Axial Compression and Bending Stiffness of Concrete-Filled Steel Tubes After ISO-834 Fire

Literature Overview

The paper by Huo Jingsi and Han Linhai (2002), published in "Journal of Earthquake Engineering and Engineering Vibration" (Vol. 22, No. 5, pp. 143-151), investigates the axial compression stiffness and bending stiffness of concrete-filled steel tubes (CFST) after exposure to the ISO-834 standard fire. The research employs numerical methods to calculate the load-deformation relationships of CFST members under both axial compression and pure bending after fire exposure. The study analyzes the influence of fire duration, material strength, steel ratio, and section dimensions on the post-fire stiffness, and derives simplified calculation formulas for engineering design. This work is supported by the Fujian Provincial Natural Science Foundation (Grant E01200001).

Core Technical Analysis

The ISO-834 standard fire curve defines a temperature-time relationship that is widely used for fire resistance testing and assessment. The temperature at the steel surface of a CFST member increases with fire duration, and the material properties of both steel and concrete degrade at elevated temperatures. The steel loses strength and stiffness at temperatures above 400°C, while the concrete experiences thermal cracking, spalling, and significant strength loss at temperatures above 600°C.

The numerical analysis in the paper captures the nonlinear material behavior at elevated temperatures, the interaction between steel and concrete, and the geometric nonlinearity due to large deformations. The load-deformation curves obtained from the analysis show a progressive degradation of stiffness with increasing fire duration. The axial compression stiffness decreases more rapidly than the bending stiffness, which is attributed to the more severe degradation of concrete compressive strength at high temperatures.

Influence of Key Parameters

The steel ratio, defined as the ratio of steel cross-sectional area to total cross-sectional area, plays a crucial role in post-fire stiffness. Members with higher steel ratios retain more stiffness after fire because the steel tube provides a load-bearing path even when the concrete core has significantly degraded. However, the steel tube itself also loses strength at elevated temperatures, so the benefit of high steel ratio diminishes at very high temperatures.

Simplified Calculation Formulas and Engineering Application

The authors derived simplified formulas for the post-fire axial compression stiffness and bending stiffness of CFST members. These formulas incorporate the temperature-dependent material properties, the geometric parameters of the member, and the fire duration. The formulas are designed to be practical for engineering design, avoiding the complexity of full finite element analysis while maintaining reasonable accuracy.

For axial compression stiffness, the formula takes the form:

K_axial = K_ambient × f(T, ρ_s, D/t)

where K_ambient is the ambient temperature stiffness, f(T, ρ_s, D/t) is a reduction factor that depends on temperature, steel ratio, and section slenderness ratio. Similarly, the bending stiffness formula follows a comparable structure with appropriate modification factors.

In engineering practice, these formulas can be used for the assessment of existing CFST structures after fire exposure. Engineers can estimate the residual stiffness based on the estimated temperature history and the known material and geometric properties. The results can then be used to evaluate the structural safety and determine the need for repair or strengthening.

Study Insights and Practical Recommendations

This paper addresses a critical gap in the knowledge of CFST structural behavior under fire conditions. While fire resistance of CFST members has been studied extensively in terms of load-bearing capacity, the stiffness degradation has received less attention. However, stiffness is a critical parameter for seismic analysis and serviceability assessment of structures after fire exposure.

The findings have direct implications for the design of CFST structures in fire-prone environments. Engineers should consider the post-fire stiffness in the seismic design of CFST structures, as a structure that has experienced a fire may have reduced stiffness and therefore altered seismic response. The simplified formulas provide a practical tool for this assessment.

Furthermore, the paper highlights the importance of steel ratio in post-fire performance. For applications where post-fire stiffness is critical, such as in nuclear facilities or bridges, a higher steel ratio may be warranted despite the increased cost. The trade-off between cost and post-fire performance should be carefully evaluated for each application.

In summary, this paper provides valuable insights into the post-fire stiffness behavior of CFST members and offers practical calculation tools for engineering application. The findings should be considered in the design and assessment of CFST structures, particularly in fire-prone environments where post-fire structural performance is critical. Engineers should adopt a comprehensive approach that considers both load-bearing capacity and stiffness degradation when evaluating CFST structures after fire exposure.