DDP,
For gravity only members, the adoption of plastic capacity in beam design does not require you to perform a material non linear analysis.
LRFD assumes the beam will fail as soon as the first plastic hinge occurs at the location where the Elastic maximum moment is. Therefore, it is ok to use elastic first order (linear) analysis to design for the beam.
However, if you are talking about a lateral frame, that's a different story. AISC requires you to perform a geometric non linear analysis or second order analysis to determine the magnified moments for the frame due to lateral loads. This analysis will still be an "ELASTIC" anlaysis.
It is very troublesome to perform a material non linear or Inelastic analysis, although we have computers to help us, but it is unwise to perform an inelastic analysis if you really understand the terminology behind; in addition, you do not need it for typical structural design.
Elastic analysis and LRFD is easy to understand and safe.
Please comment if you have nay questions.