Alternate Load Path Research Articles

Compressive arch action in beams of steel frames subjected to a column loss

AbstractSteel frames subjected to a column removal typically exhibit a complex load resisting mechanism characterised by three contributions: i) beam yielding mechanism, ii) compressive arch, and iii) catenary action. The development of compressive arch actions in the beams bridging over the lost column has not been yet thoroughly investigated in steel frames, although such effects proved to significantly contribute to the collapse‐resistance of reinforced concrete frames.This paper aims at shedding light on the compressive arch actions of steel beams in case of column removals accounting for various boundary conditions. Numerical and analytical methods were employed for quantifying the contribution of these effects to the structural robustness of steel frames. A simplified analytical model that allows estimating the magnitude of arching effects in steel beams with various types of end‐connections and horizontal restraints provided by the surrounding structure was introduced. The agreement between numerical and analytical results suggests that the proposed analytical model allows for accurate predictions. This validates the model's use for practical applications and gives promising prospects for its inclusion in consistent analytical methods for predicting the activated alternative load path in steel frames subjected to a column loss scenario.

Application of the tying force method in the design of alternative load paths in post-and-beam timber structures: A case building

This work aims to present an application of the tying force method recently proposed in the literature to a mid-rise post-and-beam timber building. Internal and edge column loss scenarios are analysed. A steel-to-timber connection is proposed and extensively evaluated as a potential solution to ensure the robustness of the structure, thereby satisfying the requirements imposed by the tying force method and effectively minimizing the risk of progressive collapse of the structure. Finally, a parametric analysis evaluating the variation of the tying force as a function of the chord rotation and different beam span lengths is carried out. The results obtained show that the tying force method represents a promising and rapid strategy for designing robust post-and-beam timber buildings falling in low and medium consequence classes.

A state-of-the-art review of progressive collapse research and guidelines for single-layer lattice shell structures

The importance of progressive collapse analysis of structures has increased significantly due to various structural collapses. Single-layer lattice shell structures are susceptible to progressive collapse, as the failure or instability of a localised region can result in a global collapse due to their lightness and wide span. The geometry of these structures plays a crucial role in the load resistance, and any damage that alters the overall geometry can initiate different instabilities, which may also result in progressive collapse. Therefore, the possibility of progressive collapse is high among these lighter structural forms. However, research on the progressive collapse of single-layer lattice shell structures is limited compared to framed structures, highlighting the need for further investigation. Therefore, this manuscript aims to provide a comprehensive review of research conducted on the progressive collapse of single-layer lattice shell structures, focusing on experimental, numerical, and theoretical investigations. Earlier studies have explored the propagation of local instabilities leading to overall failure. More recent research has primarily focused on two approaches: (1) alternate path analysis, which examines the structure’s response after removing a member, and (2) substructure analysis, which aims to identify collapse-preventive mechanisms. Based on these analyses, various methods to enhance progressive collapse resistance have been discussed, including specific local resistance, alternate load paths, compartmentalisation, and tie forces. This review also highlights the limitations present in the current literature and suggests future research directions, which helps to develop design guidelines that can effectively increase the progressive collapse resistance of single-layer lattice shell structures, making them more reliable for various structural applications.

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.

Experimental assessment of an asymmetric steel–concrete frame under a column loss scenario

Several noteworthy accidents clearly pointed out the risk of disproportioned collapse of framed structures. Design codes recently recognized it by adding a new requirement: the structural robustness. Among the different approaches to check robustness, the most popular is associated with the column loss scenario: the analysis should verify that, in case of a column loss, an alternative load path does exist, limiting the portion of structure affected by collapse. Consequently, numerous experimental and numerical studies of 2D and 3D structures were carried out in recent years to identify the mechanism of load transfer from the damaged to the undamaged part of the structure. This knowledge becomes an essential and fundamental key for assuring adequate resistance against progressive collapse by the development of catenary action in the beams and membrane action in the floor slab. Studies of reinforced concrete systems and of bare steel sub-assemblies are numerous. More recent is the focus on the response of steel–concrete composite structures subjected to accidental events. Furthermore, most of these studies focused on the characterization of 2D sub-assemblies or 3D in-scale framed structures. This paper presents an experimental assessment of the structural response of a 3D full-scale steel and concrete composite frame under the column loss scenario. The results are finally compared with the response of a frame with the same overall geometry but different columns’ layout, tested by the Authors within the same research programme.

