DESIGN WITH METHOD. 1. Introduction. 2. Material properties. Test and Design Methods for Steel Fibre Reinforced Concrete 31

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1 Test and Design Methods or Steel Fibre Reinorced Concrete 31 DESIGN WITH METHOD Lucie Vandewalle Katholieke Universiteit Leuven, Belgium Abstract The inal recommendation o the design method, proposed by RILEM TC 16-TDF, is presented in this paper. The design method is based on Eurocode and the design parameters in the relation are determined by means o a displacement controlled bending test on notched prisms. 1. Introduction The design o steel ibre reinorced concrete according to the method is based on the same undamentals as the design o normal reinorced concrete. The proposed method is valid or steel ibre concrete with compressive strengths o up to C50/60. Steel ibres can also be used in high strength concrete, i.e. concrete with ck 50 N/mm. However, care should be taken that the steel ibres do not break in a brittle way beore being pulled out. The European pre-standard ENV (Eurocode : Design o Concrete Structures - Part 1: General rules and rules or buildings) [1] has been used as a general ramework or this design method proposed. It must be emphasised that these calculation guidelines are intended or cases in which the steel ibres are used or structural purposes and not e.g. or slabs on grade. They also do not apply or other applications such as those in which increased resistance to plastic shrinkage, increased resistance to abrasion or impact, etc. are aimed or.. Material properties..1 Compressive strength. The compressive strength o steel ibre reinorced concrete (= SFR-concrete) should be determined by means o standard tests, either on concrete cylinders ( = 150 mm, h = 300 mm) or concrete cubes (side = 150 mm). The design principles are based on the characteristic 8-day strength, deined as that value o strength below which no more than 5 % o the population o all possible strength determinations o the volume o the concrete under consideration, are expected to all. Hardened SFR-concrete is classiied in respect to its compressive strength by SFR-concrete strength classes which relate to the cylinder strength ck or the cube strength ck,cube (Table 1). Those strength classes are the same as or plain concrete.

2 3 RILEM TC 16-TDF Workshop, Bochum, Germany, 003 Table 1: Steel ibre reinorced concrete strength classes: characteristic compressive strength ck (cylinders), mean ctm,l and characteristic ctk,l lexural tensile strength in N/mm ; mean secant modulus o elasticity in kn/mm. Strength class o SFRC C0/5 C5/30 C30/37 C35/45 C40/50 C45/55 C50/60 ck ctm,l ctk,l E cm Flexural tensile strength. When only the compressive strength ck has been determined, the estimated mean and characteristic lexural tensile strength o steel ibre reinorced concrete may be derived rom the ollowing equations: ctm,ax ck (1) (N/mm ) ctk,ax ct,ax 0.7 (N/mm ) () ctm,ax 0.6 (N/mm ) (3) ct,l ctk,l 0.7 (N/mm ) (4) ctm,l The corresponding mean and characteristic values or the dierent steel ibre reinorced concrete strength classes are given in Table 1. I bending tests are perormed, the ollowing method [] can be used to determine the characteristic value o the limit o proportionality (LOP) (cr. bending test) [3]: ctk, L k s (N/mm ) (5) ctm,l x p with ctk,l : characteristic value o LOP (N/mm ) ctm,l : mean value o LOP (N/mm ) s p : standard deviation (N/mm ) s n k x p ctm,l ct,l n 1 : number o specimens : actor dependent on the number o specimens; some values are given in Table. The maximum value o expression (4) and (5) can be taken as the lexural tensile strength o the SFR-concrete. (6)

