Ultimate Bearing Capacity of Dumbbell-Shaped Eccentrically Compressed Steel Tube Concrete Long Columns

Literature Overview

This paper by Chen Baochun and Sheng Ye, published in Engineering Mechanics (2008, Vol. 25, No. 12, pp. 98-105), presents experimental and finite element investigations into the ultimate bearing capacity of dumbbell-shaped eccentrically compressed steel tube concrete (SRC) long columns. The study was funded by the Fujian Provincial Basic Research Program (2003F007) and represents a significant contribution to the structural engineering understanding of non-standard SRC cross-sections under combined axial and bending loads. Sixteen test specimens were designed and tested, with slenderness ratio and eccentricity ratio serving as the two primary variables. The research directly addresses a gap in the existing design codes, which predominantly cover conventional circular and rectangular SRC columns.

Core Experimental Design and Test Results

The experimental matrix was carefully constructed to isolate the effects of two critical parameters. The sixteen specimens varied in slenderness ratio and eccentricity ratio, enabling systematic analysis of their individual and combined influences on structural performance.

The failure mode observed across all specimens was classified as global (overall) failure rather than local buckling or concrete crushing at the compression fiber alone. This is a critical finding because it confirms that the dumbbell geometry, despite its reduced second moment of area compared to a solid section of equivalent weight, maintains sufficient overall stability to fail in a ductile, global manner. The load-deformation curves exhibited a clear elastic stage followed by an elastoplastic transition and eventual softening after peak load.

The key quantitative findings are summarized below:

This dual degradation pattern is consistent with classical column theory but is particularly important for the dumbbell section because the geometry inherently concentrates material away from the neutral axis, creating higher local stress concentrations at the web-flange junctions.

Finite Element Analysis and Design Formula Development

The finite element models replicated the full loading history from initial loading through peak capacity to post-peak softening. The modeling approach captured the steel tube's elastic-plastic behavior, concrete confinement effects, and geometric imperfections inherent in the dumbbell profile.

A crucial analytical insight from the FE work is that the slenderness ratio and eccentricity ratio exert essentially independent effects on the ultimate bearing capacity. This independence allows engineers to adopt a multiplicative partial factor approach, where the stability coefficient for slenderness and the eccentricity reduction coefficient are applied sequentially rather than requiring a coupled interaction formula. This simplification has direct practical value for design offices and code development.

The stability coefficient calculation formula adopted the same expression as that used for dumbbell-shaped axially compressed long columns, demonstrating that the eccentricity effect can be decoupled and handled through a separate reduction factor. The eccentricity reduction coefficient was derived through regression fitting of both experimental data and finite element results, providing a robust empirical formula applicable within the tested parameter range.

Engineering Practice Implications and Reflections

From a materials and fabrication standpoint, the dumbbell SRC section presents specific challenges. The steel tube profile requires specialized rolling or forming equipment, and the concrete infill must be placed and vibrated in a geometry that includes concave regions where honeycombing is a risk. The experimental results confirm that despite these fabrication complexities, the section performs reliably in global stability terms, provided the steel tube thickness and concrete strength meet minimum design requirements.

For engineers specifying such columns in practice, the multiplicative factor approach offers a convenient design pathway. However, it is essential to verify that the local buckling resistance of the thin-walled dumbbell tube is adequate under the concentrated stresses at the web-flange junctions, particularly in the compression zone where the eccentricity effect is most severe. The paper's focus on global behavior does not fully address local buckling, which remains a critical check in detailed design.

The study also highlights that the tangent stiffness degradation in the elastoplastic stage with increasing slenderness and eccentricity has implications for serviceability limit states, particularly deflection and crack width control in SRC members. Engineers should not rely solely on ultimate capacity formulas but must also verify deformation performance under service loads.

This research provides a solid foundation for the rational design of dumbbell SRC long columns, and its decoupling approach to slenderness and eccentricity effects is a methodologically elegant contribution that simplifies practical design without sacrificing safety margins.