Assumptions:<br>
1) fletch plates are steel plates bolted to the top and bottom (in the bending axis) of the wooden 2x6's.<br>
2) a somewhat standard spacing of 10"-16" for the 2x6's.<br>
3) A king size water bed, 7'x7'x9"<br>
4) using standard water density of 62.4 pcf. I know that extra chemicals are added to the water bed to prevent bacteria growth but lets consider them negligible.<br>
5) walls are of sufficient strength to carry the load and moment.<br>
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If you bolt the plates to the wooden beams every 6-12", then they will carry the load of the water bed.<br>
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BTW, in general a standard residential floor will carry the weight of a waterbed without reinforcement. This assumes the floor and structure are in good condition and follow good construction and engineering practice.<br>
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Disclaimer:<br>
This does not constitute a professional opinion on any specific matter but a generic answer for informal knowledge. Please consult a local structural engineer for specific instances.