The Hardy Cross method and its implementation in Spain

En mayo de 1930, Hardy Cross (1885-1959) publicó un artículo titulado “Análisis de Marcos Continuos Mediante la Distribución de Momentos de Fin Fijo” en la Sociedad Americana de Ingenieros Civiles (ASCE). Este artículo propuso un nuevo enfoque de la teoría estructural, y su relevancia podría compararse con la del Teorema De Los Tres Momentos (también conocido como el Teorema de Clapeyron). El método Cross, como se ha llamado a menudo esta metodología de cálculo, tuvo notable importancia desde el momento en que salió hasta los años 70, cuando los nuevos métodos de cálculo se hicieron populares.Este método, así como muchas de aplicaciones adicionales, ha generado un gran número de artículos. En el presente artículo, intentaremos evaluar su impacto en lugares alejados de sus orígenes; en particular, cómo se entendió y formuló enEspaña. Como se demostrará, la importancia de este método era extremadamente relevante para la construcción de nuevos edificios y la implementación de nuevas industrias, que comenzaron a aparecer en un momento decisivo para el desarrollodel país. Aunque el método de Cross era la metodología más utilizada en ese momento, también se disponía de otros dos procedimientos a saber, los métodos Kani y Takabeya, métodos que también aparecerían en la bibliografía técnica de la época. A pesar de la infrecuente aplicación de estos otros métodos, nos hemos referido brevemente a ambos en el presente documento. Este artículo tiene como objetivo mostrar la relevancia del método Cross, así como su pronta implementación en España, utilizando la bibliografía docente de la época.In May 1930, Hardy Cross (1885-1959) published an article called ‘Analysis of continuous frames by distributing fixed-end moments’ in the American Society of Civil Engineers (ASCE). This article proposed a new approach to Structural Theory, and its relevance could be compared to that of the Three Moments Theorem (also known as the Clapeyron Theorem). The Cross method, as this calculation methodology has been often called, had remarkable significance from the moment it came out until the 70s, when new calculation methods became popular.In the present article, we will be trying to evaluate its impact in locations far from its origins; in particular, how it was understood and formulated in Spain. As will be demonstrated, the importance of this method was extremely relevant for theconstruction of new buildings and the implementation of new industries, which started to appear in a decisive moment for the development of the country. Even though the Hardy Cross method was the most widely used methodology at the time, two other procedures were also available; namely, the Kani and the Takabeya methods, methods that would also appear in the technical bibliography of the time. Despite the infrequent implementation of these other methods, we have briefly referred to both of them in the present paper. This article aims to show the relevance of the Cross method as well as its early implementation in Spain, by using academic bibliography of that time

From Galileo to Navier and Clapeyron

Galileo (1564-1642), in his well-known Discorsi (Galileo, 1638), briefly turning his attention to the fracture of a beam, starts an interesting discussion on the beam's breakage as well as its location. Could the section and breaking point of a beam have been determined beforehand? Furthermore, is it specific to the material? What Galileo did was not merely challenge a physics problem, but the prevailing knowledge of his time: namely, Aristotelianism on one hand, and Nominalism on the other. As a matter of fact, must the breakage of an element be treated as a universal or is it particular to a given material?/nThe present essay aims to prove how Galileo, confronting the structural problem and bringing it into the realm of science, was not just raising a problem but, using Salviati's words, he also established what actually takes place. Many years later, with the progress of physics, strength of materials and theory of structures, figures such as Claude Navier (1785-1836) and Benoît Clapeyron (1799-1864) confirmed once again that the Pisan turned out to be right./nThis article intends to combine technical fields such as strength of materials and theory of structures with others like the history of science and philosophy proper. A cooperative approach to these disciplines can be doubtlessly helpful to improve the knowledge, learning and teaching of their different curricula, giving the reader a global, holistic perspective./nGalileo (1564-1642), in his well-known Discorsi (Galileo, 1638), briefly turning his attention to the fracture of a beam, starts an interesting discussion on the beam's breakage as well as its location. Could the section and breaking point of a beam have been determined beforehand? Furthermore, is it specific to the material? What Galileo did was not merely challenge a physics problem, but the prevailing knowledge of his time: namely, Aristotelianism on one hand, and Nominalism on the other. As a matter of fact, must the breakage of an element be treated as a universal or is it particular to a given material/nThe present essay aims to prove how Galileo, confronting the structural problem and bringing it into the realm of science, was not just raising a problem but, using Salviati's words, he also established what actually takes place. Many years later, with the progress of physics, strength of materials and theory of structures, figures such as Claude Navier (1785-1836) and Benoît Clapeyron (1799-1864) confirmed once again that the Pisan turned out to be right./nThis article intends to combine technical fields such as strength of materials and theory of structures with others like the history of science and philosophy proper. A cooperative approach to these disciplines can be doubtlessly helpful to improve the knowledge, learning and teaching of their different curricula, giving the reader a global, holistic perspective

El castell de Montpalau. Pervivència de la jurisdicció d'un castell abandonat

Castles with own territory enclosed maintain the jurisdictional rights on their demarcation in spite of being from long time in situation of ruin or abandonment. The present work presents the case of the castle of Montpalau

Mecánica elástica, por A. Peña Boeuf. noventa años después

En el número 2427 de la Revista de Obras Públicas, correspondiente al año 1925, apareció un breve artículo1 escrito por un desconocido M. donde se glosaba la notable obra de Mecánica Elástica escrita por el reputado Ingeniero de Caminos, profesor de la Escuela Especial del Cuerpo, D. Alfonso Peña Boeuf. Pasados 90 años y, a la vez que recuperando el artículo, se referencia la importancia de dicho libro en la docencia y aprendizaje del cálculo estructural visto el prisma del tiempo discurridoPostprint (author's final draft

The vierendeel truss: past and present of an innovative typology

In the late 19th century, Belgian engineer Jules Arthur Vierendeel registered the patent for a new type of beam. This would be later on better known as the Vierendeel truss. It is characterized by the frame’s lack of diagonal members, something which would appear to contradict conditions of steadiness and balance, along with its notable deformation and difficult calculation, caused technicians in his time to be skeptical about its applicability. Nevertheless, its application surged in popularity during the 20th century, being used both in civil engineering and architecture. What are the advantages of the Vierendeel truss as compared to other types, such as diagonal trusses? In this article, the Vierendeel typology will be introduced along with its main features, its calculation as well as its implementation in civil engineering and architectural works.Postprint (published version

Com les TIC poden ajudar a l'ensenyament de la història de la ciència

L’objectiu de la present comunicació fora presentar, dins la temàtica de les TIC en la incorporació de la història de la ciència a l’ensenyament, com l’ús d’aquestes eines pot ajudar a mostrar a l’alumnat –acostumat sens dubte a aquest tipus de tecnologies– proposicions o formulacions fetes segles enrere. Aquesta implementació pot anar acompanyada en paral·lel, a l’aula, de les formulacions teòriques (de pissarra) de matèries com la física, la mecànica i fins i tot d’altres com podria ser la filosofia.Postprint (author's final draft