Shear Design with -Method

Transcription

1 Test and Design Methods for Steel Fibre Reinforced Concrete 105 Shear Design with -Method Rosenbusch, J. and Teutsch, M. Institute for Building Materials, Concrete Structures and Fire Protection Technical University of Braunschweig, Germany Abstract In the Recommendations of Rilem TC 162-TDF [1] a design method is suggested entitled Design Method, which also contains a chapter dealing with the shear design. The handling of this design method is very simple because the shear resistance not depends on the real magnitude of the strain. Within the Brite / Euram project BRPR-CT [2] tests were carried out to check this design proposal. Due to the results found within this project it can be concluded, that the shear design proposed by Rilem TC 162-TDF [1] is a simple way to calculate the shear resistance with a sufficient margin of safety. However, in the final draft of the Rilem Recommendations TC 162- TDF [3] the equivalent flexural tensile strength is replaced by the residual flexural tensile strength and the factor which takes into account the height of the member is replaced by the factor used in the final draft of the EC 2. So these changes must be adapted in the Rilem proposal. 1. Introduction This paper mainly deals with the work carried out within the framework of subtask 4.2 Trial Beams in shear of the Brite / Euram project BRPR-CT [4]. Three laboratories were involved to carry out tests investigating the shear carrying capacity of steel fiber reinforced concrete beams. The labs are: Katholieke Universiteit Leuven (KUL) Technical University of Braunschweig (UBS) Universitat Polytecnica de Catalunya (UPC) The RILEM Recommendations TC 162 TDF [1] give a proposal for the design of steel fiber reinforced concrete members. This proposal is entitled Design Method. The design in the ULS for bending and axial force depends on an assumption for the strain distribution for which the equilibrium of internal forces is satisfied. In case of shear design the real magnitude of the strain in the cross section is not taken into account. It is assumed that in all cases the maximum strain of 10 0 / 00 is reached in the ULS. The only material property of the steel fiber reinforced concrete, on which based the calculation for the shear resistance, is the equivalent flexural tensile strength f eq,3 which is related to the maximum strain of 10 0 / 00. It was the main objective to find out weather the RILEM proposal [1] is applicable for the shear design or if it leads to less safety. It has to be highlighted that it was not possible within the Brite/Euram project [2,4]to come to a completely new description of the shear carrying capacity

2 106 RILEM TC 162-TDF Workshop, Bochum, Germany, 2003 for steel fiber reinforced concrete. A new description of the shear resistance of steel fiber reinforced concrete will be shown in [5] which not only based on empirical connections and which is also related to the method. The tests carried out within the Brite/Euram project [2,4]were performed to check the sensible range for the application of beams out of steel fiber reinforced concrete. This will be members with low effects of actions because with an increase of the effects of action the use of stirrups will be unavoidable. 2. Brite/Euram Project 2.1 Test Programme An overview of the shear design in the Rilem recommendation [1] is given in fig. 1. The shear resistance can be calculated by the following equation: V Rd3 = V cd + V wd + V fd This is the equation given in the first draft of EC 2 [6] with the addition of the term for the contribution of the fibers V fd. However, the shear resistance of the plain concrete V cd is taken from the 2nd draft of the EC 2 [7] with the partial factor c =1,5. Shear Resistance of the plain concrete V cd = (0,12 k (100 l f fck ) 1/3 + 0,15 cp ) b w d k = 1+ (200/d) 1/2 V cd Shear Resistance due to the fibers V fd V fd = k f k 1 fd b w d k f = 1 + n (h f /b w ) (h f /d) k 1 = (1600 d)/1000 fd = 0,12 f eq,3 Shear Resistance due to the stirrups V wd = A sw /s 0,9 d f ywd (1 + cot ) sin 45 V wd fig. 1: Shear design for steel fber reinforced concrete members according to Rilem Recommendations [1] The test programme involved both plain concrete and steel fiber reinforced concrete. The variables were the content of steel fibers, the longitudinal reinforcement ratio, the conventional shear reinforcement ratio (stirrups) and the cross section shape (see fig. 2 and table 1). The used fiber type for all specimen was Dramix RC-65/60-BN. It was planned to check if there are influences of the addition of steel fibers on the the shear resistance of the plain concrete V cd or the shear resistance due to the stirrups V wd and if there are influences of the varied parameters (a/d, l, w, h, cross section shape) on the shear resistance due to the fibers V fd. The amount of the tested beams was about 38. All specimen were single-span beams. The reinforcements were chosen in that way, that nearly all beams were expected to fail in shear. A few of the beams were foreseen to fail in flexure to check the sensible range of the use of steel fibers as shear reinforcement. The parameters varied are shown in table 1 (columns with grey background).

