I am not an engineer and will address this straight common sense thought and with no engineering. I see two things to consider.

The supports are there to support the Rumber floor. Which is in place to support the weight of a horse standing on that spot of the floor of the trailer.  Now Rumber ( or any other material that you place over the supports) will support a certain about of weight based up the space it has to cover.  The specs will show a number of what it will support. ie that a 1200 lb horse can stand on a piece of rumber with 12" supports or a 800 lb horse can stand on it with 16" span between supports or 600lbs can stand on it with 24" supports.  You will have to get the actual specs from Rumber I threw those numbers out for an example.  You will need to ook at what you will have over the top of the area where the support was removed.  If the weight that will be in the spot after the modification is considerable less than the weight of horse. Then you might be just fine.

The second point is what effect will removing the support member have the stability of the trailer. Is that member providing a certain amount of torsional rigidity to the frame of the trailer.  I suspect that the cross member is there more to support the weight of horse standing on it and less to provider structual rigidity to the trailer.

Regardless of the purpose, there is generally ways to reinforce structural members that need to be modified.  Whether it be plate welded into the floor, addition cross member, something can be designed and added to compensate for what you are removing.

A couple of years ago I installed a tank in an Exiss trailer. This is a slant load, initally with a dressing room ahead of the stalls. The bulkhead is also on a slant, which places the front horse's weight on at least two or three different floor joists. The Exiss has a different floor construction than yours, consisting of aluminum planks welded to 2" X 4" floor joists.

I had to remove one joist to fit the tank. I cut the web at the bottom of the top plate, removing the web and bottom plate. This left the top plate and its welded construction intact and undisturbed. The welded construction and remaining plate, allowed no floor deflection whenever any one walked over the modified area.

The remaining top plate was proud of the floor by a little less than an inch. I dressed the edge of the web to the radius of the plate, eliminating any rough cut edges that might endanger cutting the plastic tank. I ripped 1 1/8" pressure treated strips on my table saw, and attached them to the top of the tank's outer flanges. With the tank in place, it did not touch the web.

The tank's length took up less than the width of the trailer, and the removed joist was not under the rear legs of the horse. I've seen some multiple tank installations, where several joists were removed to facilitate their placements.

A rumber floor is not as rigid as a plank type, aluminum welded structure. I would mark where the horse's actual weigh is located, and then check the frame's construction to see if a major structure is affected. If the tank's placement is under the dressing room, and a horse is not standing on the cut out, you should have no problem. Just remember to leave the joist's top plate in place to help support the flooring.

BOL

A couple of years ago I installed a tank in an Exiss trailer. This is a slant load, initally with a dressing room ahead of the stalls. The bulkhead is also on a slant, which places the front horse's weight on at least two or three different floor joists. The Exiss has a different floor construction than yours, consisting of aluminum planks welded to 2" X 4" floor joists.

I had to remove one joist to fit the tank. I cut the web at the bottom of the top plate, removing the web and bottom plate. This left the top plate and its welded construction intact and undisturbed. The welded construction and remaining plate, allowed no floor deflection whenever any one walked over the modified area.

The remaining top plate was proud of the floor by a little less than an inch. I dressed the edge of the web to the radius of the plate, eliminating any rough cut edges that might endanger cutting the plastic tank. I ripped 1 1/8" pressure treated strips on my table saw, and attached them to the top of the tank's outer flanges. With the tank in place, it did not touch the web.

The tank's length took up less than the width of the trailer, and the removed joist was not under the rear legs of the horse. I've seen some multiple tank installations, where several joists were removed to facilitate their placements.

A rumber floor is not as rigid as a plank type, aluminum welded structure. I would mark where the horse's actual weigh is located, and then check the frame's construction to see if a major structure is affected. If the tank's placement is under the dressing room, and a horse is not standing on the cut out, you should have no problem. Just remember to leave the joist's top plate in place to help support the flooring.

BOL

Would the tanks hang too low if they were just mounted under the joists? I will be tackling this when the weather breaks so this is good info for me..

Thanks!