Seismic behavior of braced steel frames with pipe dampers

Abstract

Steel pipe dampers offer advantages such as a simple structure, low cost, high energy absorption and dissipation, consistent functionality under cyclic loading, and ductility. Dual-pipe dampers show improved performance over single pipe dampers in terms of strength. The current study focused on the structural performance of the dual-pipe system. The seismic performance of steel-framed structures having 4, 8, or 16 stories with either a simple moment frame or a braced frame equipped with pipe dampers were subjected to seismic loading and investigated using the finite element method. The performance of the models was examined by considering the base shear and lateral displacement of the roof as well as the von Mises distribution. The stress distribution caused by the plastic damage concentration increased in the pipe dampers in the 4- and 8-story models and the base shear decreased 50% in the 4-story models equipped with a pipe damper. The results showed that, in the 16-story models, the strength in the damping system should be designed in accordance with the other elements. In addition, the strength of the damping system can be increased by increasing the number of pipes and their thickness.

Keywords

pipe damper seismic performance steel structures

Introduction

The moment frame is a superior type of steel frame that uses the rigid connections between each of its constituent members. This configuration is able to resist lateral and overturning forces because of the bending moment and shear strength that is inherent in its members and the connecting joints. Therefore, the strength and stiffness of the moment frame in seismic design depends on the mechanical characteristic of its members. AISC 341-05 (ANSI, 2005) provides detailed design requirements relating to materials, framing members such as columns, beams, column-beam joints, connections, and construction quality assurance and quality control (Ghaderi et al., 2015; Maleki and Mohammadi, 2017). In-elastic performance in the moment frame is proposed to be accommodated through the formation of plastic hinges at the column bases and the beam-column joints (Han et al., 2019; Mohsenian et al., 2020; Naghshineh et al., 2019). Plastic hinges form through flexural yielding of beams and columns and shear yielding of panel zones. In addition to the behaviors discussed above, research and common sense suggest that a number of other failure modes should also be considered when designing moment frames, some of which have not necessarily been observed in past earthquakes. These modes, associated with frame behavior and not that of other elements such as diaphragms and foundations.

The cost-effectiveness, ease of installation and replacement, and high efficiency of yielding steel dampers for alleviating damage inflicted by earthquakes and for seismic retrofits of seismically weak structures are advantages of these types of inactive dampers. The damage caused by dynamic loading from earthquakes on a structure is concentrated in the yielding dampers, allowing the other structural elements to remain in the elastic zone. In the past 40 years, various types of steel yielding damping systems have been introduced. The mechanism of plastic deflection and their shear, flexural, and torsional behavior allows energy to dissipate in these dampers (Amadeo et al., 1998; Benavent-Climent, 2006; Chan and Albermani, 2007; Hanson et al., 1993; Symans et al., 2008).

Hsu and Halim (2018) proposed a design for the steel braces equipped with steel curved dampers. They reported that the braces exhibited high energy absorption and dissipation and improved the mechanical performance of the steel frames. Qu et al. (2019) presented a design for the application of U-shaped damping sheets. They concluded that the hysteresis loop of the U-shaped steel dampers exhibited stable behavior and the proposed design showed high energy absorption and dissipation. Columns equipped with slit dampers were investigated by Liu et al. (2019). In contrast to previous designs, their slit damper was placed at the foot of the column. The results indicated that this method provides appropriate ductility for the column as well as the required stability and stiffness. Naeem and Kim (2019) suggested a design for the application of multi-slit dampers that were a combination of weak and strong dampers. The weak dampers were expected to dissipate energy generated by weak-to-moderate earthquakes and the strong dampers were expected to dissipate energy generated by strong earthquakes. This design also has been used for the seismic retrofit of concrete structures. Wei et al. (2019) proposed a novel principle for improving frame structures, which is called the partially out-shift plastic zone. They using this principle, developed a modified steel frame structure with corrugated steel plates. Ghabussi et al. (2020) focused on using steel curved dampers systems in studying the structural behavior of steel portal frames. In their study, five dampers with the same thickness and length, yet with different eccentricities and angles, had been used in the pitched roof symmetric and mono-pitch portal frames.

