In the current literature we can find mainly two approaches to the
SDE regime switching modeling. The traditional one, the externally induced
regime switching diffusions is described by the switching being derived from
a separate continuous time Markov process, with a finite, or denumerable,
state space { indexing the regimes { the random times of the regime switches
being exactly the jump times of the finite valued Markov process. There is a
first alternative approach in which the regime switching occurs whenever the
trajectory enters in some prescribed region on the state space; the regions we
consider will be mainly open intervals defined by unknown thresholds for the
trajectories; thresholds that, in principle, should also be estimated. In this
approach the partitioning of the the state space is already defined in the drift
and volatility of the SDE. In a second alternative approach the switching occurs
in a random way but at some random times defined when the trajectories hit
some prescribed thresholds, that again, must be estimated. We may designate
these two alternative approaches as auto-induced regime switching diffusions
as there is no external noise source to force the switching occurrence. We prove
a generalization of an existence result of the existence of auto-induced regime
switching SDE solutions for irregular coefficients and a result that encompasses
some of the cases of both externally and auto-induced regime switching SDE
solutions.

The interfacial behaviour between ribbed steel rebars and concrete has been extensively studied because the contribution of the adherence between these two materials is of the utmost importance for the behaviour of Reinforced Concrete (RC) structures. The majority of the available studies on this topic indicate that the local adherence between these two materials can be defined through a bond-slip relationship, which is obtained with short embedded lengths. Although this seems to be widely accepted, some incoherencies, mainly regarding the local and the global detachment process in that “conventional theory”, are identified in the present work. To facilitate the understanding of the detachment process between a ribbed steel rebar and concrete, an analytical solution is developed. An experimental program with 33 pull-out tests covering three different ribbed steel rebars with different diameters and embedded lengths was carried out. Based on the experimental load–displacement at the pulled end responses, a new local bond-slip relationship with friction is proposed. In the end, the new bond-slip relationship, as well as other known relationships, is implemented into a Finite Element (FE) commercial code and the results are compared to the experimental data. Based on these preliminary results and up to the yielding point of the steel rebars, the new proposed local bond-slip model is the only one able to clearly distinguish and simulate either the local and the global performances of the tested specimens. © 2020 Institution of Structural Engineers

The aim of the present paper is to evaluate the gravity loads effect in the behaviour of reinforced concrete beams critical zones subjected to cyclic loads. A numerical study to assess the influence of gravity load on RC beam critical zones subjected to cyclic loading is presented, assuming the level of gravity load as a variable parameter. For this purpose, the non-linear model was previously validated with an experimental campaign carried out on RC beam connection subject to cyclic loading with and without gravity loads. The consideration of the gravity load effects led to an accumulation of negative (hogging) deformation and the formation of an unidirectional plastic hinge. In order to validate this behaviour in an overall structural response, a non-linear numerical analysis of a RC frame system under cyclic loads, subject to different levels of gravity load, is also presented. The numerical results are analysed in terms of global hysterical response, accumulated energy dissipation and equivalent viscous damping ratio. In this numerical study was observed that the hysteretic response depends on the load path. In the presence of higher gravity loads levels, the structure hysteretic behaviour exhibits higher damage levels and the failure mechanism is prone to the formation of four plastic hinges. This phenomenon is analysed and discuss in the present paper. © Federation Internationale du Beton (fib) - International Federation for Structural Concrete, 2019.

The different representations of functions are assumed as central on the development of the concept of function. Being widely recognized the complexity of this concept, the different representations allow the student to understand in a representation what could not be understood in another representation. And the integration of technology into the teaching and learning process provides an easy and quick way to access different representations. This study intends to analyse the understanding of upper secondary students about the information transmitted by each of the representations of functions usually available on technology. Specifically, it intends to understand which transitions between representations are more easily understood by the students and which ones are more difficult to perform. It also intended to identify some aspects that may contribute to this. This study adopts a quantitative methodology in which the answers given by a class to a test focused on the transition from one representation to another are analysed; and a qualitative methodology based on interviews to three of the students in the class, as a way of seeking comprehension about their answers. The results achieved suggest a greater ease of understanding associated to the graphical representation and a greater difficulty associated to the tabular representation. The reasons for this seem to be related to the specific characteristics of each representation, but fundamentally with aspects related to the experiences lived by the students on the mathematics classes, being the integration of technology an influence not to neglect.

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This paper presents a study of the behaviour and load capacity of steel-fibre-reinforced concrete (SFRC) flat slabs under monotonically increased concentrated vertical loads. The SFRC was used only in the local region of the slab–column connection, as the rest of the slab was cast using normal concrete without fibres. The six experimental test specimens had a thickness of 150 mm with different longitudinal reinforcement ratios, using a non-uniform distribution over the slab width. The concretes used were made with different Dramix 4D 65/60 BG steel fibre contents (0, 0·5, 0·75 and 1·0% volume content). The slab tests were complemented by flexural tests on notched beams. This made it possible to determine the tension behaviour of the different concretes used, through a linear post-cracking behaviour and inverse analysis. The inverse analysis made it possible to define the stress–crack opening relationship that characterises the tension behaviour of SFRC and to relate it to the observed behaviour and load capacity of the tested slabs. The tests results show that the tensile behaviour of the SFRC plays an important role in the behavioural and load capacity of the slabs and that it can be considered relevant to physically based models.

This paper presents an experimental study of four flat slab specimens subjected to combined vertical and horizontal cyclic loading. Steel fibre-reinforced concrete (SFRC) was used only in the local region of the slab–column connection, while the rest of the slabs were cast using normal concrete. The specimens measured 4·15 m × 1·85 m × 0·15 m and were connected to two steel half columns by 0·25 m × 0·25 m rigid steel plates, prestressed against the slab using steel bolts, to ensure monolithic behaviour. The specimens were tested using an innovative test setup system that accounted for important factors, such as the ability of bending moment redistribution, line of inflection mobility and assured equal vertical displacements at the opposite slab borders, and symmetrical shear forces. Results show that the presence of SFRC in the slab–column connection region is effective in increasing the deformation capacity of slab–column connections, allowing the increase of horizontal drift ratios.