3 Test and Design Methods for Steel Fibre Reinforced Concrete 107 a d 180 l Variation: - Fiberdosage fig. 2: Test set-up in principle and variation of parameters 2.2. Results General results - Longitudinal Reinforcement Ratio L - Shear Reinforcement Ratio w - Shearspan to Depth Ratio a/d - Cross Section Shape All of the tested beams failed in shear, including the beams which were planned to fail in flexure. The ultimate loads are shown in table 1. The greatest deviation from the calculated ultimate loads according to Rilem [1] was found for the beams with low a/d ratio (series 2), for beams with stirrups (series 1) and for the consideration of the size effect and the flange (series 3). For beams with low a/d ratio and for beams with stirrups there was found a great underestimation of the shear resistance. The ultimate loads for beams with low a/d ratio were in a range of two times the calculated ultimate loads. The underestimation for the beams with stirrups is in the range of 25% for the beams without fibers and up to 35% for the beams with fibers.

4 108 RILEM TC 162-TDF Workshop, Bochum, Germany, 2003 Table 1: Parameters varied and test results Series 1 UBS Series 2 KUL Series 3 UPC material properties cross section system reinforcements calc. loads results specimen f c,cube,m f eq,3,m f y,w h b w b f h f a/d l l w,y f F u,rilem,cal F u,test MN/m² MN/m² MN/m² m m m m m kg/m³ [kn] kn 1.2/1 55,00 0,00-0,30 0, ,46 1,80 3,56% , /2 58,67 1,49-0,30 0, ,46 1,80 3,56% , /3 54,67 3,05-0,30 0, ,46 1,80 3,56% , /4 60,33 4,85-0,30 0, ,46 1,80 3,56% , /1 62,33 0, ,30 0, ,46 1,80 3,56% 0,07% 0 201, /2 62,67 1, ,30 0, ,46 1,80 3,56% 0,07% , /3 54,33 3, ,30 0, ,46 1,80 3,56% 0,07% , /4 63,00 4, ,30 0, ,46 1,80 3,56% 0,07% , /1 60,67 0, ,30 0, ,46 1,80 3,56% 0,14% 0 244, /2 61,00 1, ,30 0, ,46 1,80 3,56% 0,14% , /3 51,67 3, ,30 0, ,46 1,80 3,56% 0,14% , /4 63,33 4, ,30 0, ,46 1,80 3,56% 0,14% ,5 500 specimen f c,cube,m f eq,3,m f y h b w b f h f a/d l l w,y f F u,rilem,cal F u,test MN/m² MN/m² MN/m² m m m m m kg/m³ [kn] kn 2.2/1 51,04 0,00-0,30 0, ,54 2,30 1,81% , /2 51,46 1,91-0,30 0, ,54 2,30 1,81% , /3 50,37 5,60-0,30 0, ,54 2,30 1,81% , /1 50,15 0,00-0,30 0, ,50 2,30 1,15% , /2 50,05 1,35-0,30 0, ,50 2,30 1,15% , /3 48,35 4,13-0,30 0, ,50 2,30 1,15% , /1 50,15 0,00-0,30 0, ,50 2,30 1,81% , /2 50,05 1,35-0,30 0, ,50 2,30 1,81% , /3 48,35 4,13-0,30 0, ,50 2,30 1,81% , /1 51,04 0,00-0,30 0, ,04 2,30 1,81% , /2 51,46 1,91-0,30 0, ,04 2,30 1,81% , /3 50,37 5,60-0,30 0,20-4,04 2,30 1,81% ,1 234 specimen f c,cube,m f eq,3,m f y h b w b f h f a/d l l w,y f F u,rilem,cal F u,test MN/m² MN/m² MN/m² m m m m m kg/m³ [kn] kn 3.1/1 47,12 5,45-0,30 0,20 0,20 0,00 3,50 2,20 2,83% , /1 F2 48,50 5,58-0,30 0,20 0,20 0,00 3,50 2,20 2,83% , /2 47,12 5,45-0,45 0,20 0,20 0,00 3,34 3,30 3,09% , *50 48,50 5,58-0,50 0,20 0,20 0,00 3,37 3,40 2,73% , /3 47,12 5,45-0,60 0,20 0,20 0,00 3,48 4,50 2,73% , /3 F2 48,50 5,58-0,60 0,20 0,20 0,00 3,48 4,50 2,73% , *50 48,50 5,58-0,50 0,20 0,50 0,08 3,37 3,80 2,80% , /1 47,12 5,45-0,50 0,20 0,50 0,10 3,37 3,80 2,80% , *50 F2 48,50 5,58-0,50 0,20 0,50 0,10 3,37 3,80 2,80% , /2 47,12 5,45-0,50 0,20 0,50 0,15 3,37 3,80 2,80% , *50 F2 48,50 5,58-0,50 0,20 0,50 0,15 3,37 3,80 2,80% , *50 F2 48,50 5,58-0,50 0,20 0,50 0,23 3,37 3,80 2,80% , /3 47,12 5,45-0,50 0,20 0,75 0,15 3,37 3,80 2,80% , /4 47,12 5,45-0,50 0,20 1,00 0,15 3,37 3,80 2,80% ,6 412 It must be highlighted, that the beams with steel fibers shows a more ductile failure than plain concrete beams. Further for the beams of series 1 differences in the failure mechanism between beams without fibers and with fibers were observed (fig. 3). After the crack, which leads to the failure, started, the further crack propagation occurred in different ways. The course of the crack propagation was smoother for the beams with fibers. Further the time dependent crack propagation in the region of the uncontrolled crack propagation (see fig. 3) could be followed with the eyes for the beams with fibers while this was not possible for the beams without fibers. For the beams without fibers the last step before the compression zone was chopped through, the crack propagation grows in a sudden way and it was not possible to distinguish between the region of the uncontrolled crack propagation and the region where the compression zone was chopped through.

