Crack Width Calculation Ec2 Software |LINK|

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Where the spacing of the bonded reinforcement exceeds 5(c+φ/2) or where there is no bonded reinforcement within the tension zone, an upper bound to the crack width should be calculated by assuming a maximum crack spacing:

The second approach, applied in this paper, involves tracking the changes in crack formation and crack width to develop diagnostic methods for the evaluation of reinforced concrete structures whose condition depends on the intensity of cracking. Cracking intensity is the number of cracks per unit length a member and the crack width which determines the reinforcement corrosion risk. Random variables influence the crack width size; hence the crack width is also a random variable of which the probabilistic or the evaluation properties follow a normal or log-normal distribution. In terms of the limit states, In the limit states view, the maximum crack width is a quantile at β, where the probability of this event β is fixed a priori and can be a function of the purpose and durability of the structure. From a practical point of view, of particular importance is the maximum crack width estimation accuracy, which decides the risk of corrosion [18]. Corrosion significantly affects the durability of RC structures as it is the leading cause of their deterioration [6,19,20].

Although various crack width estimation methods have been developed over the years, research needs to be continued [4,5,6,7,13,21]. The proposed relationships are fairly complicated and largely based on many empirical coefficients that take account of concrete composition and strength characteristics, way of curing, loading scheme, cover thickness, type and diameter of reinforcing bars. New and simplified techniques for crack width estimation must be found, particularly reflecting the stochastic nature of the crack formation process [2]. The search for the new methods is aided by modern apparatus [3,4,22,23] that allows continuous monitoring of crack propagation and measuring crack width under dynamic loads.

Since the durability of reinforced concrete structures depends on the intensity of cracking and crack widths, a parallel topic of tracking the process of crack formation and development was undertaken. A known density function for inter-crack distances and crack widths under loading will allow the development of a method for RC structure condition diagnosis based on artificial intelligence. A diagnosis that relies on methods, i.e., acoustic emission and artificial intelligence will be much more reliable, particularly in difficult cases.

The formation of cracks and their development was recorded using the ARAMIS digital image correlation (DIC) system. The system provides a 3D real time display of strain field overlaid on live image, thereby allowing a continuous measurement of crack widths. The use of a power supply system with a controller, which was synchronized with the measuring equipment, enabled the implementation of cyclic loads.

This satisfactory agreement made it possible to use the DIC system to record and measure the quantities describing the cracking state of the beams based on consecutive images. The strain measurements were recorded over the entire prepared area of the beam, thereby enabling the measurement of distances between the cracks and crack widths at the height corresponding to the centroid of the tension reinforcement during loading to failure. The frequency of image triggering events was adjusted to each loading program. The images were captured either at a specified time or at appropriate load values. A single tripod with two cameras was used to capture images every 30 s for A2M beams and every 20 s for C2M and D2M beams.

All these characteristics are interrelated. It can easily be shown that the cracking moment is a special property of these functions (4) and (5), because for M < Mcr, the distance between the cracks would be greater than the beam length, and the crack width would be zero. The crack width and the distance between the cracks are thus strongly interrelated. Accordingly, the results of the RC beam test are presented for these three quantities.

The use of the DIC system in this study enabled the analysis of crack formation and development processes (cracking moment, crack width and distance between the cracks) for the loading program specified in Table 2.

Figure 21 and Figure 22 show an image the cracking state on the A2M-2 beam at the load level of 0.75 and 0.95, respectively, failure load. The calculation mask (deformation map) applied to the side surface of the beam after tests allows the observation of cracks at any selected load level, as illustrated in Figure 21 and Figure 22 (crack numbers are added in the middle section of the 1000 mm long beam).

Deterministic crack formation criteria lead to a description in which all cracks are formed simultaneously over the entire section of the beam, where the moment reaches the critical value for cracking. The cracking on the middle section of the beam, between the forces, proceeds gradually, despite the constant value of the bending moment in this section, and new cracks appear even at the load that significantly exceeds the cracking load. Therefore, it can be concluded that cracks in the beam subjected to pure bending action under increasing load initiate successively as a result of a random spread of strength and forming limit in tension, which proves that both the distance between cracks and crack width are, in fact, stochastic processes. The deterministic description of the distance between the cracks can only refer to the final state of the cracking process.

The size of the area surrounding the crack, where stress decreases, is generally a random function. However, in search of a simplified formula, the continuous changes of the crack width were measured using the DIC system. The measurement of the crack width development under loading indicates the linear increase of up to 0.9 of the failure force [42], as shown by examples of cracks no. 2 and 14 (Figure 29) on beam D2M-2 and crack no. 11 on beam C2M-2 (Figure 30). This was confirmed by analyzing the average crack width increase for individual beams, as shown in Figure 31. It can thus be concluded that the course of changes in the section 2aω length can be assumed as linear.

The maximum crack width was obtained from the DIC system at selected load levels for the tested five beams with a constant moment in the central segment, and the value of 2aω was calculated from Formula (7). The results of the calculations are given in Table 10 together with the fixed maximum, minimum and mean values.

When analyzing the Figure 32, it can be noticed that the point with the coordinates [0.83; 127.04] is the farthest from the solid line obtained by LSM. Considering that the durability of the concrete structure is decided by the cracks with the maximum width, crack width estimations must give safe results. Hence, the solid line obtained by LSM was shifted by the vector υ [0; 41.88] and intersects point with coordinates [0.83; 127.04], as shown in Figure 33. To stay on the safe side, to determine the bond loss segment section, relationship (9) was adopted.

Figure 34 compares the experimental results, the results calculated according to the simplified Formula (6), assuming Relationship (9), and the results of the maximum crack width calculations to EC2. The horizontal line in the drawing corresponds to the permissible crack width of 0.3 mm.

The second approach, which is presented in this paper, is the tracking of crack pattern and crack width changes, utilized toward the development of methods for the assessment of reinforced concrete structures. The process of the loading of reinforced concrete beams is accompanied by the process of crack formation. As the load increases, the initially rapid changes in the crack pattern decrease and the pattern gradually stabilizes. The crack formation process depends on many factors, but for a given element it is a function of the load. It is thus a function of one variable, and the quantities such as shape, section dimensions, type of reinforcing steel, concrete mix composition, etc., act as parameters. The combined effect of these factors determines the intensity of the process which is a function of load. The crack intensity is the number of cracks per unit length of the element and the crack width, which determines the corrosion protection of the reinforcing bars. The paper presents the results of an extensive research program on reinforced concrete beams subjected to monotonic loads, and cyclic loads. The research presented in this paper was carried out with a view to developing a method for diagnosing reinforced concrete bridges; in particular, using the acoustic emission method [24,25]. Since the durability of reinforced concrete structures depends on the intensity of cracking and crack width, a parallel study was undertaken concerning the tracing of the crack formation process and development. Knowledge of the density function describing the distribution of distances between cracks in the process of loading and changes in the crack width would provide a reliable method of assessing the RC structure condition based on artificial intelligence. Topics related to the determination of the density function describing the distribution of distances between cracks have been addressed previously [2]. However, hardware possibilities in the field of computer capacity as well as testing equipment in the field of alternating loads and continuous crack width observation available in those time have stopped further development. The use of a program able element loading controller and an ARAMIS optical system for examining the lateral surface (1.2 m × 0.30 m) of the beam between the forces, enabled the continuation of the earlier subject matter. The results of the study of 10 reinforced concrete beams loaded according to 3 programs of monotonic loading to failure, with unloads loads, and cyclic loading gave a quantitative sufficient set of data to draw conclusions from the analyses. It was found that: 2b1af7f3a8