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1

A general theoretical formulation of deformation of steel structures exposed to fire

Badowski A., Dornowski W.

Biuletyn Wojskowej Akademii Technicznej

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2018

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Vol. 67, nr 2

63--75

EN

This paper presents a proposal for the formulation of a mathematical model of a fire resistance testing process for steel beams subject to bending, carried out experimentally in a test furnace. The model for the formulation was created with a balance method by describing with the fundamental laws of thermomechanics the phenomena occurring during the experiment analysed for the formulation. The viscoplastic behave our of steel at high temperatures was described with constitutive relationships proposed by Perzyna (which form the so-called “overload model”). The general mathematical model of the experiment analysed, obtained in the form of a system of differential equations, is discussed. The authors considered the impact of known physical properties of the test material and the impact of the results of the observations made during the research on the behaviour of individual terms of the model’s equations. Based on these considerations, simplifications were proposed which optimized the mathematical description and facilitated its adaptation to a special case. As a result of the investigation, a system of equation was obtained which described the processes present during the fire resistance test. It is postulated here to accept the system of equations as the mathematical model.

PL

W artykule przedstawiono propozycję sformułowania modelu matematycznego procesu badania nośności ogniowej stalowych belek zginanych, przeprowadzanego w piecu ogniowym. W celu opracowania tego modelu posłużono się metodą bilansową, opisując zjawiska zachodzące w trakcie analizowanego eksperymentu za pomocą podstawowych praw termomechaniki. Zachowanie lepkoplastyczne stali w wysokich temperaturach zmiennych w czasie opisano, używając związków konstytutywnych zaproponowanych przez Perzynę (tzw. model „przeciążeniowy”). Uzyskany w postaci układu równań różniczkowych ogólny model matematyczny analizowanego eksperymentu poddano dyskusji. Rozważono wpływ znanych właściwości fizycznych materiału i wyników obserwacji dokonanych w czasie badań na zachowania poszczególnych składników równań modelu. W efekcie zaproponowano uproszczenia umożliwiające zoptymalizowanie opisu matematycznego i jego dostosowanie do rozważanego przypadku szczególnego. Jako rezultat przeprowadzonych dociekań uzyskano układ równań opisujący procesy zachodzące w badaniu ogniowym, który postuluje się przyjąć jako jego model matematyczny.

2

The Viscoplastic Effect in the Heat–Treated, Thin–Walled AL–6060 Alloy Profiles Subjected to Compressive Axial Impact

Mróz A.

Mechanics and Mechanical Engineering

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2014

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Vol. 18, nr 1

53--71

EN

This paper will highlight the influence of the strain rate effect occurring during pulse loading on dynamic stability of aluminium profiles. Current work is the development of the analysis carried in [1]. The C–channel cross–section beams/columns are made of 6060 T4, T5, T6 and T66 aluminium alloy. The rectangular–shape compressing pulse is analysed. The static material characteristics had been obtained from the experimental tensile tests and afterwards modified for dynamic response according to Perzyna viscoplastic model. The results of the numerical computations are presented whereas the critical load and DLF (Dynamic Load Factor) basing on the selected dynamic buckling criterion is determined.

3

Parameters’ Identification of Perzyna and Chaboche Viscoplastic Models for Aluminum Alloy at Temperature of 120◦C

Kłosowski P, Mleczek A.

Engineering Transactions

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2014

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Vol. 62, iss. 3

291-–305

EN

The main purpose of this paper is the parameters identification of the Perzyna and the Chaboche models for the aluminum alloy at elevated temperature. The additional purpose is comparison of the results for these viscoplastic models. The results have been verified by the numerical simulation of the laboratory tests. The material parameters have been calculated on the basis of the uniaxial tension test. The determination of the Perzyna model’s parameters has been made on the basis of the ideas presented in papers of Perzyna [14–16, 18]. Then the parameters identification of the Chaboche model has been performed using concept presented in [2, 5, 6]. The elastic and inelastic properties have been estimated using the non-linear approximation by the least-squares method in Marquardt-Levenberg variant [12, 13]. The correctness assessment of the performed approximation has been verified by correlation and determination coefficients.