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The problem of the rigorous derivation of one-dimensional models fornonlinearly elastic curved beams is studied in a variational setting.Considering different scalings of the three-dimensional energy and passing tothe limit as the diameter of the beam goes to zero, a nonlinear model forstrings and a bending-torsion theory for rods are deduced.

The nonlinear bending-torsion theory for curved rods as Gamma-limit of three-dimensional elasticity