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The evaluation of stress state of longitudinal tensile reinforcement is highly important while examining the technical state of under-reinforced concrete structures. The appearance of yield stress in tensile reinforcement could be treated as the start of incipient failure of the flexural structure. The state of tensile reinforcement of flexural reinforced concrete structures could be examined by observing the properties of normal cracks. This paper presents the analysis of the relationship between various parameters of a normal crack during its development. Some elements of fracture mechanics are used for analysis of stress state in flexural reinforced concrete members. The analytical data are compared to the experimental results, and the adjustment functions are proposed for flexural beams of certain cross section shape, dimensions and reinforcing ratio.

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The width of normal cracks at the level of tensile reinforcement was calculated according to various methods using the data obtained from experimental tests on reinforced concrete beams (without reinforcement pre-stress), pre-cast reinforced concrete slabs and ribbed roof slabs. Th e numerical results were compared to actual crack widths measured during the experimental tests. Also, the crack widths of pre-stressed reinforced concrete beams were calculated according to various methods and compared with each other. Th e following conclusions were reached based on the analysis of numerical and experimental results: 1) Design stresses in tensile reinforcement calculated according to [STR] and [EC] design codes are very similar, although the calculation of such stresses is more logical and simple according to [EC]. Design stresses calculated according to [RU] are greater due to the estimation of the plastic deformations of concrete in the compressive zone. Th e method proposed by Rozenbliumas (Розенблюмас 1966) estimates tensile concrete above the crack peak, and thus allows a more accurate calculation of stresses in tensile reinforcement (Fig 3). Therefore, the latter stresses in pre-stressed RC beams may be decreased by 10–12 %, when height hct ≠ 0 (Fig 1, c) and ratio M/MRd varies between 0,65 and 0,75; 2) The widths of normal cracks in conventional RC beams (subjected to load that corresponds approx. 70 % of their carrying capacity) calculated according to [STR] and [EC] design codes are almost equal to the experimentally obtained crack widths. When beams and slabs are loaded by approximately 52 % of their carrying capacity, design crack widths wk [EC] are approximately 12 % less than wk [STR], although the design crack width wk [RU] is signifi cantly greater. Here, ratio β in the beams and slabs is equal to 2 and 3.3 respectively. Th erefore, the design code [RU] ensures higher probability that the crack width will not reach the limit value (for environmental class XO and XC1) equal in all design codes mentioned in this article; 3) In case of loaded prestressed reinforced concrete beams, the calculated increases of crack widths wk [EC], wk [RU] and w [5] are greater if compared to wk [STR] (Fig 6). Th e increased reinforcement ratio ρ has more signifi cant infl uence on the increases of crack widths calculated according to other design codes if compared to wk [STR]. Tensile concrete above the crack peak has signifi cant infl uence on the design crack width when pre-stressed RC beams are lightly reinforced (ρ ≤ 0,008); 4) During the evaluation of the state of fl exural RC members, expression (5) could be used for calculating the crack width or a position of the neutral axis when the heights of the crack and the tensile zone above the crack are known (calculated or measured experimentally). Design crack widths w (5) are very similar to the experimentally obtained results.

Tensile stresses in concrete occur under the action of reinforcement rust pressure. When they exceed concrete tensile strength or concrete extension strain exceeds limit value, concrete cracks. Physical and numerical models of such cracks are proposed for analysis of formation and development based on the main assumption that in the place of the rusting bar there is an artificial cut of circular shape, the contour of which is subjected to a pressure, imitating pressure of rust. Limit pressure values and character of formation and development of cracks through concrete cover to reinforcement are compared with data of experimental investigations performed by S. Williamson. The analysis has indicated that proposed models of formation and development of longitudinal concrete cracks are based on correct assumptions and can be applied for assessing the state of cracked reinforced concrete structures.