Mechanics, and Statics as part of the aforementioned discipline, with its application topics dedicated to the study of the isostatic beams, are matters of special interest within the subjects of Physical Fundamentals of the Engineering, which are included in the Degree Programs of Technical Schools. These subjects are part of basic training and therefore provide students with the necessary previous knowledge for the study of the matters which constitute what is traditionally known as Civil Engineering. These matters not only require a full knowledge of the theory but also experimental training in the laboratory where the true behaviour of the theoretical models studied in the classroom is analysed in depth.
In this study, a beam model as well as the design of a plan of experiments to analyse the real behaviour of the theoretical patterns studied in the topics relating to the isostatic beams is presented. This model, designed so that its deflection deformation was noticeable for relatively small loads, was assembled with rectangular cross section pieces made of PVC. The pieces were been joined at their half plane with hinges. This allows for free turning regarding the perpendicular axis to the plane of symmetry of the beam. The gaps between pieces, occupied in the middle by the hinges, were filled with polyurethane sheets stuck to both adjacent pieces, so as to give rigidity to the beam, since this material presents elastic properties adequate as much to traction as to compression. This arrangement makes the pieces, when the beam is deformed, verify in an approximate way Navier’s hypothesis about the sections of a homogeneous beam (all plane sections remain plane and perpendicular to the deformed axis of the section after deformation) being the deformed axis the straight line resulting form the intersection of the horizontal and vertical planes of the beam. Besides, the model is provided with the adequate supports and weights for modelling different configurations, so that the internal stress laws were calculated and measures on the deformed beam were considered. The treatment of the experimental data and the study of their relationship with those obtained from the theoretical calculations were made with Excel.
The experimental measures were carried out on the beam on two supports at their ends subjected to its own-weight as a continuous load, and also with different punctual loads on its centre. For all the configurations, and on the deformed beam, the separation of the gaps between pieces and the deflection in the gaps as well as in the pieces were measured, relating them with the theoretical bending moment and comparing the adjusted experimental elastic curve with the theoretical one, studying the experimental elastic properties in comparison to the theoretical ones.
Once obtained the parameters that allow for the analysis of the behaviour of the model and comparing it with the theoretical one of a deflection beam, the two main important conclusions of this work are: 1) the model is simple to manage and is economic in comparison with the cost of other commercial models, and 2) this simple model is appropriate to carry out the necessary experimental measures to study its elastic behaviour, which is quite suitable in an educational laboratory.