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The only person that is truly qualified to answer that question would be a structural engineer. The beam is not the only integral part of your design. The support columns and the footings under them are also an important part that will need to be designed to support the weight that will be placed on them as well as the live load that will be added from people, furniture, etc. If I or anyone else were to give you a size for this beam we would be opening ourselves up to liability against the failure of your design. Most structural engineers will not answer this question across the internet due to problems from practicing in a state other than the one they are licensed in.
Best advice is to consult an expert in your area (Structural engineer) and have your design approved by your local building inspections department.