Energy Model in Calculating the Strength Characteristics of the Reinforced Concrete Components

Abstract

The article proposes applying energy from law deformation mechanics of the rigid body to deformation method for calculating the strength of reinforced concrete constructions with the use of diagrams illustrating the deformation of concrete and reinforcement. In terms of the energy theory of strength, concrete and rebar accumulate potential energy in the section of the construction component under stress; based on the contours of the diagram used in calculation it is possible to distinguish a stress diagram for concrete of the compressed zone. The value of the strains is equivalent to the force used for the deformation of the concrete specimen under stress (prism-or cylinder-shaped); the force is equal to the area used in the calculation of the normable diagram. The resolving balance equations are deduced with the use of the flat section hypothesis. The conditions of the stress balance in the section of the construction component are tested with the method of the successive approximation. The variable parameter of approximation is the construction component bending. General deformations (deflections) of the construction components are significantly higher than their limit stress values permitted for safe operation.

Relation between Breaking Stresses in the Strength Calculations of Reinforced Concrete Elements under the Deformation Mode in the Edition of Russian and Foreign Regulatory Documents

“…From the equations of the static moment relative to the stress axes, the gravity centers bc ε ( сc ε ) of areas db S ( dc S ) are calculated. In accordance with the energy model presented in [7], the diagrams areas for given values of the element curvature are equivalent to the forces magnitude in the compressed element zone. The strains values bc ε ( сc ε ) determine the forces application coordinates in the normal section about the neutral axis.…”

“…The strains values bc ε ( сc ε ) determine the forces application coordinates in the normal section about the neutral axis. The equation for calculating the limiting bending moment takes the form: is the force perceived by the compressed zone concrete in the limit state for a strip of unit width (b = 1), s b z z , are the forces distance, respectively, in concrete and reinforcement to the neutral element axis, calculated by the formulas in [7], χ is the element curvature.…”

“…Curvilinear diagram that has ascending and descending branches of deformation meets most fully concrete physical properties and experimental data from standard concrete samples tests. When describing compression concrete strain diagrams the edition [5,6,7,8,9], the base points are used: at the top of the diagram on the ascending branch; at the end of the falling branch where the deformations reach maximum values. The strength and strain parameters at the base points are determined by the tables of regulatory documents or by calculating the formulas with concrete strength grade B and C, which are numerically equal to the guaranteed compressive strength n R -a concrete cube with an edge of 150 mm in [1,2,3,4] and ск f -a concrete cylinder 150 mm in diameter and 300 mm in height in [1,2,3,4].…”

Evaluation of the Structures’ Reinforcement Effectiveness Based on Non-Linear Concrete State Diagrams

“…In recent years, one of the promising areas for the development of methods for calculating reinforced concrete structures is the use of a deformation model. The diagram method is widely used in the design of reinforced concrete structures and has broad prospects for the dissemination of a uniform approach that allows us to evaluate elements simultaneously by bearing capacity and stiffness, to include in the design model different in nature and intensity of load and impact [4][5][6][7][8][9][10][11][12][13][14]. The purpose of this article is to develop a diagrammatic method for evaluating the effectiveness of concrete when strengthening structures under load.…”

The Concrete Diagrams Integral Parameters in the Calculations of Reinforced Concrete Elements by Limiting States

“…Performing the stresses summation operation at each iteration step complicates the complex sections and statically indefinable systems calculating the strength computational process. In the energy calculation method proposed by the author [9,10], the forces cross section calculation of an element is performed taking into account the outline and diagrams' integral parameters, but this does not simplify the calculation algorithm. In order to simplify the method of calculating the elements strength, it is necessary to exclude the procedure for the numerical integration of stresses in determining the forces in concrete and reinforcement from the computational process.…”