Circular tube-in-tube dampers for seismic resilience of structures

Abstract

A new brace-type slit damper, called ‘Circular Tube-in-Tube Damper (C-TTD), comprises two solid steel cylinders and one circular cross-section tube equipped with slotted holes, is proposed for seismic resilience of structures. In the proposed damper, a system of bolts was used to connect up various components of the damper, allowing inspection and replacement of the damaged components without any requirement for the replacement of the entire damper. Nonlinear finite element analyses using ABAQUS were carried out to verify the experimental results and to investigate the effect of damper geometric properties on the yield load capacity of the C-TTD dampers. The seismic performance characteristics of 4-storey, 8-storey, and 15-storey steel structures equipped with C-TTD dampers were determined by nonlinear time history analyses using three different earthquake excitations. The results indicated that when the structures were equipped with C-TTD dampers, the inter storey drift decreased in the range of 8%–55%, the base shear load decreased in the range of 27%–35%, and the input energy decreased in the range of 70%–80%, depending on the number of storeys and the earthquake type, compared to the counterpart structures without the damper.

Keywords

Slit damper tube-in-tube damper energy dissipation energy absorption seismic retrofitting

Introduction

Vibration control is a set of technical methods used to alleviate the impacts of seismic loading on structures by absorbing and dissipating a high percentage of vibration energy and therefore decreasing the displacement of structures without the need for retrofitting individual structural elements. Among all vibration control systems, dampers are considered to be an economical and practical solution and are widely used for the dynamic retrofitting of structures (Council et al., 1997). The most common type of dampers is metal dampers that dissipate the energy of vibration by damper material yielding through axial, shear, and flexural deformation mechanisms (Teruna et al., 2015). Metal dampers are categorised into several groups, of them the most popular are (1) Steel Slit Dampers (SSD), (2) Buckling Restrained Brace dampers (BRB), and (3) Tube-in-Tube Dampers (TTD) (Oh et al., 2009; Takeuchi et al., 2012; Teruna et al., 2015) SSD dampers are composed of one or multiple slotted sheets that dissipate the vibration energy through shear and flexural deformation mechanisms (Chan and Albermani, 2008; Ghabraie et al., 2010; Lee et al., 2015; Zheng et al., 2015). BRB dampers consist of a steel tube surrounding a metal core, where the space between the tube and the core is filled with concrete or mortar. The central core of the BRB withstands high values of axial loads, while the outer tube, which is filled with concrete or mortar, prevents buckling of the metal core when subjected to axial compressive stresses (Filip-Vacarescu et al., 2016; Iwata et al., 2000).

SSD dampers should be embedded in a structure such a way that they sustain plastic behavior before the structural elements (Aghlara and Tahir, 2018; Aminzadeh et al., 2020; Bayat and Shekastehband, 2019). While the SSD dampers are required to be mounted on secondary structures such as bracing systems for vibration dissipation of the structures (Amiri et al., 2018; Lee et al., 2015; Teruna et al., 2015), BRB dampers are directly integrated with the primary structural system. This poses a problem post-seismic loading as non-destructive testing methods cannot be used to examine the metal core and the surrounding concrete/mortar needs to be physically removed to conduct an examination (Tremblay et al., 2006). However, the major disadvantage of this system is the limitations associated with the quality control of the system for which demolishing of the damper is required.

TTD dampers were developed to address the drawbacks associated with SSD and BRB dampers, with TTD dampers consisting of an outer and an inner square hollow section tube with different lengths that are connected using a combination of plug and fillet weld. The outer tube consists of a series of strips and slits, with the energy of vibration dissipating via elastic and inelastic deformation of the strips (see Figure 1(a)) (Benavent-Climent, 2010). Benavent-Climent showed that the SSD dampers design equations could be used for the design of TTD dampers:

Q_{Y} = \min {n \frac{f_{y} t b^{2}}{2 h^{'}}, n \frac{2 f_{y} t b}{3 \sqrt{3}}}

(1)

Q_{B} = {n \frac{f_{B} t b^{2}}{2 h^{'}}, n \frac{2 f_{B} t b}{3 \sqrt{3}}}

(2)

δ_{Y} = \frac{Q_{Y} h^{'^{3}}}{n E t b^{3}} [1 + 3 \ln \ln \frac{h + 2 r}{h^{'}}] + \frac{3 Q_{Y} h^{'}}{2 n t b G} [1 + \ln \ln \frac{h + 2 r}{h^{'}}]

(3)

h^{'} = h + ⌊ 2 r^{2} / (h + 2 r) ⌋

(4)

where Q_y is the axial yield load, Q_B is the maximum load of the strips,

δ_{y} i s

the displacement associated with yielding of the strips, b and t are the strip width and thickness, respectively, r is the radius of the slotted holes, n is the total number of strips in a damper; f_y and f_B are the yielding and maximum tensile stress of the steel, respectively, h is the height of the strip, and h^’ is the height of an equivalent strip (see Figure 1(b)). Dongbin et al. proposed a novel BRB damper with a circular cross-section, with the results showing that the hysteresis curves of the damper were stable and saturated (Dongbin et al., 2016). Torkamani and Maalek developed a novel circular tube-in-tube buckling restrained damper, with the results showing a stable hysteretic behaviour of the damper when subjected to cyclic loadings (Heidary-Torkamani and Maalek, 2017). Shao et al. proposed a new type of metal damper called bracing shear fuses to avoid the limitations mentioned in conventional BRB and SSD dampers. they concluded that the ratio of width to height of steel strip has a significant effect on the cumulative inelastic ductility of the specimens (Shao et al., 2020). Jia et al. proposed a new type of shear bracing fuses that were connected in series, where the deformation capacity of these dampers was positively related to the number of shear fuses and that the dampers ruptured due to shear stresses (Jia et al., 2020).

