For an Over-the-Road driver (OTR) it may become complicated to figure out the number of winter chains needed, because each state has its own laws and regulations to be followed. Ideally, and what the law says, each time you travel into a state, you need to be familiar with that states laws!
However, to make your life a little easier, I picked up a few of the most strict states with the winter chains laws. These apply only to a semi truck pulling a semi trailer (5 axles total).
FOR WASHINGTON you'll need 5 chains
FOR OREGON you will need 6 chains (3 pairs) when SNOW ZONE sign is posted:
Source: Here and OR CHAIN LAW