3. (45 points) A bar of length L and square cross-section with side of length a,...

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3. (45 points) A bar of length L and square cross-section with side of length a, made of a linearly elastic homogeneous and isotropic material is loaded with a tensile traction of magnitude T applied to a portion of its cross section as shown in the figure below (with T extending along the entire cross-section in the through- thickness direction). (i) What are the exact 3D boundary conditions for this square cross- section bar? (ii) What are the relaxed (St. Venant) boundary conditions? (iii) Find the stress state in the bar? T Ta/2 L a Note: For this beam, the bending moment of inertia is given by I: 12 3. (45 points) A bar of length L and square cross-section with side of length a, made of a linearly elastic homogeneous and isotropic material is loaded with a tensile traction of magnitude T applied to a portion of its cross section as shown in the figure below (with T extending along the entire cross-section in the through- thickness direction). (i) What are the exact 3D boundary conditions for this square cross- section bar? (ii) What are the relaxed (St. Venant) boundary conditions? (iii) Find the stress state in the bar? T Ta/2 L a Note: For this beam, the bending moment of inertia is given by I: 12