Figure 1.

Geometric properties of TTD dampers [14]. (a) TTD damper (b) Details of the energy-dissipative part and equivalent strip of TTD damper. TTD: Tube-in-Tube Damper.

In TTD dampers, stress concentration occurs at the corners of the square hollow section tubes and consequently causes the fracture of the tubes. Additionally, the whole system of the TTD damper needs to be replaced after any failure associated with the components of the TTD dampers because these dampers are connected via welds (Benavent-Climent, 2010). In the reported study herein, circular cross-section tubes were used to replace square hollow section tubes in the TTD dampers to eliminate the stress concentration at the corners of the square cross-section tubes. Additionally, a system of bolts was used to replace welds in TTD dampers to connect up the various components of the damper, with the use of bolts allowing inspection and replacement of the damaged components without any requirement for the replacement of the entire damper. The proposed damper is identified as ‘Circular Tube-in-Tube Damper’ (C-TTD). In this study, the effect of strip and slit dimensions on the yielding load of the C-TTD dampers was investigated, and then the seismic performance characteristics 4-storey, 8-storey, and 15-storey steel structures with and without a C-TTD damper that were subjected to various earthquake scenarios was investigated.

C-TTD damper manufacture

A C-TTD damper was composed of two steel solid cylinders and one circular cross-section tube. At one end of each of the two solid cylinders, two 89° sectors (for eliminate contact between sectors and therefore eliminate the friction when the sectors slide into each other) and a hole with 15 mm diameter having a depth of 66 mm were removed (see Figure 2(a)). The steel solid cylinders were assembled with a 90° phase difference such that the unremoved sectors could slide into the removed sectors with no friction by creating several special cuts, while at the other end of these solid steel cylinders, there were connecting plates with a hole to connect the damper to the frame using a pinned support (Figure 2(c)). A series of strips were created by cutting a series of slits on the circular cross-section tube. The corners of the slits were rounded to prevent stress concentration at the corners of the slits (Figure 2(b)). This tube was connected up to the steel solid cylinders using bolts (see Figure 2(d)). The energy of vibration was dissipated by C-TTD damper via flexural/shear yielding of the strips. The circular cross-section tube that overlapped the solid cylinders prevented any out-of-plane movement of the damper (see Figure 2(d)). The overlapping length of the circular cross-section tube was not manufactured for ease of construction and due to limitations associated with the laboratory facilities and equipment (see Figure 3(b)).

Figure 2.

Details of circular tube-in-tube damper . (a) Schematic details of steel solid cylinders (b) Circular cross-section tube with several strips on wall (c) Assembly of steel solid cylinders (d) Assemble all parts of damper.

Figure 3.

Details of test set-up. (a) View of test set-up for C-TTD damper subjected to axial load (b) Close up view of C-TTD damper. C-TTD: Circular Tube-in-Tube Damper.

The C-TTD damper was designed based on the maximum axial load that could be applied by the available actuator in the laboratory. The geometric characteristics of the C-TTD damper are given in Table 1.

Table 1.

Geometric properties of circular tube-in-tube damper.

Outer tube diameter (mm)	Inner tube diameter (mm)	Tube thickness (mm)	Width of strip (mm)	Height of strip (mm)	Radius of slotted hole (mm)	Diameter of slotted hole (mm)	Total number of strips
60.5	54.5	3	6	10	7.5	15	8

Experimental study

One end of the C-TTD damper was attached to a pinned support bolted to a portal frame to constrain the damper against any axial movement, and the other end of the damper was attached to an actuator using a pinned support (see Figure 3(a)). The test procedure involved applying axial harmonic sinusoidal load with a frequency of 0.5 Hz and a maximum amplitude of 3.5 mm. The strips behaved as a series of fixed-ended beams and deformed in double curvature when the damper was subjected to sinusoidal harmonic load. The energy of the cyclic loading dissipated through shear and flexural yielding at strips.

A total of three cycles of axial harmonic sinusoidal loading were applied on the damper during the experimental program, with the associated hysteresis curves for axial load versus strip displacement being presented in Figure 4. The results showed that the hysteretic response was stable and symmetric, and the maximum compression and tensile loading values were approximately the same, indicating negligible energy dissipation due to friction between the components of the damper. Also, the shape of the loops, which was close to a rectangle, indicated an excellent energy dissipation capability of the damper.

Figure 4.

Hysteresis curve and backbone curve. (a) Axial load-displacement relationship of circular tube-in-tube damper (b) Backbone curve.

