Problem 2 A solid rod of radius c = 40 mm is made of a steel that is assumed to be linearly elastic and perfectly plastic with E = 200 GPa and or=250 MPa. The rod is subjected to a couple of moment M that increases from zero to the maximum elastic moment My and then to the plastic moment Mp. Denoting by y the half thickness of the elastic core, write a computer program and use it to calculate the bending moment M for values of y from 40 mm to 0 using 5 mm decrements. (Hint: Divide the cross section into 80 horizontal elements of 1 mm height.)