This work is mainly concerned with the development of sophisticated yet efficient methods for
assessing the elastic buckling of steel beams with web openings, focussing on local buckling effects in
the web region. A new computational method is proposed which extends the use of the Element Free
Galerkin (EFG) method for the numerical discretisation combined with a simplified buckling
assessment approach based on the Rotational Spring Analogy (RSA). The new approach considers
several potential simplifications offering a balance between computational efficiency and accuracy in
local buckling analysis.
In the present EFG/RSA method, considerable advantage is established by separating the
planar and out-of-plane responses. Planar analysis is further enhanced using modular concepts, where
the beam is divided into unit cells, each of which resembles a super-element with a reduced number of
freedoms, and solved using a standard discrete procedure. As for the out-of-plane analysis, the
application of a ‘local region’ is adopted to significantly reduce the size of the original buckling
problem. Finally, local buckling assessment is conducted using an effective approach that utilises an
iterative procedure based on a rank 2 reduced eigenvalue problem along with a shifting local region.
Several illustrative examples are provided which highlight the efficiency and accuracy of the
developed approach in comparison with detailed nonlinear finite element analysis performed using
ADAPTIC, and which demonstrate general applicability to local buckling analysis of steel beams with
web openings of various shapes and sizes.
This work also considers the development of a simplified design-oriented method which is
presented particularly for web-post buckling. Towards this end, a simplified analytical model is
proposed based on an analogy with equivalent rectangular thin beams (RTB), where a semi-empirical
approach is used to calibrate the suggested formulation against the results obtained from the numerical
work performed earlier.