The backbone curve that was obtained from the axial load-strip displacement hysteresis relationships showed a symmetrical response in tension and compression (see Figure 4(b)). The structural parameters, namely axial yield load (Q_y), displacement associated with yielding of the strips (δ_y), initial elastic stiffness (K_e), maximum axial load (Q_B), maximum displacement (δ_max), and the ratio of the ultimate stiffness-to-the initial stiffness (K₂/K_e) were derived from the idealised backbone curve and are listed in Table 2. The ductility of C-TTD dampers (μ) is defined as the maximum displacement-to-the yielding displacement ratio. Since no failure occurred in C-TTD dampers, therefore, no ductility value was obtained for this damper type. The value of maximum axial displacement-to-the yielding displacement for C-TTD dampers was 13.46, which is slightly higher than the ductility of TiTBRB dampers reported in Ref. (Heidary-Torkamani and Maalek, 2017), i.e., μ = 12.5. The ductility value for the C-TTD damper is expected to be higher than the calculated maximum axial displacement-to-the yielding displacement (13.46), implying considerable ductility of C-TTD dampers.

Table 2.

Design parameters of circular tube-in-tube damper.

Q_y (kN)	Q_B (kN)	$δ_{y}$ (mm)	$δ_{\max}$ (mm)	K_e (kN/mm)	K₂ (kN/mm)	K ₂ /K _e	The value of maximum axial displacement-to-the yielding displacement
7.20	7.80	0.26	3.50	27.69	0.04	0.001	13.46

The metallic yielding devices are categorised as displacement dependent instruments (independent from the loading rate), in which effective damping and stiffness are the two most important nonlinear features for analytical modelling. The effective stiffness (K_eff, see Figure 4(a)), is calculated using equation (5) to determine the elastic strain energy (E_es) and the restoring force of the damper (K_eff (|δ_max ⁺| + |δ_max ⁻|)/2) in each cycle.

K_{e f f} = \frac{(| P_{i, m a n}^{+} | + | P_{i, \max}^{-} |)}{(| δ_{i, m a n}^{+} | + | δ_{i, \max}^{-} |)}

(5)

The effective damping of a system indicates the energy dissipation capacity of a device, which is related to the displacement of the device. The effective damping of a device (β_eff) is calculated using equation (6)

β_{e f f} = \frac{1 E_{l o o p}}{4 π E_{e s}} = \frac{2 E_{l o o p}}{π K_{e f f} {(| δ_{i, m a n}^{+} | + | δ_{i, \max}^{-} |)}^{2}}

(6)

in which E_loop and E_es are the total dissipated energy and the elastic strain energy, respectively (Chopra, 1995). Total dissipated energy in each cycle of hysteresis is equal to the enclosed area of a complete cycle that there are smaller amounts in the elastic zone and a considerable volume in the inelastic zone. The effective stiffness, effective damping and total dissipated energy of the damper are given in Table 3.

Table 3.

Effective damping, stiffness range and total dissipated energy of circular tube-in-tube damper.

Effective stiffness range (kN/mm)	Effective damping range (%)	Total dissipated energy (J)
4.38	28.1	94.6

The deformation of the strips during the experiment is shown in Figure 5.

Figure 5.

Test configuration of circular tube-in-tube damper.

The strips behaved as a series of fixed-ended beams and deformed double curvature when the damper was subjected to axial load. The ultimate displacement of the C-TTD damper depends on the dimension of the strips, similar to SSD dampers; therefore, selecting the strips that are proportional to the scale of the structure will visit the deformation demand of the structures.

Numerical modelling

The general-purpose finite element (FE) program ABAQUS was employed to develop a nonlinear elastic-plastic FE model for the C-TTD damper when subjected to harmonic loading. Material properties were modelled using true stress-strain values calculated from engineering stress-strain relationships, which were obtained from the tensile test on circular cross-section tubes, with the averaged results given in Figure 6.

Figure 6.

Stress-strain relationship of circular tube-in-tube damper material. (a) Average engineering stress-strain relationship (b) Close-up view of the stress-strain relationship within elastic range.

C3D20R solid elements were used to model steel tubes. The C3D20R (twenty-node brick element with reduced integration) element is a general-purpose quadratic brick element, with reduced integration (2 × 2 × 2 integration points). This element properly simulates the mechanical behaviour of isotropic materials in bending and rarely exhibits hour glassing despite the reduced integration. The General Contact algorithm was used to model the contact between the steel rigid cylinders and circular cross-section tube. Smaller mesh size was used to model the circular cross-section tube when compared to cylinders because a higher level of stress concentration occurred in the tube. Only one-fourth of the specimen was modelled due to the symmetry of the model (Figure 7).

Figure 7.

Finite element model of circular tube-in-tube damper.

One of the steel solid cylinders was constrained against axial displacement (z-direction for the longitudinal direction of the tube) and a harmonic displacement (f = 0.5 Hz and PGD = 3.5 mm) was applied at the other end of the steel solid cylinder, as shown in Figure 8.

Figure 8.

Harmonic loading protocol.

The system was subjected to an implicit dynamic analysis. Figure 9 shows the results of the analysis along with the strain rate for the C-TTD damper. Energy is dissipated by the shear/bending yields of the strips (see Figure 9).

Figure 9.

Equivalent plastic strain at the maximum displacement of finite element model.

