Bending moments redistribution in two‐span reinforced concrete beams reinforced with FRP bars based on collected data research

This article presents a review of state of the art on nonmetallic reinforcement in terms of bending moment redistribution in double‐span elements. The authors present a summary of existing research programs focused on moment redistribution in FRP (Fiber Reinforced Polymer) reinforced concrete (RC). On this basis authors created a database of concrete elements with all the important construction properties of the elements. Gathered data are presented with quantitative analysis of several variables effecting moment redistribution in published articles. In the following publication authors show a research review which includes an analysis of the influence of variable parameters from the point of view of the database, concerning: degrees of longitudinal reinforcement, ratio between degrees of reinforcement in span and over the support, type of reinforcement (FRP/steel/hybrid), concrete class and transverse reinforcement.


| INTRODUCTION
FRP (fiber reinforced polymer) reinforcement produced in several types (GFRP-glass fiber reinforced polymer, AFRP-Aramid, CFRP-carbon, BFRP-basalt) has long been available on the construction market and has been an interesting alternative to steel reinforcement.It is primarily used in special structures, where the unique properties of the FRP reinforcement, such as high corrosive resistance, electromagnetic neutrality, high tensile strength and low weight justify their usage in civil engineering structures (Table 1).
The stress-strain characteristic of FRP reinforcement is fully linear-elastic, which is significantly different from steel reinforcement with its typical linear-plastic characteristics (Figure 1).This is the reason for the significant effect of the bending moments redistribution in the multi-span beams and slabs reinforced with FRP bars.The issue of redistribution in beams reinforced with FRP bars or hybrid steel-FRP reinforcement has already been described in publications, [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] but there are still many inaccuracies regarding the adhesion of reinforcement to concrete, degree of reinforcement, modulus of elasticity, concrete compressive strength, shear reinforcement and interaction of all those parameters combined.

| ANALYSIS OF EXISTING RESEARCH
Several studies of double-span concrete elements with composite reinforcement of various types (GFRP, CFRP, BFRP, hybrid steel-FRP) have been published so far, but the impact of FRP reinforcement on the effect of bending moment redistribution in multi-span elements is not fully explained.
One of the first studies of two-span beams with nonmetallic reinforcement confirmed the possibility of bending redistribution, but the authors did not indicate a clear relationship between the degree of longitudinal reinforcement and the level of bending redistribution. 3The research program 4 was the first of the T-section elements studied along with an analysis of the effect of using main reinforcement and FRP stirrups simultaneously.Studies 5 confirmed a slight degree of bending redistribution in the beams designed according to the recommendations of ACI 440, but the results of these studies also did not indicate constructive conclusions referring to the effect of variable parameters on the level of bending moments redistribution.The subject of referring to ultimate limit states and serviceability limit states (ULS, SLS) of concrete structures reinforced with FRP-type bars in scope of European, Canadian, American, and Japanese design guidelines and reliability studies ware addressed in a publication. 22Other studies 3,6,7 confirmed the occurrence of redistribution in double-span beams with FRP reinforcement and thus became the basis for designing such elements with the assumption of moments redistribution.The study 6 confirmed that due to the bond loss of the FRP reinforcement to concrete, the effect of the bond should be taken into account, with particular reference to the different surface preparation of non-metallic reinforcement.
The issue of the transverse reinforcement effect on the bending redistribution was discussed in the same studies, 6 indicating the effect of differences in the confinement degree of beams on the bending moment's redistribution after concrete cracking.Smaller spacing of the stirrups significantly improved the bending moment's redistribution and increased the flexural capacity of members. 8The experimental program 18 focused on slabs without transverse reinforcement.
