Creep Design Calculation Formula for Steel Tube Concrete Bending Members

Literature Overview

The paper by Wang Yuanfeng, Zhu Haibin, and Han Bing, published in the Journal of Highway and Transportation Research in 2007, addresses a critical yet often overlooked aspect of steel tube concrete (STC) structural design: the long-term creep behavior of bending members. The authors, affiliated with Beijing Jiaotong University, developed a design-oriented creep calculation formula using regression analysis based on the hereditary flow theory. The work was supported by the Ministry of Education Key Research Program and the Doctoral Program Foundation for Higher Education.

Core Technical Content

The fundamental challenge in STC bending member design is that conventional concrete creep models do not adequately account for the confining effect of the steel tube on the concrete core. The authors adopted the hereditary flow theory as the theoretical foundation, which describes creep as a time-dependent process where the creep strain at any instant depends on the entire stress history. This approach is particularly suitable for STC members because the steel tube constrains lateral expansion of the concrete, modifying the creep development mechanism compared to plain concrete.

The regression analysis incorporated three primary influencing factors:

The resulting design formula is characterized by its mathematical simplicity while maintaining comprehensive consideration of physical factors. The authors validated the formula against theoretical calculations from the hereditary flow theory, demonstrating good agreement between regression results and theoretical predictions.

Technical Analysis of the Hereditary Flow Theory Approach

The hereditary flow theory, originally developed in the context of viscoelastic materials, provides a rigorous framework for describing time-dependent deformation. In the context of STC members, the theory accounts for:

1. The nonlinear stress-strain relationship of concrete under sustained loading
2. The progressive development of micro-cracks and pore structure changes in concrete
3. The interaction between concrete creep and steel tube elastic deformation
4. The redistribution of internal forces as concrete creeps under the constraint of the steel tube

The key insight is that as concrete creeps under sustained bending, the internal force distribution between the steel tube and concrete core changes. The steel tube, being essentially non-creeping under normal service stresses, progressively assumes a larger share of the bending moment. This internal force redistribution is a unique feature of composite members that does not exist in plain concrete structures.

Engineering Practice Integration

From a steel pipe manufacturing perspective, several considerations arise when applying this creep formula in practice:

• Pipe wall thickness selection: The steel ratio parameter directly relates to the wall thickness of the steel tube. Thicker walls increase the steel ratio, thereby reducing creep but also increasing material cost. Engineers must find an optimal balance.
• Steel grade selection: Higher-strength steel grades allow thinner walls for the same structural capacity, which reduces the steel ratio and potentially increases creep. This creates a trade-off between material efficiency and long-term deformation control.
• Residual stress effects: Manufacturing residual stresses in the steel tube, which arise from welding or cold-forming processes, can influence the initial stress state of the composite member and modify creep development.

In bridge engineering applications, where this formula was primarily intended, creep can lead to progressive deflection that may exceed serviceability limits over the design life. The formula provides a practical tool for checking long-term deflection at various time points, enabling engineers to verify compliance with deflection limits specified in bridge design codes.

Key Questions and Reflections

Several important questions emerge from studying this work:

First, the regression formula is derived from a specific set of theoretical calculations and may not fully capture the variability of real-world conditions. Factors such as concrete mix composition, curing conditions, environmental humidity, and temperature cycling can significantly affect creep behavior. The formula's applicability to different concrete types and environmental conditions should be verified through additional experimental data.

Second, the formula assumes uniform loading conditions, but in practical bridge structures, load histories are complex and variable. The superposition principle underlying the hereditary flow theory should theoretically handle variable loading, but the simplified regression formula may not fully preserve this capability.

Third, for steel pipes used in STC applications, the surface quality and dimensional accuracy of the tube directly affect the confinement effectiveness. Manufacturing tolerances for outer diameter, wall thickness, and straightness should be considered when applying the formula to real structures.

Study Insights and Implications

This work demonstrates the value of developing simplified design formulas from rigorous theoretical models. The regression approach successfully bridges the gap between academic theory and practical engineering application. For steel pipe manufacturers and structural engineers working on STC applications, this formula provides a quantitative tool for predicting long-term deformation behavior, enabling more accurate serviceability design. The methodology also suggests that similar regression-based approaches could be developed for other time-dependent phenomena in composite structures, such as shrinkage effects, relaxation of prestress, and fatigue under sustained loading conditions.