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Question: a questions however you must work hdepend problem 1 at...

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A questions. However you must worK hdepend Problem 1: At a point in a linaer elastic isotropic body (with E-10 Mpa and v =.35), the state of stress is given by the matrix 6 19 -5 19 66 10 [01=1-5 -Jel MPa with respect to x-y-z. a). Calculate the principal stresses 어 > σ2 > ơ3 of [o] and the Von Mises (or effective) stress b)-Calculate the principal directions n(1), n(2), and n(3) corresponding to σισ2, ando,, respectively. Express the principal directions as unit vectors in terms of the unit vectors i.j, and k. c) Calculate the magnitude mx of the absolute maximum shear stress, the outward normal d) Calculate the octahedral shear stress τ0cr and the normal stress σ0ct that acts on the same e) Calculate the traction vector p on a plane that passes through the point and is described n to the plane on which it acts, and the normal stress σ that acts on the same plane. Express the principal direction n as a unit vector in terms of the unit vectors i, j, and k. plane as τ0ct by the equation x+2y+3z-0. (Express p in terms of the unit vectors i, j, and k.) Calculate f) Calculate the isotropic part [σ] and the deviatoric part [Da] of [0]. How do the principal g) Calculate the strain energy density U, the strain energy density U associated with h) Calculate all components of the (small) strain matrix [e] with respect to x-y-z, and the normal stress σ, and the shear stress τ on the same pl stresses and principal directions of[Gd] compare to those of [o]? volume change, and the strain energy density Uod associated with distortion calculate the dilatation (i.e. volumetric strain) e.

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