Progressive Collapse Assessment of High-Rise Framed Structure Using ETABS Software

Abstract: The structures generally get collapse due to the failure of one or a few structural components which then progresses over the successive of other components. This process is referred as progressive collapse of the structure. Local damage that initiates progressive collapse is called initiating damage. In order to study the collapse in analytical way, loading pattern or boundary conditions are required to be changed so that other structural elements within the structure are loaded beyond their capacity. This leads to development of alternative load paths to initiate the redistribution of loads.

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.

“Progressive collapse analysis of flat slab building in hilly terrain using Non-Linear Analysis: A study on bracing system as a structural Remedy”

Progressive collapse is a term used to describe the failure of a structure, such as a building or bridge, due to the structure’s inability to reallocate the loads after the failure of a key component or portion of the structure. It is a cataclysmic structural failure that may occur when a primary structural member or a portion of a structure is damaged or fails, resulting in a string of structural failures that leads to the partial or complete breakdown of the structure. This research paper investigates the progressive collapse behaviour of an earthquake-resistant flat slab building lying in hilly terrain upon removal of the column at three different locations, using non-linear static analysis. The study involves the use of a finite element method-based software tool to simulate the collapse behaviour of the building. The results of the analysis indicate that the building lying in hilly terrain, designed to resist earthquake forces can be vulnerable to progressive collapse due to the abrupt removal of a crucial structural component and this can be significantly mitigated through the implementation of strategies, such as the provision of an alternate load path through the use of steel bracing systems. Evaluation of the outcomes is done in terms of vertical joint displacements at the top of the deleted column and the formation of plastic hinges in the adjacent structural members. The findings of this research paper provide valuable insights into the progressive collapse potential of a flat slab building designed for earthquake loads, in hilly terrain under extreme loading conditions. The results can be used to inform the design and construction of buildings that are more resilient and robust to extreme events, thereby lowering the possibility of progressive collapse and ensuring the safety of the occupants.

Structural behaviour of 2D post-tensioned precast beam-column sub-assemblages subjected to column loss scenario

Many previous studies have investigated alternative load path (ALP) mechanisms of 2D reinforced concrete (RC) beam-column sub-assemblages under column removal scenarios. However, how precast and prestressed RC structures respond under a column loss scenario receives far less attention, as evident from a lack of published test data. Herein, five 2D post-tensioned precast RC sub-structures subjected to a middle column loss scenario were tested by multi-point quasi-static loading. In all the specimens, individual precast members such as beams and columns were joined together through wet connection. The study focused on investigating the combined effects of post-tensioned tendon (PT) and wet connection on load-resisting mechanisms and the influence of basic parameters such as unbonded and bonded PT, T-beam effect, and boundary conditions. The test results indicated that both unbonded and bonded parabolic-shaped PT significantly enhanced compressive arch action (CAA) and catenary action (CA) beyond basic flexural capacity, and also changed the plastic hinge mechanism in the precast beams. The specimen with unbonded PT could provide greater residual capacity than bonded PT, but the former was severely damaged by fracture of normal reinforcement and crushing of concrete rather than fracture of the tendon. In addition, the effects of T-beam and boundary conditions are discussed in detail. Finally, new design criteria for precast and post-tensioned concrete structures under column removal scenarios are proposed for structural engineers to take advantage of high-strength tendons and avoid failure at critical locations by precast joints.

Robustness of a full-scale precast building structure subjected to corner-column failure

Although many analytical and experimental studies have been carried out to date on the progressive collapse and robustness of cast-in-place reinforced concrete (RC) and steel building structures, very few experimental research works have been performed on precast concrete (PC) structures. The small number of publications on these experiments have focused on analysing the behaviour of subassemblies after the sudden loss of an internal column. This paper is the first to describe the construction of a full-scale purpose-built experimental PC building to study the sudden removal of corner columns and the structure’s ability to find alternative load paths (ALPs). The connections between the precast members were designed using existing simplified guidance for robustness. The results obtained from the test using gravity loads corresponding to typical load combinations defined in building codes for accidental design situations, showed a structural response governed by Vierendeel action with a clear contribution from the floor slabs. Load increase factors were obtained from the test results which can be applied by practitioners using simplified linear finite element models to account for non-linear dynamic effects in a simplified manner. This work is expected to form part of a large database of experimental results that are useful for developing advanced numerical simulations and parametric analyses.

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.