3 Test and Design Methods or Steel Fibre Reinorced Concrete 33 Table n k xknown k xunknown In Table, k xunknown means that the coeicient o variation o the population is unknown; instead o the standard deviation o the population, the standard deviation o the spot check will be used. The mean value o the secant modulus E cm in kn/mm is also given in Table 1..3 Residual lexural tensile strength. The residual lexural tensile strength R,i, which is an important parameter characterising the postcracking behaviour o steel ibre reinorced concrete, is determined by the CMOD (crack mouth opening displacement)- or delection controlled bending test [3]. The residual lexural tensile strengths R,1, R,4 respectively, are deined at the ollowing crack mouth opening displacement (CMOD i ) or mid span delections ( R,i ): CMOD 1 = 0.5 mm - R,1 = 0.46 mm CMOD 4 = 3.5 mm - R,4 = 3.00 mm and can be determined by means o the ollowing expression: 3 FR,i L R,i (N/mm ) (7) b h sp where b = width o the specimen (mm) h sp = distance between tip o the notch and top o cross section (mm) L = span o the specimen (mm) F R,i = load recorded at CMOD i or R,i (N) (see Figure 1) The relation between characteristic and mean residual lexural tensile strength is given in. (equation (5)). Figure 1: Load CMOD diagram.

4 34 RILEM TC 16-TDF Workshop, Bochum, Germany, 003 Hardened SFR-concrete is classiied by using two parameters that are determined by the residual lexural strengths R,1 and R,4. The irst parameter FL 0.5 is given by the value o R,1 reduced to the nearest multiple o 0.5 MPa, and can vary between 1 and 6 MPa. The second parameter FL 3.5 is given by the value o R,4 reduced to the nearest multiple o 0.5 MPa, and can vary between 0 and 4 MPa. These two parameters denote the minimum guaranteed characteristic residual strengths at CMOD values o 0.5 and 3.5 mm, respectively. The residual strength class is represented as FL FL 0.5 /FL 3.5, with the corresponding values o the two parameters. For example, a SFRC with a characteristic cylinder compressive strength o 30 MPa, and R,1 =. MPa and R,4 = 1.5 MPa would have FL 0.5 =.0 MPa and FL 3.5 = 1.5 MPa and be classiied as C30/37 F L.0/ Design at ultimate limit states 3.1 Ultimate limit states or bending and axial orce General The design method was originally developed without size-dependent saety actors. A comparison o the predictions o the design method and o the experimental results o structural elements o various sizes revealed a severe overestimation o the carrying capacity by the design method. In order to compensate this eect, size-dependent saety actors have been introduced. It should be outlined that the origin o this apparent size-eect is not yet ully understood. Further investigation is required in order to identiy i it is due to a discrepancy o material properties between dierent batches, to a size-eect intrinsic to the method, or a combination o both. In assessing the ultimate resistance o a cross section, the assumptions given below are used: plane sections remain plane (Bernoulli); the stresses in the steel ibre reinorced concrete in tension as well as in compression are derived rom the stress-strain diagram shown in Figure and explained in appendix 1; the stresses in the reinorcement (bars) are derived rom an idealised bi-linear stress-strain diagram; or cross sections subjected to pure axial compression, the compressive strain in the SFRconcrete is limited to -. For cross sections not ully in compression, the limiting compressive strain is taken as In intermediate situations, the strain diagram is deined 3 by assuming that the strain is - at a level o the height o the compressed zone, 7 measured rom the most compressed ace; or steel ibre reinorced concrete which is additionally reinorced with bars, the strain is limited to 5 at the position o the reinorcement (Figure 3); to ensure enough anchorage capacity or the steel ibres, the maximum deormation in the ultimate limit state is restricted to 3.5 mm. I crack widths larger than 3.5 mm are used, the residual lexural tensile strength corresponding to that crack width and measured during the bending test has to be used to calculate 3. It is recommended that this value, which replaces R,4, should not be lower than 1 N/mm ; in some cases, as mentioned below, the contribution o the steel ibres near the surace has to be reduced. For this reason the steel ibres should not be taken into account in a layer near the surace: or exposure class (appendix ): i crack width is larger than 0. mm (serviceability limit states: see 4), the height o the cracked zone has to be

