Closure to “Mechanics and Slenderness Limits of Sway-Restricted Reinforced Concrete Columns” by Jostein Hellesland

A simplified method for instability and second‐order load effects of framed structures: Story‐based approach

“…The rotational stiffness at the upper and lower ends of the column analyzed in regular frames are considered to vary proportionally to the value The term 2 k c in the denominator in the C A and C B expressions represents the contribution of the columns to the rotational stiffness at the column ends. Therefore, a more reasonable expression is used for C A and C B , with the assumption of 2 k c = k c + k c , top and 2 k c = k c + k c , bot , The values of C A and C B are the inverse of the well‐known G factors in AISC and other American steel literature.…”

“…Where the subscript "1" denotes the first-order case and S 1 ¼ EI L 3 c 1 . The rotational stiffness at the upper and lower ends of the column analyzed in regular frames are considered to vary proportionally to the value 21,22] The term 2k c in the denominator in the C A and C B expressions represents the contribution of the columns to the rotational stiffness at the column ends. Therefore, a more reasonable expression is used for C A and C B , with the assumption of 2k c = k c +k c,top and 2k c = k c +k c,bot ,…”

“…[7] As reported in that study, the determination of the system buckling is not only a function of geometry and member properties but also a function of load arrangement.A reasonably comprehensive review of story-based approaches is given in Hellesland, [8] and similarly, this study also presents a method for the approximate story-based treatments of horizontally interacting columns in sidesway unbraced frames. The problem of taking vertical interaction into account is discussed in Hellesland [9] and Tong and Wang. [10] Salama [11] proposed some simple equations for obtaining of the effective length factors and compared those factors with the values recommended in structural specifications.…”