An innovative yielding steel damper with a pure rotational mechanism was developed by Mahyari et al. (2019) in which the story shear force, excluding the bending force, is transferred to the damper. High energy absorption and suitable ductility are among the advantages of this damper. Chen et al. (2019) introduced yielding steel dampers with two yield points that are composed of two spiral sections. Testing showed that this damper is capable of absorbing and dissipating energy and that its geometric design adequately prevents fatigue failure resulting from cyclic loading. Maleki and Bagheri (2010) proposed an inactive steel damper called a “pipe damper.” They reported that this damper is able to absorb and dissipate energy under cyclic loading. Stable cyclic performance and noticeable energy dissipation are the advantages of this system. They estimated the strength and stiffness of the pipe dampers and found that, despite their suitable ductility, it was, in fact, less than those of other types of yielding dampers. The application of dual-pipe dampers has been considered in order to improve the performance of these dampers.

Finite element modeling

Figure 1 is a schematic of a type of a dual-pipe damper as developed by Maleki and Mahjoubi (2013). Such dampers comprise two horizontal pipes that are welded to one another and to their support. The materials used to manufacture the pipe dampers should have a strain rate of at least 25% so as to provide an adequate amount of ductility. Also, St-37 steel material were used to connect the stiffened plates together. They reported that, in order to achieve optimum energy dissipation using dual-pipe dampers, the deflection limits by can be defined as:

Δ_{\max} = D / \tan θ - D [1 + \sin (100 ° - 90 °)]

(1)

Figure 1.

(a) Schematic of dual-pipe damper device and (b) maximum allowable deflection of a dual pipe damper.

where the length of line AB in the deformed dampers (L_AB)^u is equal to the arch of the two semicircles in the undeformed case (L_AB)⁰.

(L_{AB})^{u} = (L_{AB})^{0} = 2 π D (100 / 360)

(2)

\begin{matrix} θ = \sin^{- 1} {D / [2 π D (100 / 360)]} \\ = \sin^{- 1} (360 / 200 π) \approx 35 ° \\ Δ_{\max} = D / \tan (35) - 1.17 D [1 + \sin (100 ° - 90 °)] \\ \approx 0.26 D \end{matrix}

In Figure 1, the maximum deflection of the dual damper is 26 times greater than its diameter. Maleki and Mahjoubi (2013) reported that the advantages of dual dampers include their tensile hardening behavior, stable cyclic performance, excellent energy dissipation and suitable ductility. Maleki and Bagheri (2010) investigated the performance of dual dampers in a laboratory environment and confirmed the suitable performance of these types of damper.

The performance of single-pipe and dual-pipe elements subjected to cyclic loading was examined by Maleki and Mahjoubi (2013), but no study thus far has examined the seismic structural performance of these dampers. In the current research, the seismic performance of 4-, 8-, and 16-story steel structures under seismic loading has been examined using the finite element method in ABAQUS. Each structure has either a simple moment frame or a braced frame equipped with pipe dampers. Initially, a model of a steel pipe damper was simulated and validated, after which the structural models were investigated. The seismic performance of the structures was evaluated in terms of their base shear and lateral displacement.

Validation from experimental data

In order to validate the simulations, a laboratory model of the pipe damper developed by Maleki and Bagheri (2010) was simulated in ABAQUS. Figure 2 shows the details of the models.

Figure 2.

Details of Maleki and Bagheri (2010) model.

The steel used to manufacture the pipe damper complied with ASTM-A370. Tables 1 and 2 present the mechanical properties of the steel and the geometrical characteristics of the model, respectively. The diameter and thickness of the steel dampers in the validated model were 140 and 4 mm, respectively. The Young’s modulus and yield stress of the model were estimated to be 200 GPa and 355 MPa, respectively. The ultimate yield stress of the dampers was 410 MPa and the length of the pipe dampers was 75 mm.

Table 1.

Mechanical properties of pipe damper from Maleki and Bagheri (2010).

Pipe	Diameter (mm)	Thickness (mm)	Modulus of elasticity (GPa)	Yield stress (MPa)	Ultimate stress (MPa)	Breaking strain (%)
Mill-2	140	4	200	355	410	25

Table 2.

Geometrical characteristics of pipe damper from Maleki and Bagheri (2010).

