Elastic deformations of an infinitely long strip and a beam with the fixed-free end condition are considered within the range of small strains. All local governing equations are satisfied up to first order in strains, and to take into account the higher order terms neglected in the local governing equations, the overall equilibrium are imposed exactly up to the leading order. The success of the approach relies upon the semi-inverse method and the decomposition of deformations in which the classical linear theory guides the solution.
The solution bridges the gap between the two extremes the classical solutions valid only for infinitesimal deformations and the solutions from the technical theories for deformations with large rotations. The solutions may be used to confirm the technical theories and to verify numerical solutions obtained from finite element analysis.