The type of a point and a characterization of the set of external points of a conic in in PG(2,q), q odd

Recently, see [1], Alabdullah and Hirschfeld introduce the type of a point. This simple and original concept allow us to characterize the set of external points of a conic in PG, (2, q) odd, within a class of three-character sets

Validation of a New Analytical Formula to Predict the Steel Temperature of Heavily Insulated Cross-Sections

Fire protection is a popular solution to slow down the temperature increase in steel elements subjected to fire, and simple equations, such as the mass lumped formula proposed in EN1993-1-2, may be employed to estimate the steel temperature in the cross-section. The EN1993-1-2 formula assumes that the temperature of the exposed insulation surface and the surrounding gas are equal. This simplification may provide inaccurate results for heavily insulated steel sections. Therefore, a new mass lumped formula was derived, accounting for more accurate boundary conditions considering the heat flux impinging the insulation. On these premises, this work evaluates how the new simple formula fares with respect to the EN1993-1-2 formula. In this respect, a comprehensive comparison with the results of 1-D and 2-D analyses considering several insulation materials and thicknesses of insulation and steel is thoroughly presented. The proposal results in being always safe and better estimates steel temperatures relevant in the structural fire engineering context. Its use is particularly recommended for heavily insulated sections, where the ratio between the insulation and the steel heat capacities is higher than 14, and the EN1993-1-2 formula gives unsafe predictions

Implementation of a weak coupling approach between a CFD and an FE software for fires in compartment

The paper presents the assumptions and the issues that arise when developing an integrated modelling methodology between a Computational Fluid Dynamics (CFD) software applied to compartment fires and a Finite Element (FE) software applied to structural systems subjected to fire. In particular, a weak coupling approach used to simulate a fire exposed structure by modelling the fire development in the compartment, the heat penetration in the structure and the mechanical response is described. The advantages and the disadvantages of such a technique are highlighted compared to a full coupling that conversely takes into account all mutual interactions. The favourable aspect of computing the thermal response of the structure in the FE model in order to avoid modelling the structure in the CFD model is underlined, namely a sensitive reduction of computational demand. Finally, the study is enriched by an application of this methodology that concerns the simulation of a pool fire in an open compartment the results of which are compared with those obtained by employing the simplified Hasemi model included in the Eurocodes

Dynamic Increase Factors for progressive collapse anaylsis of steel structures accounting for column buckling

Man-made hazards, such as fire, explosions, or impacts, may induce the progressive collapse of structures, in which the localised failure spreads from the single affected structural component to other parts of the structure. A typical approach to model progressive collapse consists in performing static column removal analyses considering a Dynamic Increase Factor (DIF), whose determination becomes paramount to account for the dynamic effects related to a sudden column loss scenario. Current recommendations on the definition of such factor mainly consider a beam-type collapse in non-linear analyses, though different mechanisms, e.g., column buckling, may govern progressive collapse events. This paper presents the determination of the DIFs through a numerical procedure for five steel structures with an increasing number of storeys. Both global and local imperfections are modeled to account for the geometric non-linearities of the structure and column buckling. DIF values are obtained considering two different Engineering Demand Parameters (EDPs), suited for describing beam-type and column-type mechanisms respectively. The evaluated DIFs are compared with the values recommended in the current UFC design prescriptions for progressive collapse, and considerations on the choice of the appropriate DIF values are provided

A Retrofit Method to Mitigate Progressive Collapse in Steel Structures

Accidental events, such as impact loading or explosions, are rare events characterized by a very low probability of occurrence. However, their effects often lead to very high human losses and economic consequences as are likely to trigger the progressive collapse of the buildings. The pro-gressive collapse of structures attracted the attention of many researchers and the topic has been widely investigated in recent years. In addition, increasing interest has been shown also on the definition of retrofit strategies able to increase the robustness of existing structures. The present work investigates the performance and the design of a retrofit solution to increase the robustness of steel moment resisting frames. A case study structure is selected and modelled in OpenSees, including both mechanical and geometrical non-linearities. Non-linear static analyses have been carried out on the frame, simulating a column loss scenario to investigate the subsequent load re-distribution. The simulations showed that the case study was unable to redistribute the load and hence retrofitting was required. Among others, a truss system was added at the rooftop level of the building allowing the definition of an alternative load path. The analyses outcomes showed how the proposed retrofit method allows to increase the robustness of the case study structure and allowed for critical remarks on the checks required when this retrofit system is employed

Dynamic increase factors for progressive collapse analysis of steel structures considering column buckling

