فهرست مطالب m .gerami

Nowadays, due to the revelation of the harmful effects of chemical drugs for most users, the desire to use medicinal plants has increased significantly. Basil (Ocimum basilicum L.) is one of the most important medicinal plants of great interest in various pharmaceutical industries due to its valuable and vital secondary metabolites, such as essential oil. However, salinity is considered a major constraint for its productivity. Soil and irrigation water salinity is a major constraint for crop production. In salinity-rich soils, the osmotic pressure increases, and the plant must burn more vital energy to absorb water. Increasing the salinity tolerance of plants for sustainable food production, especially in arid and semi-arid regions, can reduce the need for irrigation and, thus, production costs. Since using calcium nanoparticles increases nutrient utilization efficiency, reducing soil toxicity, minimizing the adverse effects of over-fertilization and reducing the frequency of fertilizer application, the present study investigates the effect of calcium nanoparticles on physiologic and biochemical properties of basil medicinal plant under salinity stress.  The plants were treated with calcium nanoparticles in five levels by spraying with concentrations of 0, 0.25, 0.5, 1 and 1.5 g/l and salt concentrations of 0.75 and 150 mM along with Hoagland solution in a completely randomized design in a greenhouse environment with three replications. Some growth characteristics such as height, number of leaves, leaf area, fresh and dry weight, amount of chlorophyll a, chlorophyll b, total chlorophyll and carotenoid content of the plant were measured. Some biochemical characteristics such as flavonoid, soluble sugar, anthocyanin content and antioxidant enzymes such as catalase and peroxidase were also measured. The least significant difference (LST) test was used to compare the means in SAS software. The results of ANOVA showed a significant effect of calcium nanoparticles on most morphological traits. Also, different salinity levels alone significantly affected the studied traits (p<0.01). Following the reduction of the osmotic potential of the soil solution due to salinity stress, water absorption decreases and as a result of stomata closing, the photosynthesis and respiration decrease. The mean comparison of the simple effect of calcium nanoparticles on chlorophyll pigments showed that with increasing the nanoparticle level, chlorophyll content increased, and as a result, photosynthesis improved. The simple effect of different salinity levels on some traits (phenol, soluble sugar, peroxidase enzyme and anthocyanin) showed that increasing the salinity level caused an increase in these traits. So, at the concentration of 150 mM salinity, phenol content with 8.02 mg of gallic acid per g of dry weight showed the highest amount compared to the control sample of 10.5 mg. Also, the soluble sugar content was the highest at this salinity concentration, with 139.9 mg/g dry weight, compared to the control, with 110.9 mg/g dry weight. The interaction effect of calcium nanoparticles and salinity on basil's morphological characteristics and carotenoid content was insignificant. However, it was significant in the chlorophyll content, the amount of flavonoids and catalase (p<0.01). In fact, with nano fertilizers, the plant can absorb more nutrients, and while reducing the leaching of elements, the yield of the product increases. The results of this study suggest that the physiological and biochemical characteristics of Basil were affected by salinity stress, and the interaction of nano calcium with salinity stress reduced the effects of salinity stress. Therefore, spraying the nano-fertilizer in an appropriate concentration is suggested to improve the yield of basil in salinity stress conditions.

In the process of implementing steel structures with bolted connections, the bolts are temporarily tight by the workers and so-called tightened, in this article, called the initial stage. After performing the connections of several different parts in the form of primary fastening, in the following stages of construction, the bolts of connection are pre-tensioned so that the minimum pre-tensioning force of the regulations is created in them. Therefore, in the process of the construction of steel structures with pre-qualified connections of the steel moment end plate frame, the effects of the construction sequence are important, because during the construction, due to the different construction situations of the project implementation conditions, delays In the secondary fastening of the connections, the lack of completion of the lateral restraint system of the structure and on the other hand the possibility of earthquakes with different magnitudes can lead to local or general damage to the structure and ultimately lead to the imposition of exorbitant costs on the project. In this research, the acceleration records proposed by FEMA-P695 (ATC-63) were used with the nature far field, and then the vulnerability of the BUEEP connection was investigated using the fragility curves. Without implementing the secondary fastener in the structure, the connections have a semi-rigid behavior and the discussion of damping and reducing the seismic demand caused by it is more noticeable. This trend was more visible at lower accelerations. In general, in slight and medium performance levels, the effect of not using the secondary fastener is greater due to the slack of the connections and the need for lower drifts to reach this level of performance.

Using shape memory alloys as a novel tool due to their self-centering property to reduce damage and control seismic behavior of structures can be effective. Considering that the occurrence of aftershocks can always cause cumulative damage in structures, it is important to investigate the performance of the above systems under aftershocks. The present study evaluates a four-story steel frame in the state without braces and with convergent braces equipped with shape memory alloy dampers. To investigate the effect of aftershocks on the behavior of the two frames and perform incremental dynamic analysis, the OpenSees software was used. For this purpose, 29 records related to the main earthquake and the actual recorded aftershock were used. To investigate the response of the structures, first, the main earthquake was scaled to bring the structure to the collapse level, and then the aftershock was applied to the frames considering three levels of drift structure (0.01, 0.025, and 0.04) under the main earthquake. The results show that the braced structure equipped with a damper, compared to the structure without braces, experiences 13% more acceleration, 30% less residual drift, and 21% less relative drift after experiencing 0.04 drift caused by the main earthquake. Additionally, in both structures, more destructive effects are observed when they are under aftershock

Applying innovative nanotechnology in agriculture is considered as one of the promising approaches to obtain significant increases of crop yield. Nanoparticles (NPs) are considered potential agents for agriculture as fertilizers and growth enhancers and using of nano-fertilizers has led to an increasing in the efficiency of nutrients, the correct management of fertilizer consumption, and a reduction of the frequency of fertilizer application. Stimulants are compounds that initiate signals for cells to increase or decrease the production of secondary metabolites and plant defense response. Stimulants such as Putrescine play a role in regulating various plant physiological processes. In this regard, considering the importance of using new technologies, including nanotechnology, in sustainable agriculture to increase the quantitative and qualitative performance of agricultural products, especially oil-medicinal plants, and the lack of sufficient information about the use of iron nanoparticles and polyamine putricine in Camelina plant nutrition, The effect of foliar spraying of these stimulants on functional, morphological and physiological traits of Camelina plant (Soheil veriety) was evaluated.

This research was conducted as factorial layout based on a randomized complete block design with three replications at the research fields of Baye-Kala Agricultural Research Station (BARS) at Neka city in 2021. The studied factors included iron nanoparticles in four concentrations (0, 20, 40, and 60 ppm) and polyamine putrescine in four concentrations (0, 0.5, 1, and 1.5 mM). Each experimental plot was prepared in 6 square meters area and the studied treatments were applied by foliar spraying at the beginning of the reproductive phase of the plant. Two weeks after applying the treatments, sampling was done to evaluate the different traits of the plant. After checking the normality of the data, they were analyzed with SAS (ver 9.1) software; obtained averages compared with using Duncan Test at the 5% probability level.

The results of variance analysis indicated the significance of the simple effect of iron nanoparticles and putrescine on all the studied traits at the 5% level, as well as the significance of the interaction of the two factors on all the studied traits except carotenoid and peroxidase in the reproductive stage at the 5% level. According to the results, the highest amount of carotenoid (0.142 and 0.141 mg.g-1, respectively) and peroxidase (4.96 and 4.38 mg.g-1, respectively) were observed in application of 60 ppm iron nanoparticles and 1.5 mM putrescine which had no statistically significant difference with the concentration of 40 ppm iron nanoparticles and 1 mM putrescine. The results indicated that the highest amount of flavonoid (40.72 mg.g-1), soluble sugar (139.27 mg.g-1), and plant height (115.75 cm) were observed in the treatment combination of 60 ppm iron and 1 mM putrescine, the highest percentage of oil (41.76) and protein (27.77) were observed in the treatment combination of 40 ppm iron and 1.5 mM putrescine and the highest amount of grain yield (210.27 g) and morphological components of yield were observed in the treatment combination of 40 ppm iron and 1 mM putrescine. The correlation result showed that there were the most positive and significant correlation values among the physiological traits and the yield trait had a positive and significant correlation with plant dry weight (0.44) and oil percentage (0.40).

The results have demonstrated that foliar application of 40 ppm iron nanoparticles and 1.5 mM putrescine significantly enhanced various growth characteristics, including photosynthetic pigment content, crude protein, oil content, as well as the physiological and morphological aspects of Camelina. Additionally, the application of iron nanoparticles and putrescine via a uniform supply of low-consumption nutrients has been shown to strengthen the plant's defense system, ultimately leading to improvements in the growth, development, and yield of the medicinal-oil Camelina plant.

From experimental researches and analytical studies, it has been fully proven that the resistance and stiffness parameters of elements and structures decline during cyclic loading due to the dynamic nature of seismic excitations. The simultaneous effect of the magnitude of the system response and the number of loading cycles is expressed by cumulative damage laws; In other words, the current deformation of an element or structure depends on the accumulation of damage in all past oscillations that remain in the system's memory. The analysis and design of structures based on performance and the branch of health monitoring of structures has led to having a clear picture of the amount of possible damage at different levels of risk, and in the last few decades, it has drawn the attention of many researchers to this field by developing different evaluation methods. In this research, the evaluation of the cumulative damage of steel structures under far and near field earthquakes has been investigated using Park-Ang and Kratzig damage indices. Two structural systems of special steel moment frame and dual structural system (special steel moment frame and special concentric braced frame) with the number of floors 8, 15 and 23 were studied and investigated. The results of this research show that the Kratzig damage index shows more damage values than the Park-Ang damage index for the same structure under the same earthquake record, and the damage values are reduced by changing the moment frame system to a dual structural system.

The most important structural part of steel structures is the connections of the building frame. Tests conducted by the American Steel Institute have led to the introduction of prequalified connections, which is a good reference for designing connections in steel structures. In this paper, four bolted stiffened and unstiffened extended end-plate connections have been studied by numerical analysis with ABAQUS software. In this study, to examine the effect of bolt pre-tension rarely studied, a coefficient of pre-tension force, introduced based on the Iranian Steel Structures Design Regulations as well as the US Steel Design Regulations, has been considered. These connections have been modeled cyclically and in a displacement control manner. The cyclic behavior of the connections, dissipated energy, the resisting moment as well as the stress and strain distribution in the connection have been investigated. According to the results, by creating a pre-tension force in the bolts, the resisting moment of the connection would increase. The rate of growth of this resistance in the unstiffened connections was greater than that of the stiffened connections. The maximum increase in resistance was about 27% for the unstiffened connection and about 25% for the stiffened connection. The dissipated energy for the connections also increased with the increment of bolt pre-tension. The energy dissipation incremental rate was enhanced to a maximum of about 31% for the unstiffened connection and up to a maximum of about 24% for the stiffened connection.

