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Can you tell me how high the hay bales will be stacked?
What floor joist will you be using to span the 12'?
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I’d like to point out that a Professional Engineer’s standard of care typically includes a site visit to assess field conditions and get an overall understanding of the structure. This can obviously not be accomplished through the internet. The information provided here is meant for planning purposes only (general sizing and budgeting) and is based on the information provided by you. All loading cases considered are for vertical loads only, no lateral analysis has been completed. The information should be verified by a professional engineer who can visit the site to ensure that potentially important information has not been overlooked or omitted.
You can use a W24x68 (50 ksi) steel beam for your 40’ clear span beam. The beam is 9” wide and 23.75” deep. It weighs 68 pounds per foot of beam length. You will need to provide a 2”x10” wood nailer bolted to the top flange of the steel beam. You will need to provide solid mechanical connections of each of the floor joists to the wood nailer on top of the steel beam. This will provide the needed lateral bracing of the compression flange of the steel beam. You will need to have a local engineer detail your connections, size your column supports, and determine foundation requirements.
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No, the beam would need to be much larger.