Idealized structural unit method and its application to progressive hull girder collapse analysis of ships

Progressive collapse of building structures under blast and impact loads has attracted great attention all over the world. Progressive collapse analysis is essential for an economic and safe design of building structures against progressive collapse to blast and impact loads. Because of the catastrophic nature of progressive collapse and the potentially high cost of constructing or retrofitting buildings to resist it, it is imperative that the progressive collapse analysis methods be reliable. For engineers, their methodology to carry out progressive collapse evaluation need not only be accurate and concise, but also be easily used and works fast. Thus, many researchers have been spending lots of effort in developing reliable, efficient and straightforward progressive collapse analysis methods recently. In the present paper, current progressive collapse analysis methods available in the literature are reviewed. Their suitability, applicability and reliability are discussed. Our recent proposed new method for progressive collapse analysis of reinforced concrete frames under blast loads is also introduced.

Open ships inherently possess low torsional rigidity because of their open deck structural configuration. Some of the structural failures for open ships are caused by wave-induced torsional moment in combination with other load components in oblique seas. Relatively few experimental results about horizontal bending and torsional moments in oblique seas have been published, however. Further, test data for vertical shear force and vertical bending moment in oblique seas are quite scarce. A backbone model has been recently tested by the Center for Ships and Ocean Structures (CeSOS) in the towing tank and ocean basin at the Marine Technology Center. The model consists of 15 box-shaped segments, in addition to bow and stern segments, which are interconnected by an aluminum beam on the top. Model tests in oblique seas without forward speed were first carried out to provide basic comparisons. Tests in head and oblique seas with speeds were then conducted in regular waves. Irregular wave tests were also carried out to assess the spectral responses and peak distributions of cross-sectional load effects. Load effects at 7 longitudinal positions were measured through strain gauges, including vertical shear force (VSF), vertical bending moment (VBM), horizontal bending moment (HBM), and torsional moment (TM). The motivation of this paper is to perform a benchmark study by comparing numerical predictions of different computer codes with these test results. The uncertainties in the experiments and the computer codes are discussed, and conclusions are presented at the end of this paper.

The growing need for blast-resistant designs in structural engineering is driven by the rising threat of terrorism, accidental explosions, and the significant risk of progressive collapse. This study presents a numerical procedure for analyzing the progressive collapse of Reinforced Concrete (RC) framed structures due to blast loads, addressing the gap in current methodologies. Traditional approaches such as the Alternate Load Path method, which are code-based and threat-independent, mainly focus on sudden column loss scenarios but do not fully capture the dynamic nature of blast-induced, threat-dependent collapses. Hence this study addresses the need for a computationally efficient and reliable method to predict and model progressive collapse under blast loading. This study employs a comprehensive numerical investigation using Finite Element Method where a seven-storeyed RC building is assessed for progressive collapse under blast loading. Progressive collapse analysis was executed using a commercially available Finite Element Analysis software, adhering to the Linear Static Procedure specified in the General Services Administration (GSA) guidelines, while blast load scenarios were examined through a nonlinear direct integration time history analysis. Different blast parameters, including charge weight and standoff distances, are varied to evaluate their impact on the structural integrity of the building. The study differentiates between threat-independent analysis, considering four column removal locations, and threat-dependent (blast-induced) scenarios with three distinct column removal positions. The scope of this study delves only into the perimeter blast scenarios neglecting the internal explosions. Demand Capacity Ratios (DCR) of columns were calculated to determine the susceptibility of the building to progressive collapse, with a DCR greater than 1 indicating failure. The numerical model was validated against the GSA baseline model. In threat-independent analysis, 30%, 60%, 22%, and 44% of the considered columns under corner, long side, short side, and interior column removal scenarios respectively exceeded the acceptable DCR criteria. In threat-dependent analysis, 100% of the considered columns under each blast induced column removal scenario exceeded the acceptable DCR criteria. This emphasizes the need for scenario-based planning in structural design to reduce collapse risks. The identification of critical columns, for threat-independent analysis as those directly above the removed column and on the topmost floor and for threat-dependent analysis as ground floor columns adjacent to the removed column, reveals potential weak points for progressive collapse initiation. The analysis of blast-induced progressive collapse reveals significantly higher DCR values than threat-independent assessments. Even the minimum percentage increases of DCRs when transitioning from threat-independent to threat-dependent analysis reaches high values up to 995%, 325%, and 981% for corner, long side, and short side column removal scenarios respectively. This specifies the importance of integrating blast resistance into the structural design of high-risk buildings. As a result, this study contributes to the understanding of structural dynamics under blast loads and offers a framework for the analysis of progressive collapse in RC buildings.

