Finite Element Analysis of Double-Tube Buckling-Restrained Energy Dissipation Braces

Literature Overview

This paper by Deng Xuesong, Yang Yebin, Chen Zhen, Zhou Yun, and Zou Zhengmin (2011), published in Earthquake Engineering and Engineering Dynamics, presents a comprehensive finite element study on double-tube buckling-restrained energy dissipation braces. Buckling-restrained braces (BRBs) are a critical component of seismic energy dissipation systems, providing stable and symmetric hysteresis behavior under cyclic loading by preventing global buckling of the steel core tube. The double-tube configuration, which incorporates an inner steel core tube and an outer restraining tube with a controlled gap filled with mortar or grout, offers enhanced performance characteristics compared to single-tube designs. The authors designed 12 groups of 41 specimens and analyzed them using ABAQUS to systematically investigate the effects of diameter-to-thickness ratio, restraint ratio, slenderness ratio, and boundary conditions on brace performance.

Specimen Configuration and Parametric Design

The double-tube BRB consists of a steel core tube (typically square or circular hollow section) surrounded by an outer restraining tube, with the annular gap between them filled with a mortar or grout material that provides lateral restraint to prevent outward buckling of the core tube. The inner cavity of the core tube may be left empty or filled with concrete to modify the mass and stiffness characteristics.

The restraint ratio is defined as the ratio of the lateral stiffness provided by the outer restraining tube and grout to the axial stiffness of the core tube. A higher restraint ratio provides more effective prevention of local and global buckling.

Key Performance Results

The finite element analysis reveals several critical design thresholds:

The hysteresis curves of the braces that meet these criteria are described as full and stable, indicating consistent energy dissipation capacity throughout cyclic loading. The equivalent viscous damping ratio of the braces is typically in the range of 20–30%, which is significantly higher than the 2–5% typical of conventional braced frames.

Engineering Design Guidelines

Based on the parametric analysis, the following design guidelines can be extracted for practical application:

1. Core tube wall thickness: The diameter-to-thickness ratio should not exceed 24 to ensure that the core tube yields in a stable manner without premature local buckling. For Q235 steel, this corresponds to a minimum wall thickness of D/24.
2. Outer tube design: The outer restraining tube should be designed with sufficient stiffness to achieve a restraint ratio of at least 3. This typically requires the outer tube to have a significantly larger cross-sectional area and wall thickness than the core tube.
3. Grout properties: The grout or mortar filling the annular gap should have sufficient compressive strength (typically ≥ 20 MPa) and adequate bond strength to the steel tubes to ensure effective load transfer.
4. Connection design: The brace connections to the structural frame should be designed as rigid (fixed) connections to prevent rotational instability. Pinned connections are not recommended as they allow the brace to rotate and lose its buckling restraint effectiveness.
5. Slenderness management: For braces with slenderness ratios exceeding 10, the restraint ratio should be increased proportionally to maintain stable hysteresis behavior.

Fabrication and Quality Control Considerations

From a fabrication standpoint, the double-tube BRB presents several challenges:

The grout filling process is particularly critical. Insufficient grout compaction can lead to void formation, which reduces the effective restraint ratio and may cause localized buckling of the core tube. Post-grouting inspection using ultrasonic methods is recommended to verify grout density and bond quality.

Study Reflections

This paper provides a systematic parametric study that establishes clear design thresholds for double-tube BRBs. The finding that D/t ≤ 24 and R ≥ 3 are critical for stable hysteresis behavior is directly applicable to engineering design. The recommendation of fixed boundary conditions is consistent with practical observations that pinned connections in BRBs can lead to premature failure. One area for further investigation is the effect of grout material properties (compressive strength, modulus of elasticity, bond strength) on the restraint ratio and overall brace performance. Additionally, the study does not address the long-term performance of the grout under cyclic loading, which may be affected by fatigue cracking and bond degradation.

Conclusion and Outlook

The finite element analysis of double-tube buckling-restrained energy dissipation braces provides engineers with clear, quantitative design criteria for achieving stable and effective seismic energy dissipation. The diameter-to-thickness ratio limit of 24 and the minimum restraint ratio of 3 are practical and actionable design parameters that can be directly incorporated into structural design specifications. Engineers designing BRB systems should adopt these guidelines as baseline requirements and supplement them with detailed nonlinear finite element analysis for specific projects, paying particular attention to the grout quality, connection detailing, and slenderness ratio management to ensure reliable seismic performance throughout the service life of the structure.