A new damage index for plane steel frames exhibiting strength and stiffness degradation under seismic motion

► A new damage index for performance-based seismic design of steel frames is proposed. ► The damage index is defined at a section of a steel member. ► The axial force–bending moment interaction is taken into account. ► Strength and stiffness degradation, and low-cycle fatigue are taken into account. A new damage index for plane steel frames under earthquake ground motion is proposed. This index is defined at a section of a steel member and takes into account the interaction between the axial force N and bending moment M acting there. This interaction is defined by two curves in the N–M plane. The first curve is the limit between elastic and inelastic material behavior, where damage is zero, while the second one is the limit between inelastic behavior and complete failure, where damage is equal to one. The damage index is defined by assuming a linear variation of damage between the two abovementioned curves. Thus, for a given N–M combination at a member section, obtained with the aid of a two dimensional finite element program, one easily defines the damage index of that section. Material nonlinearities are taken into account by a stress–strain bilinear model including cyclic strength and stiffness degradation in the framework of lumped plasticity (plastic hinge model), while geometrical nonlinearities are modeled by including large deflection effects. The increase of damage related to strength reduction due to low-cycle fatigue is also taken into account. Several illustrative examples serve to demonstrate the use of the proposed damage index and to compare it with other well known damage indices.