Performance of RC beam-column assemblies during and after elevated temperature to resist progressive collapse

In practice, fire is one of the accidental loads that can result in the progressive collapse of buildings but the commonly used alternate load path (ALP) approach often ignores the impact of fire. Therefore, numerical models based on the finite element software ABAQUS are employed to investigate the performance of reinforced concrete (RC) beam-column assemblies during and after high temperature to resist progressive collapse. The thermal–mechanical sequential coupling method is used for analysis. The effects of fire durations, boundary conditions (middle or penultimate column removal) and side column subject to fire are studied. Previous test results demonstrated that compressive arch action (CAA) and catenary action (CA) are developed in sequence to prevent progressive collapse for the assemblies at ambient temperature. However, the numerical results show that the in-fire assemblies could not develop CA owing to severe degradation of rebar elongation and thus, the load resistance of in-fire assemblies controlled by CAA capacity. Further increasing fire duration to 90 mins, the CAA capacity of the assemblies decreases over 70% compared with that at ambient temperature. Since the rebar can recover most of its mechanical properties after cooling down, the assembly after fire (i.e., exposed to fire then cooled down) can also successively develop flexural action (FA), compressive arch action (CAA) and catenary action (CA) to resist progressive collapse, which is similar to that of intact RC frame at ambient temperature. Under the penultimate column removal scenario, the exterior side column of the post-fire specimen suffers large eccentric compression failure, which causes the highest collapse risk.

Evaluation of collapse resistance of masonry-infilled RC frame building under blast loadings

As non-structural members, the masonry-infilled (MI) walls are always ignored in the numerical and experimental study on the blast and collapse resistance of RC frame buildings, while the contribution of MI walls on preventing the large-scale collapse has been observed according to the past explosion incidents. This paper aims to propose and verify a numerical simulation approach considering the blast- and collapse-resistant effects of MI walls, and further evaluate the collapse resistance of MI RC frame buildings under blast loadings. Firstly, based on our previously validated hybrid finite element (FE) modelling approach for RC frame structures and Multi-material Arbitrary Lagrangian-Eulerian method for applying blast loadings, the simplified micro-model and compressive strut model of the MI wall were adopted to characterize its blast and collapse resistance in the near- and far-regions of building, respectively. Secondly, the out-of-plane explosion test and in-plane quasi-static collapse test were numerically reproduced to verify the applicability of adopted FE modelling approaches for MI walls. Furthermore, by establishing the hybrid FE models of prototype bare and MI RC frame buildings, the propagation of blast waves, damage modes as well as dynamic responses of RC frame buildings under two design-based threat of explosion at corner and side columns were derived and examined. Finally, the applicability of the anti-collapse design method specified by U.S. Department of Defense, i.e., alternate path method (APM), for RC frame buildings under external explosions was examined. It derives that, (i) the presence of MI walls can efficiently block the blast waves into the building structures, and relieve the upward arch of slabs and damage degree of interior columns; (ii) compared with the bare RC frame buildings, the MI walls provide sufficient alternate load paths to enhance the structural robustness and restore the gravity stability of MI RC frame buildings after the explosions; (iii) the APM is only applicable to evaluate the collapse resistance of MI RC frames under the external explosion of cargo van bomb (1814 kg of equivalent TNT) or even less charge weight.

Structural assessment of beam–slab reinforced concrete sub-structures under column loss scenario

Mobilisation of alternate load path (ALP) mechanisms in three-dimensional (3D) beam–slab systems is a key factor in designing structures against progressive collapse. Existing analytical methods on 3D beam–slab systems focusing on limited load-resisting mechanisms often lead to uneconomical and unrealistic design, while finite element models with 3D solid elements are too complicated and time-consuming for 3D beam–slab systems. To address these shortcomings, this paper aims to provide structural engineers with two simple but effective and reliable approaches to predict the structural behaviour of 3D beam–slab systems. They include (i) an analytical method and (ii) a simplified finite element model based on strip method and grillage analysis. Both approaches are validated against published test results for 3D beam–slab systems. Compared to existing approaches on 3D beam–slab systems, these two proposed methods incorporate all the load-resisting mechanisms in both the beams and slabs, giving more accurate and realistic predictions of load–displacement curves for the sub-structures considered. In addition, parametric studies on the analytical approach are presented to shed light on the role of boundary conditions and the contribution of slabs to the load resistance capacity of 3D beam–slab structures against progressive collapse.

