# Person: Gimena Ramos, Faustino

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Gimena Ramos

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Faustino

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Ingeniería

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IS-FOOD. Research Institute on Innovation & Sustainable Development in Food Chain

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0000-0001-7912-9082

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485

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Publication Open Access Pohlke theorem: demonstration and graphical solution(Springer, 2017) Gimena Ramos, Faustino; Gimena Ramos, Lázaro; Goñi Garatea, Mikel; Gonzaga Vélez, Pedro; Proyectos e Ingeniería Rural; Landa Ingeniaritza eta ProiektuakShow more It is known that the axonometric defined by Pohlke, is geometrically known as a means of representing the figures of space using a cylindrical projec-tion and proportions. His theorem says that the three unit vectors orthogonal axes of the basis in the space can be transformed into three arbitrary vectors with com-mon origin located in the frame plane. Another way of expressing this theorem is given in three segments mismatched and incidents at one point in a plane, there is a trirectangular unitary thriedra in the space that can be transformed in these three segments. This paper presents a graphical procedure to demonstrate a solution of Pohlke¿s theorem. To do this, we start from previous work by the authors on the axonometric perspective. Graphic constructions that allow a single joint invariant description of relationships between an orthogonal axonometric oblique axono-metric system and systems associated thereby. At a same time of the geometric lo-cus generated by the diagonal magnitude positioned at any direction in the plane of the picture. This magnitude is the square root of the sum of the squares of the projection of the three segments representing axonometric on arbitrary magnitude.Show more Publication Embargo Application of the elastic curve equation for the verification of structures assimilable to continuous beams(World Scientific Publishing, 2024) Gimena Ramos, Faustino; Gonzaga Vélez, Pedro; Goñi Garatea, Mikel; Valdenebro García, José Vicente; Senosiain Carasusan, María Aranzazu; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC; Institute on Innovation and Sustainable Development in Food Chain - ISFOODShow more This paper analyzes the beam under isolated and uniform loads, extending this calculation towards the structural type of the continuous beam, by means of a single expression of the elastic curve. A general expression of the bending is proposed, deduced by integrating the different differential equations of the elastica, associated to each section between discontinuities produced by the loads. In this paper, support reactions are incorporated into the load system. Therefore, the continuous beam is understood as a bar made up of sections aligned between discontinuities. With this, the isostatic beam, the hyperstatic beam and the continuous beam can be treated by means of the same integrated expression of the displacement, also called the Macaulay method. Equivalent notations are provided to the expression of bending for the cases of traction-compression and torsion, obtained through the same reasoning and sequence of operations. The formulation of elastic type and the associated operations shown allow us to cover the analysis of the generic structural form, which we can define as the beam of any number of spans, or continuous beam of >n spans. The load system is also generalized, being able to contemplate loads of a different nature and form of distribution, both static and mobile. The examples that have been developed always provide analytical results of solicitation and deformation. They intend to explain the systematic path followed from the approach of the structural problem to its mathematical modelling, and the resolution procedure developed to obtain useful values for the structural verification. In these examples, an increasing degree of complexity and generalization has been followed. The expressions obtained are validated by comparing them with those that are usual in the structural literature for the same or similar problems.Show more Publication Open Access Formulation and solution of curved beams with elastic supports(Mechanical Engineering Faculty, University of Slavonski Brod, 2018) Sarría Pueyo, Fernando; Gimena Ramos, Faustino; Gonzaga Vélez, Pedro; Goñi Garatea, Mikel; Gimena Ramos, Lázaro; Ingeniería; IngeniaritzaShow more This article presents the general system of differential equations that governs the behaviour of a curved beam, which can be solved by either numerical or analytical methods. The obtained solution represents the matricial expression of transference. The stiffness matrix is derived directly rearranging the transfer matrix. Through twelve equations are shown the elastic conditions of the support in both ends of the curved piece. By joining the twelve equations of the stiffness matrix expression with the twelve equations of support conditions, we determined a unique system of equations associated to the curved beam with elastic supports. Establishing the elastic conditions has always been a problem, since previous traditional models do not look at the whole system, of twenty four equations, with all the unknowns and all the functions. Two examples of pieces with elastic supports are developed to show the applicability of the proposed method.Show more Publication Open Access Curved beam through matrices associated with support conditions(2020) Gimena Ramos, Faustino; Gonzaga Vélez, Pedro; Valdenebro García, José Vicente; Goñi Garatea, Mikel; Reyes-Rubiano, Lorena Silvana; Ingeniería; IngeniaritzaShow more Publication Open Access Geometric locus associated with thriedra axonometric projections. Intrinsic curve associated with the ellipse generated(Springer, 2017) Gonzaga Vélez, Pedro; Gimena Ramos, Faustino; Gimena Ramos, Lázaro; Goñi Garatea, Mikel; Proyectos e Ingeniería Rural; Landa Ingeniaritza eta ProiektuakShow more In previous work on the axonometric perspective, the authors presented some graphic constructions that allowed a single and joint invariant description of the relations between an orthogonal axonometric system, its related orthogonal views, and oblique axonometric systems associated with it. Continuing this work and using only the items drawn on the frame plane, in this communication we start from the three segments, representing trirectangular unitary thriedra, joined in the origin and defining an axonometric perspective. Each is projected onto any direc-tion and the square root of the summa of the squares of these projections is deter-mined. We call this magnitude, orthoedro diagonal whose sides would be formed by the three projections axonometric unit segments. If the diagonal size is built from the origin of coordinates and onto the direction used, this describes a locus here called intrinsic curve associated with the ellipse. When the starting three segments represent an orthogonal axonometric perspective, the intrinsic curve as-sociated with the ellipse is a circle.Show more Publication Open Access Alternative approach to the buckling phenomenon by means of a second order incremental analysis(Springer Nature, 2023) Gimena Ramos, Faustino; Goñi Garatea, Mikel; Gonzaga Vélez, Pedro; Valdenebro García, José Vicente; Ingeniería; IngeniaritzaShow more This article addresses the problem of determining the solicitation and deformation of beams with geometric imperfection, also called real beams under a compression action. This calculation is performed by applying the Finite Transfer Method numerical procedure under first-order effects with the entire compression action applied instantaneously and applying the action gradually under second-order effects. The results obtained by this procedure for real sinusoidal or parabolic beams are presented and compared. To verify the potential of the numerical procedure, the first and second-order effects of a beam with variable section are presented. New analytical formulations of the bending moment and the transverse deformation in the beam with sinusoidal imperfection subjected to compression are also obtained, under first and second-order analysis. The maximum failure load of the beams is determined based on their initial deformation. The results of solicitation and deformation of the real beam under compression are compared, applying the analytical expressions obtained and the numerical procedure cited. The beams under study are profiles with different geometric characteristics, which shows that it is possible to obtain maximum failure load results by varying the relationships between lengths, areas and slenderness. The increase in second-order bending moments causes the failure that originates in the beam, making it clear that this approach reproduces the buckling phenomenon. The article demonstrates that through the Finite Transfer Method the calculation of first and second-order effects can be addressed in beams of any type of directrix and of constant or variable section.Show more