I can help
Can you take a look at the following link and answer the questions at the bottom of the sheet? Your answers will allow me to accurately model the loading and size your beam. Thanks
You say Joist #3 is 32', that seems kind of long. Is that the distance of Joist #3 and #4 together?
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 W6x25 (50 ksi) steel beam for your 13’ span exterior wall beam. This beam is 6.125" wide, 6.375" deep and weighs 25 pounds per foot of beam.
You will need to have a local engineer detail your connections, size your support columns and determine foundation requirements.
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Let me know if you have any more questions