Theoretical analysis and optimization of toggle-brace damper for cable tray system

https://doi.org/10.1016/j.jcsr.2021.106936Get rights and content

Highlights

  • Deformation calculation method for suspension frame and TBD is developed.

  • Optimization for brace connecting point location of TBD is established.

  • Influence of installation error of brace connecting point is investigated.

  • Seismic responses of cable tray systems with different dampers are compared.

Abstract

The cable tray system, one type of non-structural components, may suffer severe damage and even fall in case of earthquakes, causing interruptions to post-earthquake operations and even injuries or casualties. This paper introduces a toggle-brace damper (TBD) into the cable tray system to control its seismic response and damage. However, owing to the large deformation/rotation effect in the TBD equipped cable tray system, the traditional design method based on small deformation assumption is no longer applicable. The new deformation calculations of suspension frame and TBD subjected to displacement loading are established combining the optimization technique and the geometry relationship, respectively. After then, an optimization design method for connecting location of the damper brace is proposed, considering the installation errors, deformation constraints, and loading process. With the aid of numerical analysis, it is found that the large deformation effect and in-plane installation errors have considerable influence on the damping magnification function. Compared with typical seismic resistant elements such as the steel brace, diagonal- and chevron-brace damper, the proposed optimal TBD can dissipate more energy and effectively suppress the vibration of cable tray system.

Introduction

The impact of earthquake hazards promotes significant advance in current seismic design method, which can basically ensure the safety of building structures. For instance, during the devastating 2011 Tohoku-oki Earthquake, Tokyo was well prepared from the viewpoint of structural safety and indeed no severe structural damage occurred. However, many kinds of nonstructural components suffered severe damage [1]. The cable tray system is one type of vital non-structural components in modern buildings, which is mainly utilized to support insulated electric cables for power distribution and communication. Considering its importance in connecting the external power supply to maintain normal function of the building, it can be called as one part of the “lifeline”. In large-scale facilities, the cable mass could exceed 100 kg/m, and the fallen electric cables may easily result in injuries or casualties. During Chile Earthquake in 2010 [2], the pounding of cable trays with the main structure, pipes, ducts, ceilings, fire sprinklers, and other suspended systems caused buckling of the trays, falling of electric cables, and structural damage. Similar damage was observed in the recent Anchorage Earthquake in Alaska [3]. As reported by Kasai et al. [4] and Masuzawa et al. [5], damage to wiring electric cables was mostly caused by the failure of the hanging type cable tray system, which resulted in the loss of property, interruptions to post-earthquake operations, and even brought secondary disasters. Therefore, it is of great importance to propose effective methods to improve the seismic performance of the cable tray system.

The steel brace is commonly used to form a lateral load resisting system owing to its high stiffness and strength [6]. Both the displacement and acceleration responses of the cable tray system can be effectively controlled by incorporating different types of braces into the cable tray system (shown in Fig. 1), which have been studied through shaking table tests [7,8]. However, when suffering severe earthquakes, the main to sub beam joints (MSBJs) may fail, leading to a progressive drop of sub beams. If so, the earthquake energy is dissipated by the main frame itself in this type of cable tray system, which is of course not desired. Matsuda and Kasai [1] proposed a new type of viscoelastic damper to reduce the deformation of cable tray. Later, through a comparison of the responses of the cable tray system installed with different types of energy dissipation devices, such as viscoelastic, viscous, metallic, and friction dampers [9], it was found that the viscous damper (VD) could provide the highest damping and reduce damage to the structure. Typical configurations of VDs include diagonal-brace damper (DBD) and chevron-brace damper (CBD). Owing to the velocity-dependence nature of VDs, it requires high velocity to produce a large control force. Taylor [10], Constantinou [11], and Hwang et al. [12] initially investigated the combination of fluid dampers with a mechanical toggle-brace assembly to magnify the damper velocity. It was shown that the toggle-brace damper (TBD) could amplify the damping force. Subsequently, some complicated and novel magnification devices were successively developed [[13], [14], [15], [16], [17]].

In previous work, the TBD was applied to building structures based on a small deformation assumption. However, the TBD in the flexible frame, such as the cable tray system, is more vulnerable to large deformation, which may influence the damping efficiency of TBD in controlling the vibration responses. The importance of the connecting location of the damper brace on the magnification effect had been examined [18,19]. However, most of the design of the VD system in previous studies are focused on the optimization of the damping coefficient, configurations, and layout of dampers [[20], [21], [22], [23]] while design of the connecting location of the damper brace still needs considerable improvement.

This work aims to improve the seismic performance of cable tray system through applying TBD. To address issues such as large deformation effect and optimal connecting location of the damper brace, a series of theoretical analyses are conducted and an optimization design procedure for the connecting location of the damper brace is developed. Furthermore, to investigate the superior performance of the TBD, influence factors on damping magnification effect are investigated, and four cable tray systems installed with different types of seismic resistant elements (B-type steel brace, DBD, CBD, and TBD) are analyzed by numerical simulation. Their responses under sinusoidal waves as well as earthquakes are compared.

Section snippets

System description

A typical cable tray system used in practice is shown in Fig. 2, which is commonly suspended from the top floor or ceiling via threaded rods or cold-formed steel struts. The tray itself is a lattice frame consisting of main and sub beams. The sub beams mostly are welded to main beams, and bolted connections are rarely adopted. The constitution of a typical cable tray system is shown in Fig. 3(a). In the transverse direction (in-plane), different brace configurations of the damper can be used. A

Energy dissipation based optimization for brace connecting point of TBD

In the traditional design of damping magnification devices, the calculation of magnification factor is based on the undeformed damper braced structure and small deformation assumption, and its value is regarded as a constant [12]. Typical undeformed VD configurations and calculation method of magnification factor are shown in Fig. 6 [11]. For the DBD, f = cosθ, where θ is the angle of inclination of the damper with respect to the horizontal axis. For the CBD, whose damper is at the bottom of

Optimization design of TBD

To demonstrate the feasibility of the proposed optimization method, a design following the procedures as shown in Fig. 9 is described below. The model of cable tray systems is selected from [8]. For the in-plane admissible error of the brace connecting point, a value of 20 mm is considered tolerable.

The cross-section and material information of the in-plane frame as shown in Fig. 3(b) are summarized as follows:

Hanging bolt: length of 1 m and diameter of 14 mm.

Support member: length of 1.2 m,

Conclusions

In the present work, for understanding the deformation process of the TBD equipped cable tray and determining its optimal connecting location of the damper brace, the optimization technique is introduced firstly for the large deformation calculation of the suspension frame, and an instantaneous deformation calculation method of TBD is developed. Furthermore, optimization for maximizing energy dissipation is also proposed to determine the connecting point location of the damper brace. The

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The financial support from International Joint Research Laboratory of Earthquake Engineering of Tongji University (Grant No. 0200121005/058) is gratefully acknowledged.

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