mid-height buildings compared to tall buildings. Additionally, the results demonstrate that the FEMA-P58 method yields similar predictions regarding building behavior as traditional seismic assessment methods like pushover analysis, but in a simplified manner that benefits non-engineers by providing clear insights into the financial and temporal aspects of different structural system solutions.

Seismic Failure Mechanism and Influencing Factors of Plate-Shell Integrated Concrete Liquid Storage Structure

To study the seismic failure mechanism of Plate-Shell Integrated Concrete Liquid Storage Structure (PSICLSS), the mechanical properties of each component under earthquake are studied. The influences of excitation frequency and amplitude on seismic responses of PSICLSS are analyzed. Based on the alternate load path method, the influences of partial component failure on the seismic responses of PSICLSS are studied, and the effects of free surface and structure size on seismic responses of PSICLSS are studied. Results show that the upper connection beams, upper plate and upper shell are easily tension failure. The effect of external liquid sloshing on the seismic response of the structure is more significant. The upper beams have a more significant influence on the structural seismic response. Considering the liquid free surface will cause structural stress increases. With the increase of the structural size, the structural stress, displacement and hydraulic pressure all increase, but the liquid sloshing height does not increase as the structural size increases.

Robustness Analysis of Historical Timber Roofs: A Case Study of the Gaggiandre Shipyard at the Arsenale of Venice

In this work, a deterministic approach is adopted to analyze the robustness of the timber roof of the Gaggiandre shipyard at the Arsenale of Venice. The capacity of the traditional timber truss to withstand the design loads as a result of the damage in the strut-tie node is evaluated according to the alternative load path method. Two layouts of the trusses are analyzed and compared: before and after the Austrian retrofitting intervention, performed in the late 1800s. For both configurations, robustness analyses are carried out by using linear 2D numerical models that consider the effective rotational capacity of the structural nodes in relation to the construction methods of the timber joints. For the configuration subject to the 19th-century restoration, the 3D response of the roof is also analyzed to verify the additional contribution provided by the longitudinal bracing system to the activation of alternative load paths (bridge effect). The results obtained with the different analyses are thoroughly evaluated, providing an indication of the deterministic robustness index of the roofing system based on different assumptions. The outcomes of this work allow to draw some general considerations on the method that could be used for the robustness assessment of historical wood systems.

Evaluation of progressive collapse behavior in reinforced concrete buildings

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

Study on structural robustness to resist progressive collapse of vertical irregularly base-isolated structures

It is necessary to establish qualitative analysis of structural robustness to ensure that the design meets the engineering requirements. The existing damage analysis methods such as Incremental Dynamic Analysis and Static Pushover Analysis which are used to determine the overall response of the structure without focusing on the local damage of the single structural component. From the macroscopic point of view, the local damage on each structural component can cause the progressive collapse of the overall structure and reduce the structural robustness. Particularly for the construction of special based isolation system and superstructure, the impact of accidental bearing failure on the overall structure of the impact of progressive collapse cannot be determined directly. This study starts with the damage risk and the importance of the single component, and the failure of the single component is related to the collapse of the whole structure. Based on the Alternative Load Path Method, the quantitative analysis method of structural anti-progressive collapse is proposed, and the vertical irregular base-isolated structures are compared and analyzed. The robustness of the isolated structure after the failure of the isolated bearing is discussed. The result shows that, qualitative analysis of structural robustness proposed in this study can be used to provide reference for the selection of building scheme and analysis of structural robustness. The robustness of the structure does not only depend on the property of structure itself but also the external load applying on the structure. It is suggested that reasonable protection measures should be set for the isolation bearing with greater vulnerability coefficient which may suffer from extreme accidents and the potential risk of isolation bearing with greater component importance coefficient is eliminated or reduced.

FE modelling progressive collapse assessment of steel moment frames-parametric study

ABSTRACT Progressive collapse is the failure of primary structural components produced by natural or abnormal events that may result in a total or partial collapse of the structure. In this paper, several structure models, under different column removal scenarios, were modeled and analyzed using the FE program SAP2000 to evaluate the effect of span length, the strength of structural members, and cross-section on the steel building’s resistance against progressive collapse. The Alternative Load Path method was carried out using the linear static and nonlinear dynamic analysis following the GSA 2003 guidelines for this investigation. The material and the geometric nonlinearities must be considered in the nonlinear dynamic analysis. The contribution of span length, steel grade, and cross-section to the response of the structural system was studied through the Demand Capacity Ratio for the linear static analysis. The variation of several parameters, such as bending moments, plastic hinges status and their rotations, displacements, and ductility, was discussed based on the response of the nonlinear dynamic analysis. The main objective of this study is to demonstrate the impact of the latter parameters on the structural enhancement and the reduction of the damage level triggered by the failure of a primary structural component.

