Here's another way to install a floor system without drilling holes

http://www.horsetrailerworld.com/forum/thread-view.asp?threadid=11440&posts=13

We only wanted to raise the floor enough for minimal insulation, and to have a means to fasten the wooden flooring materials, without drilling holes into the trailer's metal floor. The final height was predetermined to be just under the lip of the door entrance. The risers or sleepers could have been made any height that was necessary.

Installing blocking between the sleepers will prevent them from racking. With the ends fastened, and if you are placing the sleepers across the width of the trailer, you should only need blocking near the center of the floor.

Without a trap, you will get sewer gasses into your trailer's interior. For a shower to work well, the drain can go into the tank's vent line. If you have both a gray and black water tank, the gray water that the shower and sink use, will not have as much odor problems as does the black tank. We only installed a black water tank, with the sink being a minimal usage, we plumbed it there. His shower was set up as a cowboy style in the first stall, and not in the bathroom.

There is an alternative to a "P" trap that does not take up any more space than a drain line. It's called a "Hepvo" waste valve. It's simple installation, uses no fluid for sealing the odors, and requires less vertical space than a trap. You might want to consider it for your installation.