Cylindrical sandstone laboratory test

Given a cylindrical sandstone laboratory test specimen of diameter D and height L subjected to a vertical load F (force), find

(a) Te forces N and T acting normal and tangential to a surface inclined at an angle θ to the vertical and
(b) Stresses, that is, the forces per unit area, σ and τ on the inclined surface in terms of the applied stress σo (F/A), where A is the area acted on by F. Illustrate with sketches. Note: The inclined surface is elliptical and has an area πab where a and b are the semi-axes of the ellipse.

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