5 Test and Design Methods or Steel Fibre Reinorced Concrete 35 or exposure classes 3 and higher : reduced by 10 mm. This rule is only applicable in the ultimate limit state. special provisions have to be taken. Figure : Stress-strain diagram and size actor h. c 3,5,0 1 3 c [ ] = 0.7 ctm,l (1.6 - d) (d in m) (N/mm ) 1 = 1 / E c = 0.45 R,1 h (N/mm ) = = 0.37 R,4 h (N/mm ) 3 = 5 E c = 9500 ( cm ) 1/3 (N/mm ) h : size actor 1,0 0,8 0,6 0,4 0, h [-] h [cm] 1,5 h 1,0 0,6 1,5 h 60 [cm] 47, h [cm]

6 36 RILEM TC 16-TDF Workshop, Bochum, Germany, 003 Figure 3: Stress and strain distribution Calculation o crack width Crack control is required in all structures. This crack control can be satisied by at least one o the ollowing conditions: presence o conventional steel bars, presence o normal compressive orces (compression - prestressing), crack control maintained by the structural system itsel (redistribution o internal moments and orces limited by the rotation capacity). In structurally indeterminate constructions without conventional reinorcement but with a compression zone in each cross section, the crack width may be determined as ollows (see Figure 4): determination o the neutral axis on the basis o Figure 4, determination o the compressive strain c,max o concrete, determination o an idealised tensile strain c,t taking into account the Bernoulli - hypothesis: c,t h x c, max (8) x calculation o the crack width in the ultimate limit state: w h x (9) c, t

7 Test and Design Methods or Steel Fibre Reinorced Concrete 37 Figure 4: Element without ordinary reinorcement. In statically determinate constructions (bending - pure tension), crack control is only possible i a high amount o steel ibres is used or i there is a combination o steel ibres and conventional reinorcement. In structures with conventional reinorcement the calculation o the crack width corresponds to that o normal reinorced concrete. However, the stress in the steel bars has to be calculated, taking into account the beneicial eect o the steel ibres, i.e. a part o the tensile orce F c,t which is taken up by the steel ibres (see Figure 5). Figure 5: Element with ordinary reinorcement. 3. Shear The calculation or shear shown here applies to beams and plates containing traditional lexural reinorcement (bar and mesh). It also applies to prestressed elements and columns in which axial compression orces are present. The approach proposed is the best possible until urther evidence becomes available. When no longitudinal reinorcement or compression zone is available, no generally accepted calculation method or taking into account the eect o the steel ibres can be ormulated.

8 38 RILEM TC 16-TDF Workshop, Bochum, Germany, 003 Bent-up bars shall not be used as shear reinorcement in beams except in combination with steel ibres and/or stirrups. In this case at least 50 % o the necessary shear reinorcement shall be provided by steel ibres and/or stirrups. For shear design o members with constant depth, the member is assumed to consist o compressive and tensile zones o which the centres are separated by a distance equal to the internal lever arm z (Figure 6). The shear zone has a depth equal to z and width b w. The internal lever arm is calculated perpendicular to the longitudinal reinorcement by ignoring the eect o any bent-up longitudinal reinorcement. Figure 6: Strut and tie model. The parameters given in Figure 6 are: : the angle o the shear reinorcement in relation to the longitudinal axis (45 90 ) : the angle o the concrete struts in relation to the longitudinal axis F s : tensile orce in the longitudinal reinorcement (N) F c : compressive orce in the concrete in the direction o the longitudinal axis (N) b w : minimum width o the web (mm) d : eective depth (mm) s : spacing o stirrups (mm) z : the internal lever arm corresponding to the maximum bending moment in the element under consideration (mm) in a member with constant depth. In the shear analysis, an approximate value z = 0.9 d can normally be used. An example o the standard method, i.e.: = 45, will be used or the shear analysis Standard method The design shear resistance o a section o a beam with shear reinorcement and containing steel ibres is given by the equation:

