Stress-strain state of damaged reinforced concrete bended elements at operational load level


 Each structure is exposed to different influences during operation. As a result, there are various defects and damages of these elements that affect their safe operation. The article presents the results of experimental studies of reinforced concrete beams with damages to stretched reinforcement made with and without initial load application. As the damages were accepted one or five Ø5.6 mm holes. In one case, the damage was made until the beam destruction (up to the 8.4 mm opening) Control samples of both series were destroyed due to crushing of the compressed zone of concrete. Samples that were damaged without initial loading collapsed due to rupture of the stretched reinforcement. The same type of failure was identified for damages at the operational load level.


Introduction
Taking into consideration the prevalence of reinforced concrete structures in construction, the study of their load-bearing capacity changes during operation is the topical issue (Azizov et al., 2019;Karpiuk et al., 2019;Vatulia, 2018). The main issue in this area is the determination of bearing capacity, taking into account the damages` occurrence Klymenko et al., 2020;Kotes et al., 2018). The most dangerous and common are damages in the compressed zone of concrete (Yogalakshmi et al., 2020). In the article (Lobodanov et al., 2021), the work of damaged reinforced concrete structures is investigated and calculation of such structures is given. The reduction of compressed elements cross-sectional area is more dangerous and important (Khmil et al., 2021b;Klymenko et al., 2019;Kochkarev et al., 2020). In such cases the damage does not only lead to load-bearing capacity decrease, but can also cause changes in the structure stress-strain state (for example, the transition from compressed to compressed-bended state of element due to damage). The study of steel corrosion for damaged RC constructions (Blikharskyy et al., 2020;Fomin et al., 2021). In the study (Lipinski, 2017), an attempt was made to analyze the effect of 20% aqueous NaCl solu-tion on the stiffness of steel as the result of corrosion. Steel stiffness and corrosion wear were determined according to the corrosion time.
An important issue is the determination of actual bearing capacity of inclined sections in bended reinforced concrete elements (Kramarchuk et al., 2021;Pavlikov et al., 2019). Their complex stress-strain state and simplified calculations can lead to depletion of bearing capacity, especially in cases of existing damages in the support zones.
Studies of the stress -strain state are important taking into consideration the necessity of such structures` further restoration or strengthening (Kotes et al., 2020;Vatulia et al., 2017). Strengthening and restoration of structural reinforcement is always carried out taking into account its real stress-strain state. As the result, is obtained the structure that has worked in different stages, with different stresses in structural layers (at initial stages), which leads to another important issue, namely the reliability of such structures (Khmil et al., 2021a).
Particular attention should be paid to the establishment of residual load-bearing capacity of structures in which new materials are proposed (for example, composite (Turba and Solodkyy, 2021;Vavrus and Kotes, 2019)), as well as for structures with complex stress-strain state (such as pre-stressed structures ).
The study of the residual bearing capacity of elements and structures is the topical issue not only in construction but also in other fields of science and technology (Ulewicz R. and Ulewicz M., 2020;Czajkowska and Ingaldi, 2019), which only emphasizes the relevance of this issue.

Test program
The total number of tested beams was equal to 12. The samples were divided into two series: two samples of the 1st series and ten samples of the 2nd series. Thee test samples had the rectangular cross-section with dimensions equal to 200×100 mm and length of 2100 mm. Samples of 1st and 2nd series had the same geometric dimensions with deviation less than 2%. For the samples of 1st series the working reinforcement was made of 1Ø16 А 500S and 1Ø20 А500Sfor the samples of 2nd series.
Compressed and transverse reinforcement is made of wire reinforcement of Ø5B500 and is identical for samples of both series. Reinforced concrete beams were made of concrete of C30/35 class.
