A pre-curved bimetallic strip that is applied with a force in an axial orientation, i.e. along its chord line, exhibits nonlinear force–displacement characteristics. For thin bimetallic strips, whereby the radius of curvature is large compared to the thickness of the strip, the non-linearity tends to be tangent related. The new theoretical formula introduced here was correlated to the results of a set of force–displacement tests, and a good overall fit of the theory to the test data was achieved. The formula put forward in this work enables the evaluation of large chord line displacements but is limited to the permissible stress limits of the material. This work can also be directly applied to thin shallow arc beams of a single material. The application of this work is in the field of bimetallic force–displacement actuators.