USE OF STEEL FIBER REINFORCED CONCRETE IN THIN SHELL STRUCTURES: EVALUATION OF FIBER PERFORMANCE THROUGH TESTING OF SHELL SPECIMENS

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1 Computational Methods for Shell and Spatial Strutures IASS-IACM 2000 M. Papadrakakis, A. Samartin and E. Onate (Eds.) ISASR-NTUA, Athens, Greee 2000 USE OF STEEL FIBER REINFORCED CONCRETE IN THIN SHELL STRUCTURES: EVALUATION OF FIBER PERFORMANCE THROUGH TESTING OF SHELL SPECIMENS Prof. A. Domingo, Ass. Prof. C. Lázaro* (1), Prof. P. Serna Department of Constrution Engineering Universidad Politénia de Valenia, Spain (1) CM Calidad S.L. Valenia, Spain Key words. Shell strutures, steel fiber reinfored onrete, bending test Abstrat. The following doument proposes the use of steel fiber reinfored onrete (SFRC) in the onstrution of shell strutures. SFRC provides bending resistane and improves shell servieability. One diretional bending tests on shell speimens will be arried on, and onlusions on SFRC shell setions performane will be drawn out on the basis of the omparison between theoretial and modeled load defletion behavior.

2 Prof. A. Domingo, Ass. Prof. C. Lázaro, Prof. P. Serna 1 Introdution Strutural design of RC shells parting from the results of a shell-type finite-element analysis faes the diffiulty of providing the required safety for the ultimate limit states of bending and shear of shell setions. The addition of steel fibers in the onrete mix allows for the development of tensile stresses along the entire raked depth of a setion. These stresses an provide the required ultimate bending strength. Steel fibers provide also other properties that improve the strutural behavior under servie loads [1]. For instane: Crak width redution More uniform distribution of raks Improvement of strutural behavior under yli loads Inrease in strutural dutility The paper fouses on the study of the behavior of steel fiber reinfored onrete (SFRC) as omposite material for onstrution of thin shell strutures. The main aims are as follows: On one hand to afford the ultimate design of setions from the results gained in a linear elasti analysis of the shell, onsidering the bending resistane developed by fibers. On the other hand, to take advantage of the strutural qualities whih fibers an bring to onrete. These ideas are being arried into pratie in the strutural design and onstrution of a hypar shell roofing struture. This roof is an eight-lobe groined-vault system, spanning 36 m between opposite supports, with a base shell thikness of 6 m. It will be onstruted at the Parque Oeanográfio Universal in Valenia (Spain). For this struture we proposed in ref. [2] a design method means an interation diagram axial fore vs. bending moment for onrete shell setions. The diagram is alulated on the basis of a stress strain ultimate model that onsiders the effets of entral reinforement mesh and the addition of steel fibers in the mix. The model is based on the one proposed in referene [3] for dimensioning flexural members with or without reinforement bars. Its main feature is the quantifying of fiber effets as a tensile stress blok ating on the entire raked depth of the setion. The amount of stress an be obtained from speial tests or from data provided by the fiber manufaturer. In order to verify the onveniene of this model for bending alulations in the ase of thin setions, one diretional bending tests on 6 m thik retangular shell speimens (1,30 x 1,80 m) were arried on in the Laboratorio de Materiales of the Universidad Politénia de Valenia (Spain). Eah speimen lies horizontally on two linear bearings. Bending fores are introdued through two load lines using one vertial jak. During the testing proess values of vertial displaements on several points are measured. Behavior of speimens up to failure will be studied. Test results will be ompared with the results from a load-defletion theoretial model of the speimen. Conlusions are being drawn out on the ability of steel wire fibers to provide the required tensile strength, and to improve shell behavior under servie loads. 2

