Concrete Cross-section Research Articles

Minimum Depth-Span Ratio of Beams in order to Control Maximum Permissible Deflection

Background: ACI code and other building codes and standards include the provisions for deflection control and depth-span limitations, also including the maximum permissible deflection for specified concrete and steel reinforcement strength. In this study, the effects of applied load intensity, steel reinforcement index amount as a ratio to the balancing reinforcement index (ρ/ρb), concrete strength (fc' ) and beam width on the depth-span ratio of the beam with different types (simply supported, fixed ended, propped and cantilever) were investigated. Objective: This study aimed to study the effect of applied load intensity, steel reinforcement index amount as a ratio to the balancing reinforcement index (ρ/ρb), concrete strength (fc' ) and beam width on the depth-span ratio of the beam of different types (simply supported, fixed ended, propped and cantilever). Methods: This study theoretically investigates the effect of applied load intensity, steel reinforcement index amount as a ratio to the balancing reinforcement index (ρ/ρb), concrete strength (fc' ) and beam width on the depth-span ratio of the beam of different types (simply supported, fixed ended, propped and cantilever). Results: The results show that the effect of the ratio (ρ/ρb) is small on the depth-span ratio, and the required depth of the beam increased with increasing the applied distributed load value and decreased with increasing the concrete strength for all beam types. Discussion: Deflection of slabs and beams can be controlled by the addition of steel reinforcement bars or using pre-stressing concrete, loading type and value, material properties (E), section properties (I), and the type of the member. The results showed that the effect of the ratio (ρ/ρb) was small on the depth-span ratio, and the required depth of the beam increased with increasing the applied distributed load value and decreased with increasing the concrete strength for all beam types. Conclusion: - A modification of ACI Code span-depth ratio is suggested to include the effect of tension reinforcement area which is represented by the reinforcement indices ratio (ρ/ρb), applied distributed load (w), concrete compressive strength (fc' ) and cross section width (b) in order to control the maximum deflection of the beam within the ACI limit of the maximum permitted deflection. - The value of span-depth ratio (N = L / h) is determined for four types of beam (simply supported, fixed ended, propped and cantilever) for concrete strengths (fc' = 21, 28, 35, 42, 63 & 84 MPa), applied distributed load (w = 14.6, 29.2, 43.8 & 58.4 kN/m), cross width (b = 150, 200, 250 & 300 mm) and (ρ/ρb = 0, 0.5 & 1) in addition to (ρt /ρb & ρmax /ρb). - The effect of the reinforced indicia ratio (ρ/ρb) is small on the span-depth ratio (N = L / h) for all values of applied load and concrete compressive strength. - The span-depth ratio (N = L / h) decreased with increasing the applied load, or in other words, the required depth increased with increasing the applied load for all values of concrete strength and beam width. - The span-depth ratio (N = L / h) increased with increasing the concrete strength (fc' ), i.e. the required depth decreased with increasing concrete strength for all values of applied loads and beam width. - The same behavior and conclusions are obtained for all beam types (simply supported, fixed ended, propped and cantilever).

Shear Performance of Reinforced Concrete Beams with Small Circular Openings Strengthened Using Rectangular and Octagonal-Shaped Reinforcement.

An experimental case study was carried out to investigate the shear performance of reinforced concrete beams with small circular openings under a cyclic anti-symmetric bending moment. The openings were strengthened by using a newly developed reinforcement continuously bent into rectangular and octagonal shapes, which was convenient for installation and effective for crack control. The presence of web opening reinforcement, the reinforcing method, and the web opening spacing were employed as main variables in the design of five specimens. The cyclic performance of all specimens was evaluated in terms of failure mode, crack pattern, strength and stiffness degradation, and strain distribution. Experimental results were discussed to assess the suitability of the proposed web opening reinforcement in RC web opening beams. It was confirmed that the proposed web opening reinforcement exhibited outstanding crack control and served as a shear resistance component in place of the concrete cross-section lost due to web openings. Finally, the shear strength of all specimens, obtained from the cyclic loading tests, were compared with those obtained from the equation proposed by Mansur (1998) and the Architectural Institute of Japan standard 2010.

