Prediction of the stress level and stress concentration in cellular beams with circular openings

Abstract

Although stress concentration in vicinity of regularly located circular openings under axial tension is well researched [1], in this work the problem was investigated in aspect of transverse bending of cellular beam, when simultaneous action of shear force and bending moment take place and pure bending.

For today the main shapes of perforations are hexagonal and circular openings, which are produced on unwaste technology. Comparison of strength of such beams for choice of optimal design solution is possible in first turn with estimation of their stress state. In spite of numerous works dedicated to estimation of stress level in perforated beams as foreign [2-14], so and Russian [15, 16] authors, there is no analytical expression for evaluation of stresses in zones of concentration. In all works the analysis of stress state is performing on base of calculation by finite element method, sometimes accompanied with experiments. More often in them there are only numerical values and colored fields of stress distribution. To generalize such results or use them for predicting of stress level in designed beam is rather difficult.

In the work it was obtained the analytical expression for maximum equivalent stresses on Mises in beams with circular openings. These beams are distinguished with wide spectrum of sizes (Fig. 1), but in this work it was changed only one parameter of perforation – relative width of web-posts. The relative depth of openings was remained unchangeable and equal to ξ=0.667. It was also investigated influence of web thickness on the stress level.

Investigation of stress distribution in cellular beams with circular openings was made under two kinds of loading:

-under transverse bending when shear force at any section is constant and flexure moment is changing on lineal law;

- under pure bending, when shear force is absent. Stress concentration was evaluated under pure bending.

DOI: http://dx.doi.org/10.5755/j01.mech.23.4.15136