Thanks for the pictures.
I’d like to point out that a Professional Engineer’s standard of care typically includes a site visit to assess field conditions and get an overall understanding of the structure. This can obviously not be accomplished through the internet. The information provided here is meant for planning purposes only (general sizing and budgeting) and is based on the information provided by you. All loading cases considered are for vertical loads only, no lateral analysis has been completed. The information should be verified by a professional engineer who can visit the site to ensure that potentially important information has not been overlooked or omitted.
I can give you a couple engineered wood options for your 13’ span beam:
5-1/4” x 11-1/4” Versa-Lam 1.7 2650 DF
7” x 9-1/4” Versa-Lam 2.0 3100 DF
These are Boise Cascade products and you can go to the following link to find distributors in your area.
You will need to have a local engineer detail your connections, size your support columns, and determine foundation requirements.
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