The significant reason of the decrease in the load carrying capacity of the beams was the loss of adhesion of the FRP reinforcement to concrete over the support published in the study. 9This topic could be explained by the progressive redistribution from the support to the span.This study confirmed that the loss of adhesion of the FRP reinforcement to concrete over the support, and the increased degree of the bending moment redistribution, did not lead to a reduction in flexural capacity.Noteworthy is the study, 10 which reported adverse impact of asymmetric loading on the degree of bending moments redistribution in the continuous beams with the FRP reinforcement.On the other hand study publication, 11 confirmed a lack of the decrease in the load bearing capacity after moment redistribution compared to elastic analysis.It should be mentioned that in the research programs, 12,13 beams were tested in the small-scale (span of elements was equal to 1 m and the height of the cross section was 120 mm).A further step of this research was creation and calibration of the numerical models based on their test results.Another interesting problem was the impact of adding to concrete BMF (basalt macro fibers) published in References (19,23) which concluded that BFM improved the structural performance of beams and lowered widening of the shear cracks and changed the failure of beams from shear to concrete crushing.
The conclusions of these studies became the basis for the consideration of the bending moment redistribution in the design of multi-span structures.The over-reinforced spans and the under-reinforced mid-support had the beneficial effect on the beam deflections.One way to reduce beam deflections and increase stiffness while maintaining increased resistance to environmental conditions was to use the additional steel reinforcement in the second layer of reinforcement.This concept was the basis of research programs, [14][15][16][17]21 which confirmed a significant reduction in deflections and a beneficial effect on the occurrence of bending moment redistribution.

| DATABASE OF EXPERIMENTAL MEMBERS
The authors collected a wide test database from the literature containing 114 double-span elements tested in bending, which summarized analysis of the parameters affecting the bending moments redistribution.The vast majority of the research adopted the five-point static bending scheme with the elastic bending moment shown in Figure 2 with the redistribution assumed to varying degrees.Moreover, Figure 2 shows the example of bending moment redistribution with an assumed value of 20% from support to span (dashed line).
Exceptional research was, 10 where the effect of asymmetric beam loading was investigated.Publication 10 investigated the effect of asymmetrical loading in the beam's spans where the symmetrical loading, increased the force in the left span to a value of 1.5 P and the left span loaded only was compared.One of the important research problem was the selection of appropriate dimensions of the tested elements to reduce the influence of the scale effect.This problem was described in the studies. 24,25The height of the cross-section was taken as the main criterion for evaluating the scale effect.In the case of beams with a height <200 mm may be classified among those in which the scale effect is significant and may have a negative effect on the degree of the bending moment redistribution.
A statistical summary of the variable parameters of the tested beams is shown in Figure 3.The vast majority contain members with a section height of more than 200 mm (89%).The most common cross-section was rectangular (81%) and the remaining elements had the T-section (19%).Most members were reinforced with GFRP bars (43%) and FRP bar hybrid reinforcement with steel reinforcement (22%) (Figure 3c).FRP bars had significantly higher tensile strength than steel, which determined the most common choice of concrete strength in the range of 40-50 MPa (Figure 3d).The important parameter in the analysis of bending moment redistribution is the reinforcement adhesion to the concrete, which is decisively influenced by the surface finish of FRP bars.7][28][29][30][31] The most commonly used surface finish was sand coating (32% of beams).Unfortunately, a large part of the publication does not consider this parameter, omitting it from the description of the materials used in the study (up to 49% of beams did not indicate a type of surface finish).The most commonly used shear reinforcement was steel reinforcement (78% of members).
One of the main advantages of FRP bars was the resistance to environmental aggression.To retain all the advantages of this reinforcement, it is necessary to use both main and shear reinforcement made of FRP bars.A combination of FRP longitudinal reinforcement and steel transverse reinforcement is not a good solution, because the use of steel stirrups in the beams with FRP main reinforcement, significantly reduces the structural resistance in environmental conditions.However, in buildings not subjected to environmental conditions the steel stirrups may applied.Another case is hybrid FRP-steel longitudinal reinforcement where steel reinforcement is in a second layer, where the initiation of corrosion effects on steel reinforcement is later due to the thicker concrete cover.

| DATABASE OF RESEARCH RESULTS
Elements with cross-section heights smaller than 200 and 150 mm for slabs were omitted from the analysis of the database.The key parameters considered in the analysis were the mode of failure (bending, shear, bar rupture, concrete crushing), the location of failure mode (span, support), the ultimate load and the cracking load.The F I G U R E 2 Typical static scheme of a bending moment redistribution before and after redistribution of bending moments (20% from support to span section).degree of bending moments redistribution (β) was calculated according to the formula: where M u,test -ultimate bending moment from experimental tests and M u,cal -design bending moment calculated in the elastic state according to Figure 2 or instructions from publications.
