Absolutely!! More aggressive chains like the v-bar will do more damage and less aggressive chains will do less, but they all do some. If you can park on plywood or rubber mats, you can lessen the damage.
Regards, Mike
In my younger and less wise days, I ran a snowblower on my craftsman tractor with chains. It would spin the tires and everywhere it spun is a nice little polished spot on the concrete. We sold that house and nothing was said, but I wasn't happy with myself when I first saw it. I can't imagine what some serious chains would do to a nice concrete finish.
Yes they sure do. My v-bars scratch the floor when I turn the wheel to back the tractor up against the wall. Other then that they don't scratch my floor much at all.
I put chains on my JD 2520 this year and keep it on concrete. I haven't noticed any marks on the concrete from driving across it. But outside where I have tried removing snow/ice that has came off the shed roof and had a chance to freeze down I noticed marking where I had spun on the concrete. If your only driving across it for storage purposes I don't believe that there will be any evidence of it. I have attached a photo of the chains that I have on my tractor.
I have chains on my JD 2010. I have marks on my pad in front of my garage from the chains. I park the JD in my pole barn on a 4x8 sheet of OSB that is cut in half the long way.
I have the same chains as Farwell. They hardly leave a mark when driving over concrete and almost invisible on asphalt. Sit and spin is another story no matter what the type chain. Plain twisted link chain will be your best bet to remain unobtrusive to concrete floor.