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A finite displacemtment theory is developed for an arbitrary plane curved Timoshenko beam, in which an elastic constitutive relation is defined not by tensor components of stress and strain but by other physical components. This selection of components makes the governing equation simple and easy to handle. The nonlinear stiffness equation, with the use of nodal positions and the appropriate selection of local coordinates, is formulated for an elastic plane straight beam element. Threedoi:10.2208/jscej.1986.368_169 fatcat:zu34oi2rnnhfnaiqxfr46epydq