9 Test and Design Methods or Steel Fibre Reinorced Concrete 39 V Rd,3 V V V (10) cd d wd with: V cd : the shear resistance o the member without shear reinorcement, given by: V cd b d (N) 0.1 k l ck cp w (11) where 00 k 1 d in mm and k (1) d A s l % (13) b wd A s = area o tension reinorcement extending not less than d + anchorage length beyond the section considered (Figure 7) (mm ). Figure 7: l or V cd b w = minimum width o the section over the eective depth d (mm). NSd cp (N/mm ) (14) Ac N Sd = longitudinal orce in section due to loading or prestressing (compression: positive) (N). In the case o prestressing, h should be used in stead o d in ormula (11). V d : contribution o the steel ibre shear reinorcement, given by: V 0.7 k k b d (N) (15) d l d w where k = actor or taking into account the contribution o the langes in a T-section : h h k 1 n and k 1.5 b (16) w d with h = height o the langes (mm) b = width o the langes (mm) b w = width o the web (mm) b b w 3b w n 3 and n h h

10 40 RILEM TC 16-TDF Workshop, Bochum, Germany, 003 k l 00 1 d in mm and k (17) d d = design value o the increase in shear strength due to steel ibres: d 0.1 (N/mm ) (18) Rk,4 V wd : contribution o the shear reinorcement due to stirrups and/or inclined bars, given by: Asw Vwd 0.9 d ywd 1 cot sin (N) (19) s where s = spacing between the shear reinorcement measured along the longitudinal axis (mm) = angle o the shear reinorcement with the longitudinal axis ywd = design yield strength o the shear reinorcement (N/mm ). When checking against crushing at the compression struts, V Rd is given by the equation: V Rd, 1 cd 0.9 d bw 1 cot (N) (0) with 0.7 ck 0.5 (ck in N/mm ) (1) 00 For vertical stirrups, or or vertical stirrups combined with inclined shear reinorcement, cot is taken as zero. 4. Design at Serviceability limit states 4.1 General When an uncracked section is used, the ull steel ibre reinorced concrete section is assumed to be active and both concrete and steel are assumed to be elastic in tension as well as in compression. When a cracked section is used, the steel ibre reinorced concrete is assumed to be elastic in compression, and capable o sustaining a tensile stress equal to 0.45 R,1. 4. Limit states o cracking In the absence o speciic requirements (e.g. watertightness), the criteria or the maximum design crack width (w d ) under the quasi-permanent combination ( *** ) o loads, which are mentioned in Table 3 or dierent exposure classes (see Appendix ), may be assumed.

11 Test and Design Methods or Steel Fibre Reinorced Concrete 41 Table 3: Criteria or crack width Exposure steel ibres + ordinary steel ibres + class (*) steel ibres reinorcement post-tensioning pre-tensioning 1 (****) (****) 0. mm 0. mm 0.3 mm 0.3 mm 0. mm decompression (**) 3 4 special crack limitations dependent upon the nature o the aggressive environment involved have to be taken 5 (*): see Appendix (**): the decompression limit requires that, under the requent combination (***) o loads, all parts o the tendons or ducts lie at least 5 mm within concrete in compression (***): see ENV [1] (****): or exposure class 1, crack width has no inluence on durability and the limit could be relaxed or deleted unless there are other reasons or its inclusion. 4.3 Minimum reinorcement The ollowing ormula is proposed or calculating the minimum reinorcement A s in order to obtain controlled crack ormation: A s Act k k k 0.45 (mm ) c p ct,e Rm,1 () s where: Rm,1 = the average residual lexural tensile strength o the steel ibre reinorced concrete at the moment when a crack is expected to occur (N/mm ), A s = area o reinorcement within tensile zone (mm ). I A s is smaller than zero only steel ibres are necessary. A ct = area o concrete within tensile zone (mm ). The tensile zone is that part o the section which is calculated to be in tension just beore ormation o the irst crack. s = the maximum stress permitted in the reinorcement immediately ater ormation o the crack (N/mm ). This may be taken equal to the yield strength o the reinorcement ( yk ). However, a lower value may be needed to satisy the crack width limits. ct,e = the tensile strength o the concrete eective at the time when the cracks may irst be expected to occur (N/mm ). In some cases, depending on the ambient conditions, this may be within 3-5 days rom casting. Values o ct,e may be obtained rom ormula (1) by taking as ck the strength at the time cracking is expected to occur. When the time o cracking cannot be established with conidence as being less than 8 days, it is recommended that a minimum tensile strength o 3 N/mm be adopted. k c = a coeicient which takes account o the nature o the stress distribution within the section immediately prior to cracking. The relevant stress distribution is that resulting rom the combination o eects o loading and restrained imposed deormations. k c = 1 or pure tension (e = M/N = 0) k c = 0.4 or bending without normal compressive orce (e =).

