. A compressive stress is to be applied along the long access of cylindrical <?x

Question

. A compressive stress is to be applied along the long access of cylindrical  <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

           rock sample that has a diameter of 0.4 inches. Determine the magnitude  

           of the force required to produce a  <?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" />                                     inch change in diameter, if the      

            deformation is entirely within the elastic range. The module of elasticity

            of rock is E = 9 x psi, and the Poisson

A compressive stress is to be applied along the long access of cylindrical rock sample that has a diameter of 0.4 inches. Determine the magnitude of the force required to produce a inch change in diameter, if the deformation is entirely within the elastic range. The module of elasticity of rock is E = 9 x psi, and the Poisson's ratio is ? = 0.25

Explanation / Answer

original dia of rock d =.4 in
required change in dia deld = 1 inch

diametrical strain = deld/d = 1/0.4 = 2.5

as poisons ratio = -(diametrical strain/longitudanal strain)

longitudanal strain eps = - posions ratio/diametrical strain = - .25/2.5 = -0.1

(-ve sign indicates compression)

as E = stress/strain

stress = E X eps = 9 X 0.1 = .9 pounds/ inch

stress = force/area

force = stress x area = 0.9 x piex(0.4^2)/4 = 0.11304 pounds

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