3 IASS-IACM 2000, Chania-Crete, Greee 2 Strutural use of steel fiber reinfored onrete (SFRC) The use of fibers as reinforement for onrete (espeially steel fibers) is a onsiderably developed tehnique. Researh in this field has token plae on the study of the behavior of several fiber types, the properties of the resulting omposite, preparation and plaing tehnologies, and the onvenient theoretial models see ref. [1]. Appliations of ast-inplae steel fiber reinfored onrete (SFRC) involve in a great extent high requirement floor slabs and pavements, and tunnel and surfae linings. Pre-ast SFRC has been applied in thin elements of redued size, thus with limited strutural requirements. On the other hand, great experiene is also available for steel fiber reinfored shotrete (SFRS), mainly in the field of slope stabilization and tunnel lining. Other appliations of SFRS inlude the onstrution of redued size dome-shaped strutures, with shotrete applied to the underside of polyurethane foam moulds to a thikness of about 40 to 100 mm (see ref. [4]). What onerns the dimensioning of SFRC setions for bending, some available approahes ref. [1] are based on onventional design methods supplemented by tensile stress fiber ontribution for the bending strength of the setion. The main differenes lie on the determination of the magnitude of the tensile stress due to the fibers. Other approahes use the fiber tensile ontribution to determine the remaining moment apaity in the raks, onsidered as plasti hinges. The onservative point of view is to analyze the setion with reinforement bars resisting the total tensile load, and is based on the fat that variability of fiber distribution an lead to dangerous redutions in strength. On the opposite side lie reent proposals suh as the one in ref. [3] (Belgium), or the methods desribed in ACI Report 544.4R-10 (ref. [7]) to standardize the ultimate design methods for onrete setions with onventional and steel fiber reinforement. These proposals inlude design methods for bending and longitudinal fores, for shear and alulation of rak width. Referene [7] desribes the method developed by Henager and Doherty in 1976 for stati flexural analysis of beams ontaining bars and fibers, whih is similar to the ACI ultimate strength design method. This method proposes the use of: a) a retangular ompression blok with a stress value of 0,85 f (onrete ompressive strength) and a depth of 0,8 x (neutral axis depth). b) a retangular tensile blok with a stress value alulated from the length, diameter, perent by volume and bond effiieny fator of fibers, developed at a ertain strain under the neutral axis. The flexural analysis method of ref. [3] is based on a more sophistiated method for the stress strain diagram for steel wire fiber reinfored onrete: 1. For onrete in ompression a paraboli-retangular behavior until maximum onrete strain (0,0035) is assumed 3

4 Prof. A. Domingo, Ass. Prof. C. Lázaro, Prof. P. Serna 2. For onrete in tension a linear behavior is assumed up to the onrete axial tensile strength. After raking stress is assumed to derease to 0,37 f t,eq,300 (equivalent flexural tensile strength of SFRC obtained in the standard bending test with ontrolled strain orresponding to a defletion of L/300) at a strain value of 0,001. From this strain value to the SFRC limit strain 0,01, stress dereases linearly to 0,37 f t,eq,150 (equivalent flexural tensile strength of SFRC orresponding to a defletion of L/150). Figure 1. SFRC stress strain diagram (soure: ref. [3]) Based upon this stress-strain diagram a plasti design or a onventional design with a tensile stress blok with the desribed form, with flexural tensile stress values gained from standard bending tests, an be arried on. Referene [3] inludes guaranteed mean values for the equivalent flexural tensile strength for different types and weight ratios of Dramix-type fibers and the orresponding analytial expressions to evaluate this parameter. These values ould be used in ase of absene of standard tests. 3 Target of this researh The strutural design and dimensioning of thin shell elements, faes an important question: the ability of the shell setion to resist bending fores. Generally thin shell strutures are designed to resist mainly membrane fores, without onsideration of bending fores. This hypothesis, traditionally aompanied by theoretial models and alulations based on the membrane theory, leads to thin shells reinfored approximately along the mean surfae with bars oriented in two perpendiular diretions. Considering this priniples fasinating reinfored onrete shell strutures, only a few entimeter thik, were built in the sixties (see ref. [10]). 4