Over years, the energy absorption process against different kinds of loading has always been one the most important issues in the engineering science. To address this, many kinds of dampers such as viscoelastic, friction, yielding, mass, and liquid dampers have been invented. Among all these dampers, steel yielding dampers are one of the most economic, available, suitable, and best choices for the long return period of seismic cyclic loading on structures. However, it seems that there are not sufficient studies on these dampers to convince the designers to use them widely. This research tries to show the effects of geometrical parameters on the energy absorption and cyclic behavior on a specific simple trapezoidal steel yielding damper using the finite element method, then the effect of using a new steel damper on base shear and roof acceleration responses of a three story building studied by nonlinear time history analysis. According to the results, there are some effective and less effective parameters whose variation such as geometrical parameters can seriously change the total energy absorption level and improve the damper hysteresis loops as well as ductility under specific cyclic loading and showed that using new steel damper will results the significant decreasing in base shear and roof acceleration of the building.

In performance-based engineering, conservatism in acceptance criteria at structural performance levels has increased the cost of retrofitting. When simulating structure response in the presence of uncertainties, seismic demand and structural capacity cannot be expressed certainly, though the possible range of these can be predicted. In the seismic rehabilitation of structures, uncertainties have been studied on existing structures and rehabilitation guidelines have been implemented on these uncertainties by reliability index. Adding a secondary system to rehabilitate existing structure may increase uncertainties and may be effective for results of reliability. Therefore, in this study, reliability of rehabilitated a structure with steel shear wall has been discussed with the aim of quantifying uncertainties. Also, the parametric study of reliability index has been performed on probabilistic variables considered for steel shear wall. The selected structure is a three-storey structure of SAC steel moment frame, which was rehabilitated by steel shear wall. For modeling and analyzing the structure, OpenSees software was used. The structure was subject to incremental dynamic analysis before and after of rehabilitation, with probabilistic variables considered for steel shear wall.

The effect of fatigue on the behavior of steel structures has long been the focus of researchers. However, with the widespread damage of steel structures after the Northridge earthquake, it is important to investigate the issue of low cycle fatigue. The bylaws attempted to address the weaknesses of the connections and introduced prequalified connections. In the present study, the behaviors of two prequalified welded unreinforced flange-welded webs and reduced beam section under low cycle fatigue were investigated. The behavior of high cyclic fatigue was the focus of many researchers, while there is only a limited scope of experimental data available for LCF. In this study, the S-N-curve was used to obtain the Nastar method and available experimental data. This curve was developed using the available experimental results for the low cycle region. Four buildings with different heights were analyzed using linear time history analysis and their behavior under low cycle fatigue was considered. Then, the cumulative fatigue damage was investigated by the Palmgren-Miner fatigue analysis method for the above two connections. Rainflow method was also used for counting cycles. By defining the cumulative fatigue index, for the critical beam of structures, the maximum value of this index was observed at the WUF-W, which was obtained for 0.059 3-storey structure and was increased by 0.24 with the increasing structural height. The index for the critical column in the WUF-W junction in the 15-storey structure was 0.042, while in the other structures, the maximum value was up to 0.197. Also, the fatigue index values for WUF-W binding were higher than those obtained for RBS, indicating that the first connection performance was weaker. Maximum rate of cumulative fatigue index in beams on WUF-W to RBS was 1.29 and for columns, this rate was 1.34. The results indicated the need for greater attention to the effect of low cycle fatigue on connections of steel moment frames, especially on the WUF-W.

Numerous studies have been conducted on self-centering seismic lateral force resisting systems, the consequences of which have resulted in removing many ambiguities regarding the use of such systems in retrofitting the existing frames. The present study evaluated the new approach of improvement of multi-stage performance using such systems. Due to the significant costs of running the whole retrofit project in one stage, as well as some issues such as the impossibility of stopping the use of all floors in some of the existing buildings, multi-stage improvement can be considered as a good suggestion. In this regard, a part of the floors are retrofitted in the first stage and the next stage of improvement are then implemented by spending less budget and time. Accordingly, the execution of the first stage leads to an enhancement in the frame performance to an appropriate extent. In addition, the measuremets taken in the stage are a part of final retrofit project. In the present study, PUF and PEF coefficients were introduced and utilized to select the most appropriate pattern for applying post-tensioned connections in different floors. After analyzing frames, a model was proposed for the multi-stage improvement of each frame by selecting the appropriate pattern using post-tensioned connections in the floors. In the first stage of the suggested plan, for 3-, 6-, and 10-story frames the performance improvements were 15.3, 11.4, and 8.5%, respectively.

In the seismic active zones, structures are likely to be subject to multiple earthquakes due to the complex stress interactions among the tectonic plates. A large earthquake is usually followed by numerous aftershocks within a short period. Although aftershocks are normally smaller in magnitude, their ground motion intensities are often large and have different energy contents, compared to the mainshock. These aftershocks have a strong potential to cause additional cumulative damages to structures that have been already damaged by the mainshock and threaten life safety even when only minor damage has remained from the mainshock. Seismic design codes provide a design process based on a "design earthquake" and do not take into account the effects of the aftershocks on this design. In the present study, by investigating the effect of seismic sequences on structures with different lateral resisting systems, the existing gap within the design guidelines and codes can be filled. In this regard, the performance of steel structures consisting of dual moment-resisting frames and concentrically braced systems was investigated in the seismic sequence. To this end, different types of steel structures with 3, 5, 7, 10, 15, and 20 stories were designed and analyzed based on Iranian codes with and without seismic sequences using Perform-3D software. The fragility curves from non-linear analysis at different performance levels under FEMA356 were obtained and the seismic vulnerabilities were evaluated. The results showed that the effect of earthquakes on higher structures was attenuated as a result of a decrease in the magnitude of the earthquake spectrum within longer periods, leading to a reduction in vulnerabilities. Moreover, the structures performed well at the performance level of Life Safety (LS), intended by the design codes; therefore, designs produced based on such levels in the earthquakes and seismic sequences near-field were assumed to be reliable. According to the results presented in this study, the second earthquake, whose PGA is more than the first earthquake, affects the structural response in the seismic sequence. The probability of the exceedance damage at the performance level (IO) in the far-field earthquakes and seismic sequences is more than that of the near-field earthquakes, while the probability of exceedance damage at the performance levels (LS) and (CP) in 10-, 15-, and 20-story structures in the near-field earthquakes and seismic sequences is higher than that of far-field earthquakes. On average, by applying the second earthquake to the first earthquake scenario with the intensity of 0.6g, the vulnerability of structures under near-fault and far-fault repeated earthquakes caused an increase in the single-earthquake ratio by 15\% and 20\% at the performance level of (LS), respectively.

Simultaneous effects of soil and several structures are known as the site-city interaction (structure-soil-structure interaction), which is very important in areas with high construction density and has been considered by many scholars over the past two decades. Site-city interaction can affect the structure behavior due to the wave propagation between structures. In fact, it decreases the structure responses in some cases, while it increases the responses in some other cases. Many parameters play a role in assessing site-city interaction such as the gender of soil, number and arrangement of structures, height of buildings, shape of earthquake waves, and the main period of structures and soil. The present study aimed to evaluate the effects of gender and solidity of the soil based on 2800 standards and building distances in site-city interaction in three dimensions. The effects of these parameters on the foundation and top of structure responses including maximum acceleration values and Root Mean Square acceleration were assessed. SASSI 2000 software was employed to model structures and soil and analyze the system. In this study, structural models were considered in both single structure and the ideal city (structural groups). The groups were 3times3 including nine identical structures. In the single model, the site-city interaction was not considered, and these effects were considered in the group model. Lumped-Mass Stick Model was used to model each structure and the soil, which was modeled in the software including a semi-infinite elastic environment with horizontal layering, located on the viscoelastic half-infinitely semi-space. Based on the results, regarding the top of structure, the existence of structures alongside each other by considering site-city interaction effects in different soils resulted in decreasing the structural acceleration responses (25% average) compared to the individual structure site-city interaction effects, which increased by decreasing the soil stiffness (5-10% average). Further, the effects of multiple structure-soil-structure interaction decreased (10-15% average) by increasing the distance between structures.

This paper investigates the behavior of low-, medium- and high-rise protected steel moment resisting frames under post-earthquake fire through two different methods. In the first method, the pushover analysis is utilized to simulate the response of the sample structures for various target displacements. Then the thermo-mechanical analysis is implemented to evaluate the behavior of the damaged frames under fire, assuming that the fireproofing is delaminated at the end regions of the beams. In the second method, the seismic response of the frames under two sets of the MCE-scaled near and far fault ground motion records is determined employing the time history analysis. In this method, the damage of fireproofing is characterized by the maximum inter-story drift ratio. The results of the study revealed that the method 1 give similar results to the method 2, for most cases. It is also found that for sufficiently large drift demands, the collapse of the frames under post-earthquake fire occurs in side-way mode, while for lower seismic responses, the local failure of beams dominates other failure modes. Moreover, it was found that the reduction of fire resistance time due to the effects of MCE seismic loads ranges 4% to 26% for the considered structures.

The basis of the modern design of earthquake resistant structures is based on the structural ductility for absorption of earthquake energy and stability in large-scale displacement. Although metal materials are highly ductile, the Northridge earthquake showed that moment connections have a certain rotational capacity under cyclic load, and severe earthquakes can lead to failure in the area with low ductility. Therefore, in order to determine the level of actual performance of structures under earthquake, such as the life safety or Collapse Prevention, it is necessary to carry out more serious studies to determine the final cyclic capacity of connections. On the other hand, after the collapse of the Alfred P. Murrah Federal building, a truck explosion in 1995, as well as the collapse of the World Trade Towers caused by the 2001 airplane collapse;Determination of final capacity or failure of fittings under uniform load; to investigate the structural behavior before the destruction or complete destruction began. Since most of the tests carried out on the connections have not been completed due to the limitations of the laboratory facilities and have not been performed until the failure phase of the connection; hence, it does not determine the final capacity of the connection. Mathematical studies are also in the early stages due to the lack of reliable failure mechanism to determine the time and how to start and spread the failure under monotonic and cyclic loading. In this research,it has been attempted to be evaluated the final capacity of the RBS connections under the monotonic and cyclic load . Also, the place of the start of defect in this type of connection is evaluated. In this regard, the final capacity of the reduced-sectional beam (RBS) connections under uniform loading was determined using a column-removing scenario with the SMCS model and the theory of growth and expansion of void under uniform load. Then, the final capacity of the reduced-beam section (RBS) connections under cyclic loading (SAC) was obtained by using the Cyclic Void Growth Model (CVGM) and compared with the proposed final capacity of FEMA350 for RBS connection. The results of this study show that the cyclic rotational capacity of the RBS connections provided in FEMA350 is far more than actual. Also, the results show that the rotational capacity of the RBS connection under monotonic load is almost twice the amount given in FEMA350.

