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 stepby-step optimization algorithm developed for uniform damage distribution, Ductilitydependent 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.

Nowadays, in most earthquake resistant design codes, structures are permitted to experience significant inelastic deformations under severe earthquake. Structural experts believe that if structures are designed properly, under severe earthquake, they can deflect in inelastic limits, and, as a result, can dissipate most of the earthquake energy.A general way to evaluate the inelastic behavior of structures is using nonlinear dynamic analyses. These kinds of analysis are usually time consuming and uneconomic and need a high level of knowledge to be undertaken. Thus, it is not always possible for practicing engineers to perform these sorts of analyses. In order to solve the problem, earthquake resistant design codes permit use of a reduction factor (R). This factor, named the response modification factor, reduces the earthquake design force so that the response of the structure is assumed elastic. In this study, the Ductility reduction factor of ordinary and special concentrically braced frames, using a combination of V and inverted V bracing systems, is investigated. According to the results, the maximum height of ordinary frames, which are braced using a combination of V and inverted V bracing systems, can increase up to 15 meters. This value is larger than that proposed by ASCE7 (10.7 m). Also, results indicate that using ordinary frames, which are braced by a combination of special inverted V and V braced systems, can have a saving of about 0 to 29 percent using materials for frames from 1 to 16 stories, in comparison with ordinary frames. According to the results of this study, the response modification factor proposed by the Iranian seismic design code (2800 standard fourth edition), (R=5.5), is more logical than the one proposed by ASCE7 (R=6). Unfortunately, for frames braced by a combination of special inverted V and V braced systems, when the stories of the frames increase up to 10, the expected Ductility demand cannot be achieved. So, as a result, for frames with more than 10 stories, the lower response modification factor should be used. In addition, frames taller than 10- stories do not experience specified target displacement and collapse before reaching the preferred mechanism. This phenomenon shows the necessity of using a different response modification factor for frames taller than 10 stories.

Study on single degree of freedom (SDOF) structures provided information on seismic demand for elastic and inelastic systems. But this information needs to be modified to become of direct use for design of real structures, which are mostly multi-degree of freedom (MDOF) systems, governed by several modes. According to the near fault ground motions have cause much damage in the vicinity of seismic sources, this paper evaluate the modification that must applied to strength reduction factors derived from simplified SDOF models in order to account for MDOF structures in near fault zones. This proposed by estimation the ratio of strength in MDOF systems that result by limiting maximum story Ductility ratio to the strength corresponding to the same ground motion and same level of Ductility in an equivalent SDOF system having a period equal to the fundamental period of the MDOF structures. Nonlinear dynamic time history analysis were carried out on four steel moment resisting frames with two distinct behavior of yield mechanism, undergoing five level of Ductility ratio when subjected to 15 near fault ground motions with forward directivity effects. Modification factors spectra were computed as a function of period and number of stories and were compared to those of corresponding spectra for far fault ground motions. The required modification factor for inelastic MDOF systems, for near fault motions was shown to be dependent on target Ductility ratio and the type of yield mechanism and to a lesser degree, period of vibration and number of stories. The result demonstrate that in the low level of Ductility ratio, during the short period range, the modification factor given from near the fault ground motions is less than those from the far fault ground motions, and this is true during all period range as the level of Ductility is increased. Finally, since the equivalent pulse of near fault ground motions have significant effect on structural response, modification factors were proposed as a function of the ratio of structural period to equivalent pulse period and Ductility ratios.

In this study, the Ductility reduction factor of Ordinary Concentrically Braced Frames (OCBFs) and special concentrically braced frames (SCBFs) which are braced concentrically in two end sides of frames, is evaluated. The results confirmed that, using SCBFs will reduce about 15 to 45 percent of total used material for one to 16 story frames respectively. In addition, for all of the 16 ordinary X-braced frames, which have 1 to 16 story height, calculated Ductility reduction factor exceeds from ASCE7’s proposed one, except for 16 stories frame. For studied frames, which are braced in two end sides, using the X-bracing system, the results confirmed that Ductility demand is achievable without any significant problem. In addition, results indicated that although the response modification factor which is proposed by Iranian seismic design code (2800 standard), is more logical than ASCE7’s one, for frames which are braced in the end sides, the response modification factor should be taken less than 5.5.

