Nicola L. Rizzi and Valerio
VaranoFacoltà di Architettura, Università degli Studi di Roma Tre Via Madonna dei Monti, 40 -- 00184 Rome ITALY
On the other hand, structural mechanics is taught prevalently by means of typical instruments of a formalized discipline, that is, a demonstrative or deductive method, and the language of mathematics. The co-existence of these two approaches poses a delicate teaching problem, which if tackled without caution and the necessary attention, can cause the students to perceive the presence of two routes that evolve in parallel, so that the students, disorientated by the differences, fail to grasp the meaning, and perhaps convince themselves that they are being subjected, for inexplicable academic reasons, to a useless and boring assignment. If on the one hand this obscures, in the student's mind, the
potential application of the knowledge of structural mechanics
(which becomes merely material for specialists, on the other
hand, it can engender the deep-rooted Instead, we are convinced that the co-existence of such different approaches will be a happy prerogative of the Architectural Faculty and constitute a precious resource to resist the insistent requests for a specialized education that often is unacceptable to the University. But how can one preserve the specificity of scientific culture and methods and achieve the objective of a strong integration of structural disciplines in the formation of architectural students? Leo, the multimedia tale which we are presenting in this document, would like to contribute to this debate.
- Difficulty in managing abstract concepts (axioms of scientific theory);
- Little interest in formal rigor (mathematical language and its esthetics);
- Difficulty in following a pure demonstrative approach (mathematical methods).
Students have difficulty in confronting the heart of abstract
scientific theories and have a strong need for concrete examples. - The abstract route which leads to the construction of theoretical models should be presented with a constant reference to selected examples.
- It is beneficial when these examples are presented with illustrations which constitute an aid to the understanding of the formal language without taking its place.
- Once the results of the theory are presented, the nature of the 'Rule of Interpretation' of the behavior of real objects must be stressed so that the student can utilize their worth in predicting outcomes of in the design process.
These considerations suggest a teaching method which is articulated in the following three phases: - observations;
- modeling;
- design.
By 'observations', we mean the description of mechanical phenomena, increasingly complex, selected with regards to their pertinence of the problem that one wants to affront, and their efficiency. One needs to induce the student to feel the need to form a reference point (or a theory) and push him to follow the process of abstractions or generalization which must be progressive and in some way personal, then to guide him in the construction of a physical-mathematical model that takes into account its formal content and stressing its importance as an instrument and has the potential for other applications. The suggestion of cues for applications stimulate the student to exercise his creative imitation, which constitutes the design phase. He is prompted to not only verify the feasibility of his design ideas, but to explain it overall using a pre-figurative (pre-vision) mental design. What we intend to propose to the student is not so much a set of notions, as a method and set of instruments for selecting experiences (for example previous design solutions) to the end of evaluating their repeatability in diverse situations, by means of a physical-mechanical reading which comes from phenomena which one finds in daily life. For this reason, Leo was created as a teaching instrument which is presented as a tale in the form of a hypertext.
Fig. 1 Incited by his own curiosity to test the resistance, he is a little puzzled to find that his construction is not able to resist modest even stress tests; in other words, the model has difficulty staying erect. He immediately makes some spontaneous attempts to improve the situation, but these attempts are substantially inefficient. This gives him the sensation of having ignored a relevant aspect of the project and not possessing the adequate conceptual instruments to affront the problem or to even consider it. Zooming into the material itself (see fig. 2), shows how miniscule parts are lined up to represent the status of internal stresses, emphasizing the change of requirements and the necessity to learn a behavioral mechanical model of structures and the materials of which it is composed. Fig. 2. An intellectual journey begins during which, through successive
abstractions, will lead to his learning physical-mathematical
models which will progressively allow him to affront the design
themes in a more knowing way. The Computer simulations have revealed themselves to be powerful and versatile instruments to represent the mechanism of progressive abstraction, the multiple possibilities of rendering, from photo realism to pure geometry, in fact, permits us to highlight aspects one at a time which are considered pertinent (that is, ones that are chosen as) evidence in the phenomenon being studied.
