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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.

Large deflection anaIysis of cantilever beams with an opening

Rahman M. A., Rahman M. S., Hossain A. H. M.

International Journal of Applied Mechanics and Engineering

2007

Vol. 12, no 1

169-181

Numerical solutions have been obtained for analyzing the elastic dellection and stresses of a cantilever beam with a variable cross-sectional area. The variable cross-section was due to a circular, an elliptical and a square openinglhole/slot having the same cross- sectional area placed at different positions of the beam's span. An extensive numerical simulation was carried out using both the smali and large dellection theories to calculate the stresses and the deflections of the same beam. A computer code in "C" has been developed using the Runge-Kutta technique for the purpose of simulation. The position of the opening over the beam's span is found to have significant effect on the beam's response under a tip load. Results show the linear theory fails to account for the change in curvature at high intensity loadings and underestimates the dellections. If same amount of material is removed considering different cross-sectional area (square, circle and ellipse), it is found that the maximum dellection is developed for the circular holes and the square slots. while the circular holes cause to develop the maximum stress. The discrepancy between the linear and nonlinear solutions is the maximum if the hollow section is near the fixed end. Among the three types of openings, the elliptic slots develop the minimum stress and tip dellections.