Analytical Method for Axial Compressive Bearing Capacity of Concrete-Confining Steel Tubes Considering Additional Confining Effect of Temperature

Literature Overview

This paper develops an analytical method for calculating the axial compressive bearing capacity of steel-confined concrete (CFST) columns that accounts for the additional confining effect induced by elevated temperatures. The research addresses the fire resistance design of CFST members by incorporating temperature-dependent material behavior and the enhanced confinement mechanism that develops as steel and concrete undergo differential thermal expansion.

Fundamental Principles

Under elevated temperature conditions, several phenomena affect the axial compressive capacity of CFST columns:

Steel loses strength progressively, with significant degradation above 600°C
Concrete experiences spalling and strength loss, typically beginning around 300°C
Differential thermal expansion between steel and concrete creates additional radial pressure
The steel tube, while losing strength, maintains geometric confinement due to its ductility

Temperature-Dependent Material Properties

Temperature (°C)	Steel Strength Retention (%)	Concrete Strength Retention (%)	Concrete Expansion Coefficient (×10⁻⁶/°C)
20	100	100	12
200	95	90	12
400	78	65	13
600	47	32	14
800	23	8	14
1000	12	2	14

Analytical Method Development

The proposed analytical method modifies the conventional confined concrete stress-strain model by introducing a temperature-dependent additional confining pressure term. The key innovation is the recognition that thermal expansion mismatch creates an additional radial pressure on the concrete core, partially compensating for the strength degradation of both materials.

The method involves:

Determining the temperature distribution through the column cross-section using heat transfer analysis
Calculating the additional confining pressure from differential thermal expansion
Modifying the confined concrete constitutive model to include temperature effects
Integrating the modified stress distribution over the cross-section to obtain total axial capacity
Adding the contribution of the steel tube at the reduced temperature-dependent strength

Key Equations and Parameters

Parameter	Expression	Description
Additional confining pressure	σ_t = α_s × T × E_s × t / D	Thermal confinement from steel tube
Modified concrete strength	f_c' = f_c × ξ(T) × (1 + k × σ_t / f_c)	Temperature and confinement effects
Steel tube contribution	N_s = A_s × f_y(T)	Temperature-reduced steel capacity
Total capacity	N_total = N_c + N_s	Combined axial capacity

Engineering Application

This analytical method has direct applications in:

Fire resistance design of CFST columns in buildings, bridges, and industrial structures
Assessment of existing CFST structures after fire exposure
Performance-based fire engineering design where structural response at elevated temperatures is explicitly calculated
Comparison of different fire protection strategies for CFST members

The method provides a rational basis for determining the fire resistance rating of CFST columns without relying solely on parametric fire tests, which are expensive and limited in scope.

Study Insights

The research highlights an important physical mechanism that is often overlooked in fire design: the thermal expansion of the steel tube creates an additional confining pressure on the concrete core, which partially offsets the strength degradation of both materials. This self-confining effect is most pronounced at intermediate temperatures (400–600°C) where the concrete has not yet spalled but the steel has already undergone significant thermal expansion. From a welding and fabrication perspective, this analysis also has implications for the design of welded joints in CFST members, as the heat-affected zone of a weld may experience localized temperature elevations during fire that trigger these same confinement mechanisms. Engineers should consider that the fire performance of a welded CFST column is not simply the sum of its parts but is influenced by the interaction between material properties, geometric constraints, and thermal gradients throughout the structural system.