Stability analysis of beam structures in civil engineering - a teaching and learning tool
During their studies, students of civil engineering are required to understand the behaviour of beam structures at risk of stability. This includes analysing the buckling shape and buckling loads of certain standardised systems. Both are essential for the design of beam structures. However, teaching experience shows that students have deficits in interpreting buckling behaviour.
With the learning tools currently used, such as graphics in lecture notes, complex dependencies cannot be visualised or only with great difficulty and cannot be shown in a striking way. Furthermore, the inflection points, which are important for the stability analysis, do not receive the attention they need, because the inflection points define the buckling length of the members contained in the system. The buckling length is one or even the most important parameter in the stability analysis of beam structures.
This is where the digital learning tool presented here comes in. On the one hand, it can be used to analyse complex systems and reduce the representation to the most important parameters and thus highlight them. In particular, the representation of the buckling figure and the inflection points contained therein is shown, which no commercial framework programme offers to date despite its fundamental importance.
Oberfläche buckL.ing
The illustration shows the user interface of the learning tool. The settings for the system under consideration can be made there. The graphical evaluation is shown in the bottom left-hand area. The undeformed structure with the point load is shown in black and the buckling figure is shown in orange. The inflection points (red) can be taken from the buckling figure, from which the buckling length shown in dashed lines can be derived. If system parameters are changed, the display of the buckling figure changes immediately. The idea is to use the tool in lectures and to demonstrate the basic behaviour of structures
In addition, students can use the learning tool in self-study to deepen these basic principles and recognise further correlations. For example, system parameters such as bending stiffness, elongation stiffness, member length and the like can be changed, on the basis of which students can draw their own conclusions.
Another function is the visualisation of the buckling length or the load increase factor over the changed system parameter or over the corresponding multiplier of a system parameter.
Petersen [1] Tafel 5.1 (links) und Verlaufskurve buckL.ing (rechts)
The diagram on the right shows the course of the buckling length under modified bending stiffness of the upper beam of the system shown in Figure 1 by buckL.ing. The two lines show the limit values under changed boundary conditions at the lower support. The lower curve is assumed in the case of restraint and the upper curve in the case of a hinged support.
The interpretation of Euler's buckling cases as interval boundaries is thus not only clearly visible, but the course within the boundaries can also be shown. On the other hand, the Petersen tables can also be digitised and flexibly applied to any type of beam structure. Figure 2 shows the comparison of the calculated values with the Petersen tables. While only one parameter is varied in the tables, all parameters can be changed in this tool and their influence can be shown directly.
Literature:
[1] Petersen, Christian (1992): Statics and stability of building structures. Elasto- and plasto-static calculation methods for structures subjected to compression; forms of verification against buckling, tilting and buckling. 2nd, ed. Ed. Brunswick: Vieweg.