All test samples were marked in following way: BС -control beam, or BD -damaged beam; the first digit is the series number, the second digit is the test sample number. For example, BС 1.2 means that the second control beam from the 1st series was tested. An index of 0.5 indicates the level at which the damage was made as the fraction from the received destructive. For conventional beams the notation * means that the test beam has five identical holes in the stretched reinforcement. The letter index "pd" (pointed damage) indicates damage with 5.6 mm hole, which corresponds to the decrease in the crosssectional area of reinforcement from Ø20 to Ø16. The index "fd" (full damaged) means that the beams were damaged until the load-bearing capacity is exhausted due to the maximum reduction of cross-sectional area.
Reinforced concrete beams were tested according to the program given in Table 1.
The experimental study was performed by applying a static load as two concentrated forces. Two samples from the 1st and 2nd series were tested as control samples (without damages). The next two samples from the 2nd series were tested as follows: damages were performed by drilling one hole of Ø3 mm. After that the diameter of the hole was increased by 0.5 mm up to Ø5.6 mm. At such damage the residual diameter of armature corresponds to Ø16 mm; -gradually, according to the research method from (Blikharskyy et al., 2020), the samples were brought to physical destruction. The other 4 samples were tested in the following sequence: -samples were loaded up to load level of 0.5 from the expected destructive value; -the Ø3 mm hole was drilled, its diameter was gradually increased in increments of 0.5 mm. up to a value of 5.6 mm; -gradually, according to the research method in (Blikharskyy et al., 2020), the samples were brought to physical destruction. The last two samples were tested in the following sequence: -samples were loaded up to the load level of 0.5 from the expected destructive value; -the Ø3 mm hole was drilled, its diameter was gradually increased in increments of 0.5 mm until the load-bearing capacity of the sample is exhausted. 5. BD 2.5-0.0pd Samples with one Ø5.6 mm hole in stretched reinforcement without initial load applied 6. BD 2.6-0.0pd 7. BD 2.7-0.5pd Samples with one Ø5.6 mm hole in stretched reinforcement at initial load level of 0.5 8. BD 2.8-0.5pd 9. BD 2.9-0.5pd* Samples with five Ø5.6 mm hole in stretched reinforcement at initial load level of 0.5 10. BD 2.10-0.5pd* 11. BD 2.11-0.5fd Samples with one hole in stretched reinforcement until the element is destroyed 12. BD 2.12-0.5fd At each stage, after increasing the diameter of the hole the readings were recorded from the devices located as shown in study .

Experimental researching
The test specimens were tested by static load application, which was applied until the physical destruction occurred.
Control samples of the 1st and 2nd series were destroyed due to crushing of the compressed zone concrete in the central part of the beam. Damaged specimens, regardless of whether they were damaged during loading or not, were destroyed due to the stretched reinforcement rupture. It was identified that the bearing capacity of the samples varied depending on the damage type and the load level at which the damage occurred (see Table 2).
In the samples BD 2.5-0.0pd and BD 2.6-0.0pd, BC 1.1 and BC 1.2 the area of working reinforcement, as well as all other parameters (concrete strength, location of frames, etc.) were the same. However, according to Table. 2, the strength of samples with damaged reinforcement with 20 mm diameter (BD 2.5-0.0pd and BD 2.5-0.0pd) is greater than the strength of samples with working reinforcement of 16 mm diameter (BC 1.1 and BC 1.2). This could be explained by the fact that in damaged samples the main working cross section of the reinforcement is the thermally strengthened outer layer. Therefore, the deviation of bearing capacity in damaged samples was at average 24%, whereas in undamaged samples with the same area of working reinforcement deviation was at average 31%. Significantly lower bearing capacity was identified for samples BC 1.1 and BC 1.2 with working reinforcement with 16 mm diameter in comparison with beams reinforced with 20 mm diameter rebar, the deviation was equal to 30.2%. In the samples damaged at load levels, the bearing capacity was approximately the same within 3.7… 13.2%. The higher bearing capacity of damaged specimens at load levels with damaged reinforcement of 20 mm diameter (the area of the damaged rebar corresponds to the area of 16 mm diameter) in comparison with samples with working 16 mm rebar could be explained by the presence of thermally strengthened layer. Namely, due to the damage, the cross-sectional area of the core (cross-section of unstrengthened part of rebar) is significantly reduced, whereas the outer thermally-reinforced layer is slightly reduced; this fact explains the higher bearing capacity results. The number of holes also affects the bearing capacity of such samples. Thus, the samples BD 2.9-0.5pd* and BD 2.10-0.5pd* had larger number of holes (5 holes compared to other samples with 1 hole), which reduced the load-bearing capacity and, accordingly, increased the deviation compared to the control undamaged samples with working 20 mm steel bars up to 24.0%. When the samples are damaged at the operational load level, the load-bearing capacity is decreased due to reduction of working rebar cross section by 35% from the initial value. However, for samples, damaged at a load level of 0.5 from the expected destructive for control samples, the load-bearing capacity was 50% from bearing capacity, which is equal to the level of damaging.

