A plastic bar of diameter d = 32 mm is compressed in a testing device by a force P = 190 N applied as shown in the figure.
(a) Determine the normal and shear stresses acting on all faces of stress elements oriented at (1) an angle θ = 0°, (2) an angle θ = 22.5°, and (3) an angle θ = 45°. In each case, show the stresses on a sketch of a properly oriented element. What are σmax and Ï„max?
(b) Find σmax and τmax in the plastic bar if a re-centering spring of stiffness k is inserted into the testing device, as shown in the figure. The spring stiffness is 1/6 of the axial stiffness of the plastic bar.

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P-190N 100 mm 300 mm 200 mm Plastic bar Re-centering spring Part (b) only) d-32 mnm