05.41: A unified catastrophe theory approach for the in‐plane buckling of steel arches under point gravitational loading

Abstract

The problem of the buckling response of various types of steel arches has been the subject of a vast number of earlier as well as recent papers and chapters of books. Namely, the majority of all these works aimed -via analytical and/or computational approaches -to establish the nature of the postbuckling response of the foregoing structures. It has been found over the years that two types of loss of in-plane stability are dominant: (a) snap-through, a characteristic of shallow (flat) arches (low height to span ratio), in a symmetric or asymmetric mode (limit point or bifurcation), and (b) sideways buckling (deep arches). In the latter situation, the axial inextensibility (being a justified simplifying assumption) becomes dominant and in the case of radial load and circular arch configuration the whole analysis is rather easy and convenient, using equilibrium considerations. On the other hand, low arches (with unavoidable shortening of their center line) can be thought of as curved beams; hence their buckling analysis may be performed from the viewpoint of energy. However, there not seems to be a unified approach overall, especially since the geometry of arches may be significantly varying, from circular to elliptical, parabolic, sinusoidal and catenary, and hence the height at the crown and the span are not the only parameters this geometry is dependent on. Moreover, if one considers a point gravitational loading acting on the arch, a case scarcely reported, then the whole analysis is multiparametric, since it involves (a) the value of the load and its position, (b) the cross-sectional and material characteristics and (c) the geometrical configuration parameters. This work aims to provide a unified approach for the foregoing problem based on the Theory of Catastrophes. The total potential energy function involving all the parameters is firstly established, and furthermore all restrictions related to boundary conditions, geometry, material and cross-sectional properties. Using an approximate 4 th order polynomial postbuckling shape, it was found that the problem at hand is governed by a singularity that strongly resembles the butterfly. The work is ongoing and will hopefully reveal interesting future results for structural design purposes.

A method of strengthening arched buildings with insufficient bearing capacity of foundations for the thrust perception

“…Distinctive features of arched buildings are the ability of quick erection, a small mass of structures, low construction costs and the need to take into account the impact of thrust support reactions when designing the foundations of arched buildings [6][7][8][9][10]. The problem of perceiving thrust structures and reducing the material consumption for the foundation construction in arched buildings constructors solve by installing tie-beams between the arches' supports [11][12][13][14][15]. Builders face some problems when installing the tie-beams in arched structures: the need for their hidden installation in the construction of the floors; the necessity to prestress them to maintain a working condition at large spans; the impossibility of standard installation of tie-beams between the arch supports when utility lines of technological objects of the building located between the arch supports.…”