A simple approach to detect the nonlocal effects in the static analysis of Euler–Bernoulli and Timoshenko beams

In this paper, the well-known Mohr analogy is applied to the computation of displacements and rotations of carbon nanotubes, and some simple formula is derived which allows the direct generalization of the Mohr theory to the nonlocal Euler–Bernoulli and Timoshenko beam theories. Finally, some examples show the effectiveness and simplicity of the proposed approach.

► Extension of the Mohr analogy taking into account the nonlocal effects.
► Additional displacements due to the nonlocal effects by solving a simple static problem.
► The approach can be applied to Euler–Bernoulli and Timoshenko beams.