Crack formation in eccentrically compressed reinforced concrete elements subjected to combined compression and torsion

A calculation methodology and analytical model are presented for determining deformation parameters and crack width in eccentrically compressed reinforced concrete elements subjected to combined compression and torsion. The analytical relationships are derived using static equilibrium equations under the simultaneous action of torsional moment and eccentric loading, taking into account the deformation effect proposed by Vl.I. Kolchunov. The physical essence of this effect lies in the fact that upon failure of the tensile concrete and crack formation, the crack opening displacements are restrained by the reaction of the reinforcing bar, resulting in a nonlinear curvature of the crack profile. This phenomenon is accounted for in the analytical relationships when determining the relative mutual displacements of concrete and reinforcement between two adjacent cracks. Using the derived analytical relationships, the crack width in a lightly reinforced eccentrically compressed concrete element under combined compression and torsion is calculated. The computational results are compared with experimental data obtained from testing structural elements under the considered stress state, as well as with results from design methods specified in Russian and international standards. It is shown that the proposed analytical relationships satisfactorily reflect the quantitative values of experimentally measured crack widths in reinforced concrete elements under the given complex stress state.