The most common failure mode was concrete crushing (50 elements) (Figure 4a), this failure mode is recommended for design, while 26 beams failed due to fracture of the bar.The majority of the beams failed in the span of 51%, 30%-in the support and 19%-span/support (Figure 4b).
Statistical analysis of the degree of redistribution was finally limited to publications, 3,6,8,10,11,14,[16][17][18][19][20][21] in which redistribution of moments from the support to the span was most common (Figure 5a).The degree of bending moments redistribution β for Figure 5a is calculated in span, therefore, β > 0 means redistribution to span.In the case of Figure 5b β is calculated in relation to the place where redistribution occurred.Redistribution of bending moments in reinforced concrete elements is mainly possible due to the yielding of steel reinforcement.FRP bars have linear-elastic characteristics (Figure 1), which significantly limits the possibility of bending moment redistribution.In the collected tests, 36% of the beams achieved a very low degree of redistribution (<5%), 82% of elements achieved an acceptable degree of redistribution of <20%, 32 (Figure 5b), and 18% of the elements achieved a degree of redistribution above 20%.A degree of bending moments redistribution up to 2% can be considered to be within the limits of measurement error, so that the occurrence of this phenomenon cannot be clearly confirmed in this case.The bending moment redistribution of the beam indicates the presence of level redistribution >5%.The vast majority of elements experienced a bending moments redistribution from the support to the span (Figure 5a).

| EFFECT OF REINFORCEMENT DEGREE AND OTHER FACTORS ON BENDING MOMENT REDISTRIBUTION
To evaluate the effect of reinforcement degree on bending moment redistribution, the reduced reinforcement degree in bending and shear was introduced as: where E f , Young modulus of FRP reinforcement; E s , Young modulus of steel reinforcement; ρ s , degree of longitudinal steel reinforcement; ρ f , degree of longitudinal FRP reinforcement; ρ sv , degree of shear steel reinforcement; ρ fv , degree of shear FRP reinforcement; ρ sp/su , degree of reinforcement in span/above support; ρ v , degree of shear reinforcement.
Based on the literature, it was found that the main parameters affecting the degree of redistribution are: degree of flexural reinforcement (ρ s , ρ f ), ratio of the flexural degree of reinforcement in span to support (ρ sp/su ), confinement of concrete, which is directly affected by the shear reinforcement (ρ v ), the compressive concrete strength (f ck ) and the elasticity modulus of FRP reinforcement (E f ).The most important data are presented in Table 2.
Table 2 presents the degree of redistribution β calculated concerning the span and the support, so depending on the cross-section chosen, the parameter β can take on positive or negative values.A negative β calculated concerning the span means that the redistribution occurs from the span to the support and a positive value when redistribution occurs from the support to the span.Quite the same was made with the calculation of β relative to the support.Table 2 summarizes the test data including: type of FRP reinforcement, dimensions of the test elements (L-span length, h-height, b-width of cross-section) and type of cross-section rectangular (T-section), degree of span reinforcement and over the support (ρ f , degree of FRP-type reinforcement; ρ s , degree of steel reinforcement with indexes 1 and 2 referring to the reinforcement in layers or the case of different Young's modulus of FRP reinforcement).The symbol column contains individual markings for reinforced concrete beams and slabs.
