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In this study, constant-ductility optimization algorithm under a family of earthquake ground motions is utilized to achieve uniform damage distribution over the height of steel moment resisting frames (SMRFs). SMRF structures with stiffness-degrading hysteric behavior are modeled as single-bay generic frame in which the plastic hinge is confined only at the beam ends and the bottom of the first story columns. Several SMRFs having different fundamental periods and number of stories are optimized such that a uniform story damage (ductility demand) is obtained under a given earthquake ground motion. Then, the optimum lateral load pattern derived from the optimization process is compared with that of the design load pattern proposed by the latest version of the Iranian code of practice, Standard No. 2800 to evaluate the adequacy of the seismic code design pattern. Results of this study indicate that, generally, the average story shear strength profiles corresponding to the optimum seismic design are significantly different from those of the Standard No. 2800 story shear strength pattern. In fact, the height-wise distribution of story ductility demands resulted from utilizing code-based design lateral load pattern are very non-uniform when compared to the corresponding optimum cases. In addition, a significant dependency is found between the average story shear strength pattern and inelastic behavior of structural elements.

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In the present study, ten steel-moment resisting frames (SMRFs) having different numbers of stories ranging from 3 to 20 stories and fundamental periods of vibration ranging from 0.3 to 3.0 second were optimized subjected to a set of earthquake ground motions using the concept of uniform damage distribution along the height of the structures. Based on the step-by-step optimization algorithm developed for uniform damage distribution, ductility-dependent strength reduction factor spectra were computed subjected to a given far-fault earthquake ground motion. Then, the mean ductility reduction factors subjected to 20 strong ground motions were computed and compared with those designed based on load pattern of ASCE-7-16 (similar to standard No. 2800) code provision. Results obtained from parametric studies indicate that, except in short-period structures, for moderate and high levels of inelastic demand the structures designed based on optimum load pattern with uniform damage distribution along the height require larger seismic design base shear strength when compared to the frames designed based on the code provisions, which is more pronounced for long-period structures i.e., the structural system becomes more flexible. This phenomenon can be associated to the P-delta effect tending to increase the story drift ratios of flexible structures, especially at the bottom stories. For practical purpose, a simplified expression which is a function of fundamental period and ductility demand to estimate ductility-dependent strength reduction factors of designed SMRFs according to code-based lateral load pattern is proposed.

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This paper presents a practical methodology for optimization of concentrically braced steel frames subjected to forward directivity near-fault ground motions, based on the concept of uniform deformation theory. This is performed by gradually shifting inefficient material from strong parts of the structure to the weak areas until a state of uniform deformation is achieved. In this regard, to overcome the complexity of the ordinary steel concentrically braced frames a simplified analytical model for seismic response prediction of concentrically braced frames is utulized. In this approach, a multistory frame is reduced to an equivalent shear-building model by performing a pushover analysis. A conventional shear-building model has been modified by introducing supplementary springs to account for flexural displacements in addition to shear displacements. It is shown that modified shear-building models provide a better estimation of the nonlinear dynamic response of real framed structures compared to nonlinear static procedures. Finally, the reliability of the proposed methodology has been verified by conducting nonlinear dynamic analysis on 5, 10 and 15 story frames subjected to 20 forward directivity pulse type near-fault ground motions.

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In present study, the effects of optimization on seismic energy spectra including input energy, damping energy and yielding hysteretic energy are parametrically discussed. To this end, 12 generic steel moment-resisting frames having fundamental periods ranging from 0.3 to 3s are optimized by using uniform damage and deformation approaches subjected to a series of 40 non-pule strong ground motions. In order to obtain the optimum distribution of structural properties, an iterative optimization procedure has been adopted. In this approach, the structural properties are modified so that inefficient material is gradually shifted from strong to weak areas of a structure. This process is continued until a state of uniform damage is achieved. Then, the maximum energy demand parameters are computed for different structures designed by optimum load pattern as well as code-based pattern, and the mean energy spectra, energy-based reduction factor and the dispersion of the results are compared and discussed. Results indicate that optimum seismic load pattern can significantly affect the energy demands spectra especially in inelastic range of response. In addition, using energy-based reduction factors of optimum structures in short-period and long-period regions will result in respectively overestimation and underestimation of the required input energy demands for code-based structures, reflecting the difference dose exists in reality between the conventional forced-based methodology and energy-based seismic design approach that can more realistically incorporate the frequency content and duration of earthquake ground motions.
 

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In this study, the investigation of maximum inelastic displacement demands in steel moment- resisting (SMR) frames designed using the Performance-Based Plastic Design (PBPD) method is conducted under both near-fault and far-fault earthquake records. The PBPD method utilizes a target drift and predetermined yield mechanism as the functional limit state. To accomplish this, 6 steel moment frames having various heights were scaled using well-known sa(T1)  method and, then, were analyzed by OPENSEES software. A total of 22 far-fault records and 90 near-fault records were compiled and employed for parametric nonlinear dynamic analysis. The near-fault records were classified into two categories: T1/Tp≥1  and T1/Tp<1 . The study aimed at investigate their impacts on the inter-story drift and the relative distribution of base shear along the height of the structure. The results revealed that the records with T1/Tp≥1   exerted the greatest influence on the drift demands of upper stories in all frames. Conversely, the near-fault records with T1/Tp<1  demonstrated the most significant impact on the lower stories of mid-rise frames. Additionally, the distribution of relative story shears was examined through genetic programming for optimum PBPD design of steel moment frame structures. As a result, a proposed relationship, denoted as b (seismic parameter for design lateral force distribution), was developed and optimized for both near-fault and far-fault records. This relationship depends on the fundamental period of vibration and the total height of the structure. The accuracy of the predicted model was assessed using R2 , which confirmed the reliability of the proposed relationship.