Layered reinforced concrete beams made of multi-modulus of elasticity concretes are increasingly used in engineering practice. The step-by-step iterative method in combination with numerical integration in the calculation of such structures using a nonlinear deformation model and real deformation diagrams is a rational solution, despite the currently lack of a generally recognized approach to assessing the stress-strain state of sections of layered beams.
Keywords: double-layer reinforced concrete beams, normal cross-sections, nonlinear deformation model, high-modulus concrete, neutral axis coordinate
The results of studies of two-layer reinforced concrete beams with a layer of various thicknesses of high-modulus concrete of the frame structure in the compressed zone and traditional heavy concrete in the rest of the section are presented. The stress-strain state of normal cross sections along the height of the beam was estimated by the values of relative deformations at the level of stretched and compressed reinforcement using the hypothesis of flat sections and actual compression and calculated tensile deformation diagrams of concrete. The influence of the thickness of a layer of high-modulus concrete on the nature of the stress-strain state between the layers is shown. The possibility of destruction of the beam on the concrete of the compressed zone was revealed due to the abrupt decrease in the actual height of the compressed zone due to the "shooting" of a layer of high-modulus concrete with its thickness less than 0.1 h0. The dependence of the relative actual thickness of the compressed concrete, i.e. the distance from the edge fiber of the compressed concrete to the neutral axis, in the studied beams on the magnitude of the bending moment is obtained. It is established that for single-layer beams, with a difference in the elastic modulus of concrete up to 20%, the dependences of the relative actual thickness of the compressed concrete layer on the bending moment are almost identical. In the studied beams, the limiting state of which is caused by the fluidity of the reinforcement, the thickness of the compressed concrete layer was 0.37 ...0.4 with a relative moment value of 0.5, and 0.33 ...0.36 with a maximum bending moment value.
Keywords: double-layer reinforced concrete beams, normal cross-sections, nonlinear deformation model, high-modulus concrete, neutral axis coordinate
Based on the research conducted by the authors, data on the stiffness and curvatures of reinforced concrete beams with a layer of various heights of concrete with frame structure are presented. Stiffness, curvature and deflections are given for cases of absence and presence of cracks in the tensile zone of beam. Formulas for describing changes in the stiffness and curvature of sections depending on the magnitude of the moment are obtained. The influence of the thickness of the layer of concrete with frame structure and the diameter of the working reinforcement on the change in the stiffness of the sections is established. The regularity of changing the position of the neutral axis for single and double-layer beams depending on the beam parameters.
Keywords: concrete of frame structure, stiffness, curvature, deflection, layered structures, bending moment, neutral axis
The method of determining crack-forming forces based on the normative approach is considered. Experimental and theoretical studies of reinforced concrete beams made of ordinary heavy concrete, self-compacting concrete with a modifier and concrete of a frame structure have been carried out. Formulas for determining the tensile strength and flexural strength depending on the compressive strength for each of the considered types of concrete are given. The calculated values of the ultimate extensibility of various concretes determined by various methods are given. Coefficients to the formula linking the reduced and initial elastic modulus of various types of concrete are obtained. The influence of the accuracy of the experimental determination of the moment of cracking on the change in the calculated dependencies is analyzed.
Keywords: cracking moment, flexural and tensile strength, frame structure concrete, self-compacting modified concrete