Creating a curved pergola

Hi all. I am trying to create a curved pergola and I would like to create horizontal members to be exactly 3" thick, 6" apart from each other. The horizontal members need to be attached on the outside surface of the beams. I can extract curves from the beams which I have done to create the current model.

Right now I have cut this surface from simple radial projection which is not exact. Is there a method to control the distance between them? I have very little knowledge of grasshopper so some help would be greatly appreciated.

Thank you.Pergola.3dm (2.0 MB)

it’s better if you don’t split the original surface ; the work will be more easier