Results and Discussion
The deformation specifics of compressed concrete and stretched working reinforcement of undamaged control samples with working reinforcement ∅20 mm (BC 2.3 and BC 2.4) are shown in Fig. 1. It should be noted that the graphs on Fig. 1 and others show the average values of both deformations and bending moments of the twin-beams.
As can be seen from Fig. 1, the deformations of the stretched reinforcement and concrete of the most compressed fiber increased gradually with the same growth of increasing load. When deformations in the stretched reinforcement reached the yield strength = at the load level of Мs,y=24.2 kNm, the bearing capacity of the samples was exhausted due to yield of the working reinforcement; accordingly, sharp increase in deformations of compressed concrete and stretched reinforcement is observed. The maximum deformations in the stretched reinforcement equal to εs,max=388·10-5 and in the most compressed fiber concrete equal to εс, max = 309·10 -5 at the bending moment of M = 27.1 kNm were recorded. After that, when the ultimate deformations of concrete were reached, the brittle fracture of the most compressed concrete fiber under load Mult = 31.1 kNm occurred. In the samples BD 2.5-0.0pd and BD 2.6-0.0pd with working reinforcement of 20 mm without applying a load the 5.6 mm-diameter hole was made in working rebar, which led to reduction of the cross-sectional area to diameter of 16 mm. However, the hole reduces the cross-section of the core of the reinforcement, while leaving a larger part of thermally strengthened cross-sectional area. As a result, no clear region of yielding could be identified, which is shown by the results of sample beams BD 2.5-0.0pd and BD 2.6-0.0pd (Fig. 2). Gradual increase in the deformation of the stretched reinforcement and concrete of the most compressed fiber could be identified. Exhaustion of bearing capacity occurred at the moment Мs, y = 24.2 kNm, when the deformation of the stretched reinforcement achieved the beginning of yielding εs, y = 285·10 -5 .
The maximum values of deformation of the most compressed concrete fiber εс, max = 195·10 -5 and of stretched reinforcement εs,max=329·10 -5 were recorded at the moment M = 19 kNm.
After reaching the moment Мult=23.5 kNm, the samples were physically destroyed due to the rupture of the stretched working reinforcement.
It is important to note the destruction specifics of the samples, which is the result of damage of much larger part of the unstrengthened layer of reinforcement and minor thermally strengthened layer reduction.
In addition, no destruction of the compressed zone concrete occurred and no achievement of limit values for the most compressed concrete fibers was identified. The destruction occurred due to the rupture of the working rebar. This could be explained by the fact that the damage of the stretched reinforcement has the local character in one place, which corresponds to the drilled hole.
When testing control samples with working reinforcement with a diameter of 16 mm, the gradual increase in deformations of stretched reinforcement and concrete of the most compressed fiber is observed (Fig. 3). At loading of Мs,y=16.9 kNm deformations of the stretched armature were equal to εs,y=285·10 -5 , which corresponds to the beginning of yielding and accordingly exhaustion of bearing capacity are reached. After achieving these deformations, there is the sharp increase in the deformations of the compressed and stretched zone.
