Grey Relational Entropy Analysis of Axial Compression Bearing Capacity in CFRP-Steel Tube Concrete Members

Literature Overview

This paper by Sun Guoshuai, Gu Wei, and Liu Chunguang (2018, Concrete, Vol. 11, pp. 26-28), funded by the National Natural Science Foundation of China (51678107) and Liaoning Provincial Department of Education (JW201615406), addresses the evaluation of axial compressive bearing capacity in CFRP-steel tube concrete composite members. The authors apply Grey Relational Entropy (GRE) theory to systematically rank the influence of key structural parameters on ultimate load capacity. The study originates from Liaoning University of Technology, Liaoning Transportation Polytechnic College, and Dalian University of Technology, representing a multidisciplinary collaboration spanning civil engineering, materials science, and structural mechanics.

Core Methodology and Technical Approach

The Grey Relational Entropy method combines Grey Relational Analysis (GRA) with information entropy theory to quantify the degree of association between multiple influencing factors and a target response variable. In this context, the target variable is the axial ultimate bearing capacity of the CFRP-steel tube concrete member, while the influencing factors include steel tube thickness, steel tube yield strength, core concrete cross-sectional area, and CFRP thickness.

The GRE analysis procedure follows these systematic steps:

1. Determine the reference series (bearing capacity data set) and comparison series (each influencing factor's data set).
2. Normalize all data sets to a common scale using the grey relational grade calculation.
3. Compute the grey relational coefficient for each pair of data points between the reference and comparison series.
4. Calculate the grey relational degree by averaging the coefficients.
5. Apply Shannon entropy to weight the relational degrees and obtain the Grey Relational Entropy value.
6. Rank the factors by their GRE values, where higher values indicate greater influence on bearing capacity.

The information entropy component is critical because it accounts for the uniformity of the relational distribution. A factor whose relational coefficients are uniformly distributed across all test conditions contributes less entropy and thus less weight, while a factor showing concentrated high relational values under specific conditions receives higher entropy weighting.

Key Findings and Technical Interpretation

The study identifies the core concrete cross-sectional area as the dominant factor governing axial compression bearing capacity, with the highest Grey Relational Entropy value among all investigated parameters. This finding is physically intuitive: the core concrete bears the majority of the compressive load in the composite member, and increasing its cross-sectional area directly increases the load-bearing cross-section.

The relatively low influence of steel tube yield strength is noteworthy from a materials engineering perspective. In CFRP-steel tube concrete members, the steel tube primarily functions as a confining element and formwork rather than a primary load-bearing component. The concrete core carries the bulk of the axial compressive load, and the steel tube's contribution is largely through confinement effects that enhance concrete strength through triaxial compression. Increasing the yield strength of the steel tube beyond a certain threshold does not proportionally increase the overall member capacity because the concrete governs the failure mode.

Connection to Engineering Practice

For engineers involved in the design and fabrication of composite structural members incorporating steel tubes, this study provides several practical insights:

• Material selection priority: When specifying steel tubes for CFRP-steel tube concrete applications, the wall thickness should be optimized before considering higher-grade steels. A thicker wall of standard Q345 steel will generally provide better confinement than a thinner wall of Q460 steel.
• CFRP wrapping design: The CFRP layer serves as a secondary confinement mechanism. Its thickness should be designed based on the required ductility enhancement rather than as a primary strength contribution.
• Concrete specification: The concrete strength grade and cross-sectional dimensions should be the primary design variables, as they have the most direct influence on ultimate capacity.

From a welding and fabrication standpoint, the steel tube manufacturing process becomes critical. For seamless steel tubes used in such applications, the uniformity of wall thickness is paramount. Variations in wall thickness (controlled by the mandrel calibration in the seamless tube rolling process) directly affect the confinement uniformity and, consequently, the composite member's bearing capacity.

Study Insights and Reflections

This paper demonstrates that classical information theory methods such as Grey Relational Entropy can provide valuable insights into structural engineering problems without requiring extensive finite element simulations or physical testing. The GRE method is particularly useful during the preliminary design stage when engineers need to identify which parameters warrant the most design attention.

However, the study has limitations. The GRE method provides a statistical ranking of factor influence but does not reveal the underlying mechanical mechanisms. For instance, it cannot distinguish between linear and nonlinear relationships between factors and response. Additionally, the method assumes independence between factors, whereas in practice, steel tube thickness and yield strength are often correlated through manufacturing constraints and cost considerations.

For practitioners in the steel pipe and fitting industry, this research underscores the importance of dimensional accuracy in steel tube manufacturing. The tight tolerance requirements for wall thickness in structural applications demand precise control of the rolling or forming processes, whether for seamless tubes produced through the Mannesmann piercing and rolling method or for welded tubes produced through HFW or ERW processes.