IN the following investigation we consider the deflection due to bending of a tapered cantilever beam carrying concentrated end and lateral loads at the free tip. The mode of taper of the beam is assumed of a generalized form, and is such that the second moment of the area of the cross‐section at any point varies as the nth power of its distance from the unsupported vertex. Detailed calculations are given for the cases n = 1,2,3,4 corresponding to the types of beams most commonly arising in practice. It is shown that fairly substantial errors may arise if the commonly used approximate treatments are adopted. The theory may also be extended to yield the value of the critical end loads for tapered struts conforming to any value of n.
Tatham, R. and Price, H.L. (1945), "Deflexion of Tapered Beams: The Case of Cantilever Beams with Lateral and End Loads", Aircraft Engineering and Aerospace Technology, Vol. 17 No. 11, pp. 312-329. https://doi.org/10.1108/eb031303
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