5 Test and Design Methods for Steel Fibre Reinforced Concrete 109 change of the course of the crack and beginning of the controlled crackpropagation beginning of the uncontrolled crackpropagation F ca. 45 chopping through of the compression zone crack initiation beam without steel fibers region of changing the course of the crack region of the uncontrolled crackpropagation F region of the controlled crackpropagation chopping through of the compression zone crack initiation beam with steel fibers fig. 3: Failure mechanism observed at beams of series 1 without stirrups Minimum reinforcement The minimum shear reinforcement is derived from the shear resistance of the plain concrete which is reached at the point of the beginning of the uncontrolled crack propagation (fig. 3). For beams with fibers this point can not be determined because the changes of the different regions of crack propagation are fluid. Further the uncontrolled crack propagation does not go off in such a sudden way as in case of plain concrete. So a necessary minimum shear reinforcement for members with steel fibers can not be defined [8].

6 110 RILEM TC 162-TDF Workshop, Bochum, Germany, Rectangular beams without steel fibers V Ru / (b w *d*k*(100*f cm *3*d/a) 1/3 0,14 0,12 0,10 0,08 0,06 0,04 0,02 =V cu,calc acc. to model code =V cu,calc acc. to EC 2 1/2001 = V cu,test without fibers = V cu,test with fibers (V Ru,test - V fu,cal ) other tests in UBS outside Brite/Euram y = 0,18x 0,33 y = 0,15x 0,33 0,00 0,000 0,005 0,010 0,015 0,020 0,025 0,030 0,035 0,040 L fig. 4: Beams with fibers and without stirrups, influence of addition of steel fibers on V c (series 1 and 2, table 1) In fig. 4 the shear resistance of the plain concrete is calculated according to model code 90 (factor 0,15) [10] and according to the EC 2 (factor 0,18) [7, 9]. It shows, that the calculation according to EC 2 is more closer to the test results. The high values related to l = 0,018 were beams with low a/d ratio. V fu,test / (b w *d*k 1 *k f *0,5*d/a) 10,0 9,0 L = 0,7% 8,0 L = 3,6% a/d = 1,5 7,0 L = 1,2% 6,0 L = 1,8% a/d = 3,5 a/d = 4,0 calculated 5,0 V fu,test = a/d = 2,5 4,0 (V Ru,test - V cu,calc ) a/d = 3,5 3,0 other tests in 2,0 UBS outside a/d = 2,5 Brite/Euram 1,0 = test results 0,0 0,0 1,0 2,0 3,0 4,0 5,0 6,0 f eqms [N/mm 2 ] fig. 5: Beams with fibers and without stirrups, dependency of V f on f eq (series 1 and 2) In fig. 5 and 6 the influence of the equivalent flexural tensile strength and the shear span to depth ratio on the shear resistance is shown. It can be seen, that the test results are in good agreement with the Rilem proposal except the beams with low a/d (lower than 2,5).

