1 Introduction

Among all earthquakes resistant structural systems, flexural frames in particular, are considered to be a good lateral load bearing system. They have high ductility and low stiffness. However, it is different for braced frames. While the concentrically braced frames (CBF) are stiff, their ductility is not adequate. On the other hand, Eccentrically Braced Frames (EBF) have a good balance of stiffness and lack of ductility. In this type of structural system, the essential role of absorption and dissipation of induced energy is played by a link beam. Due to an opening or a door next to a column, in some configurations of Eccentrically Braced Frames, it is necessary to connect a link beam to a column. The earthquake in Northridge (1994) marked the beginning of a series of important studies regarding flexural frame connections. As a result of this earthquake, many seismic design codes of flexural frames were revised and research on the link beam to column connections were carried out. The link beam bears great forces and large inelastic deformations in flexural joints. Thus, after the Northridge earthquake, it was necessary to suggest a good strategy to provide the required ductility of these connections.

Despite the studies conducted by Okazaki (2004) and Drolias (2007), as well as the surveys carried out by Prinz and Richards (2009) and Bremen et al. (2010), until now, any appropriate and satisfactory connection between link beam and column have been proposed by design codes. In the seismic criteria of AISC (2005), due to ongoing research to overcome the drawbacks of this type of connection, designers are recommended not to use this type of connection. Hence, the importance of studying beam-to-column connections in diverge braced systems has become more essential.

Based on the studies conducted on the ductile element, Kafi et al. (Abbasnia et al. 2009) took a step towards improving the convergent brace by introducing a ductile ring. Analytical results by Andalib et al. (2018), Mohammad Bazzaz et al. (2012, 2014, 2015a, b); Bazzaz et al. (2011); revealed that the performance of steel ring studied as a ductile element in an off-centre bracing system (model off-centre braced frame and ductile element in optimum place) has more ductility among the models. Also Andalib et al. (2014) investigated the ductility and performance of steel rings constructed from plates. The results of this investigation show that the hysteresis curve of the steel specimen made of steel plates is wide and that a tensile ductility factor of 8.68 is achieved.

Also, experimental and numerical evaluation of an innovative diamond-scheme bracing system equipped with a yielding damper by Pachideh et al. (2020) indicated that both great applicability and efficiency of the proposed system in energy absorption and ductility. Moreover, it was concluded that as the braces and damper are in parallel, the use of a steel ring with smaller size and thickness would result in higher energy absorption and load-resisting capacity when compared to the other existing systems. Kheyroddin et al. (2019) assessed the RC frames retrofitted by steel jacket, X-brace and X-brace having ductile ring as a structural fuse. They found that although the frame retrofitted by the X-brace showed a better performance in terms of resistance and stiffness, but the retrofitted frame with a ring also showed a better behaviour in terms of resistance and stiffness compared to the RC frame and the sample with the jacket as well as compared to the sample with the X-brace showed more ductility and energy dissipation (with a slight reduction in resistance).

The concentrically braced frames (CBFs) are one of the most widely used lateral load-resisting systems. Kachooee et al. (2018a, b) evaluated the effect of local fuse on behaviour of concentrically braced frame by a numerical study. They found that if the reduced cross-section fuse (RCF) is properly designed and also the end of brace is fixed, the CBFs with equal energy dissipation capacity, that are equipped with this fuse exhibit a better ductility than the customary CBFs. Also Rahnavard et al. (Naghavi et al. 2019; Rahnavard et al. 2017, 2020) did some research on brace. Results of Rahnavard et al. indicated dramatic improvements in energy dissipation and ductility in BRBF models as compared to equivalent CBF models.

Experimental and numerical evaluation of Y-shaped eccentrically braced frames fabricated with high strength steel by Mingzhou et al. (Lian et al. 2015; Liang et al. 2018a, b; Ling et al. 2019) indicated that the one-bay and one-story Y-HSS-EBF specimen had good load-bearing capacity and ductility capacity. Also, Results from the simplified analysis were compared with the test results. The test results indicated that the specimen had reliable lateral stiffness and the damages observed at shear links.

