An academic exercise on layout optimization of pin-jointed frames

Jose L. Fernandez Cabo, Joaquín Antuña Bernardo
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Resumen


This article describes an academic exercise recently carried out in the Escuela Técnica Superior de Arquitectura de Madrid, within the course La Estructura en el Proyecto Arquitectónico (Structure in Architectural Project). The goal was to work on the layout optimization of pin-jointed frames. The students had to design the layout of a structure with a set system of forces in equilibrium and within geometrical bounds. The students were helped by a script implemented in MATALB® in order to compute the volume of material (the primary objective function) and other derived parameters. This allowed students to focus their attention in the topic of learning, while at the same time the results of the exercise were more reliable.

Different solutions were analyzed as the basis of further discussion in the classroom. Theoretical concepts then arise naturally and are linked with their previous work, which make it easier to address abstract concepts and reinforce the learning process. The exercise shows that the key parameter is slenderness (defined as the ratio between the span and the maximum depth of the framework). The scheme is less sensitive. Once the chords of the structure are designed with an adequate slenderness, it only remains to place the web elements with angles of around 45 degrees. For slenderness higher than approx. 8 to 10, the best design is a truss with parallel chords and diagonals between 30 and 60 degrees (better from 45 to 60 degrees). For slenderness lower than approx. 8 the arch is more efficient than a truss. This means that for typical frameworks, the skills of the designer are almost restricted to the election of the slenderness.

Built examples are finally reviewed in order to see how managing the different variables of an actual structure is a subtle question, one that cannot be detected in the previous theoretical exercise. Simplicity is crucial. Techniques such as prestressing notably increase efficiency.

The article also presents architectural masterpieces built in short and medium spans, sometimes made with low efficiency structural schemes. Any real problem is complex, and good solutions must manage all of the variables. Although structural efficiency does not guarantee architectural success, both of these are compatible.


Palabras clave


educational; layout optimization; minimum weight; frameworks; pin-jointed; conceptual design; structures.

Referencias


Aroca Hernández-Ros, Ricardo. 1989/1990. "Structure, Geometry and proportion”. (Apuntes del Curso de Doctorado). ETSAM, Madrid. (Manuscript in Spanish).

Aroca Hernández-Ros, Ricardo. 1992/1993. "Structure, Geometry and proportion”. (From a course for Ph. D students in Mexico). ETSAM, Madrid. (Manuscript in Spanish).

Aroca Hernández-Ros, Ricardo. 2002/2011. "Structures of minimum weight”. Hand notes of the course La Estructura en el Proyecto Arquitectónico. ETSAM, Madrid. (Manuscripts in Spanish).

Fernandez Cabo, Jose L. 2012. Matriz de equilibrio de estructuras trianguladas de barras articuladas con cargas en los nodos. E.T.S. Arquitectura (UPM), Madrid. (in Spanish) http://oa.upm.es/10742/

MATALB®. MathWorks Co. http://www.mathworks.com MATALB®. Math- Works Co. http://www.mathworks.com

Maxwell, James Clerk. 1927 (1890) "On Reciprocal Figures, Frames and Diagrams of Forces.". Scientific Papers (From the Transactions of the R. S. of Edinburgh; Vol. XXVI; pp. 21-23); ed.; Paris. Librarie Scientifique J. Hermann. pp. 161-177.

Michell, A.G.M. 1904. "The Limits of Economy of Material in Frame-Structures". Philosophical Magazine.S.6. Vol. 8; nº 47. Nov. pp. 589-597.


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