12 4 RILEM TC 16-TDF Workshop, Bochum, Germany, 003 k = k p = In the range between e = 0 and e = : * e/h < 0.4 k c e h (3) 6 e 1 h * e/h h 1 k e c (4) h e a coeicient which allows or the eect o non-uniorm sel-equilibrating stresses. The value can be taken as 0.8 as a irst approximation. For urther details, see ENV [1]. a coeicient which takes account o the prestressing eect: e v e v k c k p 1 1 k c.4 6 (5) k c h h where: cp = the ratio o prestressing = (6) k ct,e NSd cp (N/mm ) Ac N Sd = prestressing orce (N) A c = cross section o concrete (mm ) e v = the eccentricity o the prestressing orce (mm) i e v = 0 k p 1 1 k c (7) k c or pure bending (k c = 0.4), it ollows that : k p (8) 4.4 Calculation o crack width Crack control is only possible i at least one o the conditions mentioned in 3.1. is satisied. The calculation o the design crack width in steel ibre reinorced concrete is similar to that in normal reinorced concrete. However, it has to be taken into account that the tensile stress in steel ibre reinorced concrete ater cracking is not equal to zero but equal to 0.45 Rm,1 (constant over the cracked part o the cross section).

13 Test and Design Methods or Steel Fibre Reinorced Concrete 43 Formula () can be used to calculate the reinorcement A sr (mm ) which satisies the crack width limit. With R = yk / s = 1.4 the crack width is approximately limited to 0.5 mm: A A sr ct 0.45 k c k p k ct,e Rm,1 1.4 (9) yk 1.4 In ordinary reinorced concrete, the ollowing ormula is used: w s (30) k rm sm where: w k = the design crack width (mm) s rm = the average inal crack spacing (mm) sm = the mean steel strain in the reinorcement allowed under the relevant combination o loads or the eects o tension stiening, shrinkage, etc. = a coeicient relating the average crack width to the design value. = 1.7 or load induced cracking and or restrained cracking in sections with a minimum dimension in excess o 800 mm. = 1.3 or restrained cracking in sections with a minimum depth, breadth or thickness (whichever is the lesser) o 300 mm or below. Values or intermediate section sizes may be interpolated. sm may be calculated rom the relation: s sr sm 1 1 (31) E s s where: s = the stress in the tensile reinorcement calculated on the basis o a cracked section (N/mm ). sr = the stress in the tensile reinorcement calculated on the basis o a cracked section under loading conditions causing irst cracking (N/mm ). ß 1 = coeicient which takes account o the bond properties o the bars = 1.0 or high bond bars = 0.5 or plain bars ß = a coeicient which takes account o the duration o the loading or o repeated loading = 1.0 a or single, short term loading = 0.5 or a sustained load or or many cycles o repeated loading. For members subjected only to intrinsic imposed deormations, s may be taken as equal to sr. The average inal crack spacing or members subjected principally to lexure or tension can be calculated rom the equation: b 50 srm k1 k (mm) (3) r L