In Figure 10, the axial load versus strip displacement of the C-TTD damper obtained from experiment and FE analysis are compared, with the results showing a good correlation between the test and the numerical simulation. The numerical model showed a stable and symmetric response, and the elastic and post-elastic stiffness of the model were equal at both tensile and compression modes. From Figure 10, it can be deduced that the damper yielded at a small displacement (δ_y = 0.26 mm) and exhibited a stable hysteretic behaviour with a gradual transition between the elastic and inelastic regimes. Its yielding force and its yielding displacement agree with those obtained experimentally and with the simplified models. Total dissipated energy obtained from experiment and FE analysis were 94.6 J and 103.97 J that had 9% difference from each other.

Figure 10.

Experimental versus numerical responses.

Parametric study

A parametric study was conducted to investigate the effect of wall thickness, width and height of strips, the diameter of slotted holes and diameter of circular cross-section tube on the damper designing parameters using FE analysis. 20 models were constructed and the hysteresis curves for varying parameters obtained from the FE analysis are compared in Figure 11.

Figure 11.

Axial load-displacement relationship obtained from finite element analysis. (a) Effect of strip width (b) Effect of strip thickness (c) Effect of diameter of the slotted holes (d) Effect of strip height (e) Effect of circular tube diameter.

Each specimen assigning with a code ‘Dx-by-tz-hv-dw’, in which the sub code ‘Dx’ refers to diameter of the circular cross-section tube, ‘by’ refers to the strip width, ‘tz’ refers to the thickness of strip, ‘hv’ refers to the height of strip, and ‘dw’ refers to diameter of the slotted holes of the specimen in each damper group.

In Figure 11(a), axial load versus displacement relationships of C-TTD damper with a cross-section diameter of 114.3 and various strip widths equal to b = 7, 9, 12 and 14 mm are compared with C-TTD damper with a cross-section diameter of 88.9 having various strip widths equal to b = 5, 6, 8, 10, and 12 mm. The results indicated that with increasing the width of strips, the energy absorption capacity of the damper increased. In Table 4, the values of axial yielding load and the displacement associated with yielding of the strips that were obtained from FE analyses and equations (1) and (3) are compared, with the results showing that with increasing the width of strips equation (1) gave a better prediction of the FE analysis. Additionally, from Table 4, it can be deduced that with increasing the ratio of the width of strip-to-height of the strip the axial yielding load, the ductility capacity and the effective stiffness increased, and with increasing the width of the strip, the displacement associated with yielding of strips decreased. For all the FE models, the maximum load of the strips (Q_B) was within 1–1.5 times the axial yielding load (Q_y).

Table 4.

Axial yielding load of strips and associated displacement for varying strip widths.

Model	b/h	Q_y (kN)	Q_yt (kN)	$δ_{y}$	$δ_{y t}$	Error (%)	$μ$	K _eff
Model	b/h	Q_y (kN)	Equation (1)	$δ_{y}$	Equation (3)	Error (%)	$μ$	K _eff
D114.3-b7-t4.4-h14-d19	0.50	19.84	15.46	0.26	0.15	22	30.50	5.57
D114.3-b9-t4.4-h14-d19	0.75	29.40	25.55	0.25	0.14	13	31.80	7.69
D114.3-b12-t4.4-h14-d19	0.86	52.30	45.43	0.24	0.13	13	33.00	12.16
D114.3-b14-t4.4-h14-d19	1	65.20	61.84	0.23	0.13	5	34.10	15.36
D88.9-b5-t4-h12-d16	0.42	11.04	8.42	0.27	0.14	24	29.63	4.30
D88.9-b6-t4-h12-d16	0.50	14.54	12.13	0.26	0.13	16	30.42	4.92
D88.9-b8-t4-h12-d16	0.67	25.32	21.57	0.25	0.12	15	31.84	6.65
D88.9-b10-t4-h12-d16	0.83	37.88	33.70	0.24	0.11	11	32.87	9.13
D88.9-b12-t4-h12-d16	1	51.60	48.53	0.22	0.11	6	35.40	12.17

Note. Error = $(\frac{Q_{y t} - Q_{y}}{Q_{y}}) \times 100$

In Figure 11(b), axial load versus displacement relationships of the C-TTD damper with a cross-section diameter of 114.3 having strip thicknesses of t = 2 and 4.4 mm are compared with C-TTD damper with a cross-section diameter of 88.9 mm having strip thicknesses of t = 2 and 4 mm, with the results indicating that with increasing the thickness of strips the axial yielding load and the effective stiffness of the C-TTD dampers increased, but the ductility capacity decreased. It should be noted that there is an upper bound on the amount that the strip thickness can be increased because as the thickness increases, the plastic deformation of the damper is reduced and there is a possibility that the damper will not yield before the structure. In Table 5, the values of the axial yielding load and the displacements associated with yielding of the strips obtained from FE analyses and equation (1) are given, with the results showing that the value of strip thickness did not affect the displacement associated with yielding of the strips.

Table 5.

Axial yielding load of strips and associated displacement for varying thicknesses of strips.