We have worked on a program which we think constitutes the minimum level of knowledge which must be mastered by the end of the three-year Italian program in Architecture. The corresponding hypothetical book contains the following chapters (in parenthesis appears the name of the stage in the tale): - Introduction (Entrance into Wonderland);
- Kinematics of Rigid Bodies (Boy Scout camp);
- Statics of Rigid Bodies: (The Sacred Area of Megaliths);
- Beam Theory (Construction site).
Naturally this can be integrated or modified in order to adapt to different teaching approaches. In the initial stage, some concrete fundamentals are introduced in an intuitive manner of the structural mechanics. Concepts of body, motion, deformation, force as an interaction between bodies, equilibrium, material behavior (strength, stiffness) and others, are introduced by means of a series of metaphors (such as team playing, synonymous of structural organizations), almost all of which are acted out on anthropomorphized structural elements, with the aim of relating physical concepts to the life experiences of the student himself (see figs. 2 - 4).
At first glance, it might seem contradictory to begin an exposition which declares itself to be substantially empirically inductive by treating general concepts. In reality, they are presented not as elements of a defined theory, but rather to help the student take cues from mechanical experiences that are certainly part of his life experience in order to begin a process of selecting pertinent phenomenon.
All of the examples are analyzed according to the same pattern, which utilizes substantially three areas: the screen on which the films are visualized; the dialogue box which accompanies the films; and the small bar with buttons that activate the films (see fig. 5). Each film relates to one of the three phases of the presentation: Fig. 5
To illustrate the significance of the single phases we shall refer to the first example, utilized for the presentation of the 'Kinematics of a rigid body' (linearized). (Note that in the following the text in italics refers to the specific example while the photographs are sample frames of the films in the hypertext.)
The Experience phase corresponds to a live film which demonstrates some behavior of a simple real object.
Fig. 6
However, in order to understand the behavior of an existing structure in general one can not cut it into pieces! Therefore, a Rough Simulation is proposed (see fig. 7) as an intermediate phase which permits, by means of an initial abstraction, the identification of the pertinent characteristics and a study of them by means of a simulation in a laboratory. Fig. 7 Films in the Experiment stage describe the phenomena in a clear and qualitative manner.
The proposed experiments were selected so as to be easily reproduced by students even at home, with inexpensive materials and without complex instruments (see fig. 8). Fig. 8
Here he discovers that geometry, with which a student of architecture has a certain familiarity, is an useful instrument for constructing a model with a sufficient predictability that gives a powerful support for the imagination and design process. The films of this section are realized with computer graphics and, by means of a schematic reproduction of the analyzed structure, give a geometric explanation of the behavior evidenced in Experiment phase.
Therefore, the geometric model prompts the student to propose questions for which there are no easy answers. And at this stage, the student views the film on algebra (still presented using computer graphics) and discovers that in effect, the geometric questions already raised as well as other general questions, can be formulated algebraically.
*A rigid transplacement is shown (simulated);**Its characteristics are highlighted;**The velocity is introduced (linearization);**The formula is constructed.*
Fig. 13 Fig. 14 Fig. 15
Fig. 16
These, despite their simplicity, allow the formulation of a wide range of solutions. Thus knowledge of mechanics can be a guide and stimulation for the design, rather than an obstacle or a limitation.
*A,B,C are not aligned;**directions of 3 tripod pendulums are independent;**trestle doesn't belong to a plane through A and B (see fig. 12);**single pendulum doesn't belong to a plane trough A, B, C.*
5.3.2 Complex design. In general, anyway, geometric instruments
are not sufficient to face more complex design problems, which
instead can easily be resolved utilizing algebraic formulation.
- Taking a problem as a point of departure, the better and deeper the comprehension of the problem, the greater the freedom the designer has to solve it;
- A deeper understanding is possible only by "full immersion" of real objects in "model space", and a thorough study of such models.
[2]
Lucio Russo,
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