Mixed duopolies with advance production

Production to order and production in advance has been compared in many frameworks. In this paper we investigate a mixed production in advance version of the capacity-constrained Bertrand-Edgeworth duopoly game and determine the solution of the respective timing game. We show that a pure-strategy (subgame-perfect) Nash-equilibrium point exists for all possible orderings of moves. It is pointed out that unlike the production-to-order case, the equilibrium of the timing game lies at simultaneous moves. An analysis of the public firm's impact on social welfare is also carried out. All the results are compared to those of the production-to order version of the respective game

OPTIMUM RELIABILITY OF A STEEL TAPERED PORTAL FRAME STRUCTURE EXPOSED TO FIRE

In this study, the optimum reliability of a tapered steel portal frame structure is presented for several cases. The aim of the research is to define target reliability indices for fire design situation since some research works (Balogh and Vigh, 2015a; 2015b) pointed that the achievable reliability (with using the prescriptive rules of Eurocode standards) is lower in extreme and seismic design situations than the suggested target value in (EN0, 2002). It seems that the target reliability indices of (JCSS, 2000) are preferable in these cases. In this paper, the optimum reliability is investigated as described in (Holickỳ, 2011), but total cost function is formulated with two decisive variables with respect to the amount of active and passive safety measures. The structural reliability is obtained with the help of a complex FORM (First Order Reliability Method) algorithm. The results of this investigation can help also to answer the question, whether active or passive safety measures are more effective tools to achieve optimal solutions in case of fire design of steel portal frames

Optimal fire design of steel tapered portal frames

The development of new and valuable conceptual design concepts based on structural optimization results is the global aim of the presented research in order to assist the industry in economical fire design of steel tapered portal frames. In order to find optimal configurations regarding the life cycle of the structure, a complex, reliability based structural optimization framework has been developed for tapered portal frame structures. Due to the high nonlinearity and discrete nature of the optimality problem, Genetic Algorithm is invoked to find optimal solutions according to the objective function in with the probability of failure is evaluated using First Order Reliability Method. The applied heuristic algorithm ensures that a number of possible alternatives are analysed during the design process. Based on evaluation of the results of a parametric study, new conceptual design concepts and recommendations are developed and presented for steel tapered portal frames used as storage hall related to optimal structural safety, common design practice and optimal structural fire design

Complex and comprehensive method for reliability calculation of structures under fire exposure

The reliability of structural systems has to be verified against failure caused by extreme effects, such as fire and seismic effects. To the best of the authors’ knowledge, there is a lack of studies in the literature on comprehensive reliability calculation of complex structural systems; the available studies mainly deal with the reliability calculation of simple, separated elements. In this study, a methodology is presented for the calculation of reliability of structures under fire exposure, giving a more complex and comprehensive basis for the calculation of structural reliability than earlier studies in the literature: a) the reliability calculation does not focuses on one single element but the whole structure; b) the presented methodology is able to consider any type of fire curve; c) reliability analysis includes the nonlinear analysis of the structure, in this way the highly nonlinear structural response is followed; d) the structural reliability is assessed on time basis. The applicability of the proposed algorithm is presented through reliability calculation of tapered portal frame structure protected by intumescent coating, as an example structure. The probability of failure is calculated using First Order Reliability Method. The resulted probabilities are verified using Monte Carlo Simulation

Design of frames with Buckling Restrained Braces - FEMA P695 based Evaluation of a Eurocode 8 Conforming Design Procedure

Buckling Restrained Braced Frames (BRBF) discussed in this paper are concentrically braced steel frames using continuous columns with rigid supports and BRBs as diagonal members [1]. The BRB is an innovative brace characterised by significant energy dissipation capability under cyclic loading. Because of their beneficial energy dissipation capability, BRBF are often more economical alternatives to conventional steel frame solutions. However, their application in Europe is hindered by the absence of a standardised design procedure. This paper is based on a research effort that aims to propose such a procedure that is compatible with the concepts and methodology of the Eurocode 8 standard (EC8) [2]. Evaluation of a design procedure is challenging, because of the vast number of possible design scenarios required to consider the variability in structural geometry and the seismic hazard. Until recent years the lack of computational resources impeded direct consideration of demand and capacity variability and led to simplified studies using only a small set of scenarios and crude models. The authors believe that besides being economical, the primary target of a good design procedure shall be assurance of sufficiently low failure probability with high confidence. Therefore, merits of a design procedure can only be judged by robust and reliable evaluation of collapse probability. This requires a framework for probabilistic assessment of the performance of a large number of typical structural solutions under various seismic hazard scenarios. The authors developed an extended version of the framework proposed in FEMA P695 [3] to assess the seismic performance of an EC8 conform BRBF design procedure. The paper briefly presents the design procedure, the extended framework and the results on a set of 24 BRBF archetypes. The archetypes are arranged into 8 Performance Groups; each group collects buildings with similar characteristics. Performance of each structure is evaluated using nonlinear dynamic analyses with a set of characteristic ground motion records. Detailed results for each archetype are available in [4]. All performance groups fulfilled the requirements of FEMA P695, namely that the conditional probability of failure of their structures at the design seismic intensity is less than 10%. The majority of individual collapse probabilities of the archetypes are below 3%. In spite of the good performance as per FEMA P695 the probabilities of collapse over the lifetime of structures and the corresponding reliability indices do not fulfil the limits in Eurocode 0 (EC0) for Ultimate Limit State design (P C < 0.01%). Such a stringent regulation can only be fulfilled by structures that resist extremely rare ground motions. The authors believe that it is not economical to design a structure to resist such rare effects. This observation has been made by other researchers as well [5] and it draws attention to the need for further research on this topic and an assessment of relaxed EC0 limits for seismic performance evaluation. The experienced advantageous behaviour of BRBF does not only stem from the high ductility and energy dissipation capacity of the braces, but also from application of an appropriate design procedure. The conservative approach applied in both numerical modelling and uncertainty estimation provides high confidence in the collapse assessment results. Based on the performance of BRBF archetypes, the proposed design procedure is considered appropriate for BRBF design for frames that are within the scope of the presented research. Therefore, applicability currently is limited to concentrically braced frames with chevron-type brace topology, continuous columns with rigid supports and a maximum of 6 stories. Investigation of additional archetypes in the future will lead to a better understanding of BRBF behaviour and allow relaxation of the above limits. ACKNOWLEDGMENT The work reported in the paper has been developed in the framework of the “Talent care and cultivation in the scientific workshops of BME” project. This project is supported by the grant TÁMOP-4.2.2.B-10/1-2010-0009. This paper was also supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. REFERENCES [1] López W.A., Sabelli R. 2004. “Seismic Design of Buckling-Restrained Braced Frames”. Steel Tips, Vol. 78 [2] EN 1998-1:2008 2008. Eurocode 8: Design of structures for earthquake resistance – Part 1: General rules, seismic actions and rules for buildings, CEN [3] FEMA P695. 2009. Quantification of building seismic performance factors, Federal Emergency Management Agency (FEMA), Washington, D.C. [4] Zsarnóczay Á., 2013. Experimental and Numerical Investigation of Buckling Restrained Braced Frames for Eurocode Conform Design Procedure Development, PhD Dissertation, Department of Structural Engineering, Budapest University of Technology and Economics. [5] Joint Committee on Structural Safety (JCSS) 2001 Probabilistic Model Code Part 1 – Basis of Desig