Specimen	Pipe	Diameter (mm)	Thickness (mm)	Length (mm)
Mill-2	140	4	200	355

The cross-sections and mechanical properties of the laboratory models were accurately simulated under similar loading conditions in ABAQUS. Figure 3 is a two-dimensional (2D) model of the pipe damper simulated in ABAQUS. Figure 4 shows agreement of the models subjected to loading in the laboratory and software environments and confirms the validity of the simulations.

Figure 3.

Model of pipe damper simulated in ABAQUS in the 2D case.

Figure 4.

Compatible performances of laboratory and simulated models.

Models and accelerograms

In order to investigate the performance of the steel structures equipped with pipe dampers under seismic loading, 4-, 8-, and 16-story steel structures with moment frames were designed. The height of each story was 3.2 m and the length of each span was 5 m. The models were simulated in ABAQUS in a 2D configuration. The designs of the structures adhered to AISC-ASD89. The structures were assumed to be located in type 3 soil and a very high seismic hazard zone.

Figure 5 is a schematic of the structures equipped with 3-pipe dampers with bracings placed in the middle span. The diameter and thickness of the pipes were set as 150 and 4 mm, respectively. The placement and arrangement of the pipe dampers also are shown in Figure 5. A tie constraint was selected to connect the pipe dampers to one another and to the supports. Table 3 lists the characteristics of the parts of the structures.

Figure 5.

(a) Placement and geometry of steel dampers and (b) schematic of structures under study.

Table 3.

Characteristics of structures under study.

Story	4-story building columns	4-story building beams	8-story building columns	8-story building beams	16-story building columns	16-story building beams
1	BOX 40 × 10	PG 40 × 15	BOX 40 × 15	PG 40 × 20	BOX 50 × 20	PG 50 × 20
2	BOX 40 × 11	PG 40 × 16	BOX 40 × 15	PG 40 × 20	BOX 50 × 20	PG 50 × 20
3	BOX 30 × 10	PG 40 × 10	BOX 40 × 15	PG 40 × 20	BOX 50 × 20	PG 50 × 20
4	BOX 30 × 11	PG 40 × 11	BOX 40 × 15	PG 40 × 20	BOX 50 × 20	PG 50 × 20
5			BOX 40 × 10	PG 40 × 15	BOX 50 × 20	PG 50 × 20
6			BOX 30 × 10	PG 40 × 15	BOX 50 × 20	PG 50 × 20
7			BOX 30 × 10	PG 40 × 10	BOX 40 × 20	PG 50 × 20
8			BOX 30 × 10	PG 40 × 10	BOX 40 × 20	PG 50 × 20
9					BOX 40 × 20	PG 40 × 20
10					BOX 40 × 20	PG 40 × 20
11					BOX 40 × 15	PG 40 × 20
12					BOX 40 × 15	PG 40 × 20
13					BOX 40 × 15	PG 40 × 20
14					BOX 40 × 15	PG 40 × 20
15					BOX 40 × 10	PG 40 × 10
16					BOX 40 × 10	PG 40 × 10

The accelerograms used were chosen based on the soil type and the distance between the site and the seismic source. The characteristics of these are shown in Table 4.

Table 4.

Properties of time histories used in research.

Number	Earthquake	Date	PGA (g)	Station
1	Chi-Chi, Taiwan	20-09-99	0.1	CHAY065
2	Kobe, Japan	16-01-95	0.61	Takatori
3	Northridge, US and Mexico	17-01-94	0.49	DWP75
4	Tabas, Iran	16-09-78	0.83	Ferdows

Numerical results

The base shear of each story and the displacement of the highest point of the structure were the bases for comparison of the performance of the models. The shear base was calculated as the sum of the loads imposed on the feet of the first-floor columns. The performance of each moment frame model was compared with similar models equipped with a pipe damper.

Four-story building

Figure 6 shows the von Mises stress in a 4-story moment frame structure and a 4-story building equipped with a pipe damper. The models were subjected to the time history of the Chi-Chi earthquake at a similar time.

Figure 6.

The von Mises stress in moment frame structures subjected to Chi-Chi earthquake time history: (a) 4-story moment frame and (b) 4-story building equipped with pipe dampers.