Model	b/h	Qy (kN)	Q_yt (kN)	$δ_{y}$	Error (%)	$μ$	K _eff
Model	b/h	Qy (kN)	Equation (1)	$δ_{y}$	Error (%)	$μ$	K _eff
D114.3-b12-t2-h14-d19	0.86	22.96	20.65	0.24	10	33.2	5.37
D114.3-b12-t4.4-h14-d19	0.86	52.40	45.43	0.24	13	32.96	12.16
D88.9-b10-t2-h12-d16	0.83	19.08	16.85	0.24	12	33.1	4.49
D88.9-b10-t4-h12-d16	0.83	37.88	33.70	0.24	11	32.87	9.13

In Figure 11(c), the axial load versus displacement relationships and in Table 6 the values of axial yielding load, the ductility capacity, the effective stiffness, and the associated displacement for C-TTD dampers with varying diameters of the slotted holes that were equal to d = 8 and 19 mm are compared. The results indicated that with increasing the diameter of the slotted holes the value of the axial yielding load, the ductility capacity and the effective stiffness slightly decreased while the displacement associated with the yielding load slightly increased.

Table 6.

Axial yielding load of strips and associated displacement for varying diameters of the slotted holes.

Model	b/h	Q_y (kN)	Q_yt (kN)	$δ_{y}$	Error (%)	$μ$	K _eff
Model	b/h	Q_y (kN)	Equation (1)	$δ_{y}$	Error (%)	$μ$	K _eff
D114.3-b7-t2-h14-d19	0.50	8.70	7.12	0.25	18	31.28	2.89
D114.3-b7-t2-h14-d8	0.50	9.80	8.85	0.26	10	30.76	2.50

The effect of heights of strips (h = 14, 18 and 20 mm) on the axial load versus displacement relationships for C-TTD dampers is presented in Figure 11(d), with the results indicating that with increasing the height of strips, the energy absorption capacity of the damper decreased. In Table 7, the values of the axial yielding load for various heights of strips and the associated displacements obtained from FE analyses and equation (1) are given, with the results showing that with decreasing the height of the strips the axial yielding load, the ductility capacity and the effective stiffness increased, whereas the displacement associated with yielding of the strips decreased.

Table 7.

Axial yielding load of strips and associated displacement for varying heights of strips.

Model	b/h	Q_y (kN)	Q_yt (kN)	$δ_{y}$	Error (%)	$μ$	K _eff
Model	b/h	Q_y (kN)	Equation (1)	$δ_{y}$	Error (%)	$μ$	K _eff
D141.3-b12-t8.4-h14-d20	0.86	55.31	48.54	0.23	12	34.47	13.17
D141.3-b12-t8.4-h18-d20	0.67	48.27	41.48	0.24	14	33.04	11.28
D141.3-b12-t8.4-h20-d20	0.60	43.32	38.60	0.25	11	31.76	10.35

Axial load versus displacement relationships for C-TTD dampers with various diameters of the circular cross-section tube, namely D = 88.9 and 114.30 mm, are compared in Figure 11(e), with the results indicating that the diameter of the circular cross-section tube had an insignificant effect on the energy absorption capacity of the dampers. The reason was the value of strip height and width were the same for both diameters; therefore, similar values of energy were dissipated during the structure displacement. In Table 8, the values of axial yielding load and the associated displacements obtained from FE analyses and equation (1) are listed, with the results showing with increasing the diameter the equation (1) gave a better prediction of the FE analysis. From Table 8, it can also be deduced that with increasing the diameter of the circular cross-section tube, the value of the ductility capacity and the effective stiffness slightly decreased.

Table 8.

Axial yielding load of strips and associated displacement for varying diameters of circular cross-section tube.

Model	b/h	Q_y (kN)	Q_yt (kN)	$δ_{y}$	Error (%)	$μ$	K _eff
Model	b/h	Q_y (kN)	Equation (1)	$δ_{y}$	Error (%)	$μ$	K _eff
D114.3-b10-t2-h12-d16	0.83	19.08	16.85	0.24	12	33.08	4.49
D88.9-b10-t2-h12-d16	0.83	18.80	16.85	0.25	10	31.64	4.53

In Tables 4–8, axial yielding load for varying values of widths, thickness, diameters of the slotted holes, heights of strips, and diameters of the circular cross-section tubes obtained from FE analysis are compared with the predictions by equation (1). The results indicated that the predictions by equation (1) had a close correlation with the FE results and the predictions deviated from the FE analysis by a maximum value of 24%. The value of yielding load of the C-TTD dampers depended on the number of strips and their geometric characteristics i.e., the width, the thickness, the height of the strips and the yielding stress of the strip material. Therefore, C-TTD dampers with proper dimensions can be employed for the seismic retrofitting of the structures.

Numerical analysis of multi-storey buildings with C-TTD dampers

Three multi-storey steel structures (4-storey, 8-storey and 15-storey) were designed and nonlinear time history analyses were performed for varying earthquake scenarios, namely Tabas (16 September 1978), Imperial valley (19 May 1940), Kobe (16 January 1995) using SAP2000. The earthquake scenarios were scaled for a peak ground acceleration equal to 0.35 g according to the Iranian National Building Code, (Monir and Zeynali, 2013; Zeynali et al., 2018) with the specifications of the earthquakes listed in Table 9.

Table 9.

Ground motion records for the nonlinear analysis of the multi-storey frame.

