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.
There is very little bracing under the loft floor. It may need to be framed in more to support the weight of stored items. Tires are not that heavy, but you definitely want it to be strong enough to carry the weight of a person safely. Objects falling from that height could definitely result in personal injury, or even death. If you are unsure how to reinforce it, it would be best to have a professional come in to assess.