The steel section for continuous beam is based on the maximum value of the moments according to the 0.90 rule. The design is made according to the ASD.
AISC Tables 9-3a,b, and C for the block shear-coped beam. Table 9-3a is for Tensile rupture. Table 9-3b is for Shear yielding and 9-3c is for Shear rupture.