R	Earthquake	Station	Magnitude	Latitude	Longitude
1	Tabas (1978-09-16)	Iran 9101 Tabas	7.35	33.5800	56.9200
2	Imperial vally (1940-05-19)	Array#9Elcentro	6.95	32.7940	−115.549
3	Kobe, Japan (1995-01-16)	99999 TOT	6.9	35.4850	134.2400

The plan view of the designed buildings is shown in Figure 12. The typical storey height of the buildings was 3.20 m and the span of the beams was 4 m. The buildings were designed for the p-delta effect and had a dead load of 500 kg/m² for all stories, and a live load of 200 kg/m² for all floors except for the roof, which had a live load equal to 150 kg/m², according to the Iranian National Building Code (Divisions 6 and 10). Two structural systems were considered for the seismic design of the building, including (1) a steel moment frame and (2) the same steel moment frame that was equipped with a system of C-TTD dampers. The pinned supports at the locations of the connections to the dampers were designed according to FEMA 356 (see Figure 12(b)). The C-TTD damper was modelled using multi-linear plastic link elements. The stiffness, yielding load, and displacement associated with the yielding load were modelled in the axial direction of the damper (U1 herein). The modelled dampers were in the original scale (proportional to the dimensions of the modelled structure) and had larger axial displacement capability when compared to the tested C-TTD damper, which was constructed in small size due to laboratory limitations. Therefore, the hysteresis diagrams of the dampers (axial load-displacement relationships) obtained from the FE analysis using ABAQUS were used to model the energy dissipation characteristics of the damper (Figure 13). Dampers are installed diagonally in the frame, with the deformation of the damper depending on the angle between the damper as a diagonal member and the beam placed horizontally in the frame. The damper hysteresis diagram for each storey in the numerical model is defined as a two-liner curve with no displacement limitation, according to Figure 14. The stiffness and yielding strength of the dampers were reduced from the first storey to the top storey to avoid a soft storey collapse. The optimum values for the stiffness and yielding strength were designed based on the minimum base shear load and the minimum relative displacement of the floors using a trial-and-error method (see Table 10).

Figure 12.

Structural model of 8-storey building. (a) Isometric view (b) Front view.

Figure 13.

Axial load-displacement relationship of top stories obtained from the finite element analysis using ABAQUS. (a) 4-storey (b) 8-storey (c) 15-storey.

Figure 14.

Definition of axial load-displacement relationship of dampers in numerical analysis of structures (top storey of 15-storey structures).

Table 10.

Axial yielding load of dampers for various stories.

Basic case	Axial yielding load (kN)
Basic case	1st	2nd	3rd	4th	5th	6th	7th	8th	9th	10th	11th	12th	13th	14th	15th
4-storey	140	130	120	110
8-storey	160	145	130	115	100	85	70	55
15-storey	210	200	190	180	170	160	150	140	130	120	110	100	90	80	70

In Figure 15, the maximum inter-storey drift ratios (relative translational displacement between two consecutive floors divided by the storey height) for the steel moment frames with and without dampers when the buildings (4-storey, 8-storey, and 15-storey) were subjected to various earthquake scenarios are compared. The results showed that the inter-storey drift for the frame equipped with the damper was significantly smaller than the counterpart frame without the damper. The value of inter-storey drift for the 4-storey structure equipped with dampers ranged from 8% to 55% of the 4-storey structure without a damper. For the 8-storey structure inter-storey, this value ranged from 26% to 51%, and for the 15-storey structure, this value ranged from 33% to 49%. The inter-storey drift ratio of the bottom stories for the structures with and without dampers, when analysed for the Kobe earthquake, were similar, with this behaviour depending on the properties of the ground motion.

Figure 15.

Comparison of drift ratios in the stories under earthquakes. (a) Tabas earthquake, 4-storey; Tabas earthquake, 8-storey; Tabas earthquake, 15-storey (b) El Centro earthquake, 4-storey; El Centro earthquake, 8-storey; El Centro earthquake, 15-storey (c) Kobe earthquake, 4-storey; Kobe earthquake, 8-storey; Kobe earthquake, 15-storey.

The maximum inter-storey drift ratio of the 4-storey, 8-storey and 15-storey buildings equipped with C-TTD dampers were 0.45, 0.40 and 0.47 for the Tabas earthquake, 0.74, 0.6 and 0.59 for the El Centro earthquake, and 0.95, 0.7 and 0.61 for the Kobe earthquake, respectively. These values were smaller than the life safety limit state (equal to 1.0% of the storey height), according to FEMA 356, indicating that C-TTD dampers can be employed for seismic retrofit of the existing structures.

Load-inter-storey drift responses of damper (The non-dimensionalized deformation capacity of slit dampers) under the Kobe earthquake in the storeys with maximum inter-storey drift ratio were extracted, as shown in Figure 16. The ductility value for C-TTD damper in these storeys of 4-storey, 8-storey and 15-storey buildings were 47.7, 35.43 and 25.4 respectively.

Figure 16.

Load-inter-storey drift responses. (a) 4-storey (b) 8-storey (c) 15-storey.

In Table 11, the base shear load of the multi-storey steel structures for various earthquake scenarios are presented, with the results showing that by equipping the structures with the C-TTD dampers the base shear load decreased on average by a range of 27%–35%. However, the application of this damper for a 4-storey building when subjected to the Kobe earthquake increases the base shear by 24%, attributing to the ground motion characteristics of the Kobe earthquake.

Table 11.

Comparison of maximum base shear load in multi-storey structure without and with circular tube-in-tube dampers.

