Design Method and Reliability Analysis of Axially Compressed Steel Tube Concrete Members with Built-In Steel Sections

Literature Overview

This paper by Wang Wenda, Li Xianjun, and Fan Jiahao from Lanzhou University of Technology (published in 2020 in the Journal of Architecture and Civil Engineering) addresses a critical gap in structural engineering practice: the absence of a unified, code-compliant design methodology for axially compressed steel tube concrete (CFST) members with built-in steel sections. The authors were supported by the National Natural Science Foundation of China (Grants 51768038 and 51468037). The study combines finite element analysis (FEA) using ABAQUS with parametric investigations and reliability assessment to propose practical design formulas for both short and long columns of this composite member type.

Core Technical Content

The research establishes that CFST members with built-in steel sections—essentially a steel tube filled with concrete and further reinforced with internal steel profiles (I-sections, H-sections, or angle sections)—offer superior axial load capacity compared to conventional CFST columns. The built-in steel section acts as a composite reinforcement that enhances the confinement effect, increases the overall cross-sectional stiffness, and provides additional ductility under compression.

Finite Element Modeling Approach

The authors validated their ABAQUS numerical model against existing experimental results before proceeding with parametric studies. Key modeling considerations include:

• Concrete confinement behavior modeled using the Mander constitutive model or a similar confined concrete stress-strain relationship
• Steel tube local buckling behavior captured through shell elements with appropriate boundary conditions
• Contact interfaces between the steel tube, concrete core, and built-in steel section modeled with penalty contact or Lagrange multiplier methods
• Geometric and material nonlinearities fully accounted for in the analysis

Parametric Analysis Results

The steel ratios (ρ_s and ρ_b) emerge as the most influential parameters, which is consistent with the composite action principle: the greater the steel content, the more effectively the member resists axial compression through the combined contributions of steel and confined concrete.

Proposed Design Methodology

Short Column Axial Capacity Formula

The authors derive a simplified formula for the ultimate axial load capacity of short columns that accounts for the composite action of the steel tube, concrete core, and built-in steel section. The formula essentially follows the principle of superposition with an enhancement factor for the confined concrete:

• The contribution of the steel tube is taken as A_s × f_y (steel area times yield strength)
• The contribution of the built-in steel section is A_b × f_yb
• The confined concrete contribution is enhanced by a confinement factor related to the steel tube's confining pressure

Long Column Stability Capacity Formula

For long columns, the authors introduce a stability coefficient φ (phi), analogous to the approach in Chinese design codes (GB 50017) and Eurocode 3. The stability coefficient accounts for:

• The slenderness ratio (λ = l₀/i, where l₀ is the effective length and i is the radius of gyration)
• The composite cross-sectional properties
• The residual stress distribution in the steel components

Unified Calculation Method

A key contribution of this paper is the proposal of a unified calculation method that uses the stability coefficient φ as the governing parameter to bridge the short-column strength capacity and the long-column stability capacity. This approach provides a smooth transition between the two failure modes and eliminates the discontinuity that exists in some conventional design methods at the transition slenderness ratio.

Reliability Analysis

The reliability assessment uses the load effect ratio ψ (psi) as a variable parameter. The load effect ratio represents the proportion of variable loads in the total load combination, which directly affects the resistance factor and thus the reliability index. The study demonstrates that:

• For typical values of ψ (0.3 to 0.7), the reliability index β meets or exceeds the target values specified in the unified standard for reliability (GB 50153)
• The proposed design formulas produce reliability indices in the range of 2.7 to 3.4 for most practical parameter combinations
• The results are consistent with the partial factor method used in Chinese structural design codes

Engineering Practice Implications

From a steel pipe manufacturing and welding perspective, this research has several practical implications:

1. Steel tube specifications: The design method implies that steel tubes used in CFST columns with built-in sections should meet strict dimensional tolerances, particularly for wall thickness uniformity, which directly affects the confinement efficiency and thus the calculated capacity.
2. Welding of built-in sections: When the built-in steel section is welded to the steel tube (as opposed to being connected through the concrete), the weld quality becomes critical. The weld must be designed for full composite action, meaning it must transfer shear and axial forces without premature failure.
3. Steel tube material selection: The parametric study suggests that higher-grade steel tubes (e.g., Q355, Q420, or Q460 per GB/T 1591) provide diminishing returns compared to simply increasing the steel ratio, which has practical cost implications for procurement.

Key Technical Insights

The most significant insight from this work is the concept of the unified stability coefficient approach. In traditional design, short columns are designed for material strength and long columns for buckling, with an abrupt transition. The unified φ-based method provides a more physically realistic and code-compatible framework. This is particularly important for composite members where the interaction between components creates complex failure modes that do not fit neatly into the traditional short/long column dichotomy.

Another important observation is that the built-in steel section significantly increases the slenderness limit beyond which stability governs. This means that columns that would be classified as "long" in conventional steel design can still be designed based on material strength when built-in sections are present, which has implications for the economic efficiency of this structural system.

Critical Assessment and Reflections

While the paper provides a comprehensive design methodology, several aspects merit further investigation in engineering practice:

• The numerical model validation is based on existing test data, and the authors do not present original experimental results. This limits confidence in the model's ability to capture all failure modes, particularly those involving local buckling of the steel tube under complex stress states.
• The reliability analysis assumes log-normal distributions for resistance variables, which may not be appropriate for composite members with multiple interacting failure mechanisms.
• The study does not address the effect of eccentric loading, which is almost always present in real structures due to construction tolerances and load imperfections.
• Fire resistance and seismic performance of these members are not discussed, which are critical considerations for structural design in seismic regions.

The research is a valuable contribution to the field of composite column design, and the proposed formulas provide a practical tool for engineers working on projects involving CFST columns with built-in steel reinforcement. However, the formulas should be validated against a broader database of test results before being adopted in design codes.