Shear deflections of tapered Timoshenko beams

The shear deflection of the straight sided tapering cantilever of rectangular cross section has been treated in the context of Timoshenkoʹs beam theory. With the use of elastic stresses obtained from an analogous wedge, formulae have been derived for the calculation of shear deflection of the tapered cantilever by: (i) a direct integration of Timoshenkoʹs beam equation and (ii) a suitable application of the method of virtual work. Numerical values of deflections, obtained from the formulae derived here, have been compared with finite element and experimental results. Close agreement has been observed between these results. The formulae have been applied to calculate the shear deflection component of the web post in a castellated beam.