Progressive collapse is defined as the spread of an initial local failure from a key element to adjacent elements, eventually resulting in the collapse of the whole structure or a disproportionately large part of it. As an abnormal dynamic load, blast load has the characteristic of rapid propagation, high peak value and short duration. And it is also one of the main reasons that might cause the progressive collapse of building structures. Based on the existing research achievements on the progressive collapse of building structures, in this paper the classification method for structural progressive collapse analysis is put forward. Then the current methods for progressive collapse analysis are further divided into two categories, i.e., the method for evaluation of structural progressive collapse resistance and the method for whole process analysis of structural progressive collapse. Recent progress on the evaluation of structural progressive collapse resistance and the method for whole process analysis of structural progressive collapse are presented from literatures. Finally, the conceptual design method, structural detailing and the procedure for progressive collapse resistant design of building structures against blast loading are put forward.

Occurrence of progressive collapse events invariably leads to significant economic and human-life losses. Progressive collapse analysis and design of building structures have become a research hotspot worldwide. Existing studies have proved that development of extra load-carrying mechanisms could significantly improve the resistance of structures to progressive collapse. However, limited research has been conducted to quantitatively analyze these mechanisms. This study proposed a new and unified division method for mechanisms for resisting progressive collapse; furthermore, it provides a basis for their quantitative analysis. In addition, the progressive collapse behavior of a 1/3-scaled two-story, one-bay-by-two-bay reinforced concrete (beam–slab–column) frame with an edge column lost was experimentally investigated. Additionally, a 3 D solid finite element model was established and validated based on the test results. The effects of different extensive parameters, including ideal lateral constraints, slab thickness, and beam–slab interaction, on each resisting mechanism were quantitatively investigated. Finally, a new simple method for predicting the first peak load was proposed based on the contribution of each mechanism. The results from the simple method were in agreement with the simulation results of beam–slab–column structures.

Longitudinal stresses due to combined horizontal and vertical bending moments in ships, corresponding to a return period of 20 years, are estimated by linear response analysis. In principle, the stress should be obtained by combining the stress in all sea states that can occur over a long-term period. A method to determine the desired long-term extreme stress by considering only a few short-term sea states is presented. The sea states have a certain probability of occurrence, and are each identified by a contour line in the (Hs, Tp)-plane. This approach makes it possible to estimate the extreme loads on the vessel in a practical and accurate manner. Moreover, it is shown that the long-term stress can be estimated by combining the individual long-term extreme stresses due to vertical and horizontal bending moments by using the sum-of-squares approach and accounting for the correlation between stresses. It was found that the correlation coefficient can be taken as the largest of the ones calculated along the contour line. It is shown that this correlation coefficient can even be approximated by the normalized phase angle at the wave length where the dominant response has its peak value. A comparison with the results obtained using well-known combination rules is presented. While linear analysis has been used here, it is believed that the approach can be generalized to stresses with nonlinear behavior, and hence represent a significant improvement in calculation efficiency.

In this study, the progressive collapse potential of tube‐type buildings, such as diagrid and tubular structures, composed of lateral load‐resisting perimeter frames and internal pin‐connected gravity frames, was evaluated by nonlinear static and dynamic analyses. To this end, 36‐ and 54‐storey structures were designed as analysis models and progressive collapse analyses were carried out by removing first‐storey columns. According to the analysis results, the progressive collapse of tube‐type analysis model buildings occurred when perimeter columns corresponding to more than 11% of all member cross‐sectional areas were removed from one side of the structures. When the diagonals located around a corner were removed, the ratio was reduced to 8%. It was observed that the corner columns in the diagrid system helped prevent the propagation of member failure all around the perimeter. Copyright © 2009 John Wiley & Sons, Ltd.

This paper presents a case study of a 10-story concrete frame structure designed according to the Chinese Code GB50010-2002. To reduce the potential of progressive collapse due to single column failure, progressive collapse analysis is carried out following the DoD2009 guidelines. It is observed that most of longitudinal beams in superstructure and floors above the failure column would collapse as the results of removing an exterior column, no beams and floors would collapse when an interior column at ground floor was removed, and only the beams in short span would collapse when an interior column at upper floor was removed. Adequate reinforcements in the beams of superstructure and adequate ties among floors, beams and columns can be used to avoid the progressive failure of structure, after failure of particular column.

