p$3(40$pts$)$ As a result of your structural analysis, a critical point in the beam of the previous problem presented the following stress state:

${}_x=60k,{}_y=40k,T_{xy}=-15k$

Beam is required to be made of aluminum alloy Al $6061(E=10,000$ksi,$YS=35,000,{}_f=0\mathrm{.}15).$

a$.$ Using an appropriate failure criterion, determine if the beam is either safe, or will fail.

b$.$ Your boss is questioning your previous answer and asks you to re$-$evaluate the situation using the Modified Mohr approach. What would your answer be$?$ If No$,$ please explain, if different from the previous, show your new calculations.