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Arches are constrained with rotational resistance at both edges.An energy method is used to derive variational formulation whichis used to prove the existence of equilibrium states of elasticcircular arches for the torsional spring constants rho_{-} geq0 , rho_{+} geq 0 , and rho_{-} + rho_{+} > 0 . Theboundary conditions are searched using the existence of minimumpotential energy.