Design Methodology for Buckling-Restrained Jackets in Triple Steel Pipe BRBs

Literature Overview and Research Background

The paper by Xiao Shaowen and colleagues (2019), published in Advances in Steel Construction, presents a systematic design methodology for the jacket tubes in triple steel pipe buckling-restrained braces (BRBs). This research, supported by the National Natural Science Foundation of China (Grant No. 51578322), addresses a critical gap in the design of advanced seismic energy-dissipating structural components. The triple pipe BRB configuration consists of a core steel pipe that provides axial stiffness, load-bearing capacity, and seismic energy dissipation through controlled yielding, while an outer jacket tube and an inner jacket tube jointly restrain both global buckling and local buckling of the core pipe. The fundamental premise is that once the core pipe yields under cyclic loading, the entire bending stiffness of the brace is provided by the two jacket tubes. This paper is particularly valuable for structural engineers designing seismic-resistant steel structures where ductility and stable hysteretic behavior are paramount.

Core Technical Principles and Design Methodology

The design method is rooted in the edge yielding criterion applied to the jacket tubes. The key insight is that the jacket tubes must remain elastic throughout the seismic loading cycle to ensure stable and repeatable energy dissipation from the core pipe. The methodology proceeds through the following logical sequence:

Determine the maximum permissible bending deformation of the brace such that the outer jacket edge fibers do not reach yield.
Account for the second-order bending moment transferred from the yielded core pipe to the jacket tubes.
Calculate the required bending stiffness of the jacket system based on the allowable deformation limit.
Derive the minimum section dimensions for both the outer and inner jacket tubes.

The governing relationship can be expressed as follows:

Design Parameter	Governing Criterion	Typical Range
Core pipe diameter-to-thickness ratio (d/t)	Must allow sufficient plastic deformation	15–35
Gap between core and inner jacket	Must prevent contact before yielding	0.5–2.0% of core diameter
Gap between inner and outer jacket	Must prevent contact during lateral deformation	0.5–2.0% of inner jacket diameter
Jacket edge stress	Must remain below yield stress σ_y	≤ 0.67σ_y (safety factor ~1.5)
Core pipe material	Must exhibit stable cyclic yielding	Q235, Q345, or equivalent low-carbon steel

The critical design equation considers the bending moment at the brace ends, where the jacket tubes experience the maximum flexural demand. The second-order effect of the core pipe's lateral displacement amplifies the bending moment on the jackets, and this amplification factor must be explicitly included in the stiffness calculation. The paper demonstrates that neglecting this effect leads to underestimation of jacket requirements and potential premature jacket yielding.

Finite Element Verification and Parametric Analysis

The authors validated the design methodology through comprehensive finite element (FE) modeling. The FE analysis was conducted under three parametric variations:

Different core pipe diameter-to-thickness ratios (d/t = 15, 20, 25, 30, 35)
Different inter-tube gaps (0.5%, 1.0%, 1.5%, 2.0% of respective diameters)
Different circumferential pre-stresses in the core pipe (0, 10, 20, 30 MPa)

The results consistently showed that the proposed design formulas remained applicable across all parametric combinations. This robustness is significant for practical engineering application, as it means the methodology does not require extensive case-by-case recalibration. The FE models accurately captured the nonlinear behavior of the core pipe yielding, the progressive interaction between tubes, and the elastic response of the jackets.

Engineering Practice Implications and Reflections

From a manufacturing and fabrication perspective, the triple pipe BRB design imposes specific requirements on steel pipe production. The core pipe typically uses low-carbon structural steel (Q235 or Q345) with stable cyclic stress-strain behavior, while the jacket tubes require higher yield strength to maintain elasticity. The tight dimensional tolerances needed for the inter-tube gaps (typically 1–3 mm) demand precision in pipe manufacturing and assembly. Welding connections at the brace ends must be designed to accommodate the differential stiffness between core and jacket tubes without introducing stress concentrations.

A notable engineering consideration is the fabrication sequence: the inner jacket must be inserted into the outer jacket before the core pipe is placed, requiring careful handling to avoid damaging the gap-filling material (typically foam or sand). The circumferential pre-stress in the core pipe, which can be achieved through hydraulic expansion or mechanical interference fitting, adds another manufacturing step that must be controlled to prevent residual stress effects on fatigue performance.

The paper's methodology provides a clear and practical framework that can be directly applied in structural design offices. The explicit consideration of second-order effects distinguishes this approach from simpler methods that treat the jacket system as a simple elastic spring. For engineers involved in the detailed design of seismic isolation and energy dissipation systems, this paper offers both theoretical grounding and practical formulas that can be implemented in standard structural analysis software.