Two rectangular beams are made of steel having a tensile yield strength of 80 ksi and an assumed idealized stress-strain curve. Beam A has a uniform 1 x 0.5-in. section. Beam B has a 1 x 0.5-in. section that blends symmetrically into a 1.5 x 0.5-in. section with fillets giving a stress concentration factor of 3. The beams are loaded in bending in such a way that

(a) For each beam, what moment, M, causes

(1) initial yielding and

(2) complete yielding?

(b) Beam A is loaded to cause yielding to a depth of Determine and plot the distribution of residual stresses that remain after the load is removed.