The most significant variable parameter is the span reinforcement ratio to the support reinforcement ratio, therefore, it will be the basis for further analysis.Figures 6-12 show diagrams of the bending moments redistribution ratio (β) in reference to the ratio of the reduced degree of the span reinforcement to reduced degree of the support reinforcement ratio (ρ sp /ρ su ).In Type of shear reinforcement Total load applied at failure

Failure mode
Place of failure Type of shear reinforcement For the shear reinforcement ratio ρ v < 0.4% and the concrete compressive strength f ck < 30 MPa (Figure 6) and a significantly higher degree of GFRP reinforcement over the support than in the span (ρ sp /ρ su = 0.67), the bending moments redistribution to the support was β < 5.36%.In the beams with CFRP bar reinforcement and the span-support reinforcement degree ratio of ρ sp / ρ su = 0.75, redistribution to the span was very low β < 1.36% (both beams were designed for the moment distribution with the assumption of no redistribution).The other cases (GFRP and CFRP reinforcement) referred to the beams with a degree of reinforcement higher in the span than above the support ρ sp /ρ su = 1.5, and were designed with the assumption of 20% bending moments redistribution into the span.For the beam reinforced with GFRP bars, the redistribution value was β = 13.9%,however for a beam with CFRP bars, the redistribution value was β = 24.83%.In case of BFRP reinforcement beams with ρ sp /ρ su = 1 there were no redistribution.The highest degree of redistribution to the support β = À20.76%was obtained for ρ sp /ρ su = 0.39 for beams with BFRP type reinforcement.Beam with ρ sp / ρ su = 2.59 was the opposite to the corresponding beam with the reinforcement ratio ρ sp /ρ su = 0.39 (higher reinforcement degree in support cross section than in span) but in this case the redistribution to span was lower (β = À15.46%).
Figure 7 shows a reduced degree of shear reinforcement in the range of 0.4% ≤ ρ v < 0.6% and a concrete compressive strength f ck < 30 MPa collected of only beams reinforced with the hybrid CFRP/steel reinforcement.The higher degree of redistribution was obtained in the beam with the support reinforcement made of CFRP bars and in the span of the steel bars.In this case, reduced degree of CFRP reinforcement over the support was higher than the degree of steel reinforcement in the span, the redistribution went from the span to the support.For the second beam (hybrid CFRP/steel reinforcement in span and over support) with a much higher degree of reinforcement in the span, redistribution was obtained to the span. 17he test database does not include results of beams made of concrete with the strength lower than 30 MPa and a reduced degree of shear reinforcement (ρ v ) higher than 0.6%.
Type of shear reinforcement ; first and second capital letters represent longitudinal and transverse reinforcement ("G"-GFRP, "C"-CFRP, "S"-steel), third lowercase letter represents the design load criteria "u"-ULS, "s"-SLS, fourth number represents diameter of the stirrups in millimeters, "d/2" for 120 mm spacing between stirrups or "d/3" for 80 mm spacing, last letter "e"-configuration to satisfy the elastic moment distribution and "p" allowed for plastic redistribution 18 ; first letter in the notation corresponds to the type of supporting "C"-continuously supported, second letter indicates the type of reinforcement "C"-CFRP, third and fourth letter reflects the reinforcement ratio on the bottom mid-span and over middle-support "U" for under-reinforcement, "O" for over-reinforcement ratio 8 ; first capital letter "B"-beam type element, the last digit is a sequential number 10 ; first letter represents type of the reinforcement "G"-GFRP, the second letter stands for the type of "limit state design" "u"-ULS and "s"-SLS, third letter denotes whether the beam was designed for elastic moment-"E" or redistribution "R", last symbol represent type of loading "I"-symmetrical, "II"-load P on one span and 1.5P on the other, and "III" load P on one span only 11 ; first capital letter "G"-GFPR type reinforcement, second number stands for serries of experimental program, last number ("0", "15", "25") means designed moment redistribution in percentage 15 ; first letter in the notation corresponds to the type of supporting "C"-continuously supported, second letter indicates the type of reinforcement "G"-GFRP, "H"-hybrid, the last digit is a sequential number 14 ; specimens of groups "A" are BFRP over reinforced "B", were reinforced with BFRP but under reinforced, "C" are hybrid over reinforced and "D" are hybrid under reinforced, the last digit is a sequential number 16 ; first capital letter represents type of element "B"-beam, second capital letters stands for type of reinforcement "G"-GFRP, "H"-hybrid, the last digit is a sequential number 17 ; first letter in the notation corresponds to the type of the element "B"-beam, symbols "H" represents hybrid reinforcement at the sagging and hogging region, "CH" stands for CFRP reinforcement at the hogging region and hybrid reinforcement at the sagging region 19 ; first capital letter represents type of reinforcement "B"-BFRP, the second part stands for the stirrups spacing; d/2 and d/3 stand for 120 and 80 mm stirrups spacing, the third part represents the sagging-to-hogging reinforcement ratio and the last part corresponds to the volume fractions of basalt macro fibers 20 ; the first letter indicates that the specimens are beams (B), the next number refers to the top longitudinal reinforcement ratio and the final number describes the bottom longitudinal reinforcement ratio 21 ; first capital letter "B"-beam type element, the last digit is a sequential number.