This study attempts to develop a model of energy dissipater. It consists of a ring that increases the ductility and earthquake energy absorption. Additionally, a box joined to the ring by a connection plate increases the bearing capacity. During an earthquake, a considerable portion of the energy is absorbed by the dissipater which its behaviour has transformed into non-linear and flexural plastic hinges were formed. This way, the non-linear stage of other members is prevented. Furthermore, the buckling of bracing member and the failure of the link beam are also postponed or avoided. If the proposed element fails, it can be easily replaced. In addition to its low cost, the speed of its implementation is also high. It is predicted that the proposed element can act as a dissipater member and also as a fuse for controlling the buckling of the brace and rotation of link beam. Thus, it provides sufficient ductility for the system.

2 The Research Method

This research was conducted in two phases. In the first phase, the behaviour of the different proposed elements is simulated and the optimum element is selected in accordance with the obtained results. The results of this phase were used to evaluate the behaviour of the EBF in the next phase. To select the optimum element, 15 types of proposed elements are evaluated. These differed in terms of ring and box dimensions. Furthermore, the parameters required to evaluate the behaviour of the proposed element of finite element analysis in cyclic loading are introduced.

In the second phase, the effect of using the proposed element in EBF is investigated. For this purpose, the EBFs are simulated with the proposed element, as well as without it. This is carried out in OpenSees. It is important to note that, in this study, EBF is used for the usual EBF and D-EBF is used for EBF with ductile element. The seismic performance of EBF using a non-linear dynamic analysis is evaluated according to time history. Then the results are compared. The effect of this element was also investigated in four, six and eight story frames. Figure 1 shows the placement of the element in a braced frame. It is important to note that the proposed element was joined to the brace by a welding or screw.

Fig. 1
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The position of proposed element in EBF (Salimbahrami 2013)

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3 The Research Process

3.1 Phase One: Analysing the Proposed Element

3.1.1 Introducing the Proposed Element

Figure 2 shows the proposed element. This was composed of a ring and two plates, adjoining the ring to the two half boxes. D, L, and t are the diameter, the length and the thickness of the ring, respectively. The plates dimensions were 0.17 × 0.1 × 0.02 m.

Fig. 2
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Proposed element dimension (Salimbahrami 2013)

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In this study, 15 models are considered for the proposed element. The difference in these models was the dimension of ductile steel rings. These consisted of three types of dimensions (0.15, 0.2 and 0.25 m) and five types of thickness (0.01, 0.012, 0.014, 0.016 and 0.018 m). In all of the elements, the length of the ring was 0.1 m. The dimension of the box changed proportionally to the ring diameter. Figure 2 shows the parametric dimension of the element. Parameters a, b, D, and t in Fig. 2 for 15 models are presented in Table 1.

Table 1 The dimensions of various types of the proposed elements
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One of the effective parameters for steel ring selection is steel properties. Since the role of the ring is energy dissipation, ductility becomes an important property of this ring. Thus, it is recommended to choose soft steel with high ductility. Soft steel is a type of steel with a yielding stress of less than 305,914,863.89 kg/m2. Its ultimate strain is more than 40%. Thus, taking the market into consideration, a seamless steel pipe CT20 for the ring is selected. Although this steel does not have the property of soft steel, for the evaluation of the performance of the proposed element in this phase, it is a good choice (Abbasnia et al. 2009). For the plates that join the brace to the box, St37 is used. The mechanical properties of all members of the element, such as ultimate stress and strain, yielding stress and elastic modulus, are given in Table 2.

Table 2 Mechanical properties of the component of the element
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3.1.2 Modelling and Evaluating Performance of the Proposed Element

To evaluate the performance of the ductile element under earthquake cyclic load, the proposed model presented properties that were modelled three dimensionally in ANSYS, using element SOLID185. This type of element included eight nodes. Each node had three degrees of freedom (ux, uy, uz). In the proposed non-linear analyses, it showed stress, internal forces and loading in or out of the surface. Figure 3 shows the element SOLID185.

