Examination of second-order effects in structural concrete columns and braced frames
The Canadian Standards Association Standard for Design of Concrete Structures for Buildings (CSAA213-94) and the American Concrete Institute Building Code Requirements for Reinforced Concrete (ACI 318-99) permit the use of a moment magnifier approach for the design of slender reinforced concrete and composite steel-concrete columns. This approach is influenced by the equivalent uniform bending moment diagram factor ('Cm') and the critical buckling load ('Pcr'). The computation of ' Pcr' is strongly influenced by the effective flexural stiffness ('EI'), which varies due to the nonlinearity of the concrete stress-strain curve, creep and cracking along the length of the unsupported column. 'Pcr' is also influenced by the effective length factor ('K'), which is a function of the relative stiffnesses of beams and columns framing into a joint. This study was undertaken to examine the influence of different variables on 'EI, Cm, K', and the moment magnifier ([delta]' ns') used for design of slender, tied, rectangular reinforced concrete and composite steel-concrete columns in braced frames under short-term loads. The composite columns consisted of steel shapes encased in oncrete. The columns studied were subjected to eccentric axial loads with an eccentricity applied along one axis of the principle axes of the cross-section, producing uniaxial bending. Over 35,000 isolated reinforced concrete and composite columns in symmetrical single curvature bending were simulated to generate the stiffness data. The CSA/ACI 'EI' equations were then compared with the simulated data. A new design equation that can be used to determine 'EI' of both reinforced concrete and composite columns was also developed from the simulated stiffness data and is proposed as an alternative to the existing CSA/ACI equation. To study the effects of material and geometric non-linearity and longitudinal reinforcing bars and structural steel section details on the 'C m' factor, more than 38,000 reinforced concrete and composite steel-concrete columns, subjected to unequal end moments, were simulated. These columns were used to examine the existing CSA/ACI 'Cm' equation and to develop new expressions for 'Cm'. Finally, 2960 simple braced frames were simulated to investigate the accuracy of the CSA/ACI moment magnifier procedure applied to columns in these frames. The theoretically-computed column strengths were compared to the strengths computed using several different combinations of design equations for [delta]' ns, EI, K', and 'Cm'. The study shows that the prediction accuracy of the moment magnifier method can be improved significantly by replacing the current CSA/ACI equation for 'EI' with the proposed equation for 'EI'.