1. Introduction Earthquake is an unpredictable and destructive event that affects most of the urban regions. It is a necessary job to reduce the earthquake damages to a minimum level. The supervision of an especial organization on design principles is an effective solution to minimize structures damages. On the other hand, there are plenty of buildings that have been constructed before the establishment of supervision organizations. Two solutions can be introduced to these structures. The first is demolition and reconstruction,the second is retrofitting. The first is not satisfactory because of its high cost, however, the second is usually preferred. The second solution is cost-effective and has been proved that can be useful to minimize the seismic risks. One of the methods to retrofit concrete structures is using steel bracings. Chevron bracings were used in this paper to retrofit the concrete structure. The changes in seismic parameters like the coefficient of behavior, initial stiffness, absorbed amount of energy, and ductility ratio were calculated...

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.

This paper investigates the effect of curvature of structural members on nonlinear behavior of two-dimensional building frames. The RC moment resisting frames in two groups of medium (M) and high ductility (H) level, on alluvium (A) and bedrock (R) soil were considered for the analysis respectively.Totally, sixteen frames having 5, 8, 12 and 15 stories, with four bays of each 4m long, were considered.All frames were designed for H and M ductility levels according to Iranian standard 2800 for seismic design, and Iranian concrete code of practice (ABA) and then corresponded to the regulation of ACI- 2002.IDARC computer program is utilized for the nonlinear static analysis to investigate the capability of plastic hinge formation of different members during the various state of behavior (cracking, yielding and ultimate state). Linear relation between the overall curvature ductility and the overall displacement ductility of the multi-degree of freedom system is derived. From the derived relationship, the close relationship between the fundamental period and the relative energy dissipated (ratio of overall curvature ductility to the overall displacement ductility) is clearly obtained.

Experimental studies show that an indeterminate structure or a continuous concrete beam does not fail when critical sections reach their ultimate strengths. Therefore, if a structure has adequate ductility, stress and moment redistribution will take place in the flexural members by developing plastic hinges at critical sections. This causes the other points of beams to achieve their ultimate strengths and capacities. Besides, moment redistribution allows designers to adjust the bending moment diagram computed by elastic analysis.The usual result is a reduction in the values of negative moments at the support face as well as an increase in the values of positive moments along the span.In the current investigation, a parametric study on moment redistribution in continuous RC beams with equal spans under uniform loading was performed. First, the governing equation for the allowable percent of moment redistribution was extracted using ductility demand and ductility capacity concepts. The effects of different parameters such as the concrete compressive strength, the amount and the strength of reinforcing steel, the magnitude of elastic moment at the support and the ratio of the length to the effective depth of the continuous beam on moment redistribution were then investigated. Furthermore, the allowable moment redistributions were calculated according to the regulations of different codes in each case. The results showed that, whereas the permissible moment redistribution in continuous reinforced concrete beams based on the relevant rules in the current codes is not in a safe margin in some cases, it is rather conservative in most cases.

In seismic areas, ductility is an important factor in the design of high strength concrete (HSC) members under flexure. In order to investigate this, here in this study, eight HSC beams with different percentages of  r & r’ were cast and incrementally loaded under bending. During the test, the strain on the concrete middle faces, the tension and compression bars, and also the deflection at different points of the span length were measured up to failure. Based on the obtained results, the serviceability and ultimate behavior, and especially the ductility of the HCS members are more deeply reviewed. Also a comparison between theoretical and experimental results is reported here.

Progressive collapse studies generally assess the performance of the structure under gravity and blast loads, while earthquakes may also lead to the progressive collapse of a damaged structure. In this study, the progressive collapse response of concentrically braced dual systems with steel moment-resisting frames was assessed under seismic loads through pushover analysis using triangular and uniform lateral load patterns. Two different bracing types (X and inverted V braces) were considered, and their performances were compared under different lateral load patterns using the nonlinear static alternate path method recommended in the Unified Facilities Criteria (UFC) guideline. Eventually, the seismic progressive collapse resistance of models was compared to their progressive collapse response under gravity loads. These studies showed that models under the seismic progressive collapse loads satisfied UFC acceptance criteria and limited rehabilitation objective. The structures had better performance under seismic progressive collapse than models under gravity loads because of more resistance, ductility, suitable load redistribution, and more structural elements that participated in load redistribution. Furthermore, despite studies on progressive collapse under gravity loads, the dual system with X braces showed better progressive collapse performance (more resistance, residual reserve strength ratio and ductility) under seismic loads than the model with inverted V braces.

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.

The idea of using steel plate shear wall as a lateral load resisting system in design and retrofit of structures has attracted the attention of researchers and designers for more than three decades. In this research, the ductility of thin steel plate shear walls are studied based on ATC-24 protocol and Popov’s definition. Two three-story unstiffened steel plate shear walls were tested under cyclic loading. In these tests shear walls had rigid and simple beamto-column connections. For the plate of panels, low strength steel and for the boundary frame high strength steel were used. In addition, some other valid tests on steel plate shear walls with different configurations, which were done in the world also, were considered. The results obtained from all of the tests show that the ductility factor in thin steel plate shear walls according to ATC-24 protocol and Popov's definitions can be assumed about 6.5 and 13, respectively.

Self-consolidating concrete (SCC) is a relatively new approach to making concrete, and it is characterized by its high flowability and resistance to aggregate segregation in the plastic state. A total of 3 beams were tested in this experimental investigation on the flexural ductility of reinforced concrete beams made with self-consolidating concrete. The beams were made from concrete having average compressive strength of 30 MPa and reinforcement ratio in the range of 0.15-1.38. Three self-consolidating reinforced concrete beams with different percentage of and constant amount of were cast and incrementally loaded under bending. During the test, the strains on the concrete middle face and on the tension and compression bars as well as the deflection at different points of the span length were measured up to failure. This paper compares the ductility of reinforced beams cast with SCC concrete to the theoretical calculations based on two codes (ACI, CSA) recommended for the reinforced concrete members that vibrated into place to ensure proper filling and consolidation. Based on the results obtained, effect of increasing tension reinforcement on the curvature and displacement ductility of the self-consolidating concrete reinforced members is more deeply reviewed. Comparisons between theoretical and experimental results are also reported here. Generally, it was concluded that, self-consolidating reinforced concrete beams yielded greater ductility as opposed to the theoretical calculations based on two codes (ACI, CSA) recommended on conventional reinforced concrete beams.