Fig. 3
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The geometry of the element SOLID185 (Stolarski et al. 2018)

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After creating the geometrical model and the meshing on it, loading on the 0.1 m on the junction plate to the brace was performed. A measurement of 0.1 m is chosen, as this is more adaptive to a real loading condition. At one end of the proposed element, all degrees of freedom were restrained. At the other end, all degrees of freedom were restrained in the elements except the one in the horizontal axis. The loading protocol was based on ATC24 (Krawinkler 1992) and was unrestrained at the end of the element. This type of loading was cyclic along the horizontal axis. The diagram of this cyclic load is shown in Fig. 4. Finally, the non-linear static model is analysed.

Fig. 4
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Cyclic Loading in code ATC 24 (Krawinkler 1992)

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To compare the ductility and maximum load that the element can bear, the cyclic load (shown in Fig. 5) is applied to the model. After that, the maximum allowable displacement of the ring was 0.02 m (Abbasnia et al. 2009). This was because the initial fracture sustained load decreases. With this in mind, the applied displacement is considered to the ring, shown in Fig. 5. These results established relations between ductility, maximum sustained force in the element, diameter and the thickness of the ring.

Fig. 5
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Time history loading for proposed element

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3.1.2.1 Validation

In order to validate the modelling in ANSYS, first, only the steel ring is simulated according to the mechanical specifications in the Table 2 with a diameter of 22, a thickness of 1.2 and a length of 10 cm according to the Fig. 6a. The steel ring is loaded with the ATC24 code as shown in Fig. 4. The loading of the rings started in cycles and started from small displacements and continued until the failure location of 2 cm. This stage of experiments was performed during four experiments to check the ductility, bearing capacity and maximum change in ring diameter. Then, these results are compared with the experimental results (Abbasnia et al. 2009) (Fig. 6b).

Fig. 6
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a Geometric characteristics of experimental and numerical models b Comparative push plots for experimental specimen and numerical model

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As can be seen in Fig. 6b, the initial stiffness of the experimental and finite element models is well matched, but as the finite element model is loaded, it goes out of linear condition sooner and surrenders in it. The similarity between the load–deflection curve in simulation and experiment showed that the simulation results were valid.

3.2 Phase Two: Static and Dynamic Analysis in EBF

3.2.1 Introducing the Samples in OpenSees

In order to evaluate the seismic performance of the proposed element, the usual structures are used. For the evaluation of the effect of the structure’s height, the frames in four, six and eight stories (Fig. 7) are analysed. The height of each story was assumed 3 m and the length of each opening was 5 m. To reach an EBF with more suitable stiffness and ductility, a link beam with the shear behaviour length of e = 1 m is selected. It is considered that the dead load and live load in the stories as 700 and 200 kg/m2, respectively. Additionally, the effective width of frames was 3 m, as was considered in the plan of Fig. 7. Consequently, the line dead load and live load were 2100 and 600 kg/m, respectively. These were distributed along the beam. The plan of this study was uniform (square, regular, orderly and ordered) and the height of the structure was below 50 m. Thus, the equivalent static analysis are performed. Based on the sixth topic of the Iran National Building Regulations (Code 2013), the site with high risk and soil type three were chosen for the seismic coefficient of the structure. The seismic properties static analysis were relevant to Iran 2800 code (Code 2014) and are shown in Table 3.

Fig. 7
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EBF in 4, 6, and 8 stories a Plan b EBF c D-EBF

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Table 3 Seismic properties of static analysis based on Iran 2800 Code
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3.2.2 Analysis and Design Parameters

All of the frames were designed based on the tenth topic of the Iran National Building Regulations (edition 2008) (Code 2014). For the analysis and design of the frames, ETABS (Berkeley 2015) is used. Furthermore, the UBC (1997) (UBC 1994) was used as the basis for designing. The seismic design criterion in the tenth topic of the Iran National Building Regulations (edition 2008) (Code 2014) has a number of similarities to the seismic design criterion in this code. The properties of the sections of columns and beams for four, six and eight story frames are considered as they are shown in Table 4. Previous studies have shown that the probability of brittle failure in the side link beam to the weak axis of the column is high. Thus, this type of joint has not been used.