Figure 8 shows the moments redistribution as the function of the ratio ρ sp /ρ su for the shear reinforcement degree of ρ v < 0.4% and the concrete compressive strength in the range of 30-50 MPa.For the beam with the higher degree of reinforcement over the support designed with the assumption of the lack of redistribution, the low degree of redistribution (1.98%) to the middle support was obtained.In other cases with the higher imported degree of reinforcement in the span, the significant degree of redistribution: 10.67 ≤ β ≤ 18.59% was obtained from the middle support to the span.For beams with the same degree of reinforcement ratio in the span to the reinforcement degree over the support, a slightly higher redistribution was obtained for the beam with the higher shear reinforcement degree.The beams with a reduced reinforcement degree between 1.46 and 1.75 Bending moment redistribution as a function of ρ sp /ρ su ratio for shear reinforcement ρ v < 0.4% and concrete strength f ck < 30 MPa.
F I G U R E 7 Bending moment redistribution as a function of ρ sp /ρ su ratio for shear reinforcement 0.4% ≤ ρ v < 0.6% and concrete strength f ck < 30 MPa.
F I G U R E 8 Bending moment redistribution as a function of ρ sp /ρ su ratio for shear reinforcement ρ v < 0.4% and concrete strength 30 MPa ≤ f ck < 50 MPa.
were designed with the redistribution over the middle support of 15% and 25%, respectively.According to the research, 9 the degree of redistribution was maintained at the expected level for most of the test, but shortly before the beam's failure with the reduced reinforcement ratio 1.46, there was a loss of adhesion of the GFRP reinforcement to the concrete resulting in the sudden and significant increase in redistribution to the value of 27% relative to the support (16.7% relative to the span).In the second beam, a redistribution of 18.74% was achieved (relative to the support 10.67%), that is, the intended degree of redistribution was not achieved.The slab with the highest ρ sp / ρ su without transverse reinforcement 18 achieved the bending redistribution β = 17.63% with the CFRP bars and assumption of over-reinforcement in the span and under-reinforcement in the support.The bending moment redistribution for the slabs with the opposite reinforcement-over-reinforced in the support and under-reinforced in the span resulted in 32.21% redistribution to the span which was the highest redistribution to support in the specimens reinforced with FRP type reinforcement only.Slab with similar reinforcement in span and support but with assumption of over-reinforced cross-section achieved β = À4.01%redistribution to the support.The corresponding slab with assumption of under-reinforced cross-section achieved significantly higher redistribution β = À14.06% to support.
Figure 9 shows a curve of the degree of redistribution as a function of the ratio (ρ sp /ρ su ) for the range of the shear reinforcement of 0.4% ≤ ρ v < 0.6% and the concrete compressive strength between 30 and 50 MPa.The research program 8 describes one beam designed with the assumption of no redistribution and two beams with the assumption of the bending moment redistribution but the main differing parameter was the shear reinforcement ratio.In the first case a low degree of redistribution to the span β = 3.54% was obtained, for the other cases it was possible to obtain β = 10% redistribution to the span.Reduction of the stirrups spacing and reduction of their diameter (reduction of the degree of shear reinforcement from 0.45% to 0.41%) resulted in the bending moment redistribution β = 1.71%.In this case the stirrups spacing was crucial and showed a beneficial effect on the degree of the moment redistribution.Other beams with GFRP reinforcement from research 10 were asymmetrically loaded with the simultaneous variation of the reinforcement degree in the right and left spans, which resulted in both a high ratio of the reinforcement degrees in the span to the support and the low degree of redistribution.Asymmetric loading resulted in the adverse effect on the moment redistribution degree.Members reinforced with BFRP bars 14 were the widest beam elements of the entire database (section 500 mm width and 150 mm Â 200 mm in depth).The elements were divided into groups A, B, C, and D. Groups A and B were reinforced with BFRP bars only, while groups C and D were reinforced with hybrid BFRP/steel bars.Groups A and C were over-reinforced in the span, while B and D had a degree of the span reinforcement under-reinforced close to the balanced degree of reinforcement.The varying factor was the degree of reinforcement above the support.Hybrid-reinforced members had a lower degree of redistribution than their equivalent members reinforced with BFRP bars only.Steel reinforcement reduced the development of cracks over the support and the degree of the bending moment redistribution.While for the members with the span reinforcement degree close to the balanced reinforcement, the bending moment redistribution increased with an increase in the reinforcement degree over the support.For over-reinforced elements in the span, the bending moment redistribution decreased with the ρ sp /ρ su ratio increase.