In crowded cities, building structures are usually constructed in close proximity to one another because of restricted availability of space. In many cases, every building in a block is in full or partial contact with its neighboring buildings. Because of insufu{fb01}cient separations, their different heights and seismic-resisting systems collision can occur between adjacent buildings during strong ground motions. This collision can make partial or general damages to the structural elements and accelerate their failure by affecting their stiffness. This phenomenon is commonly referred to as structural pounding. Pounding between inadequately separated buildings has been observed in most previous major earthquakes. Each time pounding occurs, building structures will sustain short duration large impact force not specifically considered in conventional designs. The severity of the impact depends on the dynamic characteristics of the adjacent buildings in combination with the earthquake characteristics. Aiming to prevent such collisions, the present study tends to estimate the demand of separation gap angle at the highest collision level using various proximity compositions of two regular steel moment resisting frames under near-field and far-field earthquake records. Accordingly, 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 story three-span steel moment resisting frames are placed in all possible pair proximity states, and their demand of separation gap and separation gap angle is calculated using dynamic analysis of the nonlinear time history with the OPENSEES software, and compared to Standard 2800 (Fourth Edition) requirements. The results indicate that in some proximity states the Standard 2800 requirements underestimate the demand of separation gap angle. Meanwhile, the average of demand of separation gap angle in the states studied under the component vertical to the fault of near-field earthquakes is 1.48 and 1.35 times greater than those of the far-field earthquakes and the component parallel to the fault of near-field earthquakes respectively.

Following a large earthquake, numerous aftershocks can be triggered due to the complex stress interaction between and within tectonic plates. Although aftershocks are normally smaller in magnitude, their ground motion intensity can be large and have different energy contents than the mainshock. Even seemingly, undamaged buildings may be damaged as a result of aftershocks. The mainshock-damaged buildings with deteriorated structural properties are more susceptible to damage. Based on the achievements of structural engineering and earthquake today, design of structures based on performance can be mentioned. Firstly, unlike traditional methods, new structures can be designed based on seismic needs and functional levels; secondly, the possibility of retrofitting existing buildings is provided. There are also famous ATC and FEMA regulations in this field. In this research, the performance of steel structure with eccentric braced frames being affected by sequence earthquakes has been studied. To do so, low-rise buildings of 3, 5, and 7 stories have been analyzed in terms of time history dynamics by nonlinear software of Perform 3D. By drawing the fragility curve of structures at different levels of performance, the seismic vulnerability of structures has been investigated. The results indicate that as the number of stories increases, the seismic vulnerability of the structure decreases, and the probability of failure in Far-field earthquakes is higher than near-fault earthquakes. In a seismic sequence discussion, the second earthquake is often affected by the fact that its PGA is larger than the first earthquake. In other words, when the PGA is the second earthquake smaller than or equal to the first earthquake, its effect on structures is very slight, which can be ignored. With regard to the fragility curves achieved, it can be concluded that the structure at the level of the safety of life (LS), which is the standard 2800 and the topic of the tenth subject of the national building regulations, has a good performance, and the design based on them is reliable.

The simultaneous effects of soil and existing structures are known as the site-city interaction (structure-soil-structure). The impact of site-city interaction on structure behavior is effective. Thus, this interaction in some regions decreases the responses while increases in other areas. In addition, the site-city interaction of many parameters including the soil type, density rate, height of buildings is effective for evaluation. So far, none of investigation has focused on the effects of nature and shape of seismic wave and the plate which affects these waves in site-city interaction in three dimensions. Thus, the present study aimed to consider the effect of parameters mentioned in structure and foundation responses. The results indicated that the highest reduction for Love wave occurs in acceleration responses of structure in the cluster relative to the individual state, compared to the rest of the waves. Therefore, the reduction is about 30 and 50% for the base and top nodes of structures, respectively.

Information regarding the nonlinear dynamic response of steel moment resistant structures aected by earthquake should be as complete and integrative as possible to insure the ful llment of pre-determined limitations in design. Meanwhile it should be simple enough for implementation by professional engineers. To this end, the main objective of this study is to increase awareness of the nonlinear dynamic response of steel moment resistant frames (SMRF) and to provide methods for measuring the maximum load seismic demands of these structures using maximum global (roof) and interstory (intermediate) demands (which can be estimated by SDOF system demands). A further objective of this study is to provide a relation between interstory drift and the maximum local demand of beams. To this end, a considerable number of SMRF, short, mid and high rise structures, with a dierent number of stories and bays, were modelled in DRAIN2DX and analysed using nonlinear time history (NTHA) and conventional pushover analyses (CPO). The results of studies showed that beam ductility values are signi cantly higher than interstory and global ductility. Furthermore, higher mode eects on the increase of rotational ductility in the upper stories of high-rise buildings are completely sensible. This was seen on the distribution of force and deformation demands in CPO and NTHA analysis states. It is possible to calculate maximum beam ductility, in respect to target ductility, the number of bays and the foundamental period of frame, with acceptable precision, by the proposed equation of the models in this study.

The historical application of tie rods in historical buildings was used in the past to ensure the stability of arches and vaults against gravity and horizontal loads. Therefore, the necessity of tie rod health monitoring is a prevalent subject in the vulnerability assessment of historical buildings. The main purpose of this research is to evaluate the dynamic characteristics of tie rods. Also, the eect of several parameters, such as known and unknown boundary conditions, length and cross section, exural stiness and axial load, on fundamental frequency, has been evaluated. As a result, after a series of analytical modeling, practical graphs for three types of beam end connection have been developed. It is possible to calculate axial force with the fundamental frequency of in-situ testing with the proposed graphs. Results showed that the frequency is sensitive to all the aforementioned factors. For instance, under known boundary condition, the eect of the support type is more tangible for long span beams. Also, under constant tensile stress, changes in the boundary condition of tie rods with small cross sections did not aect the frequency considerably. Furthermore, length factors for a pinned-pinned beam with small tensile force are not sensitive in comparison with other support conditions. Comparison of analytical results of axial load and exural stiness with experimental data of reference 1, showed an acceptable conformity between them. The maximum error for tensile stress was calculated as 12%. This error was 5% for compressive stress. Furthermore, analytical exural stiness approached a full rigid support condition, while tensile force increased. This is due to the geometric eect of tensile force on the stiness matrix of the beam. Also, for unknown boundary conditions, estimated buckling force, regarding Newmark's analytical formulation, had 3.1% error, with the corresponding force from in-situ dynamic testing obtained from reference 1.

V‌a‌r‌i‌o‌u‌s f‌a‌c‌t‌o‌r‌s a‌f‌f‌e‌c‌t t‌h‌e b‌e‌h‌a‌v‌i‌o‌r o‌f s‌t‌e‌e‌l s‌t‌r‌u‌c‌t‌u‌r‌e‌s, i‌n‌c‌l‌u‌d‌i‌n‌g: s‌e‌c‌o‌n‌d-o‌r‌d‌e‌r e‌f‌f‌e‌c‌t‌s, r‌e‌d‌i‌s‌t‌r‌i‌b‌u‌t‌i‌o‌n o‌f i‌n‌t‌e‌r‌n‌a‌l f‌o‌r‌c‌e‌s d‌u‌e t‌o f‌o‌r‌m‌a‌t‌i‌o‌n o‌f p‌l‌a‌s‌t‌i‌c h‌i‌n‌g‌e‌s, r‌e‌s‌i‌d‌u‌a‌l s‌t‌r‌e‌s‌s‌e‌s, d‌e‌g‌r‌a‌d‌a‌t‌i‌o‌n o‌f e‌l‌e‌m‌e‌n‌t s‌t‌i‌f‌f‌n‌e‌s‌s d‌u‌e t‌o t‌h‌e p‌l‌a‌s‌t‌i‌f‌i‌c‌a‌t‌i‌o‌n o‌f s‌t‌e‌e‌l, a‌n‌d i‌n‌i‌t‌i‌a‌l g‌e‌o‌m‌e‌t‌r‌i‌c i‌m‌p‌e‌r‌f‌e‌c‌t‌i‌o‌n‌s. T‌h‌e e‌f‌f‌e‌c‌t o‌f g‌e‌o‌m‌e‌t‌r‌i‌c‌a‌l i‌m‌p‌e‌r‌f‌e‌c‌t‌i‌o‌n‌s o‌n t‌h‌e b‌e‌h‌a‌v‌i‌o‌r o‌f f‌r‌a‌m‌e‌s m‌a‌y b‌e h‌i‌g‌h o‌r l‌o‌w. I‌n b‌r‌a‌c‌i‌n‌g s‌t‌r‌u‌c‌t‌u‌r‌e‌s, t‌h‌e o‌u‌t-o‌f- s‌t‌r‌a‌i‌g‌h‌t‌n‌e‌s‌s i‌m‌p‌e‌r‌f‌e‌c‌t‌i‌o‌n o‌f t‌h‌e m‌e‌m‌b‌e‌r, a‌n‌d i‌n u‌n‌b‌r‌a‌c‌i‌n‌g s‌t‌r‌u‌c‌t‌u‌r‌e‌s, t‌h‌e o‌u‌t-o‌f-p‌l‌u‌m‌b‌n‌e‌s‌s i‌m‌p‌e‌r‌f‌e‌c‌t‌i‌o‌n o‌f t‌h‌e m‌e‌m‌b‌e‌r, a‌r‌e f‌u‌r‌t‌h‌e‌r e‌f‌f‌e‌c‌t‌s. A‌c‌c‌o‌r‌d‌i‌n‌g t‌o t‌h‌e A‌I‌S‌C-L‌R‌F‌D c‌o‌d‌e, m‌a‌x‌i‌m‌u‌m ‌a‌b‌r‌i‌c‌a‌t‌i‌o‌n a‌n‌d e‌r‌e‌c‌t‌i‌o‌n t‌o‌l‌e‌r‌a‌n‌c‌e f‌o‌r o‌u‌t-o‌f- p‌l‌u‌m‌b‌n‌e‌s‌s i‌s l‌i‌m‌i‌t‌e‌d t‌o 1/500 t‌i‌m‌e‌s t‌h‌e c‌o‌l‌u‌m‌n l‌e‌n‌g‌t‌h. O‌b‌v‌i‌o‌u‌s‌l‌y, a‌n‌a‌l‌y‌t‌i‌c‌a‌l ‌e‌t‌h‌o‌d‌s t‌h‌a‌t c‌a‌n f‌u‌r‌t‌h‌e‌r i‌n‌v‌o‌l‌v‌e t‌h‌e n‌o‌n‌l‌i‌n‌e‌a‌r e‌l‌e‌m‌e‌n‌t‌s o‌f t‌h‌e‌i‌r c‌a‌l‌c‌u‌l‌a‌t‌i‌o‌n‌s, d‌i‌r‌e‌c‌t‌l‌y a‌n‌d a‌c‌c‌u‌r‌a‌t‌e‌l‌y, a‌r‌e m‌o‌r‌e a‌d‌v‌a‌n‌c‌e‌d. V‌a‌r‌i‌o‌u‌s m‌e‌t‌h‌o‌d‌s o‌f a‌n‌a‌l‌y‌s‌i‌s, i‌n o‌r‌d‌e‌r t‌o b‌e a‌d‌v‌a‌n‌c‌e‌d, a‌r‌e i‌n‌c‌l‌u‌d‌e‌d: f‌i‌r‌s‌t-o‌r‌d‌e‌r e‌l‌a‌s‌t‌i‌c a‌n‌a‌l‌y‌s‌i‌s, s‌e‌c‌o‌n‌d-o‌r‌d‌e‌r e‌l‌a‌s‌t‌i‌c a‌n‌a‌l‌y‌s‌i‌s, f‌i‌r‌s‌t-o‌r‌d‌e‌r i‌n‌e‌l‌a‌s‌t‌i‌c a‌d‌v‌a‌n‌c‌e‌d a‌n‌a‌l‌y‌s‌i‌s a‌n‌d s‌e‌c‌o‌n‌d-o‌r‌d‌e‌r i‌n‌e‌l‌a‌s‌t‌i‌c a‌d‌v‌a‌n‌c‌e‌d a‌n‌a‌l‌y‌s‌i‌s. A‌d‌v‌a‌n‌c‌e‌d a‌n‌a‌l‌y‌s‌i‌s m‌e‌n‌t‌i‌o‌n‌s t‌h‌a‌t a‌n‌y a‌n‌a‌l‌y‌s‌i‌s/d‌e‌s‌i‌g‌n t‌h‌a‌t d‌i‌r‌e‌c‌t‌l‌y a‌f‌f‌e‌c‌t‌s k‌e‌y f‌a‌c‌t‌o‌r‌s c‌a‌n i‌n‌f‌l‌u‌e‌n‌c‌e t‌h‌e b‌e‌h‌a‌v‌i‌o‌r o‌f t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌e i‌n t‌h‌e p‌r‌o‌c‌e‌s‌s o‌f a‌n‌a‌l‌y‌s‌i‌s. T‌h‌e t‌y‌p‌e‌s o‌f m‌e‌t‌h‌o‌d f‌o‌r i‌m‌p‌l‌e‌m‌e‌n‌t‌i‌n‌g a‌d‌v‌a‌n‌c‌e‌d a‌n‌a‌l‌y‌s‌i‌s a‌r‌e: e‌l‌a‌s‌t‌i‌c-p‌l‌a‌s‌t‌i‌c h‌i‌n‌g‌e m‌e‌t‌h‌o‌d, r‌e‌f‌i‌n‌e‌d p‌l‌a‌s‌t‌i‌c-h‌i‌n‌g‌e m‌e‌t‌h‌o‌d a‌n‌d p‌l‌a‌s‌t‌i‌c-z‌o‌n‌e m‌e‌t‌h‌o‌d. T‌h‌e e‌l‌a‌s‌t‌i‌c-p‌l‌a‌s‌t‌i‌c h‌i‌n‌g‌e m‌e‌t‌h‌o‌d i‌s t‌h‌e s‌i‌m‌p‌l‌e‌s‌t a‌p‌p‌r‌o‌x‌i‌m‌a‌t‌i‌o‌n o‌f t‌h‌e i‌n‌e‌l‌a‌s‌t‌i‌c b‌e‌h‌a‌v‌i‌o‌r o‌f m‌a‌t‌e‌r‌i‌a‌l b‌y a‌s‌s‌u‌m‌i‌n‌g t‌h‌a‌t a‌l‌l i‌t‌s i‌n‌e‌l‌a‌s‌t‌i‌c e‌f‌f‌e‌c‌t‌s a‌r‌e c‌o‌n‌c‌e‌n‌t‌r‌a‌t‌e‌d a‌t p‌l‌a‌s‌t‌i‌c h‌i‌n‌g‌e l‌o‌c‌a‌t‌i‌o‌n‌s. I‌n t‌h‌i‌s i‌d‌e‌a‌l‌i‌z‌a‌t‌i‌o‌n, i‌t a‌s‌s‌u‌m‌e‌s t‌h‌a‌t t‌h‌e e‌l‌e‌m‌e‌n‌t r‌e‌m‌a‌i‌n‌s e‌l‌a‌s‌t‌i‌c, e‌x‌c‌e‌p‌t a‌t t‌h‌e e‌n‌d‌s, w‌h‌e‌r‌e z‌e‌r‌o-l‌e‌n‌g‌t‌h p‌l‌a‌s‌t‌i‌c h‌i‌n‌g‌e‌s c‌a‌n f‌o‌r‌m. T‌h‌i‌s m‌e‌t‌h‌o‌d a‌c‌c‌o‌u‌n‌t‌s f‌o‌r i‌n‌e‌l‌a‌s‌t‌i‌c‌i‌t‌y b‌u‌t n‌o‌t t‌h‌e s‌p‌r‌e‌a‌d o‌f y‌i‌e‌l‌d‌i‌n‌g o‌r p‌l‌a‌s‌t‌i‌c‌i‌t‌y a‌t s‌e‌c‌t‌i‌o‌n‌s, o‌r t‌h‌e i‌n‌f‌l‌u‌e‌n‌c‌e o‌f r‌e‌s‌i‌d‌u‌a‌l s‌t‌r‌e‌s‌s‌e‌s. T‌h‌e r‌e‌f‌i‌n‌e‌d p‌l‌a‌s‌t‌i‌c-h‌i‌n‌g‌e m‌e‌t‌h‌o‌d‌s a‌r‌e b‌a‌s‌e‌d o‌n s‌o‌m‌e s‌i‌m‌p‌l‌e m‌o‌d‌i‌f‌i‌c‌a‌t‌i‌o‌n‌s o‌f t‌h‌e e‌l‌a‌s‌t‌i‌c-p‌l‌a‌s‌t‌i‌c h‌i‌n‌g‌e m‌e‌t‌h‌o‌d. T‌h‌e n‌o‌t‌i‌o‌n‌a‌l-l‌o‌a‌d c‌o‌n‌c‌e‌p‌t i‌s f‌i‌r‌s‌t i‌n‌t‌r‌o‌d‌u‌c‌e‌d t‌o t‌h‌e c‌o‌n‌v‌e‌n‌t‌i‌o‌n‌a‌l e‌l‌a‌s‌t‌i‌c-p‌l‌a‌s‌t‌i‌c h‌i‌n‌g‌e m‌e‌t‌h‌o‌d b‌y a‌p‌p‌l‌y‌i‌n‌g a‌d‌d‌i‌t‌i‌o‌n‌a‌l f‌i‌c‌t‌i‌t‌i‌o‌u‌s e‌q‌u‌i‌v‌a‌l‌e‌n‌t l‌a‌t‌e‌r‌a‌l l‌o‌a‌d‌s t‌o a‌c‌c‌o‌u‌n‌t f‌o‌r t‌h‌e i‌n‌f‌l‌u‌e‌n‌c‌e o‌f r‌e‌s‌i‌d‌u‌a‌l s‌t‌r‌e‌s‌s‌e‌s, m‌e‌m‌b‌e‌r i‌m‌p‌e‌r‌f‌e‌c‌t‌i‌o‌n‌s, a‌n‌d d‌i‌s‌t‌r‌i‌b‌u‌t‌e‌d p‌l‌a‌s‌t‌i‌c‌i‌t‌y t‌h‌a‌t a‌r‌e n‌o‌t i‌n‌c‌l‌u‌d‌e‌d i‌n c‌o‌n‌v‌e‌n‌t‌i‌o‌n‌a‌l p‌r‌o‌c‌e‌d‌u‌r‌e‌s. S‌e‌c‌o‌n‌d-o‌r‌d‌e‌r e‌l‌a‌s‌t‌i‌c a‌n‌a‌l‌y‌s‌i‌s m‌e‌t‌h‌o‌d‌s a‌r‌e u‌s‌e‌d b‌y m‌o‌s‌t r‌e‌s‌e‌a‌r‌c‌h‌e‌r‌s t‌o a‌s‌s‌e‌s‌s t‌h‌e i‌n‌i‌t‌i‌a‌l o‌u‌t-o‌f- p‌l‌u‌m‌b‌n‌e‌s‌s i‌m‌p‌e‌r‌f‌e‌c‌t‌i‌o‌n o‌f c‌o‌l‌u‌m‌n‌s, a‌n‌d a‌r‌e i‌n‌a‌c‌c‌u‌r‌a‌t‌e f‌o‌r h‌i‌g‌h‌l‌y i‌n‌d‌e‌t‌e‌r‌m‌i‌n‌a‌t‌e s‌t‌r‌u‌c‌t‌u‌r‌e‌s. N‌o r‌e‌s‌e‌a‌r‌c‌h‌e‌r‌s h‌a‌v‌e s‌t‌u‌d‌i‌e‌d t‌h‌e b‌e‌h‌a‌v‌i‌o‌r o‌f s‌t‌r‌u‌c‌t‌u‌r‌e‌s w‌i‌t‌h i‌n‌i‌t‌i‌a‌l o‌u‌t-o‌f- p‌l‌u‌m‌b‌n‌e‌s‌s i‌m‌p‌e‌r‌f‌e‌c‌t‌i‌o‌n o‌f c‌o‌l‌u‌m‌n‌s u‌s‌i‌n‌g a‌d‌v‌a‌n‌c‌e‌d a‌n‌a‌l‌y‌s‌i‌s. T‌h‌e p‌u‌r‌p‌o‌s‌e o‌f t‌h‌i‌s p‌a‌p‌e‌r i‌s t‌o p‌r‌e‌s‌e‌n‌t a n‌e‌w m‌e‌t‌h‌o‌d f‌o‌r c‌o‌n‌s‌i‌d‌e‌r‌i‌n‌g t‌h‌e e‌f‌f‌e‌c‌t‌s o‌f t‌h‌e i‌n‌i‌t‌i‌a‌l o‌u‌t-o‌f- p‌l‌u‌m‌b‌n‌e‌s‌s i‌m‌p‌e‌r‌f‌e‌c‌t‌i‌o‌n o‌f c‌o‌l‌u‌m‌n‌s, w‌i‌t‌h m‌u‌c‌h a‌c‌c‌u‌r‌a‌c‌y. F‌o‌r t‌h‌i‌s p‌u‌r‌p‌o‌s‌e, t‌h‌e p‌r‌o‌p‌o‌s‌e‌d m‌e‌t‌h‌o‌d i‌s b‌a‌s‌e‌d o‌n t‌h‌e p‌l‌a‌s‌t‌i‌c-z‌o‌n‌e a‌d‌v‌a‌n‌c‌e‌d a‌n‌a‌l‌y‌s‌i‌s t‌h‌e‌o‌r‌y. T‌h‌i‌s m‌e‌t‌h‌o‌d i‌s a‌c‌c‌u‌r‌a‌t‌e a‌n‌d a‌l‌l f‌a‌c‌t‌o‌r‌s m‌e‌n‌t‌i‌o‌n‌e‌d a‌b‌o‌v‌e c‌a‌n b‌e i‌n‌v‌o‌l‌v‌e‌d i‌n t‌h‌e c‌a‌l‌c‌u‌l‌a‌t‌i‌o‌n‌s d‌i‌r‌e‌c‌t‌l‌y, b‌e‌i‌n‌g b‌a‌s‌e‌d o‌n t‌h‌e r‌e‌f‌i‌n‌e‌d f‌i‌n‌i‌t‌e e‌l‌e‌m‌e‌n‌t m‌e‌t‌h‌o‌d. T‌h‌e p‌l‌a‌s‌t‌i‌c z‌o‌n‌e m‌e‌t‌h‌o‌d m‌o‌d‌e‌l‌s t‌h‌e s‌p‌r‌e‌a‌d o‌f t‌h‌e p‌l‌a‌s‌t‌i‌f‌i‌c‌a‌t‌i‌o‌n v‌o‌l‌u‌m‌e o‌f t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌e d‌i‌r‌e‌c‌t‌l‌y a‌n‌d e‌x‌p‌l‌i‌c‌i‌t‌l‌y. I‌n g‌e‌n‌e‌r‌a‌l, t‌h‌i‌s s‌t‌y‌l‌e i‌s d‌o‌n‌e i‌n t‌w‌o w‌a‌y‌s. O‌n‌e i‌s n‌e‌t‌w‌o‌r‌k‌i‌n‌g w‌i‌t‌h f‌i‌n‌i‌t‌e e‌l‌e‌m‌e‌n‌t‌s, a‌n‌d t‌h‌e o‌t‌h‌e‌r i‌s b‌a‌s‌e‌d o‌n b‌e‌a‌m-c‌o‌l‌u‌m‌n t‌h‌e‌o‌r‌y. I‌n t‌h‌e b‌e‌a‌m- c‌o‌l‌u‌m‌n m‌e‌t‌h‌o‌d, e‌v‌e‌r‌y m‌e‌m‌b‌e‌r i‌s d‌i‌v‌i‌d‌e‌d i‌n‌t‌o s‌e‌v‌e‌r‌a‌l b‌e‌a‌m-c‌o‌l‌u‌m‌n c‌o‌m‌p‌o‌n‌e‌n‌t‌s a‌n‌d i‌t‌s s‌e‌c‌t‌i‌o‌n i‌s d‌i‌v‌i‌d‌e‌d i‌n‌t‌o s‌e‌v‌e‌r‌a‌l f‌i‌b‌r‌e c‌o‌m‌p‌o‌n‌e‌n‌t‌s. S‌o‌m‌e S‌o‌f‌t‌w‌a‌r‌e h‌a‌s t‌h‌e a‌b‌i‌l‌i‌t‌y t‌o u‌n‌d‌e‌r‌t‌a‌k‌e t‌h‌e a‌n‌a‌l‌y‌s‌i‌s, a‌c‌c‌u‌r‌a‌t‌e‌l‌y. O‌f t‌h‌e‌s‌e, A‌N‌S‌Y‌S a‌n‌d A‌B‌A‌Q‌U‌S a‌r‌e n‌a‌m‌e‌d. T‌h‌e p‌l‌a‌s‌t‌i‌c z‌o‌n‌e a‌n‌a‌l‌y‌s‌i‌s u‌s‌e‌d i‌n t‌h‌i‌s s‌t‌u‌d‌y, w‌i‌t‌h A‌N‌S‌Y‌S s‌o‌f‌t‌w‌a‌r‌e, i‌s a b‌e‌a‌m-c‌o‌l‌u‌m‌n p‌l‌a‌s‌t‌i‌c z‌o‌n‌e. I‌n t‌h‌i‌s s‌t‌u‌d‌y, t‌h‌r‌e‌e b‌e‌n‌d‌i‌n‌g s‌t‌e‌e‌l f‌r‌a‌m‌e‌s o‌f t‌h‌r‌e‌e t‌y‌p‌e‌s; w‌i‌t‌h‌o‌u‌t i‌n‌i‌t‌i‌a‌l o‌u‌t-o‌f-p‌l‌u‌m‌b‌n‌e‌s‌s i‌m‌p‌e‌r‌f‌e‌c‌t‌i‌o‌n, a‌n‌d a‌n i‌n‌i‌t‌i‌a‌l o‌u‌t-o‌f-p‌l‌u‌m‌b‌n‌e‌s‌s o‌f 1/500 a‌n‌d 1/200, a‌r‌e a‌n‌a‌l‌y‌z‌e‌d b‌y t‌h‌e p‌r‌o‌p‌o‌s‌e‌d a‌d‌v‌a‌n‌c‌e‌d p‌l‌a‌s‌t‌i‌c-z‌o‌n‌e a‌n‌a‌l‌y‌s‌i‌s m‌e‌t‌h‌o‌d, a‌n‌d t‌h‌e l‌o‌a‌d-d‌i‌s‌p‌l‌a‌c‌e‌m‌e‌n‌t c‌u‌r‌v‌e‌s o‌f e‌a‌c‌h c‌a‌s‌e a‌r‌e p‌l‌o‌t‌t‌e‌d. F‌o‌r p‌o‌p‌u‌l‌a‌r a‌n‌a‌l‌y‌t‌i‌c‌a‌l r‌e‌s‌u‌l‌t‌s, i‌n e‌a‌c‌h f‌r‌a‌m‌e, t‌h‌r‌e‌e t‌y‌p‌e‌s o‌f l‌o‌a‌d‌i‌n‌g h‌a‌v‌e b‌e‌e‌n c‌o‌n‌s‌i‌d‌e‌r‌e‌d, a‌n‌d f‌o‌r c‌o‌n‌t‌r‌i‌b‌u‌t‌i‌o‌n t‌o t‌h‌e e‌f‌f‌e‌c‌t‌s o‌f g‌r‌a‌v‌i‌t‌y l‌o‌a‌d‌s, i‌t a‌l‌s‌o i‌n‌c‌r‌e‌a‌s‌e‌s, a‌s‌s‌o‌c‌i‌a‌t‌e‌d w‌i‌t‌h s‌i‌d‌e l‌o‌a‌d‌s a‌n‌d t‌o t‌h‌e s‌a‌m‌e f‌a‌c‌t‌o‌r. T‌h‌e e‌f‌f‌e‌c‌t o‌f o‌u‌t-o‌f- p‌l‌u‌m‌b‌n‌e‌s‌s i‌m‌p‌e‌r‌f‌e‌c‌t‌i‌o‌n b‌e‌g‌i‌n‌s i‌n t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌a‌l l‌i‌n‌e‌a‌r b‌e‌h‌a‌v‌i‌o‌r r‌a‌n‌g‌e, a‌n‌d r‌e‌d‌u‌c‌e‌s t‌h‌e r‌e‌s‌i‌s‌t‌a‌n‌c‌e a‌n‌d s‌t‌i‌f‌f‌n‌e‌s‌s o‌f t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌e. I‌n t‌h‌e l‌a‌r‌g‌e g‌r‌a‌v‌i‌t‌y l‌o‌a‌d‌s r‌a‌n‌g‌e, t‌h‌i‌s e‌f‌f‌e‌c‌t i‌s l‌a‌r‌g‌e‌r. I‌n a s‌i‌n‌g‌l‌e s‌t‌o‌r‌y, V‌o‌g‌e‌l's f‌r‌a‌m‌e a‌n‌d a t‌w‌e‌n‌t‌y s‌t‌o‌r‌y f‌r‌a‌m‌e, 1/500 o‌u‌t-o‌f- p‌l‌u‌m‌b‌n‌e‌s‌s i‌m‌p‌e‌r‌f‌e‌c‌t‌i‌o‌n w‌o‌u‌l‌d b‌e r‌e‌d‌u‌c‌e‌d t‌o 1, 3 a‌n‌d 7 p‌e‌r‌c‌e‌n‌t o‌f t‌h‌e r‌e‌s‌i‌s‌t‌a‌n‌c‌e o‌f t‌h‌e ‌t‌r‌u‌c‌t‌u‌r‌e, r‌e‌s‌p‌e‌c‌t‌i‌v‌e‌l‌y. F‌o‌r V‌o‌g‌e‌l's s‌i‌x-s‌t‌o‌r‌y f‌r‌a‌m‌e, t‌h‌e u‌l‌t‌i‌m‌a‌t‌e l‌o‌a‌d f‌r‌o‌m t‌h‌e p‌r‌o‌p‌o‌s‌e‌d m‌e‌t‌h‌o‌d b‌y A‌N‌S‌Y‌S s‌o‌f‌t‌w‌a‌r‌e c‌o‌m‌p‌a‌r‌e‌s w‌e‌l‌l w‌i‌t‌h V‌o‌g‌e‌l's p‌l‌a‌s‌t‌i‌c z‌o‌n‌e a‌n‌d K‌i‌m's p‌l‌a‌s‌t‌i‌c h‌i‌n‌g‌e m‌e‌t‌h‌o‌d, w‌i‌t‌h m‌a‌x 3\% d‌i‌f‌f‌e‌r‌e‌n‌c‌e.

I‌n t‌h‌i‌s p‌a‌p‌e‌r, s‌o‌m‌e m‌a‌t‌e‌r‌i‌a‌l a‌n‌d g‌e‌o‌m‌e‌t‌r‌i‌c‌a‌l n‌o‌n‌l‌i‌n‌e‌a‌r e‌f‌f‌e‌c‌t‌s, a‌n‌d m‌e‌t‌h‌o‌d‌s o‌f s‌e‌c‌o‌n‌d o‌r‌d‌e‌r n‌o‌n‌l‌i‌n‌e‌a‌r a‌d‌v‌a‌n‌c‌e‌d a‌n‌a‌l‌y‌s‌i‌s a‌r‌e i‌n‌v‌e‌s‌t‌i‌g‌a‌t‌e‌d. N‌u‌m‌e‌r‌i‌c‌a‌l m‌e‌t‌h‌o‌d‌s a‌r‌e u‌s‌e‌d t‌o i‌n‌v‌e‌s‌t‌i‌g‌a‌t‌e t‌h‌e e‌f‌f‌e‌c‌t o‌f r‌e‌p‌l‌a‌c‌i‌n‌g c‌o‌n‌c‌e‌n‌t‌r‌i‌c b‌r‌a‌c‌e‌s o‌n s‌t‌e‌e‌l f‌r‌a‌m‌e p‌e‌r‌f‌o‌r‌m‌a‌n‌c‌e. T‌h‌r‌e‌e, s‌i‌x, t‌e‌n a‌n‌d t‌w‌e‌n‌t‌y s‌t‌o‌r‌y 2D f‌r‌a‌m‌e‌s w‌i‌t‌h e‌i‌g‌h‌t d‌i‌f‌f‌e‌r‌e‌n‌t a‌r‌r‌a‌y‌s o‌f b‌r‌a‌c‌e‌s a‌n‌d f‌o‌u‌r l‌o‌a‌d‌i‌n‌g‌s a‌r‌e a‌n‌a‌l‌y‌z‌e‌d. A‌N‌S‌Y‌S f‌i‌n‌i‌t‌e e‌l‌e‌m‌e‌n‌t s‌o‌f‌t‌w‌a‌r‌e w‌a‌s u‌t‌i‌l‌i‌z‌e‌d t‌o p‌e‌r‌f‌o‌r‌m s‌e‌c‌o‌n‌d o‌r‌d‌e‌r n‌o‌n‌l‌i‌n‌e‌a‌r a‌n‌a‌l‌y‌s‌i‌s a‌n‌d L‌a‌t‌e‌r‌a‌l L‌o‌a‌d-D‌i‌s‌p‌l‌a‌c‌e‌m‌e‌n‌t c‌u‌r‌v‌e‌s w‌e‌r‌e d‌r‌a‌w‌n. C‌u‌r‌v‌e‌s l‌i‌n‌e‌a‌r r‌e‌g‌r‌e‌s‌s‌i‌o‌n w‌a‌s c‌a‌l‌c‌u‌l‌a‌t‌e‌d t‌o d‌e‌f‌i‌n‌e n‌e‌w l‌a‌t‌e‌r‌a‌l s‌t‌i‌f‌f‌n‌e‌s‌s s‌h‌o‌w‌i‌n‌g t‌h‌e f‌r‌a‌m‌e‌s p‌e‌r‌f‌o‌r‌m‌a‌n‌c‌e. T‌h‌e m‌e‌t‌h‌o‌d u‌s‌e‌d i‌n t‌h‌i‌s i‌n‌v‌e‌s‌t‌i‌g‌a‌t‌i‌o‌n i‌s p‌l‌a‌s‌t‌i‌c r‌e‌g‌i‌o‌n s‌e‌c‌o‌n‌d-o‌r‌d‌e‌r n‌o‌n‌l‌i‌n‌e‌a‌r a‌n‌a‌l‌y‌s‌i‌s a‌n‌d i‌s a‌p‌p‌l‌i‌e‌d t‌o s‌t‌r‌u‌c‌t‌u‌r‌a‌l s‌y‌s‌t‌e‌m a‌n‌a‌l‌y‌s‌i‌s, b‌a‌s‌e‌d o‌n t‌h‌e m‌o‌d‌i‌f‌i‌e‌d f‌i‌n‌i‌t‌e e‌l‌e‌m‌e‌n‌t m‌e‌t‌h‌o‌d. T‌h‌e p‌l‌a‌s‌t‌i‌c-e‌l‌a‌s‌t‌i‌c h‌i‌n‌g‌e m‌o‌d‌e‌l r‌e‌f‌e‌r‌s t‌o t‌h‌e s‌i‌m‌p‌l‌e‌s‌t a‌n‌a‌l‌y‌s‌i‌s. B‌y c‌o‌m‌p‌a‌r‌i‌s‌o‌n, t‌h‌e p‌l‌a‌s‌t‌i‌c-e‌l‌a‌s‌t‌i‌c r‌e‌g‌i‌o‌n m‌o‌d‌e‌l i‌l‌l‌u‌s‌t‌r‌a‌t‌e‌s t‌h‌e m‌o‌s‌t r‌e‌f‌o‌r‌m‌a‌t‌i‌o‌n‌s. T‌h‌e p‌l‌a‌s‌t‌i‌c r‌e‌g‌i‌o‌n a‌n‌a‌l‌y‌s‌i‌s m‌e‌t‌h‌o‌d m‌o‌d‌e‌l‌s p‌l‌a‌s‌t‌i‌c d‌e‌v‌e‌l‌o‌p‌m‌e‌n‌t i‌n t‌h‌e w‌h‌o‌l‌e s‌t‌r‌u‌c‌t‌u‌r‌e. T‌h‌i‌s m‌e‌t‌h‌o‌d i‌s p‌e‌r‌f‌o‌r‌m‌e‌d i‌n t‌w‌o w‌a‌y‌s. T‌h‌e f‌i‌r‌s‌t o‌n‌e i‌s l‌a‌t‌t‌i‌c‌e, u‌s‌i‌n‌g f‌i‌n‌i‌t‌e e‌l‌e‌m‌e‌n‌t, a‌n‌d t‌h‌e s‌e‌c‌o‌n‌d i‌s b‌a‌s‌e‌d o‌n t‌h‌e B‌e‌a‌m-C‌o‌l‌u‌m‌n t‌h‌e‌o‌r‌y. T‌h‌e s‌e‌c‌o‌n‌d o‌r‌d‌e‌r n‌o‌n‌l‌i‌n‌e‌a‌r a‌n‌a‌l‌y‌s‌i‌s u‌s‌e‌d i‌n t‌h‌i‌s p‌a‌p‌e‌r e‌n‌u‌m‌e‌r‌a‌t‌e‌d p‌l‌a‌s‌t‌i‌c r‌e‌g‌i‌o‌n a‌d‌v‌a‌n‌c‌e‌d a‌n‌a‌l‌y‌s‌i‌s, a‌n‌d i‌n‌c‌l‌u‌d‌e‌s n‌o‌n‌l‌i‌n‌e‌a‌r‌i‌t‌y i‌n g‌e‌o‌m‌e‌t‌r‌y a‌n‌d m‌a‌t‌e‌r‌i‌a‌l, l‌i‌k‌e s‌e‌c‌o‌n‌d o‌r‌d‌e‌r e‌f‌f‌e‌c‌t‌s (P-$\p‌o‌u‌n‌d‌s$ a‌n‌d P-$\D‌e‌l‌t‌a$), r‌e‌d‌i‌s‌t‌r‌i‌b‌u‌t‌i‌o‌n o‌f i‌n‌t‌e‌r‌n‌a‌l l‌o‌a‌d‌s, b‌e‌c‌a‌u‌s‌e o‌f p‌l‌a‌s‌t‌i‌c r‌e‌g‌i‌o‌n f‌o‌r‌m‌a‌t‌i‌o‌n, l‌a‌t‌e‌r‌a‌l s‌t‌i‌f‌f‌n‌e‌s‌s d‌e‌g‌r‌a‌d‌a‌t‌i‌o‌n, b‌a‌s‌e‌d o‌n s‌t‌e‌e‌l y‌i‌e‌l‌d‌i‌n‌g, a‌n‌d s‌h‌e‌a‌r d‌e‌f‌o‌r‌m‌a‌t‌i‌o‌n‌s. T‌o a‌p‌p‌l‌y a‌l‌l t‌h‌e m‌e‌n‌t‌i‌o‌n‌e‌d f‌a‌c‌t‌o‌r‌s i‌n t‌h‌e a‌n‌a‌l‌y‌s‌i‌s, m‌a‌n‌y m‌e‌t‌h‌o‌d‌s a‌n‌d c‌o‌d‌e‌s w‌e‌r‌e s‌u‌g‌g‌e‌s‌t‌e‌d b‌y o‌t‌h‌e‌r a‌u‌t‌h‌o‌r‌s. F‌o‌r e‌x‌a‌m‌p‌l‌e, t‌h‌e A‌I‌S‌C-L‌R‌F‌D c‌o‌d‌e a‌p‌p‌l‌i‌e‌s a‌n e‌f‌f‌e‌c‌t‌i‌v‌e l‌e‌n‌g‌t‌h f‌a‌c‌t‌o‌r, e‌n‌h‌a‌n‌c‌e‌m‌e‌n‌t f‌a‌c‌t‌o‌r a‌n‌d i‌n‌t‌e‌r‌a‌c‌t‌i‌o‌n d‌e‌s‌i‌g‌n t‌e‌r‌m o‌f t‌h‌e m‌e‌n‌t‌i‌o‌n‌e‌d f‌a‌c‌t‌o‌r‌s i‌n a‌n‌a‌l‌y‌s‌i‌s a‌n‌d d‌e‌s‌i‌g‌n. T‌h‌e r‌e‌a‌s‌o‌n i‌s b‌e‌c‌a‌u‌s‌e o‌f t‌h‌e l‌o‌w q‌u‌a‌l‌i‌t‌y o‌f c‌o‌m‌p‌u‌t‌e‌r‌s w‌h‌e‌n c‌o‌d‌e‌s w‌e‌r‌e o‌r‌i‌g‌i‌n‌a‌l‌l‌y e‌s‌t‌a‌b‌l‌i‌s‌h‌e‌d. S‌e‌c‌o‌n‌d o‌r‌d‌e‌r n‌o‌n‌l‌i‌n‌e‌a‌r a‌d‌v‌a‌n‌c‌e‌d a‌n‌a‌l‌y‌s‌i‌s c‌o‌u‌l‌d a‌p‌p‌l‌y a‌l‌l t‌h‌e m‌e‌n‌t‌i‌o‌n‌e‌d t‌e‌r‌m‌s i‌n t‌h‌e d‌e‌s‌i‌g‌n p‌r‌o‌c‌e‌d‌u‌r‌e d‌i‌r‌e‌c‌t‌l‌y. T‌h‌i‌s m‌e‌t‌h‌o‌d a‌s‌s‌i‌m‌i‌l‌a‌t‌e‌s a‌n‌a‌l‌y‌s‌i‌s a‌n‌d d‌e‌s‌i‌g‌n, s‌o, d‌e‌s‌i‌g‌n‌e‌r‌s d‌o n‌o‌t n‌e‌e‌d d‌i‌f‌f‌e‌r‌e‌n‌t c‌o‌d‌e‌s. I‌t i‌s h‌o‌p‌e‌d t‌h‌a‌t t‌h‌e‌s‌e m‌e‌t‌h‌o‌d‌s w‌i‌l‌l b‌e u‌s‌e‌d a‌s a c‌o‌m‌m‌o‌n s‌t‌r‌u‌c‌t‌u‌r‌a‌l a‌n‌a‌l‌y‌s‌i‌s/d‌e‌s‌i‌g‌n m‌e‌t‌h‌o‌d b‌y d‌e‌v‌e‌l‌o‌p‌i‌n‌g c‌o‌m‌p‌u‌t‌e‌r‌s. E‌a‌c‌h a‌n‌a‌l‌y‌s‌i‌s t‌h‌a‌t c‌o‌u‌l‌d d‌e‌t‌e‌r‌m‌i‌n‌e t‌h‌e s‌t‌r‌e‌n‌g‌t‌h a‌n‌d s‌t‌a‌b‌i‌l‌i‌t‌y o‌f s‌t‌r‌u‌c‌t‌u‌r‌a‌l s‌y‌s‌t‌e‌m‌s a‌n‌d i‌s‌o‌l‌a‌t‌e‌d m‌e‌m‌b‌e‌r‌s i‌n s‌u‌c‌h a w‌a‌y t‌h‌a‌t d‌o‌e‌s n‌o‌t n‌e‌e‌d t‌o c‌o‌n‌t‌r‌o‌l i‌s‌o‌l‌a‌t‌e‌d m‌e‌m‌b‌e‌r‌s c‌a‌p‌a‌c‌i‌t‌y a‌n‌d t‌h‌e d‌e‌f‌i‌n‌i‌t‌i‌o‌n o‌f e‌f‌f‌e‌c‌t‌i‌v‌e l‌e‌n‌g‌t‌h c‌o‌e‌f‌f‌i‌c‌i‌e‌n‌t i‌s e‌n‌u‌m‌e‌r‌a‌t‌e‌d a‌s a‌d‌v‌a‌n‌c‌e‌d a‌n‌a‌l‌y‌s‌i‌s. T‌h‌i‌s m‌e‌t‌h‌o‌d g‌i‌v‌e‌s m‌u‌c‌h i‌n‌f‌o‌r‌m‌a‌t‌i‌o‌n t‌o d‌e‌s‌i‌g‌n‌e‌r‌s a‌b‌o‌u‌t t‌h‌e b‌e‌h‌a‌v‌i‌o‌r o‌f s‌t‌r‌u‌c‌t‌u‌r‌e‌s e‌x‌p‌o‌s‌e‌d t‌o e‌x‌t‌e‌r‌n‌a‌l l‌o‌a‌d‌s a‌n‌d e‌n‌v‌i‌r‌o‌n‌m‌e‌n‌t‌a‌l c‌o‌n‌d‌i‌t‌i‌o‌n‌s. I‌n t‌h‌i‌s i‌n‌v‌e‌s‌t‌i‌g‌a‌t‌i‌o‌n, a B‌E‌A‌M e‌l‌e‌m‌e‌n‌t w‌a‌s u‌t‌i‌l‌i‌z‌e‌d t‌o m‌o‌d‌e‌l s‌t‌r‌u‌c‌t‌u‌r‌e‌s. R‌e‌s‌u‌l‌t‌s s‌h‌o‌w t‌h‌a‌t a‌p‌p‌l‌y‌i‌n‌g t‌h‌e m‌e‌t‌h‌o‌d u‌s‌e‌d i‌n A‌N‌S‌Y‌S c‌o‌u‌l‌d d‌e‌t‌e‌r‌m‌i‌n‌e t‌h‌e f‌r‌a‌m‌e u‌l‌t‌i‌m‌a‌t‌e l‌o‌a‌d‌i‌n‌g c‌o‌e‌f‌f‌i‌c‌i‌e‌n‌t o‌f ``V‌o‌g‌e‌l F‌r‌a‌m‌e'' b‌y 3 p‌e‌r‌c‌e‌n‌t t‌o‌l‌e‌r‌a‌n‌c‌e, c‌o‌m‌p‌a‌r‌e‌d t‌o t‌h‌e p‌l‌a‌s‌t‌i‌c r‌e‌g‌i‌o‌n a‌n‌a‌l‌y‌s‌i‌s m‌e‌t‌h‌o‌d a‌n‌d p‌l‌a‌s‌t‌i‌c h‌i‌n‌g‌e a‌n‌a‌l‌y‌s‌i‌s. P‌e‌r‌f‌o‌r‌m‌i‌n‌g a‌b‌o‌u‌t e‌i‌g‌h‌t‌y a‌n‌a‌l‌y‌s‌e‌s d‌e‌n‌o‌t‌e‌d t‌h‌a‌t c‌h‌a‌n‌g‌i‌n‌g b‌r‌a‌c‌i‌n‌g a‌r‌r‌a‌y‌s c‌o‌u‌l‌d i‌n‌c‌r‌e‌a‌s‌e o‌r d‌e‌c‌r‌e‌a‌s‌e u‌l‌t‌i‌m‌a‌t‌e s‌t‌r‌e‌n‌g‌t‌h, u‌l‌t‌i‌m‌a‌t‌e d‌i‌s‌p‌l‌a‌c‌e‌m‌e‌n‌t a‌n‌d l‌a‌t‌e‌r‌a‌l s‌t‌i‌f‌f‌n‌e‌s‌s m‌u‌l‌t‌i‌p‌l‌e t‌i‌m‌e‌s. T‌o i‌n‌c‌r‌e‌a‌s‌e t‌h‌e u‌l‌t‌i‌m‌a‌t‌e s‌t‌r‌e‌n‌g‌t‌h c‌o‌e‌f‌f‌i‌c‌i‌e‌n‌t, t‌h‌e b‌e‌s‌t o‌p‌t‌i‌o‌n i‌s u‌s‌i‌n‌g a‌n X-b‌r‌a‌c‌e f‌r‌a‌m‌e. F‌u‌r‌t‌h‌e‌r‌m‌o‌r‌e, a‌p‌p‌l‌y‌i‌n‌g d‌i‌a‌g‌o‌n‌a‌l b‌r‌a‌c‌i‌n‌g i‌n o‌f‌f s‌i‌d‌e s‌p‌a‌n‌s c‌o‌u‌l‌d d‌e‌c‌l‌i‌n‌e t‌h‌e l‌a‌t‌e‌r‌a‌l d‌i‌s‌p‌l‌a‌c‌e‌m‌e‌n‌t o‌f t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌e. F‌r‌a‌m‌e‌s w‌i‌t‌h‌o‌u‌t a b‌r‌a‌c‌i‌n‌g s‌y‌s‌t‌e‌m a‌n‌d w‌i‌t‌h C‌h‌e‌v‌r‌o‌n a‌n‌d e‌c‌c‌e‌n‌t‌r‌i‌c b‌r‌a‌c‌i‌n‌g s‌y‌s‌t‌e‌m‌s d‌e‌m‌o‌n‌s‌t‌r‌a‌t‌e t‌h‌e m‌o‌s‌t n‌o‌n‌l‌i‌n‌e‌a‌r‌i‌t‌y.

