The properties of a composite material are determined by the properties of the constitutive materials. In engineering practice, there are many situations in which we have composite material, but we do not have information about the properties of each phase component. The measurements we can make in such cases are on the existing material, thus being able to determine, experimentally, the global physical properties of the composite. The possibility of realizing an estimate of the mechanical properties of each component poses a problem if we start from these measurements. The paper proposes a method to achieve this, starting from the theoretical estimates established in the literature, then illustrated by an example to determine the properties of wood. Wood is a transverse isotropic material and therefore the constitutive law has symmetries that are manifested in the decrease of the number of parameters that define the stress-strain liason, defined only by five independent parameters. The proposed method can be extended to a diversity of models and materials used in the study of composite materials.

Based on the Szirtes’ modern dimensional analysis (MDA), the authors apply the theory to a real structure in order to validate by experimental measurements its applicability. After a presentation of the basic elements of the model law (ML), deduced for two relevant cases, the authors conceived the set of prototypes and models, based on the case of an actual construction pillar, physically performed at scales of 1:1, 1:2, and 1:4. The combination of these structural elements, made at different scales, resulted in three sets of prototypes and models. In this paper, taking into consideration the ML for two relevant cases, the following are presented: the original test stand of these structural elements; block diagram of the original electronic heating and control system; the basic considerations regarding the particularity of this heating system from the point of view of heat transfer; measurement data, obtained for both nonthermally protected elements and for those protected with layers of intumescent paints. In the last part of the paper, the values obtained by rigorous direct measurements with those offered by the ML on the elements considered as prototypes and models are compared. Almost identical values were obtained from the direct measurements with those provided by the ML, thus resulting in the validation of these laws. The same thermal regimes were applied to all these structural elements, with registration of every parameter related to these thermal regimes. Depending on the role of a structural element within a certain set (prototype-model), some of the measurement data were considered as data acquired directly through measurements, and others served as reference elements for those for which we had to obtain through the model law. In the last part of the paper, the sizes obtained by rigorous direct measurements are compared with those offered by the model law on the elements considered as prototypes and models. Identical practical values of the quantities were obtained from the direct measurements with those provided by the model law, thus resulting in the validation of these laws.

This paper reports experimental and theoretical result derived from research on steel structural elements’ fire-protection with intumescent paint. The experimental results were obtained by means of an original testing bench, briefly described below and some basic cases, i.e., horizontally and vertically disposed, massive and square-tubular cross-sectioned, reduced-scale straight bars heated at one end. By means of the thermocouples mounted along the bars, the temperature distribution laws were monitored, depending on the heated end’s nominal temperature. The paper describes an original approach to the temperature distribution evaluation by means of some new parameters, based on the temperature distribution laws experimentally obtained with reduced-scale models. We involved the least-square method (LSM) and the curve-fitting one in order to obtain a more accurate temperature distribution law compared to the experimentally obtained ones. We also introduced some new parameters in order to define the amount of heat loss in a more accurate way. Based on the results obtained, the authors suggest that this approach to the temperature distribution law can be efficiently applied in further thermal analyses, for both 2D and 3D structures. The paper also includes a thorough analysis of “m” variation along the square-tubular-cross-section, reduced-scale straight bars, and similar new approaches are proposed by the authors. The sub-goals of this investigation were (1) to obtain useful correlations between the magnitudes of the massivity $\zeta =P/A$ and the parameter “m” along the bar, and (2) to analyze, on reduced-scale models, the heat distribution laws on unprotected and intumescent-paint-protected 2D and 3D steel structures.

Nowadays, the real structures (considered as prototypes) subjected to fire are analysed by means of the behaviours of some reduced scale structures (defined as models). These prototype–model correlations are governed by the so-called dimensional analysis (DA) methods. These methods, starting from the Buckingham theorem, offer several dimensionless variables and based on them is the so-called Model Law (ML), which is able to foresee the predictable prototype’s answer based on the results of the experimental investigations performed exclusively on the model (usually manufactured at a reduced scale). Based on the MDA principles, in a previous paper the authors elaborated the complete ML for the heat transfer in beams with rectangular-hole cross-sections, considering unprotected as well as thermally protected structural elements. The authors, based on meticulous experimental investigations, obtained the validation of this ML for the unprotected steel members. In this contribution, the authors offer in a similar manner the ML validation for intumescent paint-protected steel members and thus the complete validation of their original ML. In their theoretical and experimental investigations, the authors involved both a real column’s element combined with its models manufactured at 1:2 and 1:4, as well as 1:10 scales too. Consequently, the obtained ML can be considered as generally valid, involving a real structural element and its model manufactured at the desired scale.

This chapter introduces a simplified and efficient approach to dimensional analysis, namely the so-called modern dimensional analysis (MDA). MDA is a simple, safe and user-friendly version of the dimensional methods that are currently widely applicable to several engineering problems, such as heat transfer, load-bearing capacity, as well as fire protection of buildings. MDA provides a unique and very simple way to obtain the complete Model Law (ML), which governs the prototype-model correlation. The inferred ML, based on the results of experimental investigations performed exclusively on the attached reduced-scale model, will predict the behaviors of the full-scale prototype. Through its facilities, MDA makes sure to attach the most suitable and flexible model to the prototype and thereby: to obtain in the best manner the required information regarding the given prototype. In this chapter, the currently used dimensional methods are described one by one, along with their advantages and limitations; the MDA principle, with its indisputable advantages; its main stages; useful applications of MDA in the field of heat transfer, as well as a series of conclusions of the authors based on more than 25 years of experience in the application of this very efficient and user-friend method. Section 2 describes the advantages and limitations of the geometric analogy, similarity and classical dimensional analysis, while Section 3: MDA with its main stages and advantages compared to the rest of the classical methods. By comparing them, the reader can confirm or deny the correctness of the authors’ claim regarding the remarkable efficiency of MDA.