5 IASS-IACM 2000, Chania-Crete, Greee The development of the FE method allows for easily arrying on linear analysis of shells with ompliated geometry. When using shell type elements, values of bending and torsional fores in the shell are obtained. If the shape of the shell is adequate, the values of the bending moments will be generally little. But in some load ases, and also near stiff zones of the shell, higher moments will appear, for whih the neessary strutural safety must be guaranteed. Only the mehanial apaity of the setion aounts for this purpose. The flexural strength of a shallow reinfored onrete setion is espeially sensible to the depth of the reinforement bars. The resisting moment depends on the distane between rebars and the entroid of the ompression blok. Thus, a little hange of the re-bar position (few mm) an ause an important relative redution of the lever arm, hene a derease of the resisting moment. In this kind of thin shell reinforement is plaed along the middle surfae, therefore it is probable that the real re-bar position lies in the upper half of the setion and the lever arm redues to 20% of the total setion depth. For suh ases, the addition of steel fibers to the onrete mix, and its tensile ontribution in the hardened onrete an mean an important inrease of the seurity resisting bending fores. The final target of this researh is to test the appliability of a flexural analysis method onsidering tensile ontribution of SFRC for shell strutures with shallow setions. For this purpose we propose the omparison of the load-defletion behavior of shell speimens, with and without steel wire fibers, tested for one-diretional bending, and the theoretial behavior of these speimens based on the model whih will be explain in the next paragraph. A value of 6 m for shell speimens thikness was hosen, onsidering that a lower thikness ould imply a violation of the requirements for overing in the appliable standards. 4 Theoretial model of SFRC behavior for bending The analytial model to predit the load-defletion behavior is based on the method of urvature integration proposed in the European standard EC-2 [9], dedued from the Maxwell-Mohr theorem. The integration is arried on with the mean urvature funtion along the piee: w = C II M dx (1) L where M is the bending moment funtion aused by a fititious unity load applied on the point where defletion w is going to be evaluated. The mean urvature C II is evaluated for eah setion from the urvature of the unraked setion C I and the urvature of the raked setion without ontribution of onrete in tension C IIo, with the following relation: C II = ( 1 ζ ) C + ζ C (2) I IIo 5

6 Prof. A. Domingo, Ass. Prof. C. Lázaro, Prof. P. Serna where ζ is the interpolation oeffiient for eah setion, varying between 0 and 1 depending on the magnitude of the bending moment (equals 0 in unraked setions). The alulation of the urvature follows the lines desribed in ref. [9] and is based on the hypothesis of plane setion and on a simplified trapezoidal stress-strain behavior of onrete (linear behavior with seant elastiity modulus until 0,85 f -onrete ompressive strength- is reahed. Unraked setion Assuming the strainε in the upper onrete fiber to be known, the orresponding stress and the ompressive fore D of the stress blok, depending on the neutral axis depth x, an be evaluated as follows: stress σ = E ε (3) ompressive fore of onrete D = α σ b x (4) where b is the setion width, and α is a oeffiient desribing the form of the ompression blok (with a value of 0,5 in the pre-raking stress triangular blok). Strain in steel and at the lower onrete fiber is alulated from the plane setion hypothesis. reinforement lower onrete fiber d x ε s = ε (5) x ε b h x = ε (6) x fore of bar reinforement T s = E ε A (7) s s s tensile fore of onrete T = α E ε b ( h x) (8) where E is the seant onrete elastiity modulus, Es is the reinforement steel elastiity modulus, d is the reinforement depth and h is the total depth of the setion. Beginning with a given value of the onrete upper fiber strain, the neutral axis depth x an be alulated onsidering equilibrium of internal fores ating on the setion: b D T + T = 0 (9) + s One the value of x is known, the unraked urvature an be evaluated from the strains in reinforement and in onrete. The orresponding bending moment an be obtained by taking moments on the reinforement position: pre-raking urvature ε ε s CI = (10) d 6

7 IASS-IACM 2000, Chania-Crete, Greee pre-raking moment M = D ( d x) + T [( d h) + γ ( h x) ] γ (11) where the oeffiient γ desribes the position of the entroid of the ompression blok, with a value of 1/3 before onrete has reahed its limit stress (0,85 fd). Craked setion no fibers Craking ours when SFRC tensile strength is reahed. With no fiber addition the fore of ompressive stress blok should internally equate the tensile fore of bar reinforement. The same proedure as in the unraked setion will be used, with some onsiderations. When the strain at the upper onrete fiber overomes ε 0 (strain orresponding to a stress equal to 0,85 f), the form of the ompression blok beomes trapezoidal and the values of α y γ are desribed with this equations: ε 0.5ε 0 α = (12) ε 2 [( ε ε 0 ) + ε 0 ( ε 2 3 ε 0 )] 2 α ε γ = 0,5 (13) These values allow the evaluation of the neutral axis depth with the following equation (9b): D + T s = 0 (9b) The tensile fore of bar reinforement Ts will be limited to the yield strength fy of the reinforing bar one the steel strain ε s0 is reahed. Curvature and bending moment an be alulated with the following expressions: urvature of the raked setion C IIo ε ε s = (14) d moment M = D ( d γ x) (11b) Craked setion with fibers In this ase the development of a retangular tensile stress blok in the fibrous onrete is assumed, with a stress value of 0,37 f t,eq,150 (equivalent flexural tensile strength for the fibrous onrete obtained from a standard bending test with ontrolled defletion orresponding to a defletion of L/150). Tensile fore of SFRC is evaluated as follows: SFRC in tension T = f b ( h ) (8b) t, eq,150 x The neutral axis depth will be alulated from eq. (9), urvature is obtained from eq. (14) and the equation for the bending moment is: moment M D ( d x) + T [( d h) + 0,5 ( h x) ] = γ (11) 7