Progressive or disproportionate collapse of structures may have severe socio-economic consequences. Aiming at buildings that can withstand such events, one solution is to prevent or minimize the propagation of damage that may lead to progressive collapse by means of robust design strategies. As a typical approach to model progressive collapse and assess robustness, the Alternate Path Method (APM) allows for static analyses, in which the dynamic effects induced by a sudden column loss are taken into account by amplifying loads through a Dynamic Increase Factor. Current recommendations for Dynamic Increase Factors to be used within non-linear static analyses have mainly considered beam-type collapse, overlooking other failure mechanisms, e.g., column buckling. The present paper investigates the dynamic effects of steel structures subjected to progressive collapse when buckling of columns is relevant. Five low- to high-rise case study building structures are considered together with three different column loss scenarios. A numerical procedure is introduced to evaluate the Dynamic Increase Factors considering two different Engineering Demand Parameters (EDPs), suited for describing beam- and column-type mechanisms, respectively. As Dynamic Increase Factors are typically assessed by increasing the loads on all the spans (DIF), a procedure was proposed for deriving factors that apply only on the spans above the removal (DIF*), consistently with UFC guidelines. The obtained DIF and DIF* are compared with the current literature and with values recommended in the UFC guidelines, highlighting the limits of current recommendations. Relevant considerations on the derived Dynamic Increase Factors and failure mechanisms involved are provided

Assessment of retrofit measures to prevent progressive collapse in steel structures

Man-made hazards, such as fires, explosions, or impacts, may have severe social and economic consequences and, therefore, should be carefully considered during the design of new, as well as, during the retrofitting of existing structures. Among others, these events could induce the progressive collapse of structures, in which the localised failure spreads from the single affected structural component to other parts of the structure. It is important to highlight that most existing structures worldwide have been designed before the introduction of design rules against progressive collapse. Therefore, it is nowadays of paramount importance to identify effective retrofit measures to renovate existing structures and return safer buildings to the community, including explicit design considerations against progressive collapse. The present paper investigates the effectiveness of three different retrofit measures, namely roof-truss, bracing, and cable systems, conceived to increase the structural robustness and hence mitigate the progressive collapse risk in steel structures. A case study steel moment resisting frame (MRF) was studied by performing non-linear static analyses in OpenSees and investigating its response before and after retrofitting. The progressive collapse was simulated by considering central column loss scenarios, and the ability to prevent the spread of failures of the original and retrofitted structures was examined. The present study sheds some light on the effectiveness and limitations of the considered retrofit measures in improving the overall robustness of the frame. The results show that, after the column removal, the original configuration of the selected MRF fails due to column buckling. Therefore, only the roof-truss and bracings strategies effectively improve the frame’s robustness and allow the creation of alternative load paths. Additionally, some critical aspects to be carefully considered in the design of the retrofit measures are indicated

Retrofit of existing steel structures against progressive collapse through roof-truss

The paper presents the results of a comprehensive study on the evaluation of the effectiveness of a retrofit strategy of existing steel buildings against progressive collapse. In this respect, it investigates the performance and the design of a retrofit solution to increase the robustness of steel Moment Resisting Frame buildings. A truss steel system added at the building's rooftop level (i.e., ‘roof-truss’), and intended to define an alternative load path, was investigated as a retrofit solution. The numerical model key components, including the plastic hinges and the beam-column connections, were validated against available experimental results. The validated models were then used to study the robustness of the structure under column loss scenarios by means of non-linear static and dynamic analyses performed in OpenSees. The simulations allowed for the identification of possible failure modes and alternative load paths together with the definition of the Dynamic Increase Factor (DIF). In this regard, it is shown that column buckling is critical for the selected case study. Moreover, the outcomes showed how the proposed retrofit solution allows the definition of effective alternative load paths when subjected to column loss scenarios and informs on the critical details that should be checked by employing this retrofit system

Minimized Training of Machine Learning-Based Calibration Methods for Low-Cost O₃Sensors

Low-cost sensors (LCSs) show a huge potential toward enabling the pervasive and continuous monitoring of crucial environmental parameters, supporting environment preservation, and informing citizens' well-being through ubiquitous air quality data. The main drawback of LCSs is that their data is usually biased, even if LCSs are calibrated by their manufacturer at production time. More accurate in-field calibration methods based on machine learning (ML) and neural networks (NNs) are being considered in some recent studies. They typically imply LCSs colocation with reference measurement stations certified by environmental agencies. Due to seasonality effects, however, the correlation between LCSs and their reference may rapidly degrade once the LCSs are moved from the calibration site, making even really accurate calibrations useless. In this work, we specifically target this problem by optimizing the training settings of the most popular ML and NN calibration models for LCSs when a sequential split schema is adopted to separate training and test sets. Then, we assess the degradation of the calibration over time based on the R2 score, when the splitting of the dataset between training and test sets is different from the classical 80%-20% ratio. This method is applied to real data gathered from an O3 sensor deployed in co-location with a certified reference station for a period of six months. Eventually, we show that, in the case of long-short term memory NNs, using 20% of the dataset for the training is a trade-off condition that minimizes the calibration effort and still yields a robust and long-lasting calibration.</p