Table 4 Section properties in EBF
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3.2.3 Accelerometer

Accelerometers are used to determine the displacement of the earth. These should be as close as the real displacement of the earth in earthquake in the place that the structure constructed. In this study, the accelerometers are using parameters such as shear wave velocity in the soil where the accelerometer records, the distance of the accelerometers to the fault and the frequency content. As shown in Table 5, three accelerometers are chosen based on code 2800. These accelerometers had the following three features:

  • Their shear wave velocity was in a range that was based on code 2800 (the soil could be classified as type three).

  • They were far from fault and

  • They had a wide range of frequency content in the district of structure period inclusion.

Table 5 Properties of selected accelerometer records
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These accelerometers were for earthquakes in Imperial Valley, Tabas and Northridge.

3.2.4 Procedure of Modelling in OpenSees

EBF with the proposed element and without it was modelled in 2D (Fig. 8). It was modelled in OpenSees (Mazzoni et al. 2006). The modelling of the columns and beams was used from the non-linear beam-column element with non-elastic fibre sections. For beams, columns and braces, the Giuffer-Menegotto-Pinto (Menegotto 1973) material is exploited. This had isotropic strain stiffening, yielding stress of 24,000,000 kg/m2 and the tangential modulus of 2.1e10 kg/m2 (steel 02 with Fy = 24,000,000 kg/m2). The proposed element was also modelled with the same material (steel 02) with regard to the relations between the force in the brace and its dimension, yielding stress and elastic model. This was concluded from the behaviour of the proposed element in ANSYS. The yielding stress and the elastic modulus of the ring with the diameter of 0.18 m and thickness of 0.012 m were 29,585,000 and 19,400,000,000 kg/m2, respectively. It is important to note that the bearings of frames were considered as hinge.

Fig. 8
figure 8

Input model in OpenSees

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For validation of the OpenSees model, the vibration modes resultant of modal analysis in SAP (SAP 2005) are compared with OpenSees for a four story (Fig. 8). The validation of the OpenSees model is presented in Table 6. To model the link beam in EBF, the assumed method of Remdan and Ghobarah (1995) is used, along with the modification by Richard (Richards 2004). According to Table 6, there is a good correlation between the results of SAP and OpenSees.

Table 6 The comparison of vibration mode between SAP and OpenSees
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3.3 Results of Modelling of the Proposed Element in ANSYS

3.3.1 Von Misses Stress Distribution in the Proposed Element

It is demonstrated that the Von Misses Stress Distribution in the proposed element with one cycle loading, as seen in Fig. 9. The inner stress of the ring was greater than the outer one. Thus, failure initiating from the inner part and extending outwards is anticipated. As the metals were weaker, the failure most likely occurred when the ring was under pressure and the inner part carried maximum compression stress.

Fig. 9
figure 9

Von misses stress distribution in proposed element

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3.3.2 The Sustainable Force and the Amount of Energy Dissipation by the Proposed Element

Figures 10 and 11 show the relations between the exerted force and energy dissipation in the proposed element. This is with regard to the thickness to diameter ratio and exerted force and the energy dissipation diagram in the proposed element for the 15 modelled elements with the mentioned dimension. A second order regression (Figs. 10a and 11a) is used to achieve good relations between the sustainable force and energy dissipation in the proposed element, with respect to the thickness to diameter ratio. Figures 10b and 11b show that, by decreasing the ring diameter and increasing its thickness, the amount of force and energy dissipation increases.

Fig. 10
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a The relation between applicable Force in element and portion of thickness to diameter b the diagram of applicable force in proposed element

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Fig. 11
figure 11

a The relation between energy dissipation and the portion of thickness to diameter b The diagram of applicable energy dissipation in proposed element

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3.3.3 Force Response Curve to the Displacement in the Proposed Element

Figure 12 shows the force response curve to the displacement of the proposed element. Taking this figure into consideration, one could argue that the proposed element has the same performance in compression and tension. This suggests that the model is reliable.

Fig. 12
figure 12

Force response to the displacement in proposed element

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3.3.4 The Hysteresis Curve of the Proposed Element

Figure 13 shows the hysteresis curve for one sample of the proposed element with the diameter 0.15 m and thickness of 0.18 m. As illustrated in this figure, the curve for this sample is wide and regular. This hysteresis curve indicates that the model dissipates energy efficiently.

