I'm not sure how much they weigh. I assume around 50lbs a piece. Here is the area I will store them in:
Any specific way I should arrange the load or am I worrying too much?
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I'm no expert, but I suspect that there won't be any harm in storing them there. I assume, they are just your seasonal tires? Someone had to be up there to install the shelving, which would have been more weight concentrated in a smaller area (a foot). So the distributed weight of the tires should have no effect. In my In-laws garage, they store all sorts of stuff up there, bins and boxes full of clothes and other things.