Complete Equation for Stress–Strain Relationship of Normal to High Strength Concrete under Uniaxial Compression

The stress-strain relationship is a decisive parameter in assessing the behavior of any engineering material. It is necessary to propose a simple and universal stress-strain model that applies not only to normal strength concrete but also to high strength concrete. It is also essential that the mathematical form of this model be expressed in term of easily measurable parameter in laboratory. This not only ensures the model’s applicability across a wide range of concrete grades but also makes it easily operable for determining various index properties. To achieve this objective, unconfined concrete cylinders (150×300 mm) were cast with different grades of concrete such as M20, M40, M50, M60 and M75 and tested in displacement-controlled compression testing machine. A mathematical model was developed using a fourth-degree polynomial equation through linear regression analysis of the test data. The model comprised of the cylindrical compressive strength of concrete as the only input parameter. Furthermore, the proposed model was calibrated by comparing the predictions with reported stress-strain curves in the literature. It was found effective in predictions for both ascending and descending portions of the curve for the concretes having strength ranging between 18 to 86 MPa. Additionally, the ratios of predicted to measured values for the chord modulus and initial tangent modulus were 0.88 and 1.02 respectively, demonstrated excellent accuracy in predicting index properties too. This study will enable engineers to enhance the effective analysis and design of flexural members made of normal to high strength concrete by proposing new and realistic stress block.