this is not an engineered beam and may not be approved by all
inspectors, a careful builder can construct a strong and durable
built-up beam of almost any length using 2x joist lumber. A three joist
beam is shown above. To use standard metal hardware such as post
brackets, hangers and post caps, 1/2" plywood can be used as shims.For
greater strength use four
2x's as it will be close to the same strength as a solid 6x beam.
See this table of IRC spans for headers and girders.