7 Test and Design Methods for Steel Fibre Reinforced Concrete 111 V fu,test / (b w *d*k 1 *k f *0,5*f eq ) 3,0 2,5 2,0 1,5 1,0 0,5 V fu,test = (V Ru,test - V cu,calc ) y = (a/d) -1 L = 1,8 % L = 1,8 % L = 3,6 % = calculated values = test results other tests in UBS outside Brite/Euram L = 1,8 % L = 1,2 % L = 0,7 % 0,0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 a / d fig. 6: Beams with fibers and without stirrups, dependency of V f on a/d (series 1 and 2) Rectangular beams with stirrups In fig. 7 are shown the results of the beams with stirrups. On first sight it can be found a great underestimation of the calculated values. Further it can be found that with an f eq3 of 3,0 MN/m 3 a shear reinforcement ratio w of approximately 0,07 % can be replaced. 0,30% 0,25% f eq3,ms = 0,00 MN/m 2 f eq3,ms = 1,49 MN/m 2 calculated w = a sw / b w 0,20% 0,15% 0,10% f eq3,ms = 3,05 MN/m 2 f eq3,ms = 4,85 MN/m 2 range of minimum reinforcement for the used concrete (EC 2) range of V R,max for the used concrete 0,05% 0,00% V R /(b w *d) [MN/m 2 ] fig. 7: Range of test results for beams with stirrups compared with V R,max (series 1) Beams with different heights and T-Beams without stirrups Fig show the results of beams with different heights and cross section shapes (T beams) [11]. Looking at the rectangular beams (fig. 8) it can be found that with increase of the height the crack load and the ultimate load increases, as expected. Except for the 30 cm deep beam there is no significant size effect (fig. 9).

8 112 RILEM TC 162-TDF Workshop, Bochum, Germany, a F b 20x60-SFRC 2 Load (kn) x50-SFRC 2 20x60-SFRC 1 20x45-SFRC 1 20x30-SFRC 2 20x30-SFRC 1 b= const h= var Load-point deflection (mm) fig. 8: Influence of the height of the beam on the load-deflection response [11] (series 3). 5,00 Load / b.d (MPa) 4,00 3,00 2,00 h = 30 cm h = 45 cm h = 50 cm h = 60 cm 1,00 SFRC Max. Load SFRC Crack load Plain concrete 0,00 1,40 1,8 Log. of beam depth fig. 9: Influence of the height of the beam on the ultimate and crack load [11] (series 3) The test results of the T beams with constant flange height and different flange width are shown in fig. 10. It can be seen, that the ultimate loads of the T beams were much higher than the ultimate load of the rectangular beam. But within the tested T beams there can be found no influence of the width of the flange [11].

9 Test and Design Methods for Steel Fibre Reinforced Concrete 113 Load (kn) Rectangular beam T15x75-SFRC 1 T15x50-SFRC 1 T15x100-SFRC 1 b f = var. h = const. h f = const. T15x100-SFRC 1 T15x75-SFRC 1 T15x50-SFRC 1 R 45- SFRC Load-point deflection (mm) fig. 10: Influence of the flange width on the load-deflection response [11] (series 3) To find out if there is an influence of the flange height on the ultimate load, the flange width is kept constant. It can be seen in fig. 11, that only for the beam with a height of the flange of 23 cm there is a great increase of the ultimate load. Between the beams with hf = 10 cm an 15 cm there can be found no difference in the maximum load [11]. Load (kn) T15x50-SFRC 2 Rectangular beam T23x50-SFRC 2 T10x50-SFRC 2 b f = const. T23x50-SFRC2 T15x50-SFRC2 T10x50-SFRC2 h f = var. R 50- SFRC Load-point deflection (mm) h= const. fig. 11: Influence of the flange height on the load-deflection response [11] (series 3) 2.3 Conclusions derived from the Brite/Euram Project General conclusions In comparison with plain concrete the beams with addition of steel fibers shows a more ductile failure and a multiple cracking. The Rilem proposal with the 3 additional terms is a simple way to calculate the shear resistance with a sufficient margin of safety. Due to the fact that the Rilem Proposal is a very conservative design method (standard method) it can be assumed that the proposal also leads to a sufficient margin of safety for the