Reliability interpretation of redundancy on design and seismic behaviour of steel conveyors

ABSTRACT This study investigates the effect of redundancy incorporation as static indeterminacy and possibility to utilise alternative load paths in design and seismic behaviour of steel truss bridge conveyors by conducting complementary reliability assessments. The results could be supportive in adjusting the degree of indeterminacy, especially for long structures, to convince the design goals. It is conceived that the design approach with lower indeterminacy donates to less structural weight in addition to a bit more fundamental period contributing to less earthquake-induced demands and easily controllable lateral drifts in the end reference points which are very crucial in view of connecting to the adjacent structures. On the other hand, providing more indeterminacy in conveyor design could bring about more ductility, nonlinear displacement and earthquake energy dissipation as well as closer nonlinear behavioural parameters to the amounts recommended by the design code. In reliability assessments by increasing the degree of indeterminacy, the failure probability is reduced which contributes to the design with higher reliability indexes and higher collapse safety margin and it is expected that the incorporation of redundancy effects would be more perceivable by providing models with more redundancy discrepancy.

Performance-Based Retrofits of Long-Span Truss Bridges Based on the Alternate Load Path Redundancy Analysis

Existing long-span truss bridges typically undergo significant retrofits to improve their resistance against extreme load events, such as the seismic loads, for which the bridge may not have been designed or considered originally. However, the conventional seismic retrofit measures recommended in most existing codes and specifications may not be effective in providing sufficient alternative load path (ALP) redundancy to a bridge that is vulnerable to sudden member-loss scenarios because of the significantly different magnitude of demands. This paper proposed a performance-based retrofit (PBR) approach for long-span truss bridges that are vulnerable to sudden member-loss scenarios. The performance of the bridge has been evaluated by using the demand-to-capacity ratio (DCR) or strain ratio (SR) on the member/component level or the displacement factor on the bridge system level as indicators. Based on the analysis results, the argument is made that the proposed PBR approach allows bridge designers to meet the predetermined performance objectives for sudden member-loss loading conditions. Increase in weight of steel because of such the ALP retrofits is less than 10%. The retrofitted bridge would meet the desired performance levels in the event of sudden loss of any members on the primary trusses of the bridge.

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.

Study on mechanism and influential factors of progressive collapse resistance of base-isolated structure

The progressive collapse of the structure caused by the partial failure of the structure will cause severe consequences and massive losses, and structural progressive collapse resistance has always been a hot topic of current research. In order to study the progressive collapse mechanism of base-isolated structures, the test study and numerical simulation of the base-isolated structures were carried out based on the vertical Pushover method and analysis of the variation rule of the capacity of the remaining structure and influence mechanism. The isolation bearing failure position, the size of the beam of the seismic isolation layer, the type of the isolation bearing, and the horizontal stiffness of the seismic isolation layer on the capacity of the remaining structure were compared and analyzed. The results show that the non-uniformity of the beams and the concentrated loading at the nodes were easy to form a linear catenary mechanism, resulting in more severe beam end damage than mid-span damage. In the case of side isolation bearing failure, due to the lack of sufficient lateral restraint, the capacity was significantly lower than other conditions, which were more likely to cause partly collapse. Therefore, setting more transfer paths to improve the structure’s resistance to progressive collapses was necessary. Increasing the size of the beam of the seismic isolation layer could improve the capacity of the remaining structure of the alternate load path in the base-isolated structure. The changes in the horizontal stiffness of the seismic isolation layer and the type of the isolation bearing have little effect on the progressive collapse resistance capacity of the remaining structure.

Data-based modeling of the punching shear capacity of concrete structures

Flat slabs have been widely used in construction in recent decades because they allow greater clear heights and more versatile architectural layouts compared to beam-column solutions. In such structures, punching shear failure is often critical. This type of failure is brittle and occurs without pronounced advance notice, and the alternative load paths cannot be ensured. Therefore, this failure can lead to progressive collapse. For this reason, proper reliability assessment of slabs against punching is of great importance. Improved accuracy and minimization of uncertainty in the predictive models are critical. Currently, there is a wide debate in the international community about the best predictive model for punching shear capacity and there is no clear consensus among researchers. This study focuses on the development of predictive models for punching shear capacity of concrete structures using machine learning (ML) algorithms such as the Gaussian Process Regression (GPR) and Support Vector Regression (SVR). The models were developed using a set of 501 experimental punching shear tests from existing theses, dissertations, technical papers, and research reports. The performance of the developed prediction model is evaluated statistically and by comparison with EC 2. Based on the soft computing approach of the ML model, it is possible to achieve precise and accurate prediction of the ultimate punching shear capacity with significant speed. Thus, this method is suitable for implementation in probabilistic models in a reliability framework. And it can be used to explore parameter sensitivities of the punching shear failure mechanism. The results of this study indicate that the Gaussian Process Regression and specifically the Matern 5/2 algorithm can describe very accurately the punching shear capacity and it is suitable for probabilistic evaluations.

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.