I am trying to do some beam calculations..

I am building a pergola in the back yard, and need to calculate what size of square pipe steel to buy.... The span is 24', and the load will be a vine. This load weight has been approximated to a couple hundred pounds. The span will have a 3" contact point end. For cross beams i am using 5"X3"X1/4" angle iron, with the 5" side angled down.

Right now i am thinking of using 1/8" square pipe steel for the 24' runs, with a width and height of 4"X6" and a length of 288". I have calculated that this choice can handel 14.57lb/in.. However, i am unable to determine the amount of deflection, this is due to my lack of conceptual understanding... This is the part that i am stuck on.

Any help would be greatly appreciated.