The paper deals with the general case of a curved beam whose center line is a plane curve not necessarily circular. The body-stress equations and the compatibility equations for stresses in their general form are found for the chosen system of co-ordinates and put in their simplest form. Solutions for the equations with the aim of finding the stresses when the beam is subjected to a torque and to a bending out of its plane of initial curvature are obtained for both elliptic and circular cross sections of the beam. The case of a concentrated load at one end perpendicular to the plane of initial curvature is also considered.

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