Axial Compression Ultimate Bearing Capacity of Variable Cross-Section Concrete-Filled Steel Tube Lattice Columns

Literature Overview

This paper by Ou Zhijing, Yan Qiaoling, Xue Jianyang, and Chen Baochun (2016), published in the Journal of Chongqing University, addresses the axial compression ultimate bearing capacity of variable cross-section concrete-filled steel tube (CFST) lattice columns. The research was funded by the National Natural Science Foundation of China (Grants 51408128 and 51178118). Variable cross-section columns are increasingly used in tall buildings, transmission towers, and industrial structures where the load demand varies along the column height, making uniform cross-sections inefficient. The study proposes an equivalent length concept and a corresponding calculation method for the axial compression capacity of four-limb variable cross-section CFST lattice columns.

Core Technical Findings

The experimental results demonstrate two clear trends: as the specimen height increases, the ultimate load decreases, and as the limb slope decreases, the ultimate load also decreases. These findings are consistent with fundamental stability theory, as both factors reduce the effective buckling resistance of the lattice column. The authors then develop an equivalent length method that extends the existing calculation framework for constant cross-section CFST lattice columns to the variable cross-section case.

The equivalent length concept is particularly valuable because it allows engineers to use familiar constant cross-section design formulas while accounting for the variable geometry. The practical algorithm proposed for four-limb variable cross-section CFST lattice columns is validated through finite element analysis, confirming its suitability for engineering applications.

Technical Analysis of the Equivalent Length Method

The equivalent length method essentially maps the variable cross-section geometry onto an equivalent constant cross-section column of the same overall behavior. This approach is conceptually similar to the equivalent length factor used in the stability design of built-up columns in GB 50017 and AISC 360. The key innovation in this study is the adaptation of this concept specifically for CFST lattice columns, where the composite action between the steel tube limbs and the infill concrete introduces additional complexity.

From a pipe manufacturing perspective, the limb slope of a variable cross-section lattice column directly affects the geometry of the steel tubes used as column limbs. In practice, these limbs are often fabricated as tapered tubes or as constant cross-section tubes cut at an angle. If tapered tubes are used, the manufacturing process becomes significantly more complex. Seamless tapered tubes can be produced by piercing and elongation, but this is limited to small diameters. For larger diameters, tapered tubes are typically fabricated from flat steel plates using a roll-forming process followed by longitudinal welding (LSAW or submerged arc welding). The welding quality at the tapered section is critical because the varying wall thickness and geometry create complex residual stress patterns that can affect the buckling behavior.

Standards and Design Considerations

The study references the need to improve the existing CFST design code (GB 51248-2017, which supersedes earlier versions). The equivalent length method proposed here could be incorporated into future revisions of this code. For international practice, the relevant standards include EN 1993-1-1 for general structural steel design, EN 1993-1-5 for composite structures, and ISO 15590 for welded hollow structural sections. The DNV-ST-F101 standard for offshore steel structures also addresses composite columns and could benefit from the equivalent length approach for variable geometry members.

When designing variable cross-section CFST lattice columns, the following quality control measures should be implemented:

1. The longitudinal welds in tapered tube limbs should be inspected using phased array ultrasonic testing (PAUT) or time-of-flight diffraction (TOFD) to detect internal defects.
2. The gusset plate connections between limbs and cross-bracing should be designed for the higher stress concentrations that occur at the transition sections.
3. The concrete infill in tapered tube limbs should be carefully placed and vibrated to ensure full compaction, particularly near the narrower end where the cross-sectional area is reduced.

Key Questions and Reflections

A significant question that arises from this study is how the equivalent length method performs when the variable cross-section is not linearly tapered but follows a more complex profile, such as a parabolic or exponential variation. The study focuses on linearly tapered limbs, which is the most common case in practice, but the methodology should be verified for other geometric profiles.

Another reflection concerns the interaction between the variable cross-section geometry and the buckling mode. In constant cross-section lattice columns, the buckling mode is well understood, but in variable cross-section columns, the buckling mode may shift toward the weaker end of the column. This shift could lead to a more localized failure pattern that is not captured by a simple equivalent length approach. Engineers should therefore perform a detailed finite element buckling analysis for critical variable cross-section CFST lattice columns, particularly when the taper ratio exceeds certain thresholds.

Study Insights and Implications

This study makes a meaningful contribution to the design methodology for variable cross-section CFST lattice columns. The equivalent length concept provides a practical and intuitive design tool that bridges the gap between the well-established constant cross-section design methods and the more complex variable geometry case. For engineers working on tall building cores, transmission towers, and industrial structures, this approach offers a straightforward way to estimate the axial compression capacity without resorting to full-scale finite element analysis for every design iteration. The validation through finite element analysis adds confidence to the proposed method, and the study provides a clear pathway for incorporating these results into future revisions of the CFST design code.