Figure 10 shows the curve of the bending moment redistribution for the shear reinforcement ρ v > 0.6% and F I G U R E 9 Bending moment redistribution as a function of ρ sp /ρ su ratio for shear reinforcement 0.4% ≤ ρ v < 0.6% and concrete strength 30 MPa ≤ f ck < 50 MPa.concrete compressive strengths in the range of 30-50 MPa.The highest redistribution degree of 19.59% was obtained for the beam designed according to the serviceability limit state.The results of 15 showed a simultaneous increase in the degree of steel reinforcement in the span and above the support with a constant degree of the GFRP reinforcement for ρ sp /ρ su = 1, causing a change in the type of redistribution from the support to redistribution to the span.An increase in ρ sp /ρ su for the hybrid beams with GFRP reinforcement resulted in an increase in the degree of redistribution to the span.The same effect was observed for the beams with BFRP reinforcement.For specimens with ρ sp /ρ su = 1.5 increasing the amount of BMF (basalt macro-fibers) in concrete mix increased the capability of beams for bending moment redistribution.Increasing of the concrete confinement by decreasing the spacing of stirrups also increased bending moment redistribution, although in both cases: confinement and BMF fibers positive impact was very low, about 1%. 19igure 11 shows the range for a reduced shear reinforcement ratio lower than 0.4% and a concrete strength higher than 50 MPa.In this range, the highest redistribution to the support (À13.65% relative to the span) was obtained among beams reinforced with GFRP bars only.The beam was reinforced with the assumption of no bending moment redistribution resulting in a significantly higher degree of reinforcement over the support than in the span.For the other beams reinforced with GFRP bars, an increase in ρ sp /ρ su resulted in an increase in redistribution into the span.For GFRP beams, a higher degree of redistribution was achieved than planned.Beams reinforced with CFRP bars with the assumption of over-reinforcement relative to the balanced degree of reinforcement achieved a higher degree of moment redistribution than beams with a degree of reinforcement lower than the balanced degree of reinforcement.
The experimental results didn't include cases for concrete strengths higher than 50 MPa and reduced shear reinforcement ratio between 0.4% and 0.6%.
Figure 12 shows the results for a range of reduced shear reinforcement higher than 0.6% and concrete compressive strength higher than 50 MPa.For this range, the database includes beams reinforced only with hybrid F I G U R E 1 0 Bending moment redistribution as a function of ρ sp /ρ su ratio for shear reinforcement ρ v > 0.6% and concrete strength 30 MPa ≤ f ck < 50 MPa.
F I G U R E 1 1 Bending moment redistribution as a function of ρ sp /ρ su ratio for shear reinforcement ρ v < 0.4% and concrete strength f ck ≥ 50 MPa.
GFRP-steel reinforcement.Following trends observed in Figure 6-12, beams with a higher ρ sp /ρ su ratio have a higher degree of redistribution.In the case of beams with ρ sp /ρ su = 1 degree of steel reinforcement was the same but the degree of GFRP reinforcement significantly increased (from ρ = 1.31% to ρ = 2.18%) for the beam which achieved low redistribution to the span β = 1.02%, for beam with lower GFRP reinforcement beam had redistribution to the support (À5.09% relative to the span).
Figures 7 show the results of two beams, presenting too limited data to clarify appropriate conclusions, so it was excluded from further analysis.
