• Structural Engineering and Mechanics
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• v.52 no.1
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• pp.19-33
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• 2014

Structural robustness refers to the ability of a structure to avoid disproportionate consequences to the original cause. Currently attentions focus on the concepts of structural robustness, and discussions on methods of robustness based structural design are rare. Firstly, taking basis in robust $H_{\infty}$ control theory, structural robustness is assessed by $H_{\infty}$ norm of the system transfer function. Then using the SIMP material model, robustness based design of grid structures is formulated as a continuum topology optimization problem, where the relative density of each element and structural robustness are considered as the design variable and the optimization objective respectively. Generalized elitist genetic algorithm is used to solve the optimization problem. As examples, robustness configurations of plane stress model and the rectangular hyperbolic shell model were obtained by robustness based structural design. Finally, two models of single-layer grid structures were designed by conventional and robustness based method respectively. Different interference scenarios were simulated by static and impact experiments, and robustness of the models were analyzed and compared. The results show that the $H_{\infty}$ structural robustness index can indicate whether the structural response is proportional to the original cause. Robustness based structural design improves structural robustness effectively, and it can provide a conceptual design in the initial stage of structural design.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.1063-1093
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• 2015

Structural robustness has become an important design variable. However, based on the existing definitions of structural robustness it is often difficult to analyse and evaluate structural robustness, and sometimes not efficient since they mix structural robustness with several other structural variables. This paper concerns the development of a new structural robustness definition, and structural robustness and structural fragility indices. The basis for the development of the new indices is the analysis of the damage energy of structural systems for a given hazard scenario and involves a criterion to define an "unavoidable collapse" state. Illustrative examples are given detailing the steps and calculations needed to obtain values for both the structural robustness and the structural fragility indices. Finally, this paper presents the main advantages of the newly proposed definition and indices for the structural risk analysis over existing traditional methods.

• Structural Engineering and Mechanics
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• v.76 no.2
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• pp.193-205
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• 2020

The growing need for assuring efficient and sustainable investments in civil engineering structures has determined a renovated interest in the rational design of such structures from designers, clients and authorities. As a result, risk-informed decision-making methodologies are increasingly being used as a direct decision tool or as an upper-level layer from which performance-based approaches are then calibrated against. One of the most important and challenging aspects of today's structural design is to adequately handle the system-level effects, the known unknowns and the unknown unknowns. These aspects revolve around assessing and evaluating relevant damage scenarios, namely those involving unacceptable/intolerable damage levels. Hence, the importance of risk analysis of disproportionate collapse, and along with it of robustness. However, the way robustness has been used in modern design codes varies substantially, from simple provisions of prescriptive rules to complex risk analysis of the disproportionate collapse. As a result, implementing design for robustness is still very much a grey area and more so when it comes to defining means to quantify robustness. This paper revisits the most common robustness frameworks, highlighting their merits and limitations, and identifies one among them which is very promising as a way forward to solve the still open challenges.

• Structural Engineering and Mechanics
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• v.65 no.6
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• pp.689-698
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• 2018

This study focuses on a novel procedure for the robustness assessment of reinforced concrete (RC) framed structures under threat-independent damage scenarios. The procedure is derived from coupled dynamic and non-linear static analyses. Two robustness indicators are defined and the method is applied to two RC frame buildings. The first building was designed for gravity load and earthquake resistance in accordance with Eurocode 8. The second was designed according to the tie force (TF) method, one of the design quantitative procedures for enhancing resistance to progressive collapse. In addition, in order to demonstrate the suitability and applicability of the TF method, the structural robustness and resistance to progressive collapse of the two designs is compared.

• Earthquakes and Structures
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• v.3 no.6
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• pp.805-820
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• 2012

An enhanced and efficient methodology is proposed for evaluating the robustness of an uncertain structure with passive dampers. Although the structural performance for seismic loads is an important design criterion in earthquake-prone countries, the structural parameters such as storey stiffnesses and damping coefficients of passive dampers are uncertain due to various factors or sources, e.g. initial manufacturing errors, material deterioration, temperature dependence. The concept of robust building design under such uncertain structural-parameter environment may be one of the most challenging issues to be tackled recently. By applying the proposed method of interval analysis and robustness evaluation for predicting the response variability accurately, the robustness of a passively controlled structure can be evaluated efficiently in terms of the so-called robustness function. An application is presented of the robustness function to the design and evaluation of passive damper systems.

