Lateral Torsional Buckling in a W section beam

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Pooty
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Hey everyone, so I am in an Adv. Steel Design Course and I am supposed to design a beam under a given distributed DL+LL and Concentrated DL+LL. We are supposed to design the beam under two different conditions... a.) It has continuous lateral support b.) Lateral support is provided at the ends and at the concentrated load. So my question is for the condition a.), do we even need to check the beam for lateral torsional buckling? It seems that we wouldn't since it is braced continuously on it's lateral sides... And for case b.) we would need to calculate Cb and then Fcr to check LTB, right? Since these questions are not qualitative, I don't think I still need to show my work... Thanks guys.
 
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When checking for lateral torsional buckling of a W-section beam, if your Mn value is greater than your Mp value (AISC Steel Manual Equation F2-2), do you have to choose a new W section or do you then just use the Mp value as the governing nominal moment capacity? Then multiply that by Phi and check that it exceeds your Ultimate Moment?