Pergola 13x15 floor space what is 2x6 WRC maximum span?
Simpson Strong-Tie just created a pergola designer software last week. You can access it by creating an account at the link below.

Use this as a tool to check your framing sizes and spacing. If you can't select the member size you want, it's because that member size is not strong enough for the spans that you've specified.

It also shows you the connections you need and gives you a detailed report of all the material quantities you need. This is a perfect step to take before your trip to the hardware store. 

https://deckplanner.strongtie.com/pergolaplanner/#login