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Collapse loads of cantilever beams under end shear

Traglast eines einseitig eingespannten, durch Querkraftverteilung, belasteten Balkens

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Summary

Results ofOnat andShield and ofGreen on the collapse loads of symmetrically tapered cantilever beams under a uniformly distributed end shear are extended to cover the entire range of geometric parameters. Close bounds are obtained except for very short beams. In addition, the effect of a parabolic distribution of end shear upon the lower bound is investigated and found to be small. For large beams complete solutions are exhibited. Finally, an optimum design problem is considered: for fixed beam length and end load find the angle of taper which minimizes the weight. The minimum is always achieved for a taper angle (top and bottom) between zero and fifteen degrees.

Zusammenfassung

Ergebnisse vonOnat undShield, sowie vonGreen, über die Traglast von symmetrisch sich verjüngenden, einseitig eingespannten Balken, die durch eine an ihrem Ende angreifende uniform verteilte Querkraft belastet sind, werden erweitert um den gesamten Bereich der geometrischen Parameter zu erfassen. Mit Ausnahme sehr kurzer Balken werden eng zusammenliegende Schranken erhalten. Zusätzlich wird der Einfluß einer parabolischen Verteilung der Querkraft untersucht und als klein befunden. Für den Fall sehr langer Balken wird eine vollständige Lösung gegeben. Abschließend wird ein optimales Entwurfsproblem betrachtet: Für eine vorgegebene Balkenlänge und Belastung finde man den Verjüngungswinkel, der das Gewicht zu einem Minimum macht. Dieses Minimum wird immer für einen Verjüngungswinkel (zwischen Ober-und Unterseite) zwischen O und 15° angenommen.

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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, Burnaby 2, British Columbia, Canada

    W. P. Chen &  E. M. Shoemaker

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  1. W. P. Chen
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  2. E. M. Shoemaker
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With 3 Figures

This investigation was supported by the National Research Council of Canada

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Chen, W.P., Shoemaker, E.M. Collapse loads of cantilever beams under end shear. Acta Mechanica 13, 191–203 (1972). https://doi.org/10.1007/BF01586792

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