8 Prof. A. Domingo, Ass. Prof. C. Lázaro, Prof. P. Serna These equations allow for plotting the moment urvature diagrams, with or without fibers, as shown in the next figure: ft,eq=1 ft,eq=0 d=30 mm Moment (KN*m) ft,eq=1 ft,eq=0 d=20 mm ,1 0,2 0,3 0,4 0,5 0,6 Curvature Figure 2. Moment Curvature diagrams. Analytial model In order to interpolate urvatures onstant values for C I (unraked state) and for the interpolation oeffiient ζ have been onsidered. The latter is omputed with the bilinear method proposed in Euroode EC-2: M CI = (15) E I M r 2 ζ = 1 (16) M The results of the urvature integration are shown in the following load-defletion diagrams: 50 Load (KN) f t,eq,150 =2MPa f t,eq,150=1mpa f t,eq,150=0mpa f t,eq,150 =2MPa f t,eq,150 =1MPa f t,eq,150=0mpa d=35mm d=25mm Defletion (mm) Figure 3. Load defletion urves Analytial model 8

9 IASS-IACM 2000, Chania-Crete, Greee 5 Laboratory tests 5.1 Objetives of the tests. The experimental program was arried on in the Laboratorio de Materiales (Universidad Politénia de Valenia), and had the following objetives: - Chek the adequay of the proposed numeri model, omparing the theoretial results with the ones obtained by tests on retangular shell speimens. - Verify, by means of standard tests, the mehanial harateristis of the onrete with and without fibers, and afterwards ompare them with the ones proposed by the fiber produer. Following variables were analyzed: - Risks related to the shell reinforement positioning and the onsequenes aused by its movement during the onstrution in the shell mehanial apaity. Due to the fat that reinforement bars lie in two diretions, the bar entroid differs from one diretion to another, at least, in the same distane as the bar diameter. - Advantages in using SFRC. Fibers provide onrete to have flexural tensile strength after raking. At the same time fiber addition enables to ontrol rak width. Provided that the fiber effetiveness of fibers depends on several variables (mixture proportions, size, slenderness...) we deided to redue them to the minimum, fixing as the only variable the presene or not of fibers. - Making proess. Possible diferenes between ast in plae SFRC vs. shotreted SFRC were testesd. Figure 4. Shell speimen reinforement Figure 5. Fresh SFRC 9

10 Prof. A. Domingo, Ass. Prof. C. Lázaro, Prof. P. Serna 5.2 Testing program Tests on shell speimens Twelve shell-speimens were made, as speified in the following tables: No. of speimens Conrete type Plaement Speimen position Setting 4 RC Cast in plae Horizontal Vibration 4 SFRC Cast in plae Horizontal Vibration 2 RC Shotreted 60º SFRC Shotreted 60º --- Table 1. Shell-speimens Two different kinds of shell-speimens were made: the first were ast in plae in ideal onditions, horizontal position and fit on a shaking table, and the seond shotreted on a 60 degrees inlination surfae. Both kinds are retangular shaped and its dimensions are 1800 mm x 1300 mm x 60 mm. A base reinforement φ 8 to 150 mm was plaed in both main diretions (figure 4). Materials had the following features: Conrete type Shotreted Shaked All No fibers With fibers Cement I-42,5 R Water 180 Gravel 7/ Crushed Sand Round Sand Superfluidifiant (melanine) (0,8 %) 2,3 (1,2 %) 3,5 Maximum gravel size 12 mm Fibers (when plaed) 50 Kgr/m 3 Fiber Type Dramix fibers with the following features were used: Steel lass Length (l mm) Diameter (φ - mm) Slendern. (l / φ) Type Low arbon 35 0, /35 Table 2. Conrete mixture and properties of materials 10

