This paper proposes a novel simplified framework for progressive collapse assessment of multi-storey buildings, considering sudden column loss as a design scenario. The proposed framework offers a practical means for assessing structural robustness at various levels of structural idealisation, and importantly it takes the debate on the factors influencing robustness away from the generalities towards the quantifiable. A major feature of the new approach is its ability to accommodate simplified as well as detailed models of the nonlinear structural response, with the additional benefit of allowing incremental assessment over successive levels of structural idealisation. Three main stages are utilised in the proposed assessment framework, including the determination of the nonlinear static response, dynamic assessment using a novel simplified approach, and ductility assessment. The conceptual clarity of the proposed framework sheds considerable light on the adequacy of commonly advocated measures and indicators of structural robustness, culminating in the proposal of a single rational measure of robustness that is applicable to building structures subject to sudden column loss. The companion paper details the application of the new approach to progressive collapse assessment of real steel-framed composite multi-storey buildings, making in the process important conclusions on the inherent robustness of such structures and the adequacy of current design provisions.

The companion paper presents the principles of a new design-oriented methodology for progressive collapse assessment of multi-storey buildings. The proposed procedure, which can be implemented at various levels of structural idealisation, determines ductility demand and supply in assessing the potential for progressive collapse initiated by instantaneous loss of a vertical support member. This paper demonstrates the applicability of the proposed approach by means of a case study, which considers sudden removal of a ground floor column in a typical steel-framed composite building. In line with current progressive collapse guidelines for buildings with a relatively simple and repetitive layout, the two principal scenarios investigated include removal of a peripheral column and a corner column. The study shows that such structures can be prone to progressive collapse, especially due to failure of the internal secondary beam support joints to safely transfer the gravity loads to the surrounding undamaged members if a flexible fin plate joint detail is employed. The provision of additional reinforcement in the slab over the hogging moment regions can generally have a beneficial effect on both the dynamic load carrying and deformation capacities. The response can be further improved if axial restraint provided by the adjacent structure can be relied upon. The study also highlights the inability of bare-steel beams to survive column removal despite satisfaction of the code prescribed structural integrity provisions. This demonstrates that tying force requirements alone cannot always guarantee structural robustness without explicit consideration of ductility demand/supply in the support joints of the affected members, as determined by their nonlinear dynamic response. Keywords IntroductionA new relatively simple yet sufficiently accurate methodology is presented in the companion paper [1] , which aims at appraising the efficacy of multi-storey buildings to resist progressive collapse triggered by sudden local column failure, as a consequence of an extreme loading event. The potential for progressive collapse is assessed in three independent stages based on the ductility demand and supply in the critical regions of the affected structural members. A significant advantage of the developed procedure is that it can explicitly account for the dynamic effects associated with the instantaneous column removal through a simplified energy equivalence approach, thus avoiding the need for nonlinear dynamic analysis. With respect to its applicability, the proposed method accommodates both simplified and detailed models of the nonlinear static response. Moreover, it can be implemented at various levels of structural idealisation, depending on the required level of sophistication, the feasibility of model reduction and the availability of analytical tools [1] . These levels correspond to either the full structure, excluding the damaged column, or critical sub-structures in which ductility demands are concentrated.The componen...

