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Hoist Capacity

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Looking for a practical approach for setting a limit on some existing hoists.  Spans are in the 7' to 7'-6" range for an S6x12.5, with the crane capacity of 1 ton installed. Crane is hung from the bottom flange, so there is the tendency to self right itself against lateral buckling of the compression flange.  Total rail length is about 20' with no actual bracing of the compression flange.  Any thoughts on allowable Fb?  Thanks.
Chic Gilligan, PE
Brielle, NJ