Thermal Strains

The nonlinear temperature distribution within the concrete cross section results in nonlinear thermal strains. Such strains violate the plane section assumption. To force a linear thermal-strain distribution, self-induced thermal stresses are developed within the section. These stresses are in self equilibrium. The final linear thermal-strain distribution is characterized by the unrestrained thermal parameters: the unrestrained-thermal-axial strain (measured at the section centroid), and the unrestrained curvature.

The tool given below allows estimating the unrestrained-thermal parameters for a beam exposed to fire from three sides (left, bottom, and top). These parameters can be used to estimate the unrestrained-thermal deformations.

For more information, please refer to:

El-Fitiany S.F., Youssef M.A., 2009, “Assessing the Flexural and Axial Behaviour of Reinforced Concrete Members at Elevated Temperatures using Sectional Analysis”, Fire Safety Journal, 44(5): pp. 691-703. 

Simplified, rational, and practical models that account for effect of elevated temperatures on concrete and steel properties are needed. These models will enable engineers to design and assess Reinforced Concrete (RC) structures to satisfy specific fire performance criteria. This paper introduces a simple method that predicts the flexural and axial behaviour of RC sections during exposure to elevated temperatures. The method is based on using Finite Difference analysis to estimate the temperature distribution within a concrete section and a modified version of the well-known sectional analysis approach to predict the axial and/or flexural behaviour. A rational approach is proposed to convert the two-dimensional temperature distribution to one-dimensional distribution. This approach converts a complex problem to a simplified one and thus enables engineers to better understand the behaviour and have higher confidence in the results. The predictions of the proposed method are validated using experimental and analytical studies by others. Additional tests are needed to further validate and improve the proposed method.

El-Fitiany SF, Youssef MA, 2013, “Unrestrained Thermal Deformations of Concrete Elements Exposed to Fire”, 3rd Specialty Conference on Disaster Prevention and Mitigation, May 29 to June 1, Montreal, QC, Canada, DIS-043, 10 pp, DOI: 10.13140/2.1.4709.6326. 

Fire impacts Reinforced Concrete (RC) members by raising the temperature of the concrete mass. This rise in temperature dramatically reduces the mechanical properties of concrete and steel and induces new strains, thermal and transient creep. As a result, heated RC members undergo considerable thermal deformations during fire events. This paper presents a comprehensive parametric study to evaluate the unrestrained thermal deformation parameters, curvature and axial strain, for rectangular RC sections during ASTM-E119 fire exposure. These parameters describe the section’s free thermal expansion at different fire durations. The proposed expressions can be used by engineers to estimate the restraint effect in indeterminate RC structures exposed to fire.



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