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The strain energies in straight and bent single-walled carbon nanotubes(SWNTs) are calculated by taking account of the total energy of all theoccupied band electrons. The obtained results are in good agreement withprevious theoretical studies and experimental observations. The Young's modulusand the effective wall thickness of SWNT are obtained from the bending strainenergies of SWNTs with various cross-sectional radii. The repulsion potentialbetween ions contributes the main part of the Young's modulus of SWNT.  The wall thickness of SWNT comes completely from the overlap of electronicorbits, and is approximately of the extension of  $\pi$ orbit of carbon atom. Both the Young's modulus and the wall thicknessare independent of the radius and the helicity of SWNT, and insensitive to thefitting parameters.  The results show that continuum elasticity theory can serve well to describethe mechanical properties of SWNTs.Comment: 12 pages, 2 figure

Strain energy and Young’s modulus of single-wall carbon nanotubes calculated from electronic energy-band theory