Floor support??
			 
			 
			
		
		
		
		Brad, there's no way that is going through the floor unless you have some dry rot or carpenter ants.  Another question; how long a span do the joists cover? 
 
Check it out the best you can but seriously with the weight spread out over ten square feet I can't see a problem.   
 
Disclaimer: I may or may not have a clue what I'm talking about.  Use above advice at your discretion. 
		
	
		
		
		
		
		
	
		
		
	
	
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