Post back with the following answers, and I can help you. Your question is like: x + y = 26 What does x equal?
1. What is the trellis made of? 2. How many supports are we talking about? Is there only a post on each corner (4) or are there more than that? 3. How much snow do you get, and how much snow do you think your trellis design will be asked to support? 4. Do you live in a really windy area? 5. How deep are your posts going to be set into the ground? (How are you going to keep this structure from falling over to one side? Bracing?
Your question indicates you will be supporting the trellis on a 20' clear span, but I don't know exactly what you are supporting with it. Is this several 20' beams spaced every 24" or so for 30 feet, or what?
If you can explain this design better, I can tell you how big the beam will have to be.
In general, I would not advise trying to construct an engineered laminated beam on your own, especially if you don't already know how big it would have to be. Purchasing these items could be very economical, and in fact, the places that make them can provide you with very specific answers to your question as well, because they have professional engineers on staff whose licenses depend on it, instead of taking the word of who knows who I am on the internet.
Post back with your answers, and I'll help you out the best I can. Be painfully descriptive...