Fig. 13
figure 13

Hysteresis curve for proposed element

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3.4 Results of the Non-linear Dynamic Analysis of the EBF in the Form of Time History

3.4.1 Maximum Relative Lateral Displacement in Stories

Figure 14 shows the maximum relative lateral displacement in stories of the frames with EBF and D-EBF under Imperial Valley, North‌Ridge, and Tabas earthquakes. The relative lateral displacement of the stories is an important and sensitive factor in the performance evaluation of structure. This is due to the amount of inserted damage to the structural and non-structural part in each story which is directly related to it. Consequently, this parameter can be considered as an index of damage. The achieved results indicate that the relative displacement in most of the stories decreased and, therefore, can reduce the amount of damage to the structures. The reduction in lateral displacement begins from the second story.

Fig. 14
figure 14

Maximum relative displacement under earthquake for EBF and D-EBF in stories a Imperial Valley b Northridge c Tabas

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3.4.2 Plastic Rotation in the Link Beam

Figure 15 shows the non-elastic measured rotation angle of the link beam in D-EBF, under the Imperial Valley, Northridge and Tabas earthquakes. By comparing and contrasting the results of maximum relative displacement in stories with plastic rotation of link beam, it is examined that the non-elastic rotation angle of link beam in structure level is very similar to the maximum relative displacement of each story in structure level. Thus, the relative displacement of each story can be considered as damage index.

Fig. 15
figure 15

Non-Elastic measured rotation angle of the link beam in EBF and D-EBF a Imperial Valley b Northridge c Tabas

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3.4.2.1 Maximum Base Shear and Last Story Displacement

Table 7 shows the maximum base shear and last story displacement in D-EBFs under the Imperial Valley, Northridge and Tabas earthquakes.

Table 7 Comparison of maximum base shear and roof displacement in EBF and D-EBF
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The existence of the proposed element in EBF led to a decrement in base shear of about 55%. This is compared to EBF and results in construction cost reduction, improving the foundation of the structure and the displacement reduction of the last story of approximately 10%.

3.4.2.2 Shear Amount of Link Beam

Figure 16 shows the maximum shear force of the link beam of stories. The existence of the proposed element led to a reduction of shear force in the link beam.

Fig. 16
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Maximum sheer force of link beam in EBF and D-EBF under a Imperial Valley b Northridge c Tabas

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4 Conclusion

Studies on Eccentrically Braced Frames show that using ductile element acts like a fuse and decreases the rotation of the link beam. The results of this research are as follows.

  1. A.

    Analysis Result of the Proposed Element

  2. •

    It is possible to increase the capacity of the ductile ring element using the proposed element. It is also expected that this element can dissipate a great amount of plastic energy.

  3. •

    The amount of bearing force and energy dissipation increase as the diameter of the steel ring decreases.

  4. •

    Since the maximum applied load to brace is equal to the maximum bearing force of the proposed element, the element can be designed in a way to ensure that buckling does not occur.

  5. •

    The relationship between the bearing force of the proposed element and the amount of dissipated energy with a regression of 99% was achieved. This is efficient for design purposes.

  1. B.

    Dynamic Analysis Result of the Eccentrically Braced Frames

  • Due to the relations between damage rate structural and non-structural members to relative displacement rate in stories, obtained results show a reduction in the maximum relative displacement in the stories with yielding rings in the D-EBFs. This trend occurs from the second to the last story.

  • The rotation of the link beam with the proposed element in D-EBFs in the last stories decreases considerably. This highlights the importance of the dissipation energy of the proposed element.

  • The amount of base shear in D-EBF including the yielding rings is about 55% of EBF.

  • The displacement rate in the D-EBF including the yielding rings is about 10% of EBF.

  • The existence of the proposed element leads to a reduction in the bearing shear force in the link beam in D-EBF.

To approach the modelling of the structure with eccentrically brace frame and considering all the items of the regulations, It is recommended that the structure in this research be modelled in 3D and its results with Compare the results of 2D modelling.

Also in this research, the proposed element is located in a place between the beam-to-column connection plate and the brace. Therefore, it is suggested that research be done on the location of the proposed element in a frame with EBF.