Collapse Resistance Model and Deformation Mechanism of Shear Wall Replacement

Structural elements can be damaged or defective due to man-made and natural disasters, which will result in structural resistance below the design value. Component replacement can effectively improve the safety of the structure and does not affect its later use. However, this construction process must dismantle defective components. If the process is not properly operated, it will cause progressive collapse of the structure. There are few studies on progressive collapse resistance based on field tests. In this paper, the alternate load path method is used to study the deformation mechanism of reinforced concrete shear wall structures when partial members fail. The maximum vertical displacement and strain of the beam end near the failure walls are obtained, and load transfer laws are analyzed. Based on the component replacement construction of a high-rise shear wall structure, the progressive collapse resistance mechanism of the shear wall structure is verified, which provides theoretical guidance for component replacement construction.

Simplified analytical method for the robustness assessment of precast reinforced concrete structural systems

The article presents the simplified implementation of alternative load path method based on the energy balance approach. This method should be used to check the global resistance of a damaged structural system after the occurrence of an accidental event. Basic assumptions of simplified analytical models for modelling resistance of horizontal ties in a damaged structural system, taking into account the membrane (chain) effects, were presented. An approach to modelling the dynamic resistance of a damaged structural system based on the energy balance method is described. Calculated dependencies for checking the robustness of a prefabricated multi-storey building with hollow-core slabs after the loss of the central column are proposed and considered using an example. On the considered example, a comparison of the required tie sections area with the dynamic resistance designed using the energy balance method (EBM) and according to the current standards, and a statistical assessment of the reliability of the load-bearing capacity models are carried out. In the end, a brief algorithm for the simplified calculation of the dynamic resistance of a damaged structural system is proposed.

Assessment on the Progressive Collapse Resistance of a Long-Span Curved Spatial Grid Structure with Main Trusses

The progressive collapse resistance of the terminal building of Zhongchuan Airport in Lanzhou, China was studied, which is a long-span curved spatial grid structure with main trusses. Firstly, the finite element model was built using MSC. Marc software adopting the fiber model based on material. Secondly, an improved method of zoned concept judgment and sensitivity analysis was proposed to determine the key components. Thirdly, the initial failure components were removed individually based on the alternate load path method (AP method). The responses of remaining structure were calculated using nonlinear dynamic analysis method. Lastly, the influences brought by the cross-sectional sizes of grid members were investigated through conducting parametric analysis. According to the results, the proposed selection method can avoid omitting the key components. The structural responses are significant when removing the concrete filled steel tubular (CFST) column SC14 directly supporting the front middle part of the roof, with a maximum vertical displacement of 10 m at cantilever end, which should be focused on for this kind of large-span spatial structure. In addition, the tensile strength and cross-sectional area of the upper and lower chords should be increased by 20% to enhance the progressive collapse resistance of the structure, and the changes of axial compression ratios of the columns supporting the roof have little effects.

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.

Evaluating the effect of Buckling-Restrained Braces in Steel Buildings against Progressive failure using Different Simulation Strategies

Ignoring the primary damage to structural components due to blast load or fire is the alternate load path (APM) method's weakness in progressive failure analysis. The new technique used in this study examines the structure's more realistic responses by considering the initial cause of the failure. Also, buckling-restrained braces (BRBs) are applied to diminish the potential for progressive failure in braced steel buildings. Variables include the type of primary local loading (APM, blast loading, and heat caused by fire), the position of column removal in the plan (inner and outer frame), the type of brace (BRB and CB), and the number of stories (3, 5, and 8 stories). The buildings were simulated using ABAQUS. The results showed that BRBs in steel buildings under blast load, compared to conventional braces, reduce the potential of progressive failure. The use of BRBs provides much more energy absorption than conventional bracing systems due to brace buckling prevention.

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.

Investigation of progressive collapse in reinforced concrete buildings with slab-wall structural system

Nowadays, Reinforced Concrete (RC) wall-slab systems are being used more extensively due to their effective performance seen in past earthquakes. Progressive collapse is a phenomenon in which all or part of a structure is damaged due to damage or collapse of a small relevant part. The majority of research done in the field of progressive collapse has been on frame-shaped structures. Further, the performance of RC wall-slab structural systems, especially against progressive collapse, has been less studied. In this study, at first, nine concrete buildings of five, ten and fifteen stories with wall-slab structural systems, with the ratio of spans length to the story height (L/H) of 1, 1.5 and 2 and a structural height of 2.75 meters in each story, were designed by the ETABS V16 software. Then, using the SAP2000 software and nonlinear shell-layered elements, nonlinear static analysis was performed by the Alternative Load Path (ALP) method on the models and the results were evaluated. The results demonstrated the relatively high strength of buildings with wall-slab structural systems in withstanding progressive collapse. The rate of vertical displacement of the removal location, the maximum von Mises stress in rebar, the maximum compressive stress and strain in concrete in the interior wall removal scenarios were less extensively compared to the corner wall removal scenarios. In contrast, progressive collapse potential increased significantly with increasing number of stories and the L/H ratio. Also, it was found that, buildings with the wall-slab structural system may exhibit brittle failure behavior influenced by progressive collapse.