USING CARBON FIBER STRIPS IN JOINTS STRENGTHING OF BOX SEGMENTAL SELF-COMPACTING CONCRETE BEAMS

The main objective of this research is to study the effect of carbon fibers used to strengthen the joints of the box segmental beams. For this research, four beams were produced and tested. One of these beams, monolithically, was cast as a reference beam and the three others were segmental beams. All beams were produced with Self-Compact Concrete (SCC) and box cross section. Each segmental beam consisted of three precast concrete segments were connected by post tensioning tendons. The three segmental beams have same characteristics, but different in joint types between the segments. The types of joints used were (dried, epoxied and dried strengthen by CFRP sheets). All beams were tested under static two point loads up to failure. For each test, deflections at mid-span location were recorded for each (5kN). Also, first cracking, mode of failure and ultimate loads values were recorded as well as the concrete surface strains at the specified locations for both loadings.

Cross-section modeling of the non-uniform corrosion due to chloride ingress using the positional finite element method

In this paper, we propose an original and alternative FEM strategy to simulate the expansion and damage in cross sections of concrete elements due to non-uniform corrosion associated with chloride ingress. The strategy embed two-dimensional particle elements in two-dimensional matrix elements to simulate the stress distribution in the steel/concrete interface. This approach is different from the usual ones in which the steel rebar is replaced by forces and the contribution of the reinforcement stiffness is neglected. The reinforced concrete cross section is made by the composition of matrix and particle elements by means of nodal correspondence. This ensures that the number of degrees of freedom is not affected by the reinforcement, which makes the technique highly economical from the numerical point of view. A damage model contributes to the process of concrete degradation due to corrosion. The numerical applications ensure the accuracy of the developed model, showing its applicability in the analysis of non-uniform corrosion propagation in cross sections of reinforced concrete structures.

Betonarme Dairesel Kolonların Eğilme Momenti-Eğrilik ve Hasar Sınırlarının Analizi

In this study; the effect of axial load levels, longitudinal reinforcement ratio, transverse reinforcement diameter and transverse reinforcement spacing were investigated on the moment curvature relationships of reinforced concrete columns. For this purpose, circular reinforced concrete columns having different parameters were designed considering the regulations of the Turkish Building Earthquake Code (2018). The behavior of the columns were investigated from the moment-curvature relation, by considering the nonlinear behavior of the materials taken into account. The moment-curvature relationships of the reinforced concrete column cross-sections having different axial load levels have been obtained by considering Mander model, which considers the lateral, confined concrete strength. Moment-curvature relationships were obtained by SAP2000 Software, which takes the nonlinear behavior of materials into consideration. The designed reinforced concrete cross section models are considered to be composed of three components; cover concrete, confined concrete and reinforcement steel. The examined behavioral effects of the parameters were evaluated by the curvature and moment carrying capacity of the cross-sections. From the obtained moment-curvature relationship, cracking and destruction in cover and core concrete, yield and hardening conditions in reinforcement steel were calculated and the results were presented in charts and graphs. The confining effect in the core concrete is taken into account in the calculations. The behavior of the circular column sections and the types of refraction were interpreted according to the results obtained from the moment-curvature relationship of the sections. It is observed that the variation of the axial load, longitudinal reinforcement ratio, transverse reinforcement diameter and transverse reinforcement spacing have an important effect on the moment-curvature behavior of the reinforced concrete columns. The load bearing capacity of reinforced concrete column sections ends by destruction of the core concrete. Reinforced concrete column sections damaged by reinforcement yield before crushing of cover concrete exhibit more ductile behavior.

Crack Spacing Prediction of Fibre-Reinforced Concrete Beams with Lap-Spliced Bars by Machine Learning Models

Reduction of spaces between flexural cracks is one of the crucial factors in protecting reinforcements from corrosion. Different parameters, such as concrete cover, concrete compressive strength, specimens’ dimension and spacing of longitudinal and transverse reinforcements, influence the crack spacing. Insufficient lap-spliced length reduces the strength and increases the crack spacing. In this study, the effects of lap-sliced length, a cyclic number, steel fibre percentage, longitudinal rebar diameter, concrete compressive strength, cross-section height and width on flexural crack spacing are investigated. Multilayer perceptron (MLP) neural network, adaptive neuro-fuzzy inference system, support vector regression and least mean squares regression are utilized to predict the flexural crack spacing. The obtained results illustrate that the MLP model yields better accuracy compared to other ones in the prediction of cracking spacing. The proper features for predicting crack spacing are prioritized based on mutual information between features. Furthermore, it is found that the available codes are unable to determine the crack spacing within reinforced concrete beams with lap-spliced bars.