		4-storey structure (kN)			8-storey structure (kN)			15-storey structure (kN)
		Without damper	With damper	Error (%)	Without damper	With damper	Error (%)	Without damper	With damper	Error (%)
Tabas	x	1147.8	942.6	18	1577.6	1235.9	22	2278.2	1482.1	35
Tabas	y	1127.9	961.8	15	1622.3	1265.2	22	2282.9	1428.5	37
El centro	x	2127.4	1132.6	47	1604.2	1139.8	29	3260.6	1625.2	50
El centro	y	2122.0	1142.8	46	1852.9	1158.4	37	3278.5	1690.6	48
Kobe	x	1215.2	1504.3	−24	1432.2	1070.9	25	1590.6	1550.3	3
Kobe	y	1222.1	1525.5	−25	1569.1	1097.1	30	1722.5	1549..6	10

In Figure 17, the internal and the absorbed energy have been shown for the multi-storey buildings when subjected to the three scaled earthquakes.

Figure 17.

The input and the absorbed energy in multi-storey buildings under earthquakes. (a) Tabas earthquake, 4-storey; Tabas earthquake, 8-storey; Tabas earthquake, 15-storey (b) El Centro earthquake, 4-storey; El Centro earthquake, 8-storey; El Centro earthquake, 15-storey (c) Kobe earthquake, 4-storey; Kobe earthquake, 8-storey; Kobe earthquake, 15-storey.

Figure 17 shows that a considerable amount of energy delivered to the structure is absorbed by the dampers. By adding these dampers to the structures, the average energy absorbed by the structures decreased, but total dissipated inelastic energy in the frames equipped with the damper was much higher than the frames without the damper and almost all the energy was dissipated in the dampers. Input energy to the structures, energy absorbed by the dampers and the ratio of energy absorbed by the dampers to input energy are listed in Table 12, with the results showing that about 70%–80% of the input energy was dissipated by the dampers. Therefore, the contributions of beams and columns to energy absorption due to inelastic deformation decreased in the structures with dampers. Moreover, adding C-TTD dampers to the structures resulted in the concentration of damage to the dampers rather than the structural elements. These dampers are installed and removed easily. Hence, after a severe earthquake, the structures equipped with dampers can be rehabilitated by replacing the damaged parts of dampers, allowing seismic performance in line with their original design.

Table 12.

Comparison of maximum input energy and absorbed energy by dampers in structures without and with circular tube-in-tube damper.

	4-storey			8-storey			15-storey
	Input energy (kJ)	Absorbed energy (kJ)	Ratio^a (%)	Input energy (kJ)	Absorbed energy (kJ)	Ratio (%)	Input energy (kJ)	Absorbed energy (kJ)	Ratio (%)
Tabas	15.7	13.6	0.87	273.6	216.5	0.79	536.5	386.1	0.72
El centro	341.2	277.5	0.81	441.6	316.3	0.72	837.1	543.0	0.65
Kobe	731.3	569.4	0.78	769.5	550.0	0.72	1237.2	872.0	0.71

^aRatio = Absorbed energy/Input energy.

The equivalent viscous damping ratios of the structures equipped with C-TTD dampers were determined by analysing the multi-storey structures with no dampers and changing the viscous damping ratios of these structures until the displacements observed in the damper-equipped structures were achieved. The equivalent viscous damping ratios of the 4-storey, 8-storey and 15-storey buildings for various earthquake time-histories are given in Table 13, with the results showing that the average viscous damping ratio of the structures equipped with C-TTD dampers were 19%, 16% and 14%, respectively.

Table 13.

Equivalent viscous damping ratios in multi-storey structures equipped with circular tube-in-tube dampers.

	4-storey		8-storey		15-storey
	Viscous damping ratio	Average	Viscous damping ratio	Average	Viscous damping ratio	Average
Tabas	0.21	0.19	0.19	0.16	0.16	0.14
El Centro	0.20		0.15		0.14
Kobe	0.17		0.13		0.12

Future research plan

While TTD dampers proposed by Benavent-Climent were flat, C-TTD dampers proposed in the current study reported herein were curved. Although a series of parametric studies were performed in Parametric study, a comprehensive parametric study is required to offer an equation to predict the strength and stiffness evaluation of the newly proposed C-TTD dampers.

In the study reported herein, three earthquakes were selected for studying the seismic response of steel frame structures equipped with C-TTD dampers. For future research studies, it is recommended the seismic excitations be selected according to the design seismic spectrum of a seismic design code to arrive at more convincing conclusions.

The response of structures equipped with C-TTD dampers will then be different from the structural response reported earlier in Numerical analysis of multi-storey buildings with C-TTD dampers.

Conclusion

In the reported study herein, a new brace-type slit damper called ‘Circular Tube-in-Tube Damper’ (C-TTD) was proposed for improving the seismic resilience of the structures. C-TTD dampers are composed of two steel solid cylinders and one circular cross-section tube equipped with slotted holes, with the components connected using bolts. C-TTD dampers offer the advantages of easier inspection and replacement of the damaged components when compared to conventional TTD, which require complete replacement of the entire damper if a component is damaged. The effect of strip and slit dimensions on the axial yielding capacity of the C-TTD dampers were investigated using FE modelling. Additionally, the seismic performance characteristics of 4-storey, 8-storey and 15-storey steel frame structures that were equipped with C-TTD dampers were analysed for varying earthquake ground motions and the results were compared with the response of counterpart buildings with no dampers. Conclusions drawn are listed as follows:

1. Theoretical models that were developed by Benavent-Climent (Benavent-Climent, 2010) for predicting the axial yielding capacity of the steel slit dampers were found to be in good agreement with the yielding capacity of C-TTD dampers and therefore can be used for the design of C-TTD dampers.

