Incorporating Residual Strains in the Flexural Rigidity of RC Members with Varying Degrees of Prestress and Cracking

Abstract

The deformation of reinforced concrete columns and beams is controlled by the variation of the flexural rigidity (EI) both along the member and with applied loads and time. Currently, the moment-curvature (M/χ) approach is used to quantify EI. Prior to cracking, the M/χ approach provides a pure mechanics based solution for EI; that is, the only components of the model that have to be determined empirically are the material stress-strain relationships. However after cracking, the M/χ approach has to be semi-empirical, that is EI has to be determined empirically because the M/χ approach cannot simulate the mechanics of tension-stiffening. An alternative approach for quantifying EI using a moment-rotation (M/θ) approach is described in this paper. It is shown that the M/θ approach gives exactly the same results as the M/χ approach prior to cracking but after cracking has an advantage over the M/χ approach in that it can quantify the mechanics of tension-stiffening, that is allow for bond slip and its effect on crack spacing and crack widths. This paper deals with the mechanics of incorporating creep, shrinkage, prestress, relaxation and thermal gradients (broadly referred to as residual strains) on the flexural rigidity of RC beams and columns at all levels of loading prior to concrete softening.