Rigidity of reinforced concrete structures in the presence of different cracks

Abstract

Abstract. It is proposed a method for rigidity calculating of reinforced concrete structures in the presence of cracks, suitable for rod and flatstrained concrete composite structures. It is based on the operating conditions and includes a new, more complete classification of the various cracks, models of a special crack, the calculation of the two-console model; a special cantilever model to determine the parameters of the joint between the concrete; calculation model of the block with the working section at the beginning and end of the crack to determine the horizontal (vertical) projections of various cracks with the involvement of analytical relationships. They are based on the extremum of a function of many variables and Lagrange multipliers, as well as attracting level model of multi-level development of the various cracks, which allow to find the distance between the cracks and width of their disclosure, with considering the effect of discontinuities. This effect can greatly simplify the process of determining the rigidity of reinforced concrete structures (including composite ones), despite the complexity and diversity of the crack pattern.

The Second Stage of Stressed-Deformed Condition of Reinforced Concrete Structures When Turning With Bending (Case 2)

“…The upper, lower and lateral longitudinal reinforcement (in the presence of multi-tiered), in In the spatial section k for block 2, cut off by a complex section passing along a spiral-shaped spatial crack and along the broken section of the compressed zone, all the reinforcement [12,19] falling into this section are taken into account ( Figure 2). Moreover, in the compressed upper longitudinal reinforcement, cut off in sections I -I and III -III, the impact effect is not taken into account, and in the rest of the longitudinal and transverse reinforcement, the components of the impact effects are taken into accountthey are determined using a special second-level model [1,2,13,15] The need to use a complex broken section of the compressed concrete zone is due to the fact that its destruction occurs (according to the experimental studies) in a certain volume, located not along the entire length between points A and B (Fig. 1, 2), but only in a certain volume located in the middle part .…”

“…In relation to the average section I-I, under conditions of complex resistancetorsion with bending ( Figure 5), it is advisable to take into account the fact that a significant part of this section is subject to tension. It is known [1,2,15] that in a stretched concrete there are a number of adjacent spatial cracks that affect the stress-strain state of the middle section I-I. We will take into account this effect of adjacent cracks using the parameter , R T  : If the torque changes along the longitudinal axis of the reinforced concrete structure, an additional dependence is introduced, which is a proportional relationship between the torques in section k and section I-I.…”

“…qc          , using equations (1)- (23), and equating the partial derivatives with respect to all variables included in it to zero, we obtain an additional system of equations [13,15]:…”

“…Building computational models of complex resistance -torsion with a bend is becoming increasingly relevant [1,2], firstly, because there are relatively few such studies [3][4][5][6][7][8][9], and secondly, because the urgent need to take into account the spatial work of the majority of original reinforced concrete structures and buildingss that significantly change the architectural appearance of modern cities [10][11][12]; thirdly, it becomes a generally accepted postulate that there is nothing more practical than a good theory for calculation of reinforced concrete structures [13][14][15][16][17][18][19][20][21][22][23].…”

“…For the calculated forces, the resolving equilibrium and strain equations are compiled. The projection of a dangerous spatial crack is determined as a function of many variables using Lagrange multipliers [13,15].…”