Calculating Load Question


Hi,​I'm building a "roof" for a deck area in my backyard and trying to figure out how to calculate the load and determine what structure I need. Its not a covered roof - just 2x6's that are connected to the house on one side and will be supported by a beam with 2 posts on the other. So no snow or other weights pushing down on it.​I've used all my MS Paint skills to make this terrible concept: https://imgur.com/a/CQTBbyt​Ideally I would like to span a distance of 23'9" (7.23m) I calculate the total lumber load at ~700 lbs (~317 kg).​The angle is a flat 10 degree slope with one side securely connected to house; the support beam will be concrete sonotube into ground, and beam that spans isn't taking load at the end - but has a 1' overhang area.​Just looking at it I'd suspect that a 6x6x24' would easily handle the load - but how do I math this?

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