Effective Stiffness of Reinforced Concrete Columns

The assumed stiffnesses of the structural members of a building strongly influence the computed response of the building to ground shaking. For linear analysis, the member stiffnesses control predictions of the period of the structure, the distribution of loads within the structure, and the deformation demands. For nonlinear analysis, an accurate estimate of the member stiffness is required to reliably estimate the yield displacement, which in turn, affects the predicted displacement ductility demands. Practical, accurate procedures are needed to estimate the effective stiffness up to yielding of each structural component. This research digest compares the measured effective stiffnesses of reinforced concrete columns from the PEER Structural Performance Database (Berry et al. 2004) with stiffnesses calculated following the Federal Emergency Management Agency (FEMA) 356 seismic rehabilitation guidelines (ASCE 2000). The FEMA 356 procedure substantially overestimates the stiffness of columns with low axial loads, in which there can be significant bar slip in the beam-column joints or footings. The digest provides practical recommendations for improving estimates of effective stiffness. Effective Stiffness Model The yield displacement of a column can be considered as the sum of the displacements due to flexure, bar slip, and shear: y flex slip shear ∆ = ∆ + ∆ + ∆ [1] Assuming the column is fixed against rotation at both ends and assuming a linear variation in curvature over the height of the column, the contribution of flexural deformations to the displacement at yield can be estimated as follows: