Several catastrophes caused by earthquakes have recently taken place (e.g. in Haiti, Chile and Japan) and it has been revealed that both the building processes and construction materials are key points, which determine the success of the mechanical response, even in the case of low or moderate seismic forces (1, 2). By using lighter materials, the overall structural weight is reduced. This tends to increase the ductile behaviour of buildings, which is a desirable characteristic regarding the seismic forces. In contrast, throughout history, the optimisation of structures has been a fundamental issue in construction (3). The search for better mechanical response has led to the development of safe and economical structures that must be further improved with the aim of reducing both environmental impact and building costs. At this point, steel may be highlighted as one of the most used building materials due to its properties (e.g. ductile behaviour, good adherence and compatibility with other materials) and the feasibility for assembling and fitting to other building elements (4).

The bending and tensile strengths are also of great importance. For instance, horizontal structural elements (beams) made by steel profiles can achieve a larger distance between columns than other construction materials, even timber frames. However, steel structures possess two major issues.

First, steel is generally highly vulnerable to fire (5, 6) and corrosion (7, 8). This issue has been faced by improving the chemical formulation of steel, by improving construction techniques and by applying coating materials (9).

Second, the thickness of the steel profiles must be considered. Because of the high density and the aforementioned steel properties, the profile cross section tends to be reduced.

In spite of this, better performance is found in the case of beams, since columns are commonly highly affected by buckling. In addition, horizontal loads (e.g. seismic forces, wind, water and so on) highly increase this effect (10, 11).

Hence, in order to solve this issue, braces or infill walls are commonly used for complying with the technical codes in force. However, with the aim of choosing the most feasible and economical solution, this study only considers the assessment of braces. Furthermore, from the available braces, the most economical have been selected for assessing the most suitable location within the building frame structure, i.e., simple braces (SBs). Obviously, prior to such a study, a comparison between chevron braces (CBs), SBs, Saint Andrew's cross (SAC) and a bare frame (i.e. without braces) was conducted in order to determine the differences among such methods. It is concluded that no significant improvement can be highlighted when economical, scheduling and technical values are considered.

Despite several authors have improved building structure performance by paying attention to materials properties (12), there are few studies related to the assessment of the location of braces (13). Besides, these papers have been conducted for reinforced concrete rather than for steel structures. Among the studies related to steel structures, some authors have paying attention to the optimal number of braces and the most effective location (14). It was observed that the angle of about 45 degrees, which is typically used for tall buildings in practice does not guarantee minimum shear lag effect on structure. Besides, the structural stiffness, strength, and ductility can be enhanced simultaneously when the brace volume is appropriate but out of this value the ductility may be highly reduced (15, 16). Thus, this paper aims to provide a useful guide for steel building designers when lateral loads are of importance (17).

The paper is organised as follows. The methodology section shows the building model and the carried out assumptions and calculations. It also shows the different cases to be analysed. Afterward, within the structural analysis section, the results carried out by the non-linear static performance analysis (push-over) are given and discussed by considering the regulatory standards. Finally, the conclusions summarise the major findings.

The results obtained from the EC-8 approach (Table 2) and those carried out by considering NCSE-02 (Table 3) show similar values for the most unfavorable frames when no braces were installed (i.e. bare frames), which verifies the convergence of both methods.

Figure 4 shows the capacity curves of the buildings with the three types of bracing systems (i.e. CB, SAC and SB), including the frame without any bracing (i.e. bare frame). In contrast, Figure 5 shows the capacity curves of the frames with the 16 bracing locations. This Figure shows the yielding points (DY), the collapse points (DU) and the maximum displacements in the upper floor of the dynamic analyzes considering the Lorca record (Reg) and the scaled Lorca record (2º Reg). The scaled register (2nd Reg.) is the result of multiplying by 2 the accelerations of the Lorca Register (Reg.). The use of this amplification coefficient is due to the damage state of the structures, reaching the ultimate limit state in some cases.

The use of braces in the frames significantly improves the shear behavior, caused by the effects of wind or earthquakes among others. Therefore, it solves the possible buckling effects of the columns. The versatility of the use of steel in buildings with large lights and heights (industrial buildings) makes the use of these elements essential due to the significant slenderness of the columns. For example, the use of CB is a more effective solution in architectural design than the SAC. For instance, more space is available for glazing solutions. However, it is barely effective in structural behavior since SAC adds higher rigidity.

The continuity of these bars significantly improves the shear behavior and the ductility of the frames. In contrast, the existence of the bare frame decreases the structural performance of the building.

The use of European codes leads to the application of the obtained results in many countries, which have incorporated such a standard.

The results obtained under the Spanish earthquake-resistant Standard (NCSE-02) corroborate this statement. Table 4 shows the most significant results from the capacity curves derived from the initial analysis, i.e., where different braces type devices (SB, CB and SAC) were compared to the bare frame.

As shown in the capacity curves, the damage thresholds were evaluated from the idealized bilinear capacity spectrum according to Lagomarsino and Penna (41), using the yielding displacement (dy) and the ultimate displacement (du). These four damage thresholds are:

representing ‘Slight’, ‘Moderate’, ‘Extensive’, and ‘Complete’ damage states.

The structural behavior of the frames with braces significantly improves the bare frame. The use of braces in the structures, improves by 132%, 224% and 329%, the base shear of the frames using SB, CB and SAC, respectively. The best ductility corresponds to SAC and the frames with aligned braces. Yielding displacements are reduced by 67% in frames with SB and with CB and 53% using SAC, compared to bare frames. Yield and ultimate displacement and the basal shear are similar in all the analyzed cases, with the exception of the frames that do not have braces in some of their plants, where the shear diminishes significantly. The increase in the rigidity of the structures is one of the factors causing the increase in the basal shear of the structures, as shown in table 5.

Table 5 shows the effect of different locations, in accordance with cases showed in Table 1. The higher strength occurred in frames c6, c7, c9, c15 and c16, and the highest ductility occurred in frames c1, c7 and c15. On the other hand, the stiffer frames were c8, c9 and c16. The D_u and D_y values have been set automatically by Seismostruct (25).

There was no collapse in any case by considering both the NCSE-02 and EC-8. All the results, (Tables 4 and 5) in terms of base shear and displacement were lower than the ones carried out by considering the push-over analysis, regardless of whether EC-8 or NCSE-02 are considered. Furthermore, collapse was not reached in any case and most of cases remained within the elastic zone.

All carried out results have been drawn in Figure 6 according to the two main key factors of structural design: ductility and basal shear. Hence it is possible to highlight the most preferred locations depending on the ductility behavior (c1, c7 and c15) or the base shear resistance criteria (c6, c7, c9, c15 and c16).

Non-linear dynamic analysis (42, 43) were performed in discrete time following (44) as discussed above. The time period (∆t) used in the analysis was 0.01 s to match the data from the Lorca earthquake register of May 11, 2011 (45, 46) for the direction N-S (Figure 8), the most unfavorable direction. The Lorca earthquake (35, 47, 48) has been one of the largest destructive earthquakes that occurred in Spain in recent years despite its moderate magnitude (M _w = 5.1); This severity is due to its shallow hypocentral depth (2 km) and the almost zero distance between the epicenter and the center of the city of Lorca. The Lorca earthquake has an impulsive character in the N-S component (49) considered in the dynamic analyzes of this research. The dimensionless Manfredi index takes the value I_D=2.57 (index that is defined as the integral of the square of the acceleration over the total duration and the product of the maximum values of acceleration and velocity). For comparison purposes with the Standard, Figure 7 shows the spectra of the record used for each direction with the spectrum of the Standard for a type I soil; In this image it can be seen that the spectral accelerations of the record clearly exceed the requirements of NCSE-02 (50) for almost all periods, especially for the N-S direction.

The choice of this record in this investigation has been chosen randomly considering the catastrophic effects it had in reality, in order to justify the behavior that buildings with steel frame structures with braces could have had, reducing the effects caused by earthquakes such as the one in Lorca (Spain). On the other hand, the choice of this structural typology is due to its abundance in areas that are not excessively seismic such as in Spain. This impulsive and superficial record (epicenter near the surface), was outside the scope of the Spanish Regulations (NCSE-02), as shown in the accelerations shown in Figure 7. On the other hand, the scaling used in this research was to demonstrate more conclusively the effectiveness of these devices in frame structures, because as has been shown in the dynamic results using the real record, the use of these devices would have significantly improved the structural behavior of existing buildings, reducing the damage and effects caused in reality.

The structure buffer (understood as the visual representation model used by the “Seismostruct” (40), software to represent the structure of the building) was represented by the Rayleigh model (Chopra) with a damping factor of 5%, an average value of our two modes damping values (4% and 6%) which has been used in diverse studies conducted in recent years for this type of frames.

Figure 9 shows the displacement of the upper floor from the time-history responses frames, corresponding to the North-South register acceleration data shown in Figure 8. This accelerogram was chosen as it was the most severe. The building structures were selected for this analysis as they were deemed to be the most representative of real-life settings. On the other hand, Lorca's record has been scaled up to collapse in the most unfavorable frames. Figure 9 shows the displacement of each frame, considering the log without scaling and scaling. The scale coefficient used in the records is 2.

Table 6 shows the maximum displacements of the time-history analysis (dynamic analysis), belonging to the upper parts of the frames, considering the Lorca record of the year 2011 and the scaled Lorca record (the coefficient used is 2). On the other hand, the maximum axial compression of the braces in each case, considering the Lorca record (Reg) is lower than Euler's critical load, affirming what was previously mentioned that the braces do not buckle. On the other hand, in the displacements indicated in table 6, a series of gray colors of different shades are shown, related to the state in which the buildings are located considering the damage indices of Lagomarsino and Penna (41). The associated gray codes are as follows:

From the dynamic analysis, it is established that taking Lorca's record into account, no frame would enter the plastic regime. However, considering the scaled Lorca frame, only cases c2, c3, c6, c7, c8, c9, c12, c15 and c16 would not enter the plastic regime. On the other hand, frames c1, c4 and c5 would start to plastify, while frames c10, c11, c13 and c14 would collapse.

Finally, as shown in Figure 9, considering the scaled records, half of the frames (c1, c3, c4, c5, c10, c11, c12, c13 and c14) show significant permanent deformations at the end of the dynamic analysis.

This study has demonstrated that SB may lead to a similar performance to CB or even SAC. This last case shows higher basal shear but equal ductility. Hence, more sustainable, and economical building structure may be obtained. The conclusions obtained from the non-linear static analysis (Push-over) and the static analysis carried out with the EC-8 and NCSE-02 Standards, using the seismic forces obtained, are similar. Detailing the results obtained with both standards, it can be observed that the analysis carried out with the European Standard (EC-8) are a little more restrictive than the analysis carried out with the Spanish Standard (NCSE-02). The design seismic forces vary between 25% and 15% as the height increases. These differences are practically insignificant in the displacements produced in the structures by carrying out the static calculations, due to the great rigidity that the structures have with the braces. Therefore, it is possible to obtain more sustainable and economical building which meets the mandatory requirements, as well.

Regarding the displacements of the damage states of the buildings, there are differences in the displacements, shears and ductilities with respect to the bare cases, evidencing the effect that these devices have on the structures of frame buildings. The smallest displacements occur in the CB case, but there are no major differences with respect to the SB case. However, the lowest base shears occur in the case of models without devices, considering their lower rigidity.

In spite of the most suitable locations for SB correspond to cases c2, c6, c7, c9, c15 and c16, the analysis determines that diagonals and central part of buildings lead to the better results regarding both base shear and ductility.

Considering the dynamic analysis, it is concluded that the frames that have floors without any brace are the most unfavorable and weak (c1, c4 and c10). While the frames with braces in the center (c2, c6, c7 and c8) and diagonals along the frames (c3, c9, c15 and c16) are the most resistant. After analyzing all the variables studied in this research, it could be concluded that the best structural behaviors occur in cases c8 and c15.

Half of the frames (c1, c3, c4, c5, c10, c11, c12, c13 and c14) show significant permanent deformations at the end of the dynamic analysis.

In general, cases that present greater ductility and effective stiffness are cases that have better dynamic behavior.

The structural behavior of the braced models determines that the maximum displacements occur in cases C1 and C15 and that the maximum plastic displacements occur in cases C1 and C3, cases in which the models have at least 2 braces on all floors, coinciding with a uniform arrangement of these devices along the heights of the models. The greatest shear forces occur in case C7, where the braces are concentrated symmetrically in the central part of the frame. The maximum ductility occurs in case C15, coinciding with the cases of greatest displacements and the lowest ductility in C13, where half of the floors of the model do not have braces, demonstrating the importance of having braces on all floors of the structural frame (eliminating the effects of “soft floors”), generating a solution that is too fragile. On the contrary, the maximum rigidity occurs in case C8, coinciding with a symmetrical arrangement on both axes of the structure in the form of a double St. Andrew's cross, and the lowest rigidity in case C14, coinciding with the case in which the upper half of the height of the frame has no braces, making a structure that is too weak.

As far as some researchers have explored new steel formulation, it is suggested to develop these manuscript findings by considering new material behaviors. In addition, it should be investigated higher building, i.e., from 15 stories in order to determine whether the obtained results are also valid.

The struts used in all cases never buckled considering the earthquake that occurred in Lorca.

The increase in the basal shear of the different cases studied is due to the significant increase in the rigidity of the frames.

c8, c12 c13, c14 and c15, are the cases that have no damage once the Lorca earthquake occurred. However, by doubling the accelerations, c13 and c14, they become severely damaged.

Regarding the dynamic analysis, although there are no major differences in the displacements (6 cm), there are differences in the structural behavior. Considering the accelerations of the Lorca record without scaling, the smallest displacements occur in cases C8 and C15, not reaching the point of plasticizing, as occurs in cases C12, C13, C14, although these are on the limit of beginning to plasticize. Doubling the accelerations of the record, changes in the structural damage are evident, reaching the point of plasticizing the models, even so, cases C8 and C9 are those with the smallest displacements in the structure, followed by cases C2, C6, C7, and C15, corresponding to structural models with braces on all floors. On the other hand, doubling the seismic accelerations of the record causes a significant worsening of some models, such as cases C13 and C14, curiously coinciding with the cases that do not have braces on half of the floors.

For future studies related to this research, it is advisable to conduct similar studies on frame buildings with different heights, with different structural configurations (structural design and different materials) and in different locations. What can be concluded is the structural improvement that these frame buildings have with the inclusion of braces and that ductility is beneficial for better structural behavior as stated in the earthquake-resistant regulations and in scientific theory.