Figure 6 shows that the maximum stress was concentrated in the pipe dampers of the 4-story building equipped with dampers. For the simple moment frame structure, the stress was concentrated in the panel zone. The peak stress in the simple moment frame was greater than in the frame equipped with pipe dampers (in the panel zone/point), which is the key to retaining structural stability during seismic loading in a simple moment frame. The damage concentration in the model equipped with pipe dampers occurred at the location of the dampers. The base shear of the structures with simple moment frames and those equipped with pipe dampers are presented in Figure 7 for the Chi-Chi, Kobe, Northridge, and Tabas time histories, respectively. It can be seen that, except for the time history of the Tabas earthquake, the base shear of the models equipped with pipe dampers decreased by nearly 60%.

Figure 7.

Base shear of structure with simple moment frame and 4-story building equipped with pipe damper subjected to four earthquake records.

Figure 8 compare the roof displacement in the structures with simple moment frames and the moment frames equipped with pipe dampers under the time histories of Chi-Chi, Kobe, Northridge, and Tabas earthquakes, respectively. Aside from the time history of the Tabas earthquake, maximum displacement in the 4-story structures in both models was almost identical. Roof displacement in the structures equipped with steel pipe dampers sharply diminished after the first few cycles with respect to the simple moment frame structures. Roof displacement decreased 50% to 70% by the third cycle onwards for the structures equipped with pipe dampers.

Figure 8.

Roof displacement for structure with simple moment frame and 4-story building equipped with pipe damper subjected to four earthquake records.

Eight-story building

Figure 9 shows the von Mises stress in the 8-story building with a simple moment frame and that equipped with pipe dampers. In these two structures, the peak stress was concentrated in the beams and the panel zones of the simple moment frame and in the dampers of the structure equipped with pipe dampers.

Figure 9.

Von Mises stress in: (a) 8-story simple moment frame structure and (b) structure equipped with pipe dampers.

In all the time histories, except for Tabas, it was observed that the base shear in both the 8-story simple moment frame structure and that equipped with pipe dampers was the same in the initial cycles. The base shear in the structures equipped with pipe dampers decreased in subsequent cycles. Comparison of the results in this section with those of the 4-story structures, reveals that it will took more time for the base shear in the 8-story structure equipped with pipe dampers to dissipate under an earthquake record. Moreover, the dissipation of the base shear in the 8-story buildings equipped with pipe dampers was 30% to 50% less than for the simple moment frames. Figure 10 compare the base shear in an 8-story structure with a simple moment frame and that with a moment frame equipped with pipe dampers.

Figure 10.

Base shear for structure with simple moment frame and 8-story building equipped with pipe damper subjected to four earthquake records.

Figure 11 show the roof displacement of the 8-story structure with a simple moment frame and that equipped with steel dampers. In all time histories except for Tabas, roof displacement decreased in the structure equipped with pipe dampers a few seconds after the onset of the earthquake. It should be noted that the maximum decrease occurred in the Northridge earthquake time history.

Figure 11.

Roof displacement for structure with simple moment frame and 8-story building equipped with pipe damper subjected to four earthquake records.

Sixteen-story building

Figure 12 compares the stress in a 16-story structure with a simple moment frame and that equipped with pipe dampers. The stress increased slightly in the simple moment frame, indicating a fault in the damping system. It can conclude that, in high-rise structures, the pipe damping system should be reinforced by increasing the thickness and/or length of the damping pipe.

Figure 12.

Stresses in a 16-story structure subject to Chi-Chi time history: (a) simple moment frame and (b) structure equipped with pipe dampers.

Figure 13 show the base shear in 16-story structures with a simple moment frame and those equipped with pipe dampers. The base shear in the structure equipped with pipe dampers decreased up to 45% under the Chi-Chi earthquake, but only 38% under the Kobe earthquake. No major differences were observed in the base shear of the structures under the Northridge and Tabas earthquakes.

Figure 13.

Base shear of a 16-story structure with simple moment frame and structure equipped with pipe damper subjected to Chi-Chi time history.