The experience of previous earthquakes shows that the inelastic response of structure is related to the intensity and content of ground motion. In this case, the evaluation of nonlinear response of structure demonstrates the reduction in the base shear force. This reduction which leads to inelastic base shear is defined by Behavior factor (strength reduction factor) in seismic codes. One of the important parts in R factor is Ductility reduction factor Rm. While Rm is related to the type of earthquake, it seems that for near fault motions there would be a different value in comparison to ordinary earthquakes. For the near fault earthquakes, due to the direction of fault rupture from the site, the directivity effect becomes an important parameter. Previous researches show that for forward directivity effect, there would be two components for earthquakes. One is normal strike and the other is parallel strike. In this paper, these components are regarded as SN and SP. Also, in the concept of performance-based design, the ratio between inelastic and elastic response of structure is an important index in calculating the target displacement. This ratio is called CR, hereafter. It is good to mention that CR factor is defined as C1 coefficient in FEMA440. In previous researches, the evaluation of CR for near and far fault motions has less been considered.To evaluate Rm and CR, the extended number of SDOF systems (from 0.2 to 4 Sec.) are considered for four levels of target Ductility (2, 3, 4 and 5). Accordingly, Rm and CR are calculated for near field (normal and parallel component) and far fault earthquakes. The normal strike component is traced by a sensitivity analysis, changing the strain hardening ratio and inherent damping. To perform the analysis, the nonlinear time history analysis was selected in Opensees. The steel material was also defined to be bilinear. To set the required Ductility with the prescribed target Ductility -during trial and error procedure- the yield strength of SDOF was changed, since the target Ductility was achieved. To solve the inelastic equation of motion, the Newmark-Beta method was selected. The inelasticity in Opensees was modeled with distributed plasticity using the fiber element. Finally, to calculate Rm and CR for near and far field motions, approximately 84000 nonlinear time history analyses were carried out. In addition, to study the sensitivity of Rm and CR to damping and strain hardening ratio for the normal strike earthquake, approximately 22400 nonlinear time history analyses were carried out.The results show that for all three sets of earthquake, the Rm increases up to a specific value and after that, becomes constant while the fundamental period (T) increases. For small values of Ductility (m), increase in T may lead to convergence of Rm to target Ductility. In the near field, when the values of T and μ are increased, Rm becomes almost greater than μ. However, for small values of T, Rm is not dependent on demand m. The study shows that: using far field value of Rm for near field motions may lead to a non-conservative value. Furthermore, while T increases, the CR value converges to the unit. In the short period, CR depends on m and T, severely. Using CR of far field against SN component leads to Non-conservative result. For a constant value of m and T, increase in damping may increase CR. Using C1 for near field motions is non-conservative for near field motions. Also, for short periods and high Ductility demand, CR, corresponding to SN component is about 40% greater than C1. Evaluation of the ratio of displacement modification factor to behavior factor shows that the Cd/R ratio for T -greater than 1 Sec.- converged to the unit. For small period values, this ratio is significantly dependent on the duration. Also, using Cd/R of far field for near field motions may lead to inaccurate results.

The idea of using steel plate shear wall (SPSW) has been noted for last three decades as a lateral load resisting system in design and retrofit of buildings. Knowing the short life of researches on this system and the necessity for replying to some design problems, in this research, it has been tried to determine the effect of Ductility factor on force modification factor of SPSWs by using results of two cyclic tests on ductile SPSW's with three stories and other creditable experiments which have been done around the world. In the three-storey tests, two different connections (simple and fixed) and for panel’s plate, easy-going steel (EGS) are used. Assessment in this area shows that, the force modification factor of thin SPSWs with constant overstrenght factor based on Uang's methode is more than this factor of moment resisting frames.

Ductility demands of structures are increased during strong ground motion as a consequence of the dissipation of hysteretic energy caused by cyclic load reversals. This phenomenon is called Low-cycle fatigue. The monotonic Ductility capacity could not take into account Low-cycle fatigue. Hence this Ductility capacity should be reduced in design procedures (equivalent Ductility factor) and should be used instead of the conventional monotonic Ductility supply in design procedures. The equivalent Ductility factor is applied for determination of force reduction factor. In this study, the effect of low-cycle fatigue on Ductility capacity factor is examined. For this reason the replies of a single degree of freedom system was evaluated using nonlinear dynamic analysis. Seven records related to soil type II from strong ground database are extracted. Three models have been proposed to determine the equivalent Ductility factor taking into account cumulative damage. The first two models based on the maximum displacement and maximum dissipation energy are the upper and lower values. The third one model is Park-Ang model. According to the Park-Ang model, the damage is related to hysteretic energy and concluded of maximum displacement and maximum dissipation energy. The parameter γ controls the hysteretic energy and depends on maximum displacement and natural frequency of the system. In order to obtain the quantity of the parameter g, a parametric study of the inelastic response of SDOF systems was carried out. In the parametric study, input ground motion, as well as the initial stiffness (period), strength, Ductility, hysteretic behavior and damping of SDOF systems, was varied. In this paper the variation of this parameter was considered and the effect of the Ductility factor, force reduction factor, time history acceleration and damping ratio was evaluated.The results show that the reduction of the Ductility factor due to low-cycle fatigue (controlled by parameter g) is significant. It is proved that the parameter is relatively stable during all length of periods. If approximate values for γ are used, the determination of equivalent Ductility is very simple, and thus appropriate for design purpose. The parameter g varies from 0.6 to 1.2. For practice peruses it is assumed that the value of g is 0.9. Using this assumption it is possible to determine equivalent Ductility factor taking into account low cycle fatigue.

The importance of Ductility in absorbing energy and its improving the structural behavior under earthquake loading is well-established. Some researchers have noted that the Ductility ratio may also be an important parameter for designing structures against explosion induced forces. However, their works were mainly qualitative and based on the Ductility of the structural members. In this article, nine short steel frames with different spans and numbers of storeys, subjected to different blast loadings have been investigated. Nonlinear pushover blast force-displacement curves are evaluated for each frame and the Ductility parameters are extracted. The results indicate the significant effects of Ductility ratio on the structural response. Also, it is found that the Ductility reduction factor under blast loading increases with increasing Ductility ratio, irrespective of the period of vibration of the system.