Satisfactory behaviour of structures under severe seismic loading is usually largely dependent on the ability of key components to undergo significant inelastic deformations. In the case of concentrically braced frames, the critical elements are the diagonal bracing members which are expected to experience repeated cycles involving yielding in tension and member buckling in compression. The performance of bracing members depends on various factors, including local slenderness, global slenderness, material yield strength, section shape and end restraint [1]. Due to the difficulty in modelling the non-linearity and cyclic plasticity accurately, numerous experimental studies have been carried out to study the cyclic inelastic behaviour of bracing members.The interest of researchers in the early days was primarily in the load-displacement hysteretic response of the braces. Models were proposed to predict residual elongation at zero load, loss of compressive strength, the area under the hysteresis loops which represents the amount of energy dissipation, and other key characteristics of the hysteresis loops [2][3][4][5]. It was generally concluded [4,5] that global slenderness was the most important parameter influencing the hysteretic behaviour of braces. Slender members lost compressive resistance more rapidly than stocky members, resulting in fewer inelastic response cycles and lower amount of energy dissipation.More recently, attention has shifted to examination of the factors influencing the fracture life of bracing members. Through experimental testing, both global and local slenderness were found to be important factors in determining fracture life. Tang and Goel [6] proposed one of the first empirical equations for predicting the fracture life of bracing members, which suggests that fracture life is proportional to both the aspect ratio of the cross-section and the global member slenderness but inversely proportional to the square of the local slenderness. However, the validity of this prediction method is limited to bracing members in inverted V braced frames. Further developments [7][8][9] in the prediction of fracture life of brace members have utilised this basic proposed equation and generalised the applicability to bracing members in other concentrically braced frame configurations.A more general relationship was established following a comprehensive survey of the experimental cyclic behaviour of steel bracing members conducted by Tremblay [7], in which buckling resistance, post-buckling resistance in compression, tensile resistance, fracture life and a number of other properties from about 50 members were assessed. Shaback and Brown [8] carried out tests on square hollow section bracing members and calibrated a more sophisticated expression of fracture life, defined as Revised Manuscript Click here to view linked References 2 the weighted sum of normalised compressive and tensile deformation, in terms of global slenderness, local slenderness, aspect ratio of the cross-section and material yield strengt...

This paper focuses on examining the uniaxial behaviour of concrete materials incorporating rubber particles, obtained from recycled end-of-life tyres, as a replacement for mineral aggregates. A detailed account of a set of material tests on rubberised concrete cylindrical samples, in which fine and coarse mineral aggregates are replaced in equal volumes by rubber particles with various sizes, is presented. The experimental results carried out in this investigation, combined with detailed examination of data available from previous tests on rubberised concrete materials, show that the rubber particles influence the mechanical properties as a function of the quantity and type of the mineral aggregates replaced. Experimental evaluation of the complete stress-strain response depicts reductions in compressive strength, elastic modulus, and crushing strain, with the change in rubber content. Enhancement is also observed in the energy released during crushing as well as in the lateral strain at crushing, primarily due to the intrinsic deformability of the interfacial clamping of rubber particles which leads to higher lateral dilation of the material. The test results and observations enable the definition of a series of expressions to estimate the mechanical properties of rubberised concrete materials. An analytical model is also proposed for the detailed assessment of the complete stress-strain response as a function of the volumetric rubber ratio. Validations performed against the material tests carried out in this study, as well as those from previous investigations on rubberised concrete materials, show that the proposed models offer reliable predictions of the mechanical properties including the full axial and lateral stress-strain response of concrete materials incorporating rubber particles

a b s t r a c tCyclic material tests in the low and extremely low cycle fatigue regime were carried out to study the properties of structural carbon steel and stainless steel. A total of 62 experiments were performed in cyclic axial and bending configurations, with strain amplitudes up to ±15%. Materials from hot-rolled carbon steel (S355J2H), cold-formed carbon steel (S235JRH) and cold-formed austenitic stainless steel (EN 1.4301 and EN 1.4307) structural sections were tested and the results were compared. The strain-life data from the axial tests were used to derive suitable Coffin-Manson parameters for the three materials; two further extremely low cycle fatigue life prediction models were also considered. The results revealed that the three materials exhibit similar strain-life relationships despite significantly different elongations at fracture measured in monotonic tensile tests. The hysteretic responses of the materials at different strain amplitudes were used to calibrate a combined isotropic/kinematic cyclic material hardening model which can be incorporated into numerical models of structural members. The stainless steel specimens displayed significantly greater levels of cyclic hardening than the corresponding carbon steel samples. A relationship between the results obtained from axial and bending test arrangements was established through consideration of energy dissipation, enabling strain-life models to be derived from either means of testing.