When I modified my 235 to an IO320 engine in 1968,  I added a horizontal rib to stiffen the tail.  It is wedge shaped about 2 feet long and sits at the height of the stabilizer and butts against the little bulkhead back there.   There is a natural "ledge" on each side where the vertical fin attaches to the fuselage.   The rib is shaped to fit this ledge and anchored with hysol and 3bid tapes top and bottom. 

This was done on the advice of Ray Modert who made this modification after one of his friends reported some serious "buzz" in the tail at 220 mph. The rib is 1/2" plywood with 3 bid on each side. Sitting on the rib is a 12 lb chunk of lead, which balances the extra 40 lb. of engine and propeller weight. I think I'm still a little nose heavy, but not enough to cause any problem bringing the nose up to flare at 75 kts. My new empty weight is 1035, up from 970.

 If you apply a torsional load to the tail section by pushing down on one end of the stabilizer, you can see that it is not real stiff,  torsionally.    A whack on the vertical fin or stabilizer would produce a noticeable vibration.    

 I made a crude measurement of before and after torsional strength by  putting a lead brick on the outer end of the stabilizer and measuring  the deflection. . I have attached a note which describes the test  

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