Concrete constitutive relationships under different stress-temperature paths

The behavior of concrete exposed to fire is highly influenced by stress-temperature path. Any stress-temperature path consists of two basic paths: the path of constant temperature but subjected to increasing stress (TS path), and the path of constant stress but subjected to elevated temperature (ST path). The concrete mechanical strain for the TS path can be obtained experimentally, but it is difficult to obtain the mechanical strain for the ST path due to nonuniform temperature distribution within the concrete specimen. In this paper, through analyzing the stress versus mechanical strain curves of concrete from test results for the TS path, a new concept, known as the "temperature-flow mapping" method, is proposed. Based on this concept, temperature versus mechanical strain relationships of concrete for the ST path can be obtained from those curves for the TS path. Mathematical expressions for the concept are also given in the paper. It is found that the predictions based on this concept are in good agreement with experimental results.