Fully nonlinear analysis of steel-concrete composite girder with web local buckling effects

A reliable and advanced program for nonlinear inelastic analyses of steel girders and steel-concrete composite girders subjected to flexural loadings has been developed in the current article. Effects of geometric nonlinearities, material nonlinearities, and residual stresses on flexural behaviors of different steel girders and steel-concrete composite girders have been thoroughly investigated. The concrete slab and steel I-beam cross-sections are discretized into fiber elements to formulate an equivalent effective cross-section. The P − δ effect of beam-column elements is investigated by using stability functions, wherein the plasticity spreading phenomena in the element cross-section are captured at different integration points along the longitudinal direction of the element based on constitutive relations in each fiber. The local buckling phenomenon that possibly occurs in web plates of noncompact composite sections has been considered by considering its effective width formulas for the first time. The generalized displacement control method is applied to solve nonlinear equilibrium equations. The proposed program validated by experimental results shows its accuracies in capturing the structure behaviors and its efficiencies in computing time compared with finite element analyses performed in ABAQUS. Different parametric studies are conducted yielding notable observations. The proposed program might be used as an efficient tool in practical advanced analyses and designs of steel girders and steel-concrete composite girders with high nonlinearities and complexity.

Nonlinear analysis of square concrete-filled double-skin steel tubular columns under axial compression

This paper studies the characteristics of square concrete-filled double-skin steel tubular (CFDST) short columns with inner circular steel tube by performing a series of nonlinear finite element (FE) analysis. The precise definitions of the behavior of the material are the initial requirement of numerical modeling. The existing models for predicting the behavior of the concrete core confined by the circular tube are not suitable since the mechanism of the concrete confinement in square composite columns is different from that of the circular ones. Also, ignoring the confinement effects on improving the concrete strength may lead to conservative results. In this paper, the confinement effects provided by the steel tubes on the concrete core in square CFDST columns are taken into account in the concrete constitutive model. The verified FE model is utilized to investigate the effects of important parameters on the ultimate axial strength, energy absorption capacity, ductility, and interaction performance of CFDST columns. A new design equation is suggested based on stress distribution over the concrete cross-section. It is shown that material properties and dimensions of composite columns can highly affect their performance. Also, the thickness of the inner tube must be controlled to prevent its premature failure. Validation of the design equation shows that it leads to the satisfactory predictions of the ultimate strengths of square CFDST short columns under axial loading.

A novel means of improving the performance of reinforced concrete beams using the welded wire mesh as core zone reinforcement

The present practice of using shear reinforcement in the form of stirrups, which go round near to the periphery in reinforced concrete beams, leaves the core zone of the cross section, where there is existence of high shear stress, un-reinforced. This leads to sudden appearance and propagation of cracks, leading to brittle failures under shear. The performance of the reinforced concrete beam will get improved if such core zone is also reinforced. This paper presents a novel means of using prefabricated mesh either as transverse reinforcement in place of conventional stirrups or as longitudinal core reinforcement apart from stirrups/ties, which not only reinforces the core zone of reinforced concrete cross section but also provide resistance against diagonal tension due to shear in continuous manner. The pilot experimental investigation conducted on RC beams provided with welded wire mesh as core zone reinforcement indicated improved performance compared to the ultimate resistance of RC beams provided with only conventional stirrups.

Betonarme Kolonlarin Eğrilik Sünekliğinin Analitik Olarak Araştırılması

In this study; the effect of axial load, longitudinal reinforcement diameter, transverse reinforcement diameter and transverse reinforcement spacing were investigated on the moment curvature relationships of reinforced concrete columns. Reinforced concrete columns having different geometries were designed considering the regulations of Turkish Building Earthquake Codes (2018). Investigations of the effect of axial load, longitudinal reinforcement diameter, transverse reinforcement diameter and transverse reinforcement spacing on the behavior of the concrete columns are the main purpose of this study. The behavior of the columns was investigated from the moment-curvature relation, by considering the nonlinear behavior of the materials taken into account. The moment-curvature relationships of the reinforced concrete column cross-sections having different axial load levels have been obtained by considering Mander model which considers the lateral confined concrete strength. The examined effects of the parameters on the column behavior were evaluated in terms of curvature ductility and the moment capacity of the cross-section. In the designed column cross-sections, different parameters effecting the moment-curvature relationships were calculated and compared. It is observed that the variation of the axial load, longitudinal reinforcement diameter, transverse reinforcement diameter and transverse reinforcement spacing have an important effect on the moment-curvature behavior of the reinforced concrete columns.

