First, welcome to the TFG forums...
I would have to let others speak to your query, as there really isn't nearly enough information (for me at least...being visual and kinesthetic in understanding) to track the possible dynamics that this post may be subjected to.
I can share that it can depend on the species of tree, types of joinery, possible load vectors the post is subjected to, post location within a frame and even the type of roof system, among other things besides size alone. Vernacular systems to have a part in this.
A sketch and other information would be helpful on what this frame may look like...