The surface effect from surface stress and surface elasticity on the elastic behavior of nanowires in static bending is incorporated into Euler-Bernoulli beam theory via the Young-Laplace equation. Explicit solutions are presented to study the dependence of the surface effect on the overall Young's modulus of nanowires for three different boundary conditions: cantilever, simply supported, and fixed-fixed. The solutions indicate that the cantilever nanowires behave as softer materials when deflected while the other structures behave like stiffer materials as the nanowire cross-sectional size decreases for positive surface stresses. These solutions agree with size dependent nanowire overall Young's moduli observed from static bending tests by other researchers. This study also discusses possible reasons for variations of nanowire overall Young's moduli observed.

The influence of surface stress on the resonance frequencies of bending nanowires was studied by incorporating the generalized Young–Laplace equation into Euler–Bernoulli beam theory. Theoretical solutions are presented for three different boundary conditions. The overall Young’s modulus was used to study the surface stress influenced mechanical behavior of bending nanowires and a comparison was made for the overall Young’s modulus calculated from nanowires in resonance and static bending. It was found that the overall Young’s modulus can be simply related to a nondimensional surface effect factor via empirical formulae.

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