Using your aisc manual lrfd option, select the most economical (lightest) section for an fy=50 ksi assuming full lateral bracing for the compression flanges of a simply supported beam of 16 feet, with wdl= 1.0 k/ft and wll=3.0 k/ft, and a concentrated load in the center of 20 kips (one column from a story above that during live performances transfer the load to the center of your beam) which you can consider a live load. the self-weight of the beam you are designing for is not included and you need to check your design with your selected beam. the young’s modulus is e=29,000 ksi. the owner (client) asks you to
(1) select the lightest section that can carry these loads for flexure
(2) check shear capacity of the given section
(3) check that your design satisfies deflections are under l/600.