Optimum design of reinforced concrete counterfort retaining walls using TLBO, Jaya algorithm

In this study, the optimum design of a reinforced concrete counterfort retaining wall for minimum cost is investigated by using TLBO and Jaya algorithms. There are 17 design variables in the problem of reinforced concrete counterfort retaining wall created in the study. These design variables are related to the wall geometry and steel reinforcement in various parts of the wall. There are a number of charts used in the technical literature to determine the cross-sectional effects of the stem and heel slabs of the wall. However, it is seen that these charts have been prepared at certain aspect ratios of the plates. In this case, Open Application Programming Interface of SAP2000 Software (called SAP2000-API) is used within the algorithm to realize a more realistic structural analysis. Thus, the desired structural analysis can be performed by applying external loads on the wall model prepared in SAP2000 Software through MATLAB Software where the algorithm is encoded. The desired cross-sectional effects are taken from this Software and used in the algorithm. The problem has a total of 46 constraints which consist of checks of sliding, overturning, and bearing capacity of the wall, reinforced concrete cross-section controls, and conditions related to size and reinforcement. The performance of the algorithms according to the findings from the optimum design performed on a numerical application is evaluated with standard statistical data and Wilcoxon test. According to Wilcoxon test, it is also observed that TLBO algorithm is more successful than Jaya algorithm for this problem.

Experimental investigation of reinforced concrete beams using post- tension

The paper presents the results of an experimental investigation of statically determinable pre-stressed concrete beams with tension on concrete (using post-tension). The authors consider the existing practice of applying post-tension in reinforced concrete structures, the current regulatory documents of the Russian Federation containing information on the strength and deformation properties of post-tension. The paper contains information about the loading pattern, beam-fixing conditions, geometric characteristics of a reinforced concrete beam, physical characteristics of concrete and reinforcement of an experimental sample, technical characteristics of pre-stressed reinforcement. The authors present the research results using graphs of structural deflection changes under load, the distribution of relative strain along the depth of a concrete cross-section, as well as cracking and failure schemes of experimental samples. The research presented in the paper showed that the destruction of the samples occurred along a standard cross-section and was brittle. As a result of processing the results of experimental data, loads of crack formation and critical crack width were determined. The authors confirmed the effect of pre-stressing on crack resistance and the magnitude of the deflection of bent reinforced concrete elements.

Resistance of corroded RC beams: Extending fib Model Code 2010 models

AbstractThe residual resistance of corroded reinforced concrete members depends on steel and concrete cross section loss and deterioration of material properties for steel, concrete, and bond. The paper considers these phenomena in models for resistance calculations, starting from the cross section and stress field models in Model Code 2010. The aim of this study is to develop models proposed by Coronelli et al., using a recently proposed approach by Blomfors et al. to model bond of corroded reinforcement based on the Model Code 2010 bond stress–slip relation. Flexure, shear, and anchorage resistance of corroded reinforced concrete beams are studied. The verification is carried out by comparison with tests on corroded beams with different shear span‐to‐depth ratios. The bond deterioration leads to changes in the inclination of the stress fields in B regions and anchorage failures. The reduced resistance and the changes of the failure modes caused by the deterioration phenomena are captured by the modeling approach.

INVESTIGATION OF THE MOMENT–CURVATURE RELATIONSHIP FOR REINFORCED CONCRETE SQUARE COLUMNS

In this study; the effect of the material model, axial load, longitudinal reinforcement ratio, transverse reinforcement ratio and transverse reinforcement spacing on the behavior of reinforced concrete cross-sections were investigated. Squared cross-section column models have been designed. The effect of axial load, transverse reinforcement diameter and transverse reinforcement spacing on the behavior of reinforced concrete column models have been analytically investigated. The behavior of the columns was evaluated from the moment-curvature relation by taking the nonlinear behavior of the materials into account. The moment-curvature relationships for different axial load level, transverse reinforcement diameter and transverse reinforcement spacing of the reinforced concrete column cross-sections were obtained considering Mander confined model. Moment-curvature relationships were obtained by SAP2000 Software which takes the nonlinear behavior of materials into consideration. The examined effects of the parameters on the column behavior were evaluated in terms of ductility and the strength of the cross-section. In the designed cross-sections, the effect of transverse reinforcement diameter and transverse reinforcement variation on the confined concrete strength and the moment-curvature relationship was calculated and compared for constant longitudinal reinforcement ratio. The examined behavioral effects of the parameters were evaluated by comparing the curvature ductility and the cross-section strength. It has been found that transverse reinforcement diameters and transverse reinforcement spacing are effective parameters on the ductility capacities of the column sections. Axial load is a very important parameter affecting the ductility of the section. It has been observed that the cross-sectional ductility of the column sections increases with the decrease in axial load.

