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The Telescopic Cantilever Beam: Part 2 - Stress Analysis

机译:伸缩悬臂梁:第2部分-应力分析

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This paper is an extension to a Part 1 analysis of the deflection for a telescopic cantilever beam [1]. The Tip Reaction Model, proposed in that paper, establishes reactions at the tips of the overlapping portions as the mechanism of transfer of the external loads between sections of the telescopic beam. In Part 1 a three-section telescopic beam was analysed for deflection using these forces within a repeated integration method. In Part 2 the bending and shear stresses for the three-section cantilever, are obtained both analytically and numerically. A check upon stress levels is provided from a parallel study upon an equivalent, two-stepped, continuous beam. Graphical presentations of the beam stresses, found from applying the two methods to each structure, are self-validating. That is, the continuous beam theory provides a check upon numerical stress levels from FEA and, in turn, FEA provides a check upon the analytical stresses calculated from tip reactions within a telescopic beam. The fact that comparable stress levels were found confirms that the analytical technique proposed is perfectly adequate for a telescoping beam, just as the classical theory is adequate for continuous beams. Taken together, Parts 1 and 2 provide an analytical theory for bending of a discontinuous beam that did not exist heretofore, thereby obviating the need for a numerical solution.
机译:本文是对伸缩式悬臂梁[1]挠度的第1部分分析的扩展。该论文提出的尖端反应模型建立了在重叠部分尖端的反应,作为伸缩梁各部分之间外部载荷传递的机制。在第1部分中,在重复积分方法中使用这些力分析了三段式伸缩梁的挠度。在第2部分中,通过分析和数值计算得出了三段式悬臂的弯曲应力和剪切应力。通过对等效的两步连续梁进行平行研究,可以对应力水平进行检查。通过将两种方法应用于每个结构而发现的梁应力的图形表示是自验证的。也就是说,连续束理论对来自FEA的数值应力水平进行了检验,而FEA则对由伸缩梁内的尖端反应计算出的分析应力进行了检验。发现可比较的应力水平的事实证实,所提出的分析技术完全适用于伸缩梁,就像经典理论适用于连续梁一样。总而言之,第1部分和第2部分提供了一种用于弯曲迄今不存在的不连续梁的分析理论,从而消除了对数值解的需要。

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