Over the last 10 years, two United States government agencies have developed guidelines for the design of their structures to resist progressive collapse: 1. The General Services Administration, "Progressive Collapse Analysis and Design Guidelines," (GSA Guidelines) and 2. The Department of Defense Unified Facilities Criteria 4-023-03 "Design of Buildings to Resist Progressive Collapse" (UFC 4-023-03). Although both documents incorporate some of the same approaches, there are notable differences in the application of these procedures. Within both approaches, the main direct design procedure is the Alternate Path (AP) method, in which a structure is analyzed for collapse potential after the removal of a column or section of wall. Different analytical procedures may be used, including Linear Static (LS), Nonlinear Static (NLS), and Nonlinear Dynamic (NLD). Typically, NLD procedures give better and more accurate results, but are more complicated and expensive. As a result, designers often choose static procedures which tend to be simpler, requiring less labor. As progressive collapse is a dynamic and nonlinear event, the load cases for the static procedures require the use of factors to account for inertial and nonlinear effects, similar to the approach used in ASCE Standard 41 "Seismic Rehabilitation of Existing Buildings" (ASCE 41). It is important that the design requirements incorporate appropriate dynamic and nonlinear factors such that the linear static and nonlinear static designs are more representative of the actual nonlinear and dynamic response of the structure.

The progressive collapse analysis of reinforced concrete (RC) moment-frame buildings under extreme loads is discussed from the perspective of modeling issues. A threat-independent approach or the alternate path method forms the basis of the simulations wherein the extreme event is modeled via column removal scenarios. Using a prototype RC frame building, issues and considerations in constitutive modeling of materials, options in modeling the structural elements and specification of gravity loads are discussed with the goal of achieving consistent models that can be used in collapse scenarios involving successive loss of load-bearing columns at the lowest level of the building. The role of the floor slabs in mobilizing catenary action and influencing the progressive collapse response is also highlighted. Finally, an energy-based approach for identifying the proximity to collapse of regular multi-story buildings is proposed.

Simplified nonlinear progressive collapse analysis of welded steel moment frames

Progressive collapse analysis on modular steel construction based on a simplified joint model

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

With the expectation of hull girder asymmetry and corresponding shift in elastic neutral axis resulting from collision damages and other forms of structural deteriorations, the interaction of vertical and horizontal hull girder capacities become quite significant in the assessment of ship structural safety. This paper therefore extends the application of a previously proposed interactive-numerical probabilistic based methodology for structural safety to assess the hull girder ultimate strength reliability of a damaged ship by means of a user-defined numerical framework. Hull girder capacity is calculated using the NS94D ultimate strength code, which is based on the Smith’s progressive collapse method. The resulting deterministic responses have been interactively linked to the NESSUS probabilistic framework so that the reliability of the damaged hull girder is predicted using an implicit limit state function defined based on a transformation of coordinates to appropriately account for any shift in the neutral axis. Random deviations of the constituent variables are directly applied to calculate the ultimate strength deterministic responses, thereby circumventing the need to characterize any correlated strength variable, which is at best subjective. The conventional approach of characterizing ultimate strength by an assumed coefficient of variation and distribution type was found to be conservative in predicting structural safety of ships relative to the proposed method. Application of the interactive-numerical technique for structural reliability is therefore considered significant for problems involving correlated random variables with unknown statistical characteristics. The method is being considered to predict the safety of cracked hull girders by accounting for the residual strength and further load bearing capabilities of deteriorated and adjacent elements.

Progressive collapse is a critical structural phenomenon where local damage triggers a chain reaction and potentially leads to disproportionate failure of the entire system. In this study, the progressive collapse behavior of multi-story reinforced concrete (RC) structures is investigated using numerical analysis methods. This situation poses a serious danger, especially for high-risk types of structures. In the study, the effect on the collapse tendency is evaluated by considering different structural models. Numerical analyses are performed using a nonlinear finite element method. This study offers a general exploration of the progressive collapse behavior of multi-story RC frames, focusing on robustness evaluation under various structural scenarios. The aim of this study is to improve the understanding of structural responses and to support the development of safer, more durable design strategies.