Long Columns: Ultimate Strength Analysis of Restrained Columns

Theoretical analyses are presented for the ultimate strength of long restrained reinforced concrete columns. The analyses are based on the same principles as the analyses of the ultimate strength of long hinged columns presented in the first paper of this symposium. The treatment of concentrically loaded columns is founded on the tangent modulus theory suggested by Engesser, the treatment of eccentrically loaded columns follows the principles advanced by Kármán, and both treatments utilize the stress-strain relationship for concrete determined by Hognestad from tests of short eccentrically loaded columns. The consideration of the end restraints requires the addition of a new assumption and necessitates new methods of solution.

The results of the analyses are presented in dimensionless graphs. The following variables are included: (1) concrete strength, (2) percentage of reinforcement, (3) yield point of reinforcement, (4) end restraint, (5) eccentricity, (6) slenderness ratio, and (7) duration of loading.