Stretch and twist of rotating prismatic beam

A turbine blade is modelled as a uniform isotropic prismatic beam of general cross-section and “setting angle” rotating about one end, and is analysed according to the linear theory of elasticity. A semi-inverse solution is presented which reduces the three-dimensional problem to one of two dimensions, and explicit stress and strain components given for the mathematically amenable elliptic cross-section. As expected, the planar stresses σ_x,σ_y, and τ_xy arising from the two-dimensional problem are found to be small. For the general section, the theory predicts small curvature of the blade centre line, and a twisting moment which tends to reduce the “angle of set”.