Fundamental Investigation on Seismic Retrofitting Method of Aging Concrete Structural Wall Using Carbon Fiber Sheet‐Constitutive Law of Rectangular Section

Aging building structure has become a world problem. This problem is particularly serious in developing and underdeveloped countries. The multihazard resilience and sustainability (e.g., seismic performance) decrease at the aging building. A construction method for strengthening aging‐reinforced concrete buildings by wrapping structural members with carbon fiber sheets has been proposed and implemented in recent years. Authors aim to develop a seismic retrofitting method of aging concrete structural wall with a rectangular cross section using carbon fiber sheets. In this paper, authors examined the stress‐strain relationship of concrete elements with rectangular cross sections reinforced by wrapping with carbon fiber sheets. Monotonic uniaxial compression tests were performed on 21 specimens using the ratio of the long side to the short side and the ratio of the element height to the short side of the concrete cross section, the weight of the carbon fiber sheet, and the chamfer radius of section corners as variables. The tests revealed that (1) the compressive strength decreases and ultimate strain increases as the ratio of the long to short side (longitudinal ratio) of the cross section increases even in a range the ratio exceeds 2 and (2) the ratio of the element height to the short side does not significantly affect the stress‐strain relationship. Furthermore, authors proposed evaluation formulas for the constitutive law of concrete elements with rectangular cross sections including the longitudinal ratio which exceeds 2 reinforced by carbon fiber sheets and confirmed that the formulas can reproduce the test results with good accuracy.

Experimental and numerical investigation of rectangular reinforced concrete columns under contact explosion effects

The response of reinforced concrete (RC) members subjected to contact explosion effects is more severe than the response to non-contact explosions due to local material failure. The shock-wave reflection within the RC member causes severe local material damage. The resulting loss of concrete cross-section reduces the axial load and bending capacity of the RC member. It is hypothesized that the concrete loss from the sides can be prevented by increasing the aspect ratio of the cross-section. In a low aspect ratio RC column, the reflection is from three faces whereas in RC slabs and high aspect ratio columns the shock-wave reflection from the back-face only is significant. This study experimentally investigates the response of rectangular RC columns with varying widths of the cross-section, subjected to contact explosion effects. A range of aspect ratios was investigated to preclude the side face damage for a given depth of rectangular RC column. High fidelity numerical models were developed to predict the blast-response and the residual axial capacity of the blast-damaged rectangular columns. The numerical models were validated, and the results show a good correlation with the experimental results. Using a rectangular RC column aspect ratio with a width that precludes the side face spall significantly improves the residual axial capacity of the blast-damaged columns. Furthermore, parametric analyses were performed to numerically investigate the influence of the width on the residual axial load carrying capacity of rectangular RC columns subjected to contact explosion effects of breach-charge mass required for the provided depth. An increase in the width of the column improved the damage resistance even though the rectangular column was breached around the point of detonation. Hence, increasing the width of the rectangular RC columns can be effectively used to mitigate contact explosion effects.

Main results of experimental studies of reinforced concrete structures of high-strength concrete B100 round and circular cross sections in torsion with bending

Aim of the research to verify the proposed calculating apparatus and accumulate new experimental data on the complex resistance of reinforced concrete structures, experimental studies of such structures made of high-strength concrete of circular and circular cross-section were conducted at the testing base of the South-West State University. Method is experimental-theoretical. Results of experimental research the plots of the deflections and rotation angles, the dependency of deformations of concrete according to the testimony of the outlets of electrodesorption with respect to the calculated cross section 1-1. The main deformations of elongation and shortening of concrete were determined; the reinforcement was selected in such a way that in the stage preceding the destruction, it reached fluidity, so the stresses in the reinforcement are known. It is established that for reinforced concrete structures made of high-strength concrete of circular cross-section, as a rule, there is the development of two cracks, i.e. the round shape of the cross-section slightly reduces the concentration due to the structure of high-strength concrete. For the annular section there were several cracks, of which stands out the one on which the destruction occurs. On the steps preceding the destruction, this crack begins to prevail over the rest and has a maximum opening width. On the basis of experimental studies of reinforced concrete structures made of high-strength concrete of square and box sections, reliable data on the complex stress-strain state in the studied areas of resistance, such as: the values of the generalized load of cracking , and destruction ,, its level relative to the limit load; the distance between the cracks at different levels of cracking (up to the moment of destruction, as a rule, two or three levels are formed); crack widths at the level of the axis of the working armature, at a distance of two diameters from the axes of the armature and along the entire crack profile at various stages of loading, from which it follows that the crack opening at the level of the axis of reinforcement in 2-3 times less compared with the crack opening on the removal of 1.5-2 diameters of the working axis (longitudinal and transverse) reinforcement; the coordinates of the spatial formation of cracks; schematic drawings on tablets of education, development and opening of cracks of reinforced concrete constructions in torsion with bending. Thus, the experimental studies and the result provide an opportunity to test the developed computational model and its working hypotheses for assessing the resistance of reinforced concrete structures made of high-strength concrete in torsion with bending.

