Verification of Dependences Approximating the Diagrams of Deformation of Cement and Polymer Concrete by the Method of Normalized Indicators

Abstract

The article verifies some approximating power-law and hyperbolic dependences between stresses σ and deformations ε for experimental deformation diagrams of cement concrete and polymer concrete. When analyzing the state and residual life of reinforced concrete structures, one has to solve the problem of determining the relationship between stresses and deformations in various design sections of structures. The traditional approach, based on the selection of the approximating function "σ – ε" from the numerical values of the deformation diagram obtained by testing samples (cubes, prisms, cylinders), is practically impossible. Therefore, an alternative approach is proposed based on the selection of an approximating function according to standardized indicators: ultimate strength (σ_bu); modulus of elasticity (E_b0); ultimate deformation (ε_bu). The numerical values of the normalized indicators can be determined at a given point by analyzing the results of indentation of the indenter into the material of structures. As approximating ones, consider the power functions that are most preferable for materials with a fractal structure. Various boundary conditions are considered for determining the constant coefficients α and β according to the system of normalized indicators. The graphs of changes in tangent modules are analyzed.

Determination of Bending of a Beam From a Nonlinear Deformable Material by Ritz-Timoshenko Methods and Finite Differences Taking Into Account Degradation Functions of Cross Section Rigidity

“…where the constants = ( ) 3,16 10 , = ( )/ 5, 12 10 are determined from the condition of conformity of the approximating function (2) to the normalized indicators [26].…”