Energy-based plastic design of steel moment resisting frames considering cumulative damage

It is well known that damage induced by seismic loading may be due to large deformation
demands as well as cumulative damage produced by low-cycle fatigue. This paper presents
an energy-based plastic design method for steel moment-resisting frames that considers deformation
and cumulative damage as design criteria. The concept is based on the relationships
between the elastic input energy, the hysteretic energy, and the equivalent monotonic response
curve. The relationships are represented by parameters called energy factors. Single-degree-offreedom
systems were first analyzed under selected ground motions to obtain the energy factors.
By using these factors, the relationships among the structural strength, maximum deformation,
elastic input energy, and hysteretic energy can be established. The proposed energy-based
design method could be utilized for computing the required base shear of a structural system,
given the elastic input energy and the target ductility and damage level. The plastic design
is used to ensure that the response follows the intended monotonic response, which could
then be used as the link to the other key input energy contents. The energy-based damage
model is also used for the estimation of the cumulative damage. Three-story, six-story, and
nine-story steel moment-resisting frames are selected as example structures. The frames are
designed with a strong-column-weak-beam (SCWB) sway mechanism using plastic analysis. The
proposed energy-based method was used to derive the required strength of the structure and
assess the cumulative damage to the structural elements. Nonlinear static and nonlinear time
history analyses were conducted to evaluate the seismic performance of those moment-resisting
frames. The results illustrated that the deformation and the approximated cumulative damage
level met the targets predefined early. The findings show that the method can be applied in an
energy-based design framework for SCWB structures.