Effect of recycled concrete coarse aggregates on service-load deflections of reinforced concrete columns

This paper describes a numerical parametric investigation for the effects of coarse recycled concrete aggregates (RCA) on the time-dependent vertical deflections of reinforced concrete columns under sustained service loads. The deflections were analyzed for interior (concentric) and exterior (eccentric) column loading conditions, with different volumetric replacement of the coarse aggregate, R, concrete strength, column width, column depth, column length, longitudinal reinforcement area, ultimate shrinkage strain, ultimate creep coefficient, and ambient relative humidity. In addition, the quality of RCA was quantified and varied through the water absorption, Arca (viewed as a measure of aggregate porosity), and deleterious material content, Drca (e.g., wood, asphalt). The results show that increased R resulted in larger deflections, and increased Arca and Drca resulted in larger deflections for the same R. High quality RCA with low Arca and Drca resulted in deflections that were not much greater than those for natural aggregate (NA) concrete columns. The increase in deflection due to RCA was larger for columns with larger concrete strength and cross-section dimensions and smaller longitudinal steel ratios, and larger for interior columns than exterior columns with flexural cracking. RCA was also found to have larger effect on the initial column deflections than the time-dependent deflections.

Experimental study on the effect of reinforcement ratio on the ultrasonic velocity and modal frequency of concrete members

In order to study the effect of reinforcement ratio on ultrasonic sound velocity and modal frequency of reinforced concrete members, 13 concrete circular cross-section short columns were designed to detect the ultrasonic sound velocity and self-strain of short columns with different cuff ratio and longitudinal reinforcement ratio. Compared with non-reinforcing short columns, the results show that the stirrup reinforcement ratio is from 0.4% to 1.667%, the ultrasonic sound velocity is increased by 3.4%, the modal frequency is increased by 1.8%; the longitudinal reinforcement ratio is from 1.772% to 2.657%, the ultrasonic sound velocity is increased by 3.5%, and the modal frequency is increased 4.1%; the reinforcement can improve the ultrasonic sound velocity and the natural vibration frequency of the concrete to a certain extent, the change of the reinforcement ratio causes the same regular change of the sound velocity and the modal frequency.

MODELING BASICS OF MULTILEVEL NORMAL CRACKS FORMATION IN REINFORCED CONCRETE ELEMENTS AND STRUCTURES

The model of consistent multilevel normal cracks formation is an integral part of the generalized deformation and force model of reinforced concrete elements and structures resistance by force influences. It is based on the most important patterns of reinforcement adhesion with concrete. It is based on the fundamental relationships of the mechanics of a deformed solid, which are expressed by the generally recognized system of static, geometric, and physical relations. To reveal the internal static uncertainty of the reinforced concrete elements cross-section, this system is supplemented by the analytical dependence of the state diagram of the reinforced concrete element and the function of compressed concrete boundary deformation.The first normal cracks occurrence of the first level in the reinforced concrete element is determined by the boundary deformations of the stretched concrete, which are fixed by the extreme criterion of its strength.The distances between the cracks are determined by the equilibrium of the maximum forces in the stretched concrete and the active adhesion forces in the area between the cracks. The force of reinforcement active coupling with concrete is proposed to be calculated by the nonlinear function of the average stresses of this coupling, justified by the power of expression. It is shown that for a centrally stretched reinforced concrete element, the distance between the first level cracks is inversely proportional to its reinforcement coefficient. The magnitude of the normal stresses in the tensile reinforcement at which cracks of the second level will begin to form is established.It is substantiated why for bending reinforced concrete elements the distances between normal cracks of new and previous levels will always differ from each other. In the developed model, the width of the most dangerous normal crack opening is calculated from the positions of successive accumulation of reinforcement and concrete mutual displacements.The developed technique is the basis of the engineering method of calculating the formation and discrete cracks opening at the operational stages of reinforced concrete elements deformation.