• International Journal of High-Rise Buildings
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• v.9 no.2
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• pp.127-154
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• 2020

Disproportionate collapse triggered by local structural failure may cause huge casualties and economic losses, being one of the most critical civil engineering incidents. It is generally recognized that ensuring robustness of a structure, defined as its insensitivity to local failure, is the most acceptable and effective method to arrest disproportionate collapse. To date, the concept of robustness in its definition and quantification is still an issue of controversy. This paper presents a detailed review on about 50 quantitative measures of robustness for building structures, being classified into structural attribute-based and structural performance-based measures (deterministic and probabilistic). The definition of robustness is first described and distinguished from that of collapse resistance, vulnerability and redundancy. The review shows that deterministic measures predominate in quantifying structural robustness by comparing the structural responses of an intact and damaged structure. The attribute-based measures based on structural topology and stiffness are only applicable to elastic state of simple structural forms while the probabilistic measures receive growing interest by accounting for uncertainties in abnormal events, local failure, structural system and failure-induced consequences, which can be used for decision-making tools. There is still a lack of generalized quantifications of robustness, which should be derived based on the definition and design objectives and on the response of a structure to local damage as well as the associated consequences of collapse. Critical issues and recommendations for future design and research on quantification of robustness are provided from the views of column removal scenarios, types of structures, regularity of structural layouts, collapse modes, numerical methods, multiple hazards, degrees of robustness, partial damage of components, acceptable design criteria.

• Steel and Composite Structures
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• v.14 no.4
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• pp.379-395
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• 2013

Aim of this paper is to apply to a steel truss bridge a methodology that takes into account the consequences of extreme loads on structures, focusing on the influence that the loss of primary elements has on the structural load bearing capacity. In this context, the topic of structural robustness, intended as the capacity of a structure to withstand damages without suffering disproportionate response to the triggering causes while maintaining an assigned level of performance, becomes relevant. In the first part of this study, a brief literature review of the topics of structural robustness, collapse resistance and progressive collapse takes place, focusing on steel structures. In the second part, a procedure for the evaluation of the structural response and robustness of skeletal structures under impact loads is presented and tested in simple structures. Following that, an application focuses on a case study bridge, the extensively studied I-35W Minneapolis steel truss bridge. The bridge, which had a structural design particularly sensitive to extreme loads, recently collapsed for a series of other reasons, in part still under investigation. The applied method aims, in addition to the robustness assessment, at increasing the collapse resistance of the structure by testing alternative designs.

• International Journal of High-Rise Buildings
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• v.9 no.3
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• pp.245-253
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• 2020

With the ever-increasing height of timber buildings, the complexity of timber as a structural material gives rise to behaviors not previously studied by engineers. An urgent call is needed regarding their performance in damage scenarios: activating alternative load paths in tall timber buildings is not the same as in tall buildings made with steel and concrete. In this paper we propose a robustness framework covering all building materials, whose application in timber may lead to new conceptual designs for the next generation of tall timber buildings. Qualitatively, the importance of building scale and the distinction between localized and systematic exposures are discussed, and how existing supertall structures can be an example for future generations of tall timber buildings. Quantitatively, the robustness index is introduced alongside a method to calculate the performance of a given building regarding robustness, in order to find the most cost-effective structural solutions for improved robustness. A three-level application recommendation is made, depending on the importance of the building in question. Primarily, the paper highlights the importance of conceptual design to achieve structural robustness and encourages the practicing engineering community to use the proposed framework to quantitatively come up with the new generation of tall timber buildings.

• Structural Engineering and Mechanics
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• v.45 no.6
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• pp.803-819
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• 2013

This paper addresses two main issues relevant to the structural assessment of buildings subjected to explosions. The first issue regards the robustness evaluation of steel frame structures: a procedure is provided for computing "robustness curves" and it is applied to a 20-storey steel frame building, describing the residual strength of the (blast) damaged structure under different local damage levels. The second issue regards the precise evaluation of blast pressures acting on structural elements using Computational Fluid Dynamic (CFD) techniques. This last aspect is treated with particular reference to gas explosions, focusing on some critical parameters (room congestion, failure of non-structural walls and ignition point location) which influence the development of the explosion. From the analyses, it can be deduced that, at least for the examined cases, the obtained robustness curves provide a suitable tool that can be used for risk management and assessment purposes. Moreover, the variation of relevant CFD analysis outcomes (e.g., pressure) due to the variation of the analysis parameters is found to be significant.

• Ecology and Resilient Infrastructure
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• v.3 no.2
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• pp.117-125
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• 2016

Current cities encounter various types of water problems due to rapid urbanization and climate change. The increasing significance of urban water problems calls for the establishment of resilient alternatives to prevent and minimize social loss that results from these phenomena. As a background research for establishing resilient infrastructures for the mitigation of urban water problems, we evaluated the robustness of structural alternatives for urban flood as a representative case. Combining the robustness index (RI) and the cost index (CI), we suggested the robustness-cost index (RCI) as an indicator of the robustness of structural alternatives, and applied the index to assess the existing infrastructures and structural alternatives (i.e., sewer network expansion, additional storage tank construction, and green roof construction) at a site prone to floods located around Gangnam-station, Seoul, Korea. At a rainfall intensity frequency range of 2 to 20 years, the usage of a storage tank and a green roof showed relatively high RCI value, with a variation of an alternative showing greater RCI between the two depending on the size of design rainfall. For a rainfall intensity frequency of 30 years, installing a storage tank with some green roofing was the most resilient alternative based on the RCI value. We proposed strategies for establishing resilient infrastructures for the mitigation of urban floods by evaluating the robustness of existing infrastructures and selecting optimal structural alternatives with the consideration of scales of design disaster.