Samples BD-2.7-0.5pd and BD-2.8-0.5pd were damaged according to the above indicated procedure at a load level of 50% of the bearing capacity of the control undamaged samples. The bending moment at which the damage was performed corresponded to M =16.3 kNm. Deformations of the working stretched reinforcement and concrete of the most compressed fiber increased smoothly and had the linear character (Fig. 4).
During the gradual damage of the working reinforcement by drilled holes of increasing diameters at bending moment M = 16.3 kNm deformations increased at a constant load level. With growth of load higher than M = 16.3 kNm in the beams and with reduced working rebar area due to damage, more intense increase in deformation was identified. The deformations of the reinforcement reached the beginning of the yield strength and, accordingly, the samples reached the depletion of the bearing capacity for the yield of the reinforcement at Мs,y = 21.5 kNm. The maximum deformations were recorded at load of M = 22.5 kNm, which for stretched working reinforcement were equal to εs,max=316·10 -5 . The largest deformations for the most compressed fiber concrete were equal to εс,max=234·10 -5 .
When the bending moment M = 25.5 kNm was reached, physical failure occurred due to rupture of the working reinforcement.
Similarly, to the case of working reinforcement damage for the deformation of concrete of the most compressed fiber and stretched reinforcement, the uniform increase of linear nature is observed (Fig. 5). At the bending moment M = 16.3 kNm was performed damage of the stretched working reinforcement. For samples with damages was identified an increase in the deformation of the working reinforcement and concrete of the most compressed fiber at constant load level. The average deformation graphs of stretched reinforcement (left) and compressed concrete (right) of damaged beams BD-2.9-0.5pd* and BD-2.10-0.5pd* After reduction of the reinforcement cross section by 36% (the cross-sectional area reduction which corresponded to working rebar of 16 mm diameter), similarly, the linear increase in deformation is observed. When the rebar deformations reached the yielding at the bending moment Мs,y = 18.4 kNm, the bearing capacity of the samples was exhausted due to the working reinforcement yielding.
Control samples BC 2.3 and BC 2.4 showed the bearing capacity higher by 30.2% compared to samples of the 1st series. Samples damaged without the initial level of load showed the bearing capacity quite close to the samples of the 1st series. Therefore, the damage simulated the reduction of the reinforcement diameter from Ø20 to Ø16 quite accurately. At the load level of 0.5 of the expected destructive of control samples, the load-bearing capacity of the specimens damaged by points (with one hole) is higher by 11%. Accordingly, for the case of the damages along the length (by 5 holes) the increase of load-bearing capacity is 24% higher. Therefore, the load level affects the load-bearing capacity of the samples that are damaged.

Conclusion
1. The level of load and damage specifics (point or distributed) affect the depletion of bearing capacity, namely: -in the case of point damages, the bearing capacity of samples is higher by 11% (in comparison with similar undamaged samples); -in the case of damages along on sample length bearing capacity is higher by 24% in comparison with control samples. 2. Reinforced concrete beams with working reinforcement of ø20, the area of which was decreased by damage to the area analogous to the ø16 rebar had a final bearing capacity higher than reinforced concrete beams reinforced with ø16 rebar without damage. This could be explained by the fact that the damage of the ø20 rebar by drilling holes, in the greater extent the core with smaller physical and mechanical properties was damaged, whereas the outer thermally strengthened layer with higher physical and mechanical properties was damaged to a lesser extent.
3. Analysis of the results shows that in the case of damaged thermally-strengthened reinforcement, it is necessary to take into account the presence of an outer thermally strengthened layer within the rebar cross section, which has higher physical and mechanical characteristics, as well as the presence of inner core with lower physical and mechanical characteristics. With partial or complete damage of the outer thermally strengthened layer of steel bars, their physical and mechanical characteristics can be significantly reduced, which will affect the final load-bearing capacity of structures.