A ductile bar of square cross section with sides a = 12 mm is subjected to bending mome...

A ductile bar of square cross section with sides a = 12 mm is subjected to bending moments M about the z axis at its ends (Fig. P12.12). Determine the magnitude of M at which (a) yielding impends; (b) the plastic zones at top and bottom of the bar are 2-mm thick.