Mathematical model of concrete strain diagram under heating

Abstract

New regulatory documents have been adopted and they have significant differences. Firstly, this is a new concept of calculation, a nonlinear deformation model, and secondly, new approaches to the assessment of reliability, loads and impacts, methods of construction. The calculation consists of two stages. The first begins with the determination of the concrete class at temperature of 20ºC. At the second stage, the calculation is carried out at high temperatures according to Eurocode 2 part 1-2. Comparison of the “stress - strain” diagram of concrete class at compression and temperature of 20ºC by two formulae showed their big gap. There was a need to improve the mathematical model of the ratio of stress-strain of the concrete under elevated temperatures. The method of determination of maximum strain based on energy approach has been developed in the work and allowed to formulate the adjusted dependence of the limit strain on temperature, dependence of maximum strain on temperature, values of the parameters of stress-strain diagram.

Major Issues of Theory and Practice of Fire Resistance of Reinforced Concrete Structures and Buildings

“…For carrying out elastic and inelastic calculations in the software complexes also the values of the modulus of elasticity of compressed Ec,θ and stretched concrete Etc,θ, deformations εc1,θ, εtc1,θ,, corresponding to the compressive strength fc,θ and tensile ftc,θ, εcu,θ, εtcu,θ and the boundary stresses corresponding to σcu,θ and σtcu,θ both at normal temperature and at elevated temperatures are required. A particular problem is the clear and correct formulation of the corresponding mathematical model of the compressed concrete deformation diagram [10]. The diagram should be described by a nonlinear and continuous mathematical function that simultaneously includes ascending and descending branches.…”