A numerical investigation regarding ductility evaluation of steel buildings with moment resisting steel frames is conducted. Bending (µ_Lϕ) and tension (µ_Lδ) local ductilities as well as story (µ_S) and global ductilities are studied. Global ductility is calculated as the mean values of story ductilities (µ_GS) and as the ratio of the maximum inelastic to yielding top displacements (µ_Gt). The ductility capacity is associated to drifts of about 5%. Ductility values significantly may vary with the strong motion, ductility definition, structural element, story number, type of analysis, and model. µ_Lϕ is much larger for beams than for columns. Even though the demands of µ_Lδ are considered an important issue they are less relevant than µ_Lϕ. µ_S is much smaller than µ_Lϕ for beams. µ_GS for dynamic analysis give reasonable values, but µ_Gt does not. µ_Lϕ, µ_S and µ_GS obtained from pushover are larger than those obtained from dynamic analysis and unlike the case of dynamic analysis, µ_Lϕ tend to increase with the story number showing an opposite trend. Considering that: µ_Gt for dynamic analysis results in unreasonable values, pushover analysis does not consider energy dissipation, the strong column–weak beam (SCWB) concept was followed in the model designs, and µ_Lδ is not relevant in framed steel buildings, the ratio (R_LG) of global to local ductility capacity is calculated as the ratio of µ_GS to µ_Lϕ of beams, for dynamic analysis. A value of 1/3 is proposed. Thus, if bending local ductility capacity is stated as the basis for the design, the global ductility capacity can be easily estimated.

Ductility plays a central role in seismic analysis and design of steel buildings. A numerical investigation regarding the evaluation of energy dissipation, ductility, and ductility reduction factors for local, story, and global structural levels is conducted. Some steel buildings and strong motions, which were part of the SAC Steel Project, are used. Bending local ductility capacity (µ_Lϕ) of beams can reach values of up to 20, as shown in experimental investigations. The values are larger for medium than for low‐rise buildings, reflecting the effect of the structural complexity on µ_Lϕ. Most of the dissipated energy occurs on beams; however, resultant stresses at columns are also significantly reduced by beam yielding. A value of 1/3 is proposed for the ratio of global to local ductility; thus, if local ductility capacity is stated as the basis for the design, global ductility capacity can be calculated by using this ratio. It is implicitly assumed in seismic codes that the magnitude of the global ductility reduction factor is about 4; according to the results found in this paper, it is not justified; a value of 3 is observed to be more reasonable. According to the well‐known ratio of the ductility reduction factor to ductility, this ratio should be unity for the models under consideration; the results of this study indicate that, for global response parameters, a value of 3/4 is more appropriate and that, for local response parameters, values larger than 2 can be reached; the implication of this is that using simplified methods like the static equivalent lateral force may result in nonconservative designs from a global structural point of view, but in conservative designs from a local point of view. A value of 8 is proposed for the ratio of the global ductility reduction factor to the global normalized energy.

Shear walls, integrated into conventional reinforced concrete (RC) moment-resisting frame systems (RC frame–shear wall building), have proven to be effective in improving the structural performance and reliability of buildings; however, the seismic behavior of the building depends directly on the location of these elements. For this reason, this paper evaluates the structural reliability of ten medium-rise RC buildings designed based on the Mexico City Building Code, considering different shear wall configurations. With the aim to estimate and compare the seismic reliability, the buildings are modeled as complex 3D structures via the OpenSees 3.5 software, which are subjected to different ground motion records representative of the soft soil of Mexico City scaled at different intensity values in order to compute incremental dynamic analysis (IDA). Furthermore, the parameter used to estimate the reliability is the maximum interstory drift (MID), which is obtained from the incremental dynamic analysis in order to assess the structural fragility curves. Finally, the structural reliability estimation is computed via probabilistic models by combining the fragility and seismic hazard curves. It is concluded from the results that the structural reliability is maximized when shear walls are symmetrically distributed. On the other hand, the configuration with walls concentrated in the center of the building tends to oversize the frames to reach a reliability level comparable to that of symmetrical arrangements.

In the last few years, several mainshock–aftershock sequences have demonstrated their effects on structures; especially after the occurrence of an earthquake with high magnitude, the number of aftershocks tends to increase. For this reason, several studies have been oriented to estimate the influence of aftershocks on the structural response, most of them in terms of peak or residual displacement; however, energy plays an important role for long-duration earthquakes. In this paper, several bilinear SDOF systems with different post-yielding stiffness are subjected to long-duration seismic sequences, considering different levels of intensity of the aftershocks with the aim to compute constant-ductility spectra for input energy (E_I), hysteretic energy (E_H) and the ratio between them (E_H/E_I). The results suggest that although the energy demands tend to increase as the intensity of the aftershock increases, it is observed that the ratio of input and hysteretic energy is very similar for the selected aftershock intensity levels; hence, analytical equations to predict this ratio are proposed. The equations can be used toward earthquake-resistant energy-based design of buildings.

The response of steel moment frames is estimated by first considering that the mass matrix is the concentrated type (M_L) and then consistent type (M_C). The effect of considering more than one element per beam is also evaluated. Low-, mid- and high-rise frames, modeled as complex-2D-MDOF systems, are used in the numerical study. Results indicate that if M_L is used, depending upon the response parameter under consideration, the structural model, the seismic intensity and the structural location, the response can be significantly overestimated, precisely calculated, or significantly underestimated. Axial loads at columns, on an average basis, are significantly overestimated (up to 60%), while lateral drifts and flexural moments at beams are precisely calculated. Inter-story shears and flexural moments at columns, on average, are underestimated by up to 15% and 35%, respectively; however, underestimations of up to 60% can be seen for some individual strong motions. Similarly, if just one element per beam is used in the structural modeling, inter-story shears and axial loads on columns are overestimated, on average, by up to 21% and 95%, respectively, while the lateral drifts are precisely calculated. Flexural moments at columns and beams can be considerably underestimated (on average up to 14% and 35%, respectively), but underestimations larger than 50% can be seen for some individual cases. Hence, there is no error in terms of lateral drifts if M_L or one element per beam is used, but significant errors can be introduced in the design due to the overestimation and underestimation of the design forces. It is strongly suggested to use M_C and at least two elements per beam in the structural modeling.

The nonlinear seismic responses of steel buildings with perimeter moment resisting frames (MRF), modeled as complex 3D MDOF systems, are calculated and the ductility demands, ductility reduction factors and the force reduction factors ( R ), are studied. Equivalent 3D models with spatial MRF, two-dimensional models, and equivalent SDOF systems (SD), are also considered. Results indicate that the global and local force reduction factors significantly vary from one structural representation to another and that they are much larger for the SD models. One of the reasons for this is that, although there is equivalence between the SD and MDOF models, the dissipated energy and the number of incursions in the inelastic range are significantly larger for the SD models. In addition, while for the SD models total plasticization occurs, for the SAC and EQ models, even for significant yielding, plastic hinges are developed only in a relatively small number of structural members; therefore, using the R factors of the SD models may be conservative. According to the results obtained in this research for the more realistic representation of the steel building (3D), the value of 8 suggested in many codes for the R factor for ductile MRF cannot be justified. It is only justified for the SD systems. The implication of this is that non-conservative designs may be obtained if so large value is used. More transparence is needed in the codes regarding the magnitude and the components involved in the R factor.