14 44 RILEM TC 16-TDF Workshop, Bochum, Germany, 003 where: 50/(L/) 1 b = the bar size in mm. Where a mixture o bar sizes is used in a section, an average bar size may be used k 1 = a coeicient which takes account o the bond properties o the bars; k 1 = 0.8 or high bond bars and 1.6 or plain bars. In the case o imposed deormations, k 1 should be replaced by k 1 k, with k being deined in 4.3. Minimum reinorcement k = a coeicient which takes account o the orm o the strain distribution. = 0.5 or bending and 1.0 or pure tension r = the eective reinorcement ratio, A s /A c,e where A s is the area o reinorcement contained within the eective tension area A c,e. The eective tension area is generally the area o concrete surrounding the tension reinorcement o depth equal to.5 times the distance rom the tension ace o the section to the centroid o reinorcement [1] L = length o steel ibre (mm) = diameter o steel ibre (mm) For steel ibre reinorced concrete, s and sr in (31) are calculated taking into account the postcracking tensile strength o the steel ibre reinorced concrete, i.e Rm,1, in the cracked part o the section. 5. Detailing provisions The rules applicable to normal reinorcement (bar, mesh) and prestressing tendons can be ound in ENV [1]. Only requirements applicable to steel ibre reinorced concrete will be discussed below. 5.1 Shear reinorcement in beams A minimum shear reinorcement is not necessary or members with steel ibres. But it must be guaranteed that the ibres have a signiicant inluence on the shear resistance. Fibre type and ibre dosage must be suicient so that a characteristic residual lexural tensile strength Rk,4 o 1 N/mm is achieved. 6. Reerences [1] European pre-standard: ENV : Eurocode : Design o concrete structures Part 1: General rules and rules or buildings. [] ENV : Eurocode 1: Basis o design and actions on structures - Part 1: basis o design, Annex D.3.: Statistical evaluation o resistance/materials tests, 1994, pp [3] Vandewalle, L. et al, Recommendations o RILEM TC16-TDF: Test and Design Methods or Steel Fibre Reinorced Concrete: bending test (inal recommendation), Materials and Structures, Vol.35 (00) pp

15 Test and Design Methods or Steel Fibre Reinorced Concrete Appendix 1 The stresses and 3 in the diagram are derived rom the residual lexural tensile strength as explained below. The residual lexural tensile strengths R,1 and R,4 are calculated considering a linear elastic stress distribution in the section [3] (Figure 1.1a). However, in reality, the stress distribution will be dierent. To calculate a more realistic stress in the cracked part o the section, the ollowing assumptions have been made (Figure 1.1b): - the tensile stress in the cracked part o the steel ibre concrete section is constant; - the crack height is equal to ±0.66 h sp at F R,1, to ±0.90 h sp at F R,4 respectively. Requiring M 1 = M, can then be expressed as:,1 = 0.45 R,1,4 = 0.37 R,4. Figure 1.1: Stress distribution

16 46 RILEM TC 16-TDF Workshop, Bochum, Germany, Appendix. Exposure class Examples o environmental conditions 1: dry environment interior o buildings or normal habitation or oices (1) humid environment a without rost b with rost 3: humid environment with rost and de-icing salts - interior o buildings where humidity is high (e.g. laundries) - exterior components - components in non-aggressive soil and/or water - exterior components exposed to rost - components in non-aggressive soil and/or water and exposed to rost - interior components when the humidity is high and exposed to rost interior and exterior components exposed to rost and deicing agents 4: seawater environment a without rost b with rost - components completely or partially submerged in seawater, or in the splash zone - components in saturated salt air (coastal area) - components partially submerged in seawater or in the splash zone and exposed to rost - components in saturated salt air and exposed to rost The ollowing classes may occur alone or in combination with the above classes: 5: aggressive chemical environment () a b c - slightly aggressive chemical environment (gas, liquid or solid) - aggressive industrial atmosphere moderately aggressive chemical environment (gas, liquid or solid) highly aggressive chemical environment (gas, liquid or solid) (1): This exposure class is valid only as long as during construction the structure or some o its components is not exposed to more severe conditions over a prolonged period o time (): Chemically aggressive environments are classiied in ISO/DP The ollowing equivalent exposure conditions may be assumed: Exposure class 5 a: ISO classiication A1G, A1L, A1S Exposure class 5 b: ISO classiication AG, AL, AS Exposure class 5 c: ISO classiication AG, A3L, A3S