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### Mathematical Model of Compressive and Flexural Strength of Concrete Subjected to Elevated Temperature Using Dimensional Analysis—Buckingham’s Pi Theorem

#### Abstract

The effect of elevated temperature, its duration and cooling condition on compressive and flexural strength of concrete is a complex phenomenon and its characterization is governed by several other parameters related to concrete. The destructive testing of concrete subjected to elevated temperature for evaluating its compressive and flexural strength consumes time and put constraints on field schedules and hence there is need to develop the mathematical model which can provide an accurate range of results based on previous data. This paper presents the capability and application of dimensional analysis using Buckingham’s 𝜋 theorem approach for predicting compressive and flexural strength of M-20 and M-40 grade concrete subjected to elevated temperature. A mathematical model is developed using Buckingham’s 𝜋 theorem. The functional relationship of variables of concrete is expressed in the form of an exponential equation which is dimensionally homogeneous. A dimensional constant is determined from the physical characteristics such as grade of cement, initial setting time, final setting time, fineness of fly ash, consistency of cement, room temperature, elevated temperature and the dimensionless parameters are then, formed by grouping together the variables of like parameters. Concrete of M-20 and M-40 grade was cast and subjected to temperature 600 and 8000C for different durations .The natural cooling and cooling by water jet was achieved. The performance of the concrete was, and then tested for compression and flexure. The validation of mathematical model is done with experimental results and the correlation coefficient (φ) is developed which indicates the best fitting of model results with experimental results