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1 International Journal of Applied Mechanics and Engineering

1 2008

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Effect of end-shortening on the response of a steel cantilever beam with an opening

Rahman M. A., Kowser M. A., Siddiqui M. T.

International Journal of Applied Mechanics and Engineering

2008

Vol. 13, no 3

735-751

This study is a continuation of our previous study that comprehensively dealt with the response of a slender cantilever beam with an opening of different geometry (circular, elliptical and square, respectively), having the same cross-sectional area, placed at different positions of the beam's span. The effect of end-shortening that becomes important at a high load is included in the present analysis. Obviously, stresses in these beams increase significantly due to the opening. Based on numerical calculations considering geometric nonlinearity and the effect of end shortening, it is found however, that the maximum values of the stresses are actually much smaller than their predictions are by linear theory without considering end-shortening. These stresses remain well below the proportional limit of highly elastic steel. Further, a similar analysis was performed for the case of a cantilever beam of a constant cross-section. It is found that the nonlinear analysis with end-shortening is much more important for a beam with an opening than it is for a beam of a constant cross-section. Though the topic chosen for this paper corresponds to a highly nonlinear boundary value problem, the numerical simulation scheme devised is sound enough to predict the response of the variable cross-section beams with high accuracy. Experimental results obtained by another research group have been compared by simulation; a very good agreement proves the soundness of the present numerical simulation scheme.