2. By equipping the steel frame structures with C-TTD dampers the inter-storey drift of the stories decreased by a range of 8%–55%, and the structures remained elastic by decreasing the life safety limit state of the storeys below 1.0% of the storey height.

3. The numerical analysis showed that C-TTD dampers absorbed 70%–80% of the vibration energy of the structures. The average viscous damping ratio for a 4-storey structure equipped with C-TTD dampers was 19%, for an 8-storey structure was 16% and for 15- storey structure was 14%.

4. The base shear load in steel frame structures in earthquake scenarios decreased by a range of 27%–35% when C-TTD dampers were equipped.

In the reported study herein, a single C-TTD damper geometry was studied, and therefore these findings are not yet conclusive, and further experimental and numerical studies must be carried out to validate the results and the applicability of the developed equation by Benavent-Climent (Benavent-Climent, 2010) for other sizes of C-TTD dampers.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Neda Fazlalipour

References

Aghlara

Tahir

(2018) A passive metallic damper with replaceable steel bar components for earthquake protection of structures. Engineering Structures 159: 185–197.

Aminzadeh

Kazemi

Tavakkoli

(2020) A numerical study on optimum shape of steel slit dampers. Advances in Structural Engineering 23(14): 2967–2981.

Amiri

Najafabadi

Estekanchi

(2018) Experimental and analytical study of block slit damper. Journal of Constructional Steel Research 141: 167–178.

Bayat

Shekastehband

(2019) Seismic performance of beam to column connections with T-shaped slit dampers. Thin-Walled Structures 141: 28–46.

Benavent-Climent

(2010) A brace-type seismic damper based on yielding the walls of hollow structural sections. Engineering Structures 32(4): 1113–1122.

Chan

Albermani

(2008) Experimental study of steel slit damper for passive energy dissipation. Engineering Structures 30(4): 1058–1066.

Chopra

(1995) Dynamics of Structures: Theory and Applications to Earthquake Engineering. Englewood Cliffs, NJ: Prentice Hall.

Council

Rojahn

Shapiro

, et al. (1997) NEHRP Guidelines for the Seismic Rehabilitation of Buildings. DIANE Publishing.

Dongbin

Xin

Peng

, et al. (2016) Experimental study and finite element analysis of a buckling-restrained brace consisting of three steel tubes with slotted holes in the middle tube. Journal of Constructional Steel Research 124: 1–11.

10.

Filip-Vacarescu

Vulcu

Dubina

(2016) Numerical model of a hybrid damping system composed of a buckling restrained brace with a magneto rheological damper. Mathematical Modelling in Civil Engineering 12(1): 13–22.

11.

Ghabraie

Chan

Huang

, et al. (2010) Shape optimization of metallic yielding devices for passive mitigation of seismic energy. Engineering Structures 32(8): 2258–2267.

12.

Heidary-Torkamani

Maalek

(2017) Conceptual numerical investigation of all-steel tube-in-tube buckling restrained braces. Journal of Constructional Steel Research 139: 220–235.

13.

Iwata

Kato

Wada

(2000) Buckling-restrained braces as hysteretic dampers. In: Behavior of Steel Structures in Seismic Areas. CRC Press, 33–38.

14.

Jia

L-J

Xie

J-Y

Wang

, et al. (2020) Initial studies on brace-type shear fuses. Engineering Structures 208: 110318.

15.

Lee

C-H

Min

J-K

, et al. (2015) Non-uniform steel strip dampers subjected to cyclic loadings. Engineering Structures 99: 192–204.

16.

Monir

Zeynali

(2013) A modified friction damper for diagonal bracing of structures. Journal of Constructional Steel Research 87: 17–30.

17.

S-H

Kim

Y-J

Ryu

H-S

(2009) Seismic performance of steel structures with slit dampers. Engineering Structures 31(9): 1997–2008.

18.

Shao

Jia

L-J

, et al. (2020) Experimental study on damage detectable brace-type shear fuses. Engineering Structures 225: 111260.

19.

Takeuchi

Hajjar

Matsui

, et al. (2012) Effect of local buckling core plate restraint in buckling restrained braces. Engineering Structures 44: 304–311.

20.

Teruna

Majid

Budiono

(2015) Experimental study of hysteretic steel damper for energy dissipation capacity. Advances in Civil Engineering 2015: 631726.

21.

Tremblay

Bolduc

Neville

, et al. (2006) Seismic testing and performance of buckling-restrained bracing systems. Canadian Journal of Civil Engineering 33(2): 183–198.

22.

Zeynali

Monir

Mirzai

, et al. (2018) Experimental and numerical investigation of lead-rubber dampers in chevron concentrically braced frames. Archives of Civil and Mechanical Engineering 18(1): 162–178.

23.

Zheng

Guo

(2015) Analytical and experimental study on mild steel dampers with non-uniform vertical slits. Earthquake Engineering and Engineering Vibration 14(1): 111–123.