11 IASS-IACM 2000, Chania-Crete, Greee The following fabriation proess was followed: Shell speimens in ideal onditions These eight shell-speimens were fabriated in the pre-asting firm PREVALESA. Two onrete mixes were made; one with fibers and another without them. Conrete was prepared in a vertial axis mixer, and the speimens were made on a shaking table. Figure 6 shows the seond four speimens. Speimens were unmoulded and stoked after 24 h. Shotreted shell speimens These shell-speimens were prepared in the firm HORMIGONES PROYECTADOS S.A. Conrete was prepared in dry way (water addition ourred in the projetion gun). Figure 7 shows the shotreting proess. The shell-speimens were left for seven days in the work-site and afterwards they were moved (unmoulded) to the laboratory Figure 6. Making in a shaking table Figure 7. Shotreting Complementary tests. In order to establish the onrete harateristis of the shell-speimens, two prismati test moulds for eah mixture were prepared. From eah of them, by sawing or by extration, we obtained the following speimens to examine: a) 1 prismati speimen 500x500x140 mm - 4 speimens φ70x140 mm, for ompression tests. - 3 speimens 100x100x500 mm, for bending tests. b) 1 prismati speimen 500x500x60 mm. - 4 speimens 60x60x120 mm, for ompression tests. - 3 speimens 100x60x500 mm, for bending tests. Axial loading tests to speimens φ70x140 mm and 60x60x120 mm were made aording to the Spanish standard UNE SFC tenaity determination to ompression. During eah test the omplete urve stress/strain was reported, measuring the applied stress with a pressure gauge, and the strain with a gauge that measured the relative displaement between press plates. Loading was ontrolled for onstant speed strain growth. Tests went on until the speimen s whole rak or until the strain exeeded 0,0075. Figure 8 shows an example of the urves obtained by these tests. 11

12 Prof. A. Domingo, Ass. Prof. C. Lázaro, Prof. P. Serna 50 Stress (MPa) SFRC RC ,5 5 7,5 10 Strain (0/00) Figure 8. Stress/Strain urves - ompression test Bending tests on prismati speimens sized 100x100x500 mm and 100x60x500 mm were arried on. Loads were applied at thirds of span with ontrolled strain speed aording to the Spanish Standard UNE SFRC, strength to first rak determination, tenaity and tenaity fator determination on a bending test o the Belgium Standard NBN B Test on fiber-reinfored onrete Bending test on prismati sample. Figure 9 shows the typial shape of this kind of urve. First rak load and flexural tensile toughness (area below the load urve up to a defletion of L/150) were measured Se. 100x100 SFRC Load (KN) 10 Se. 100x100 RC Se. 100x60 SFRC Se. 100x60 RC Defletion (mm) Figure 9. Load/defletion urves - bending test. Figure 10 shows a speimen in the bending test and figure 11 shows how steel-fibers joins the two piees of the broken onrete. 12

13 IASS-IACM 2000, Chania-Crete, Greee Figure 10. Speimen during bending test. Figure 11. Steel Fibers Figures 8 and 9 also show that the performane of both onrete types (with and without fibers) is very similar until first rak load is reahed. The urve for onrete without fibers finished when the speimen showed the first rak. However, SFRC allows muh higher strain and is able to resist inreasing loads after the first rak. Conrete Compressive strength (MPa) Conrete C 37,8 SFC 33,9 Shotrete C 31,7 SFC 42,1 Table 3. Compressive test values. Conrete Shotrete CONCRETE C SFC C SFC Flexural tensilestrength (MPa) First rak Maximum Area strength 0,37 ft,eq, x100 4,22 100x60 4,55 100x100 3,78 4,68 1,34 100x60 3,67 5,67 2,38 100x100 2,71 100x60 3,35 100x100 2,97 4,73 2,2 100x60 3,25 3,25 1,75 1,17 1,17 Table 4. Bending test values. 13

