The 10-mm-diameter shank of the steel bolt has a bronze sleeve bonded to it. The outer diameter of this sleeve is 20 mm. If the yield stress for the steel is (σy)_st = 640 MPa, and for the bronze (σy) _br = 520 MPa, determine the largest possible value of P that can be applied to the bolt. Assume the materials to be elastic perfectly plastic. E_st =200 GPa, E_br = 100 GPa.

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P P 10 mm 20 mm