10 114 RILEM TC 162-TDF Workshop, Bochum, Germany, 2003 cases of higher fiber contents, shear reinforcement ratios and longitudinal reinforcement ratios. Anyway the use of steel fibers as shear reinforcement is sensible in first line for members with low effects of actions. The point loads near the support has to be considered in a special way. A minimum shear reinforcement is not necessary for members with steel fibers Rectangular beams without stirrups There is a good agreement between the test results and the calculated ultimate loads. It is found that the addition of steel fibers has no influence on the shear resistance due to the plain concrete V c if the shear resistance due to the fibers is calculated accordingly to the Rilem proposal. There is no significant size effect Rectangular beams with stirrups For the tested beams the Rilem proposal leads to results with a sufficient margin of safety. The shear resistance for beams with stirrups and fibers is underestimated specially for beams with w higher than the minimum reinforcement ratio. But this was also find for beams without fibers. It should be considered to take into account a different inclination of the compression strut T-beams without stirrups The presence of a flange increases the ultimate shear load-carrying capacity significantly in comparison with a rectangular beam. Within the range of these tests, the flange width does not have a significant effect on the load carrying capacity. The test results suggest that there is a limit in the flange depth beyond which there is a significant increase in the load-carrying capacity and ductility. For beams with lower flange depth and rectangular beams there can be found no significant influence of the flange depth on the first-crack and maximum load while there is a big increase of the loads for the beam with a large flange depth. The exact depth limit can not be defined within these tests. 3. General Changes in the Rilem Recommendations The main material parameters for the design in the ULS and SLS of steel fiber reinforced concrete in the Rilem Recommendations [1] were the equivalent flexural tensile strength f eq,2 and f eq,3. The related strain to the value f eq,3 was 10 0 / 00. These parameters are replaced in the final draft of the Recommendations [3] by the residual flexural tensile strength f R,i. The equivalent flexural tensile strength is derived from the contribution of the steel fibers to the energy absorption capacity (area under the load-deflection curve) while the residual flexural tensile strength is derived from the load at a definitely crack mouth opening displacement (CMOD) or midspan deflection ( R ) (fig. 12). The value which is used for the ULS is f Rk,4 (CMOD 4 = 3,5mm, R,4 = 3,0 mm) which is related to the strain of 25 0 / 00.

11 Test and Design Methods for Steel Fibre Reinforced Concrete 115 F u f area D BZ,3,I F u Load F in N f area D BZ,3,II Load F in N F R,4 0 b D BZ 0 Fu deflection in mm 3 0,3 2,35 CMOD, deflection CMOD 4 = 3,0 mm R,4 = 3,5 mm f eq,3 = 3/2 (D f BZ,3,I/2,65 + D f BZ,3,II/2,5) L/(b h sp2 ) f R,4 = (3 F R,4 L)/(2 b h sp2 ) fig. 12: Equivalent flexural tensile strength (left) and residual flexural tensile strength (right) 4. Consequences for the shear design 4.1. Material parameter Due to the change from the equivalent flexural tensile strength to the residual flexural tensile strength it might be necessary to tune the design formulas. The relation between f eq,i and f R,i for the fibers used within the Brite/Euram project is shown in fig 13. For the shear design follows by replacing f eq,3 by f R4, that the design formula has to be multiplied with the factor 1/0,87. residual flexural tensile strength f R [N/mm 2 ] 8,0 7,0 f R1, f eq 2 f R4, f eq 3 f R1 = 0,95 f eq2 + 0,48 6,0 5,0 f R4 = 0,87 f eq3 4,0 3,0 2,0 1,0 0,0 0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 equivalent flexural tensile strength f eq [N/mm 2 ] fig. 13: Relation between equivalent flexural tensile strength and residual flexural tensile strength [12] for the fibers used within the Brite/Euram project But the relation shown in fig. 13 depends on the post-cracking behaviour of the steel fiber reinforced concrete. In case that the branch in the post cracked region is nearly on the same level, the value for f eq,3 and f R,4 will be approximately the same, while in case of a great decrease in the post-cracked branch the ratio f R,4 / f eq,3 may be lower than in fig. 13. So it is proposed to replace f eq,3 by f R,4 without tuning the design formula.