Figures 6, 8-12 confirm that the leading factor influencing the redistribution of bending moments is the ρ sp /ρ su ratio, but that a higher ρ sp /ρ su ratio does not confirm the degree of moment redistribution, due to other variables: such as the mode of loading (symmetric or unsymmetric), degree of shear reinforcement, the compressive concrete strength, degree of the flexural reinforcement relative to the balanced degree of reinforcement and the proportion of steel reinforcement for cross-sections reinforced with hybrid FRP-steel.Figures 6, 8-12 show that high degrees of bending moments redistribution can be observed in each of these ranges, with a higher degree of shear reinforcement not necessarily resulting in a higher degree of bending redistribution, which is analogous with the compressive concrete strength.
Figure 13 shows a graph of the degree of redistribution as a function of the reduced degree of shear reinforcement.The presence of vertical columns presenting the results of the collected tests in terms of the values of the degree of redistribution for the different degrees of reinforcement (from zero to high values of more than 20%) shows that in the analyzed case other parameters are changing, while the degree of shear reinforcement was an additional parameter.The highest degree of redistribution was obtained in the beams with a degree of shear reinforcement close to 0.4%, and it can be concluded that this value may be assential for a high degree of redistribution.
The results of beams with concrete compressive strengths below 65 MPa showed the highest degrees of redistribution (Figure 14).For beams with strengths above 50 MPa and FRP type reinforcement, the degree of moment redistribution did not exceed 20%.Most of the beams confirmed the highest degree of redistribution in the compression strength range of 40-50 MPa.In reference Figure 13, the redistribution concerning the compressive strength of the concrete (Figure 14) shows that the diagrams of the moment redistribution degree in the range of the most commonly used variable parameters (concerning types of bars), with a very high variability of the moment redistribution degree, indicated the complexity of the moments redistribution in beams with FRP reinforcement.However, there is no globally explicit parameter determining the degree of moment redistribution.This fact makes it possible to conclude that when preparing research in this area, special emphasis should be placed on designing elements in such a way as to limit the number of variable parameters mainly to only one.
In publications, [14][15][16][17]21 the effect of FRP-steel hybrid reinforcement was investigated, depending on the reduced FRP reinforcement degree to the steel reinforcement degree at the bending moment redistribution point (Figure 15). Asthe lower is ρ f E f /E s /ρ s , the higher is the percentage of steel reinforcement in a given cross-section.The highest degree of redistribution to the support was obtained in the beams where the reinforcement over the support was made of CFRP bars, while the steel reinforcement was located in the span.For this particular case, a value of ρ f E f /E s /ρ s = 1 (Figure 15) was set.In the case where CFRP/steel reinforcement was used in the span and over the support, the bending redistribution degree of 9.29% was obtained.For the other cases where hybrid reinforcement was used simultaneously in the span and over the support, the highest degree of moment redistribution was obtained for the BFRP/steel reinforcement (31.09%) with a ratio of reduced FRP reinforcement degree to steel reinforcement degree of 0.36.However for another case and the same value of ρ f E f /E s /ρ s = 0.36 in the section to which the redistribution occurred, a redistribution degree close to zero was obtained due to the ρ s / ρ f ratio, which in this case was equal to 1 and significantly reduces the redistribution capacity of the element.Similar effect was observed for the beams with GFRPsteel reinforcement.A lower proportion of the steel reinforcement in the span resulted in a lower redistribution capacity of the element in terms of bending moments, noting that such a system is very sensitive to the effect of ρ s /ρ f .While the beneficial effect of an increased proportion of steel reinforcement in span can be offset by a change in the span reinforcement ratio to the support, an increase in the stirrup spacing or any other additional variables confirming the need to reduce variable parameters in the test.A key problem is change in the nature of the redistribution from redistribution to the support to the redistribution to the span when the proportion of steel reinforcement class increases, that is detailly described in publication.15 F I G U R E 1 4 Redistribution of moments concerning the compressive strength of concrete.
F I G U R E 1 5 Redistribution according to the ratio of reduced FRP reinforcement degree to steel reinforcement degree.
The objectives of the individual research programs were different, so that the results cannot be directly compared, but it is possible to identify variable parameters with a significant influence on the phenomenon of bending moment redistribution on the basis of the developed state of knowledge.