Figure 14 show the results of roof displacement for a 16-story simple moment frame structure and that equipped with pipe dampers under the time history of the four earthquake records. The roof displacement in the structures with pipe dampers increased up to 25% in the initial loading cycles. In the Kobe earthquake, roof displacement of both types of structure was similar during the initial cycles, but a slight decrease was observed in the last cycles for the structure equipped with pipe dampers. The decreases for the Northridge and Tabas earthquakes were not significant.

Figure 14.

Roof displacement of a 16-story structure with simple moment frame and structure equipped with pipe dampers subjected to four earthquake records.

Seismic response of steel frame in terms of the story drift ratio

Another parameter under consideration in the dynamic analysis of frames is drift between stories. The peak drift ratios of the braced frames were recorded at Tabas earthquake records. Figure 15 plots the distributions of the peak drift along steel building height for the 4-, 6-, and 12-story frame equipped with and without pipe dampers. The following results can be observed from Figure 15:

(1) There is a significant difference in peak drift ratio response between the story drift of frame equipped with and without pipe dampers in most floors. Note that, frame equipped pipe dampers has much higher strength in its brace-intersected beams than that in frame without pipe dampers. This observation shows that usage of the pipe dampers will have substantial impact on the peak drift ratio response.

(2) A comparison of a four-story steel frame drift with and without a damper shows that the maximum drift is on the third floor and its value for the frame with damper and without damper is 0.00482 and 0.0128, respectively. Accordingly, under these conditions, the frame drift without the damper is about 63.3% more than the corresponding drift with the damper frame.

(3) As shown in Figure 15, the maximum intermediate drift in high-rise buildings under consideration in the last floors is higher and this event can be due to the effect of using the damper in the frame.

(4) According to the general interpretation of the figures, it can be seen that short-story buildings are less likely to be relocated due to their difficulty. Now, due to the higher height of the buildings, this softness created in the structure causes the larger locations to change in the structures with dampers, and this in itself causes a difference in the frame drift with each other.

Figure 15.

Drift distribution along steel frame height.

Conclusion

Pipe dampers are inactive, yielding steel dampers with a simple mechanism and a good ability to absorb and dissipate energy. Although a number of studies have investigated the performance of these dampers, no study has examined their structural behavior. The current study investigated the performance of 4-, 8-, and 16-story moment frame steel structures equipped with pipe dampers under the time histories of four earthquakes.

The performance of the models was examined based on the von Mises stress distribution, base shear, and lateral displacement of the roof of the structures. The strength and geometry of the pipe dampers used for all models were the same. On the basis of the results, it was concluded that:

The von Mises stress distribution in the 4-story structures equipped with pipe dampers lowered in comparison with that of the simple moment frame. In the structure with pipe dampers, the plastic damage was concentrated in the area around the damper, whereas this occurred in the panel zone in the simple moment frame.

The base shear in the 4-story structures equipped with pipe dampers decreased up to 50% compared to the simple moment frame for all records, except for that of the Tabas earthquake.

The roof displacement of the 4-story structures of both types were similar in the initial loading cycles. However, displacement in the structures equipped with steel dampers decreased 50% to 70% after a number of cycles.

The stress distribution of the 8-story structures equipped with pipe dampers was more suitable than of that with a simple moment frame and the plastic damage was concentrated in the dampers.

The base shear and roof displacement in the 8-story structure equipped with pipe dampers decreased up to 50% with respect to the simple moment frame.

The stress distribution in the 16-story structure equipped with pipe dampers did not improve because the base shear and roof displacement did not change considerably. In some models, the simple moment frame outperformed the models equipped with pipe dampers. The reason can be attributed to the incompatibility of the strength of the damping system compared to the other structural elements. This indicates that that the strength compatibility between the damping system and the structural elements should be examined.

Maximum drift of structure equipped with pipe dampers is decreased up to 63.3%, 60%, and 58% compared to frames without pipe dampers for the 4, 8, and 16-story frames, respectively. Also, the average displacement reduction reached 66%, 57%, and 26% compared to those of frames.

Footnotes

Acknowledgements

The author would like to express his deepest gratitude to Dr. Shakiba Zandi for always giving encouragement and providing invaluable suggestions.

Authors’ Note

Hossein Abdollahiparsa is now affiliated with Department of the Built Environment, Eindhoven University of Technology, Eindhoven, Netherlands.

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

Hossein Abdollahiparsa

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