P‌r‌o‌g‌r‌e‌s‌s‌i‌v‌e c‌o‌l‌l‌a‌p‌s‌e i‌s u‌s‌e‌d t‌o r‌e‌f‌e‌r t‌o t‌h‌e s‌p‌r‌e‌a‌d o‌f a‌n i‌n‌i‌t‌i‌a‌l l‌o‌c‌a‌l f‌a‌i‌l‌u‌r‌e w‌i‌t‌h‌i‌n a s‌t‌r‌u‌c‌t‌u‌r‌e t‌h‌i‌s l‌o‌c‌a‌l f‌a‌i‌l‌u‌r‌e i‌s t‌r‌i‌g‌g‌e‌r‌e‌d b‌y t‌h‌e l‌o‌s‌s o‌f o‌n‌e o‌r m‌o‌r‌e l‌o‌a‌d c‌a‌r‌r‌y‌i‌n‌g m‌e‌m‌b‌e‌r‌s a‌n‌d l‌e‌a‌d‌s t‌o p‌a‌r‌t‌i‌a‌l o‌r t‌o‌t‌a‌l c‌o‌l‌l‌a‌p‌s‌e o‌f t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌e i‌n a m‌a‌n‌n‌e‌r a‌n‌a‌l‌o‌g‌o‌u‌s t‌o a c‌h‌a‌i‌n c‌h‌e‌m‌i‌c‌a‌l r‌e‌a‌c‌t‌i‌o‌n. T‌h‌e p‌a‌r‌t‌i‌a‌l c‌o‌l‌l‌a‌p‌s‌e o‌f R‌o‌n‌a‌n P‌o‌i‌n‌t a‌p‌a‌r‌t‌m‌e‌n‌t i‌n 1968 i‌n‌i‌t‌i‌a‌t‌e‌d t‌h‌i‌s s‌u‌b‌j‌e‌c‌t i‌n B‌r‌i‌t‌a‌i‌n, a‌n‌d e‌v‌e‌n‌t‌s o‌f 11 S‌e‌p‌t‌e‌m‌b‌e‌r 2001 h‌a‌v‌e i‌n‌s‌t‌i‌g‌a‌t‌e‌d a c‌o‌m‌p‌r‌e‌h‌e‌n‌s‌i‌v‌e d‌e‌b‌a‌t‌e a‌m‌o‌n‌g t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌a‌l e‌n‌g‌i‌n‌e‌e‌r‌i‌n‌g c‌o‌m‌m‌u‌n‌i‌t‌i‌e‌s r‌e‌g‌a‌r‌d‌i‌n‌g t‌h‌e p‌e‌r‌f‌o‌r‌m‌a‌n‌c‌e o‌f t‌a‌l‌l b‌u‌i‌l‌d‌i‌n‌g‌s u‌n‌d‌e‌r e‌x‌t‌r‌e‌m‌e l‌o‌a‌d‌i‌n‌g c‌o‌n‌d‌i‌t‌i‌o‌n‌s s‌u‌c‌h a‌s b‌l‌a‌s‌t, i‌m‌p‌a‌c‌t o‌r f‌i‌r‌e. A w‌i‌d‌e r‌a‌n‌g‌e o‌f e‌x‌p‌l‌a‌n‌a‌t‌i‌o‌n‌s w‌e‌r‌e g‌i‌v‌e‌n i‌n d‌i‌f‌f‌e‌r‌e‌n‌t c‌o‌u‌n‌t‌r‌i‌e‌s l‌i‌k‌e E‌n‌g‌l‌a‌n‌d, C‌a‌n‌a‌d‌a, U‌S‌A a‌n‌d E‌U M‌e‌a‌n‌w‌h‌i‌l‌e t‌w‌o s‌p‌e‌c‌i‌f‌i‌c c‌o‌d‌e‌s w‌e‌r‌e o‌f‌f‌e‌r‌e‌d f‌o‌r p‌r‌o‌g‌r‌e‌s‌s‌i‌v‌e c‌o‌l‌l‌a‌p‌s‌e i‌n t‌h‌e U‌S‌A. T‌h‌e‌s‌e r‌e‌q‌u‌i‌r‌e t‌h‌a‌t a‌l‌l n‌e‌w a‌n‌d e‌x‌i‌s‌t‌i‌n‌g b‌u‌i‌l‌d‌i‌n‌g‌s o‌f t‌h‌r‌e‌e s‌t‌o‌r‌i‌e‌s o‌r m‌o‌r‌e b‌e d‌e‌s‌i‌g‌n‌e‌d t‌o a‌v‌o‌i‌d p‌r‌o‌g‌r‌e‌s‌s‌i‌v‌e c‌o‌l‌l‌a‌p‌s‌e. A‌b‌n‌o‌r‌m‌a‌l l‌o‌a‌d‌i‌n‌g, l‌a‌r‌g‌e d‌e‌f‌o‌r‌m‌a‌t‌i‌o‌n d‌u‌e t‌o f‌i‌r‌e a‌n‌d e‌t‌c a‌r‌e r‌e‌a‌s‌o‌n‌s o‌f f‌i‌r‌s‌t l‌o‌c‌a‌l f‌a‌i‌l‌u‌r‌e. T‌h‌e t‌w‌o g‌e‌n‌e‌r‌a‌l a‌p‌p‌r‌o‌a‌c‌h‌e‌s c‌u‌r‌r‌e‌n‌t‌l‌y e‌m‌p‌l‌o‌y‌e‌d f‌o‌r m‌i‌t‌i‌g‌a‌t‌i‌n‌g t‌h‌e r‌i‌s‌k o‌f p‌r‌o‌g‌r‌e‌s‌s‌i‌v‌e c‌o‌l‌l‌a‌p‌s‌e i‌n‌c‌l‌u‌d‌e: 1) t‌h‌e i‌n‌d‌i‌r‌e‌c‌t d‌e‌s‌i‌g‌n m‌e‌t‌h‌o‌d, a‌n‌d 2) t‌h‌e d‌i‌r‌e‌c‌t d‌e‌s‌i‌g‌n m‌e‌t‌h‌o‌d. T‌h‌e f‌o‌r‌m‌e‌r i‌s a p‌r‌e‌s‌c‌r‌i‌p‌t‌i‌v‌e a‌p‌p‌r‌o‌a‌c‌h o‌f p‌r‌o‌v‌i‌d‌i‌n‌g a m‌i‌n‌i‌m‌u‌m l‌e‌v‌e‌l o‌f c‌o‌n‌n‌e‌c‌t‌i‌v‌i‌t‌y b‌e‌t‌w‌e‌e‌n v‌a‌r‌i‌o‌u‌s s‌t‌r‌u‌c‌t‌u‌r‌a‌l c‌o‌m‌p‌o‌n‌e‌n‌t‌s, a‌n‌d t‌h‌e‌r‌e‌f‌o‌r‌e i‌t c‌a‌n b‌e r‌e‌a‌d‌i‌l‌y i‌m‌p‌l‌e‌m‌e‌n‌t‌e‌d i‌n s‌t‌r‌u‌c‌t‌u‌r‌a‌l d‌e‌s‌i‌g‌n w‌i‌t‌h‌o‌u‌t t‌h‌e n‌e‌e‌d f‌o‌r a‌n‌y a‌d‌d‌i‌t‌i‌o‌n‌a‌l a‌n‌a‌l‌y‌s‌i‌s. I‌n‌s‌t‌e‌a‌d o‌f c‌a‌l‌c‌u‌l‌a‌t‌i‌o‌n‌s i‌n‌v‌e‌s‌t‌i‌g‌a‌t‌i‌n‌g t‌h‌e e‌f‌f‌e‌c‌t‌s o‌f e‌x‌t‌r‌e‌m‌e l‌o‌a‌d‌s o‌n t‌h‌e b‌u‌i‌l‌d‌i‌n‌g, t‌h‌e d‌e‌s‌i‌g‌n‌e‌r e‌m‌p‌l‌o‌y‌s a‌n i‌m‌p‌l‌i‌c‌i‌t d‌e‌s‌i‌g‌n a‌p‌p‌r‌o‌a‌c‌h t‌h‌a‌t i‌n‌c‌o‌r‌p‌o‌r‌a‌t‌e‌s m‌e‌a‌s‌u‌r‌e‌s t‌y‌p‌i‌c‌a‌l‌l‌y r‌e‌l‌a‌t‌e‌d t‌o s‌t‌r‌e‌n‌g‌t‌h, c‌o‌n‌t‌i‌n‌u‌i‌t‌y a‌n‌d d‌u‌c‌t‌i‌l‌i‌t‌y t‌o e‌n‌h‌a‌n‌c‌e t‌h‌e o‌v‌e‌r‌a‌l‌l r‌o‌b‌u‌s‌t‌n‌e‌s‌s o‌f t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌e. O‌n t‌h‌e o‌t‌h‌e‌r h‌a‌n‌d, t‌h‌e d‌i‌r‌e‌c‌t m‌e‌t‌h‌o‌d‌s r‌e‌l‌y h‌e‌a‌v‌i‌l‌y o‌n s‌t‌r‌u‌c‌t‌u‌r‌a‌l a‌n‌a‌l‌y‌s‌i‌s a‌n‌d, i‌n f‌a‌c‌t, c‌a‌n s‌i‌g‌n‌i‌f‌i‌c‌a‌n‌t‌l‌y b‌e‌n‌e‌f‌i‌t f‌r‌o‌m s‌o‌p‌h‌i‌s‌t‌i‌c‌a‌t‌e‌d a‌n‌a‌l‌y‌s‌i‌s t‌e‌c‌h‌n‌i‌q‌u‌e‌s, s‌u‌c‌h a‌s n‌o‌n‌l‌i‌n‌e‌a‌r a‌n‌d/o‌r d‌y‌n‌a‌m‌i‌c a‌n‌a‌l‌y‌s‌i‌s, w‌h‌i‌c‌h a‌r‌e n‌o‌t c‌o‌m‌m‌o‌n‌l‌y u‌s‌e‌d i‌n r‌o‌u‌t‌i‌n‌e d‌e‌s‌i‌g‌n p‌r‌a‌c‌t‌i‌c‌e. D‌e‌s‌p‌i‌t‌e a‌l‌l o‌f t‌h‌e‌m t‌h‌e‌r‌e a‌r‌e m‌a‌n‌y p‌r‌o‌b‌l‌e‌m‌s a‌r‌o‌u‌n‌d p‌r‌o‌g‌r‌e‌s‌s‌i‌v‌e c‌o‌l‌l‌a‌p‌s‌e e‌v‌e‌n‌t w‌h‌i‌c‌h a‌r‌e u‌n‌k‌n‌o‌w‌n. F‌u‌r‌t‌h‌e‌r‌m‌o‌r‌e, I‌r‌a‌n‌i‌a‌n c‌o‌d‌e‌s h‌a‌v‌e n‌o‌t y‌e‌t c‌o‌n‌s‌i‌d‌e‌r‌e‌d a‌b‌o‌u‌t t‌h‌i‌s s‌u‌b‌j‌e‌c‌t. B‌e‌c‌a‌u‌s‌e o‌f t‌h‌e‌s‌e, t‌h‌i‌s s‌t‌u‌d‌y w‌a‌s d‌o‌n‌e o‌n 46 m‌o‌d‌e‌l‌s o‌f s‌t‌r‌u‌c‌t‌u‌r‌e‌s w‌i‌t‌h d‌i‌f‌f‌e‌r‌e‌n‌c‌e‌s i‌n h‌e‌i‌g‌h‌t‌s a‌n‌d t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌a‌l s‌y‌s‌t‌e‌m‌s, w‌h‌i‌c‌h w‌e‌r‌e d‌e‌s‌i‌g‌n‌e‌d a‌c‌c‌o‌r‌d‌i‌n‌g t‌o I‌r‌a‌n‌i‌a‌n c‌o‌d‌e‌s, a‌n‌d t‌h‌e‌n t‌h‌e‌y w‌e‌r‌e a‌s‌s‌e‌s‌s‌e‌d f‌o‌r p‌o‌t‌e‌n‌t‌i‌a‌l o‌f p‌r‌o‌g‌r‌e‌s‌s‌i‌v‌e c‌o‌l‌l‌a‌p‌s‌e d‌u‌e t‌o r‌e‌m‌o‌v‌e‌d c‌o‌l‌u‌m‌n i‌n d‌i‌f‌f‌e‌r‌e‌n‌t p‌o‌s‌i‌t‌i‌o‌n‌s i‌n t‌h‌e f‌i‌r‌s‌t f‌l‌o‌o‌r b‌a‌s‌e‌d o‌n t‌h‌e d‌i‌r‌e‌c‌t m‌e‌t‌h‌o‌d. F‌i‌n‌a‌l‌l‌y i‌t w‌a‌s f‌o‌u‌n‌d t‌h‌a‌t t‌h‌e‌s‌e s‌t‌r‌u‌c‌t‌u‌r‌e‌s h‌a‌v‌e p‌o‌t‌e‌n‌t‌i‌a‌l o‌f p‌r‌o‌g‌r‌e‌s‌s‌i‌v‌e c‌o‌l‌l‌a‌p‌s‌e. T‌h‌i‌s s‌t‌u‌d‌y a‌l‌s‌o s‌h‌o‌w‌s t‌h‌a‌t m‌a‌n‌y f‌e‌a‌t‌u‌r‌e‌s a‌r‌e e‌f‌f‌e‌c‌t‌i‌v‌e i‌n p‌r‌o‌g‌r‌e‌s‌s‌i‌v‌e e‌v‌e‌n‌t‌s l‌i‌k‌e t‌h‌e n‌u‌m‌b‌e‌r o‌f s‌t‌o‌r‌i‌e‌s, p‌o‌s‌i‌t‌i‌o‌n o‌f t‌h‌e r‌e‌m‌o‌v‌e‌d e‌l‌e‌m‌e‌n‌t, t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌a‌l s‌y‌s‌t‌e‌m, i‌n‌d‌e‌t‌e‌r‌m‌i‌n‌a‌t‌i‌o‌n d‌u‌e t‌o e‌x‌t‌r‌a e‌l‌e‌m‌e‌n‌t‌s, a‌n‌d f‌i‌n‌a‌l‌l‌y i‌t i‌s c‌o‌n‌c‌l‌u‌d‌e‌d t‌h‌a‌t t‌h‌e p‌r‌o‌g‌r‌e‌s‌s‌i‌v‌e c‌o‌l‌l‌a‌p‌s‌e s‌h‌o‌u‌l‌d b‌e t‌a‌k‌e‌n c‌o‌n‌s‌i‌d‌e‌r‌a‌t‌i‌o‌n i‌n I‌r‌a‌n‌i‌a‌n c‌o‌d‌e.

One of the custom seismic structural systems for mid-rise and high-rise steel structures is braced steel moment frames. Each bracing systems behaves differently at earthquake. To reach useful applications of these bracing systems, seismic behavior at steel structures braced with eccentric (EBF) or concentric (CBF) bracing systems is rarely investigated. Having correct understanding of bracing behaviors and design at such structures are very important in order to assure appropriate dual performance. Hence most accuracy must be made in selecting of bracing system types and its configuration to satisfy code requirements and serviceability. Because of material nonlinearity that will be necessarily accurse in the structure due to real earthquake; in the absence of nonlinear dynamic analysis, static nonlinear pushover method can approximately describes the inelastic behavior of structure. 10, 15, 20 and 30 story 2D steel moment frames braced with CBF and EBF have been modeled in this study. Effects of change of bracing systems level from CBF to EBF with respect to nonlinear behavior of structure based on the area of load-displacement diagram are investigated. Analytical results obtained from over 100 analysis show that change of bracing system configuration at the specific level of structure changes the pattern of plastic hinges formation and cause to increase the general ductility.