• The moment redistribution in beams depends not only on the ductile properties of the reinforcement, but also on the concrete deformability.The ratio of elements (in particular the effective cross section height) and the rotation capacity over the support, makes beams redistribution with FRP reinforcement possible.• The main common variable parameter is the reinforcement degree with simultaneous assumption of the over-reinforcement cross-section.• The longitudinal reinforcement ratio in span and over support (ρ sp /ρ su ) are the main factors influencing the bending moments redistribution.The highest redistribution was obtained in beams with ρ sp /ρ su = 1 ratio and BFRP reinforcement.• Many studies confirmed several variable parameters (different bar diameters, shear reinforcement spacing, concrete strength) which presented making it impossible to accurately assess the influence of each variable parameter on the bending moment redistribution.Moreover, it is likely that the additional correlation of the variable parameters may have been an extra factor.Impact of the other factors than degree of longitudinal reinforcement is smaller and usually in the range of a few percent.It is recommended to limit the variable parameters as much as possible.• In the most research programs, steel stirrups were used to avoid the shear failure, which somewhat contradicts the uniformity of the reinforcement, but it is justified by the technical simplicity of the steel stirrups.• Shear reinforcement (stirrup spacing, diameter, and type) improves concrete confinement, which can result in better bending moments redistribution.Reduction of the stirrup spacing increases ability of bending moment redistribution.The approximate range close to 0.4% of the reduced shear reinforcement for selected elements makes higher redistribution ratio than for elements with lower shear reinforcement.This range can be considered to favor a high degree of the bending moment redistribution.• The highest degree of redistribution was obtained in beams made of concrete compressive strengths in the range of 40-50 MPa.For compressive strengths higher than 50 MPa, the degree of redistribution did not exceed 18% in span and À26% to support (calculated in span).
• In the case of hybrid reinforcement, an increase in the proportion of steel reinforcement resulted in an increase in the element's ability to redistribute bending moments, with the best redistribution effect to the support being achieved for a beam reinforced uniformly with CFRP bars over the support and uniformly with the steel reinforcement in the span.• The most frequent failure mode was concrete crushing of the beams occurred most often in the span.• Adding to concrete macro-fibers could improve the structural performance and ability for the bending moments redistribution and changed type of failure.

| DIRECTIONS FOR FURTHER RESEARCH
Beam elements are the most common choice for investigating bending moments redistribution and in the case of elements reinforced with FRP bars, there is only one experimental program with CFRP type reinforcement studying this phenomenon on slab elements.In order to estimate the influence of the longitudinal reinforcement degree on the bending moments redistribution, it was decided to study slabs (with a reduction in the degree of reinforcement over the support in order to highlight the redistribution phenomenon).Furthermore, in the slab elements without additional shear reinforcement, the influence of concrete confinement will be significantly reduced, thus reducing the number of variable parameters.A series of such tests slab with GFRP reinforcement have already been carried out in the Department of Concrete Structures Laboratory and the results are being developed and will be the subject of future publications.

T A B L E 1 20 F
Strength characteristics of FRP bars (ACI 440.1R-15 1 and fib Bulletin 40 2 ) and steel bars.I G U R E 1 Comparative stress-strain characteristics of FRP and steel bars (database; ACI 440.1R-15 1 and fib Bulletin 40 2 ).

F
I G U R E 4 (a) Beams failure mode and (b) place of failure.F I G U R E 3 Summary of selected double-span beams reinforced with FRP bars: (a) section type; (b) height; (c) type of reinforcement; (d) concrete compressive strength; (e) surface finish; and (f) type of shear reinforcement.

F I G U R E 5
Redistribution of bending moments parameter β; (a) Type of redistribution β < 0-redistribution from span to support; β > 0-redistribution from support to span; (b) degree of redistribution (calculated in relation to the place where redistribution occurred).

F I G U R E 1 2
Bending moment redistribution as a function of ρ sp /ρ su ratio for shear reinforcement ρ v ≥ 0.6% and concrete strength f ck ≥ 50 MPa.F I G U R E 1 3 Redistribution of moments as a function of the reduced degree of shear reinforcement.