Shear Stress in a Tapering Beam

IN the course of stressing certain front cross members of an engine mounting it was found necessary to determine the shear'stress on various sections of the cross members as accurately as possible. These cross members were by no means of uniform cross‐section, so that it was considered desirable to investigate, a formula which would give shear stress in a tapered beam. The “classical” methods evolved by Messrs. Coker and Filon in their Treatise on Photo‐elasticity and by Mr. Atkin in AIRCRAFT ENGINEERING, Vol. X, November and December, 1938, pp. 347–351 and 371–374 were found to be too elaborate. In September, 1942, Messrs. Pugsley and Weatherhead contributed an article entitled “The Shear Stresses in Tapered Beams”, to the Journal of the Royal Aeronautical Society. These authors start with a standard expression for shear stress based on the equilibrium of a portion of a beam and apply it to the solution of some examples. In the course of my investigations, it has been found possible to extend the “engineering” analysis of shear stress in beams of uniform section to beams of variable cross‐section. The expression for the determination of shear stress thus arrived at is very convenient and quite suitable for graphical methods. However, in the case of symmetrically tapering beams, an approximate formula has been developed for the shear stress in terms of shear force, bending moment, taper angle and section inertia and this formula is much more convenient and simple to apply than the standard expression used by Messrs. Pugsley and Weatherhead.