Experimental Study and Load-Bearing Capacity Analysis of Double-Cone Variable Cross-Section Rectangular Steel Tubes

Overview of the Literature

The paper by Luo Yaozhi and colleagues from the Zhejiang University Spatial Structure Research Center addresses a structurally significant topic in the field of advanced steel construction: the behavior of double-cone variable cross-section rectangular steel tubes (VCFST) under combined loading conditions. These members represent a hybrid structural element in which both ends adopt a tapered (conical) geometry while the central portion maintains a uniform rectangular cross-section. The research was supported by the National Key Technology R&D Program and the National Natural Science Foundation of China, reflecting its importance in the context of large-span spatial structures such as stadiums, exhibition halls, and airport terminals.

The authors first derive a theoretical formula for determining the critical cross-section location where failure is most likely to occur in such variable-section members. They then present extensive experimental results from compression-bending and compression-bending-torsion tests, documenting failure modes, plastic hinge development, and ultimate load-bearing capacities under various loading configurations. Finite element analysis (FEA) is employed to complement the experimental data and to compare member performance across different moment-to-axial-force ratios.

Core Technical Findings

Critical Section Determination

In a prismatic (uniform cross-section) member, the critical section for failure is typically at the location of maximum moment or at a point of geometric discontinuity. However, for a variable cross-section member such as the double-cone VCFST, the critical section can shift depending on the loading configuration. The authors derive an analytical expression that identifies the most unfavorable cross-section by considering the interaction between the varying section properties (moment of inertia, section modulus, wall thickness distribution) and the applied load path. This formula accounts for the fact that the tapered end regions possess reduced section properties compared to the constant central region, yet they may also experience higher bending moments due to geometric eccentricity.

The key insight is that the critical section does not necessarily coincide with the minimum cross-section. Instead, it is determined by the combined effect of local section weakness and the global moment distribution. This analytical tool is invaluable for engineers designing variable-section members, as it allows for a priori prediction of the failure location without relying solely on numerical simulation.

Failure Modes and Plastic Hinge Development

The experimental results reveal that the failure mode of the double-cone VCFST is highly dependent on the loading configuration and the moment-to-axial-force ratio. Under pure compression, the member fails by local buckling of the tapered walls, typically initiating at the thinnest wall region near the cone apex. Under combined compression and bending, the failure shifts toward the mid-span region where the plastic zone develops most extensively. Under combined compression, bending, and torsion, the failure mode becomes more complex, involving coupled local buckling and lateral-torsional instability.

The plastic hinge development process is particularly noteworthy. In a prismatic member, the plastic hinge forms at the location of maximum moment, which is often at or near the member end where it connects to the supporting node. In contrast, the double-cone VCFST exhibits a distinctive behavior: the plastic hinge tends to form in the transition region between the tapered end and the constant central section, rather than at the very end of the member. This is attributed to the gradual variation in section properties, which provides a natural "plastic hinge zone" that distributes plastic deformation over a finite length rather than concentrating it at a single point.

Load-Bearing Capacity Comparison

The most significant finding of this study is that the double-cone VCFST demonstrates higher load-bearing capacity under bending-dominated loading compared to an equivalent prismatic member with the same end conditions. This counterintuitive result can be explained by the enhanced section modulus at the tapered ends, which effectively increases the moment resistance at the critical regions. The finite element analysis confirms that this advantage persists across a range of moment-to-axial-force ratios, although the degree of improvement diminishes as the loading becomes more compression-dominated.

Engineering Practice Implications

The research findings have direct implications for the design of spatial steel structures where variable-section members are employed to optimize material usage and structural aesthetics. The key engineering takeaways are as follows:

1. Design methodology: Engineers should adopt the derived critical section formula to identify the governing cross-section for strength verification, rather than assuming failure at the minimum section.
2. Ductility enhancement: The natural plastic hinge zone in the transition region of VCFST members provides inherent ductility advantages. This is particularly beneficial for seismic design, where energy dissipation through plastic deformation is a key performance objective.
3. Fabrication considerations: The tapered geometry requires careful attention during manufacturing, particularly during the welding of the transition joints. Welding-induced residual stresses and geometric imperfections at these critical transition regions can significantly reduce the actual load-bearing capacity.
4. Connection design: Since the plastic hinge avoids the end nodes, the connection design can focus on strength requirements without the additional constraint of accommodating large plastic deformations at the joint.

Study Insights and Reflections

This paper represents a mature and rigorous approach to understanding the behavior of non-prismatic steel members. The combination of analytical derivation, experimental validation, and numerical simulation provides a comprehensive picture that is directly applicable to engineering practice. What stands out is the practical insight that geometric variability, often viewed as a design complication, can actually be leveraged to improve structural performance. The natural plastic hinge distribution in VCFST members is an elegant example of how form and function can be harmonized in structural design. For practicing engineers involved in spatial structures, this research provides both theoretical tools and practical guidance for the rational use of variable-section rectangular steel tubes.