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Reinforcing existing steel members

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Yesterday Mr. Hempstad spoke as follows:
 
 
"....the heat input would expand the reinforcement
 more than the core, resulting in (very small) net tension on the
reinforcement and compression on the core."
 
I believe this statement is incorrect.  The reinforcement
would be in compression and the core would be in tension.
 
Not trying to be picky here but thought I would try to help
out Mr. Carter seeing as he is staying up nights now.
 
Gary Bunkers P.E.