12 116 RILEM TC 162-TDF Workshop, Bochum, Germany, Single point load near the support In the shear tests of sub task 4.2 it was found, that it is necessary to consider a single load point near the support in a special way. It is proposed to take over the procedure of EC 2 [9]. For the shear resistance of the plain concrete and the shear resistance for members with conventional shear reinforcement the treatment is given in EC 2 [9]. It is proposed that the shear resistance due to the steel fiber shear reinforcement may be increased in the same way as the shear resistance of a member with conventional shear reinforcement. The magnitude of V fd can be estimated as V fd = (0,75*a u /0,9*d) * k f * k 1 * fd * b w * d This considers in fundamental a strut and tie model with = 45 (standard method) where the region in which the steel fibers acts as shear reinforcement in vertical direction is about 0,9*d (fig. 14). 0,9 d fig. 14: Region in which the steel fibers acts as shear reinforcement 4.3 Minimum shear reinforcement A minimum shear reinforcement is not necessary for steel fiber reinforced concrete members. But it must be guaranteed that the fiber dosage has a significant influence on the shear resistance. That can be assumed if the residual flexural tensile strength is at least f R,4 = 1,0 N/mm 2. Similar proposals were made in the German DBV-guideline [13] and the planed DAfStb guideline [14] 4.4 Influence of the height and cross section shape In the Rilem Recommendations [1] the influence of the height for the shear resistance due to the steel fibers V fd is taken into account by the factor k 1 = (1600 d)/1000. This is the factor k d used in the first draft of the EC2 [6].It is proposed to use the factor k = 1 + (200/d) 1/2 used in the formula for the shear resistance of the plain concrete because this is more closer to the final draft of the EC2 [9]. The relation between both factors is shown in fig. 15.

13 Test and Design Methods for Steel Fibre Reinforced Concrete 117 3,0 2,5 2,0 k =1+(200/d) 1/2 k, k d 1,5 1,0 k d =1,6 -d 0,5 k d /k 0,7 (1,6 - d)/(1 + (200/d) 1/2 ) 0, d [mm] fig. 15: Relation between k d (k 1 ) and k Within the tests of the Brite/Euram project a significant influence of the height on the shear resistance could not be found. But due to the small number of test specimen and the scatter it is not clear if this is valid in general. So the consideration of an influence of the height as mentioned above will be retained. The tests shows that there is a great influence of the presence of a flange on the shear resistance. With respect to the design formulas the scatter makes the analysis difficult. It appears that for the beams with wider flanges, the limitation of k f of 1,5 leads to more conservative design. So this factor also will be retained. 5. References 1. Rilem TC 162-TDF: Test and design methods for steel fiber reinforced concrete: Recommendations, design method, Materials and Structures, Vol.33, Nr. 226 (2000) 2. Brite-Euram Project , BRPR-CT : Test and design methods for steel fibre reinforced concrete, March 1999 March Rilem TC 162-TDF: Test and design methods for steel fiber reinforced concrete: Recommendations, Final Recommendations, June Rosenbusch, J., Teutsch, M. et al.: Trial Beams in Shear, Final Report Sub task 4.2, Brite-Euram Project , BRPR-CT : Test and design methods for steel fibre reinforced concrete, January Rosenbusch, J.: Zum Querkrafttragverhalten von Bauteilen aus Stahlfaserbeton, Doctoral Thesis in preparation, ibmb TU Braunschweig, March European Committee for Standardization: Eurocode 2: Design of concrete structures Part 1: General rules for buildings, EN (1. draft), June European Committee for Standardization: Eurocode 2: Design of concrete structures Part 1: General rules for buildings, pren (2. draft), January Rosenbusch, J.: Schubtragverhalten von Stahlfaserbetonbauteilen, in: Beiträge zum 40. Forschungskolloquium des DAfStb, Deutscher Ausschuss für Stahlbeton, Berlin European Committee for Standardization: Eurocode 2: Design of concrete structures Part 1: General rules for buildings, pren (Final draft), October Comite Euro-International du Beton: CEB-FIP Model code Final Draft. Lausanne, July Gettu, R., Barragan, R. E. et al.: Trial Beams in shear: Test Programme 3, Annex of final report Sub task 4.2, Brite-Euram Project , BRPR-CT : Test and design methods for steel fibre reinforced concrete, January Rosenbusch, J.: Relation between equivalent flexural tensile strength and flexural tensile strength of steel fiber reinforced concrete, ibmb TU Braunschweig, Deutscher Beton- und Bautechnik-Verein E.V.: DBV-Merkblatt Stahlfaserbeton, Fassung Oktober 2001, Berlin Deutscher Ausschuss für Stahlbeton: Richtlinie Stahlfaserbeton, in Vorbereitung