Analytical model to predict the resistance of cellular beams with sinusoidal openings

• Need for a new analytical model because existing design methods are not adapted.
• The analytical model is for the design of cellular beams with sinusoidal openings.
• Local buckling of web panels is considered through the study of equivalent plates.
• A model for the buckling stress coefficient of cantilever plates is proposed.
• The proposed model considers the Vierendeel mechanism and is validated by FEM.

Experimental and numerical investigations have been conducted on cellular beams with sinusoidal openings. They showed specific failure modes, in comparison with common opening shapes, mainly the local buckling of the panels around the opening. Detailed analysis of the stress distribution around the openings allowed understanding the behavior of those beams at ultimate limit state with the aim to develop a specific analytical model. The direct application of existing analytical approaches to beams with sinusoidal openings showed that the predictions need to be improved. Indeed, in order to obtain an accurate prediction of the buckling strength of the web sinusoidal parts, the analytical model is modified. In this paper, an analytical approach is proposed, based on the existing methods for multiple openings and on the plate buckling theory. A formula for the calculation of the critical stress coefficient is proposed and a simple method is described to take into account the additional strength provided by the intermediate web-post to the adjacent web panel. This approach considers simple equivalent rectangular plates. The analytical model is validated against finite element results regarding the values of critical stress coefficient obtained through an Eulerian calculation. Then, the ultimate strengths of cellular beams with sinusoidal openings are evaluated through a comparative study with FEM for different parent beam profiles and opening shapes.