Static Bending of Pre-Twisted Cantilever Blading

Abstract

In the present paper the static bending of pre-twisted cantilever blading is examined. The blading is pre-twisted linearly about the centroid of its cross-section to a maximum angle of π/2 radians and is considered to be mounted encastré at the root. The behaviour of such blading, particularly when bending under a distributed load, is of considerable practical importance. By the application of variational calculus, static equilibrium equations are derived from expressions for the total potential energy of blades subject to either concentrated or uniformly distributed bending loads. Solution of the equilibrium equations yields expressions for the static deflexions. Over a range of pre-twist angles between 0 and π/2 radians deflexions are calculated for blades of (1) narrow rectangular cross-section when subjected to either method of loading, (2) narrow aerofoil cross-section when subjected to a uniformly distributed load. Sets of steel cantilever blades of narrow rectangular cross-section are loaded laterally at their free ends and the deflexions determined by measurement. The experimental values of deflexion compare reasonably with the relevant calculated ones. Small discrepancies between the two sets of results are not yet fully explained and further investigation of the problem is under consideration. For blades where the pre-twist angles do not exceed π/2 radians, the agreement obtained between the two sets of deflexions for the concentrated load system is such that the validity of the theory, when it is applied to other loading systems, can safely be assumed without further recourse to experiment.