14 Prof. A. Domingo, Ass. Prof. C. Lázaro, Prof. P. Serna Tables 3 and 4 show the results of the tests. Compressive test results inlude the mean values of the ylinder and prismati speimens. Results also inlude the experimental value of the equivalent flexural tensile strength f t,eq of SFRC alulated with the bending test with the following equation from referene [3]: f t,eq =F m l/bh 2 (17) Where l, b and h are, respetively, span, width and depth of the speimen, F m is the medium value of the load applied between the defletion values 0 and l/150. Referene [3] shows also an equation for the analytial omputation of the equivalent flexural tensile strength f tm,,eq depending on the following parameters: f t,eq = (180 W f λ f d f 1/3 / (180 f k +W f λ f d f 1/3 )) (0,3 f k 2/3 / 0,6) /100 (18) Where W f,d f and λ f are, respetively, onrete fiber dosing (Kg/m 3 ), fiber diameter (mm) and slenderness defined as the quotient between length and diameter. The obtained values have been used in the theoretial model omputations. The values obtained in these tests for f t, eq are superior to the ones grated by the manufaturer. It is also important to be notied the great tenaity improvement obtained both ompression and flexure thanks to the fibers Shell-speimens tests. Bending tests were arried on the shell speimens. Speimens were disposed resting over its extremes leaving 1,5 m span. Load was applied in two transverse lines plaed at thirds of span. Figure 12 shows the test plan and figure 13 shows a test piture. P Cotas en mm Figure 12. Test draft Figure 13. Test devie 14

15 IASS-IACM 2000, Chania-Crete, Greee The tests were arried on to failure, with onstant speed defletion growth. During the test, 4 displaement power gauges ontinually reorded load and defletion in the midst of the span R Conrete speimen 3 Re-bar depth 28 mm Load (KN) Test results Theoretial values Defletion (mm) Figure 14. Comparative load/defletion behavior (RC) 50 SFR Shotrete speimen 9 Re-bar depth 30 mm 40 Load (KN) Test results 0.37 ft,eq,150=0 0.37ft,eq,150=1 0.37ft,eq,150=2 Theoretial values Defletion (mm) Figure 15. Comparative load/defletion behavior (SFRC) 15

16 Prof. A. Domingo, Ass. Prof. C. Lázaro, Prof. P. Serna 6 Analysis of results Figures 14 and 15 show the tested load - defletion urve of shell speimens with and without steel fibers. This urves are ompared with the theoretial behavior (desribed model) with different values of the equivalent flexural tensile strength. Values for this parameter vary from the values given by manufaturers to those obtained on the omplementary tests. The theoretial urve is drawn with the real plaement of reinforement bars obtained by measurement in the broken setion after the test. Test urve shapes are quite right up to the theoretial reinforement yielding value. The analytial load-defletion behavior diverges at this point beause yielding stress of reinforement is onsidered to be 500 MPa in the analytial model, whereas the atual values of steel yielding stress are higher. To analyze the oherene between the model and the experimental tests, we tried to relate the areas below the experimental load/defletion urve and the theoretial urve up to a defletion of 150 mm (L/100), so the effet of the reinforement yielding is obviated. For this purpose, three values of 0,37 f ft,eq in SFRC shell speimens have been onsidered: 0 (no influene of steel fibers), 1 Mpa (manufaturer s value) and 2 MPa (experimental value). RC speimens SFRC speimens Speimen No. Area Speimen No. Area relation for different 0,37f t,eq relation 0MPa 1MPa 2MPa 1 0,79 5 0,99 0,89 0,85 2 0,81 7 1,04 0,96 0,86 3 Shaked 0,76 8 Shaked 1,20 1,15 1,10 4 1,02 11 Shotreted 1,27 9 Shotreted 1,11 1,02 0, , ,55 1,43 1,26 Mean value 0,99 Mean value 1,18 1,09 0,99 Dispersion 27% Dispersion 23% 23% 18% Table 5. Area relation below load-defletion urves Table 5 shows these area relations. The obtained medium value of the area relation (experimental analytial) is quite good (0,99) for the shell speimens without steel fibers, but values have a very high dispersion (27%). For SFRC shell speimens the best adjustment is provided for a value of 0,37 f ft,eq, equal to 2 MPa (experimental value). Moreover, the use of fibers redues the dispersion down to 18%. The effet of fibers on SFRC seems notieable and the model suffiiently aurate. 16

17 IASS-IACM 2000, Chania-Crete, Greee 7 Conlusions 1. The flexural behavior of thin reinfored onrete shells, after raking, is very sensible to the depth of the reinforement. It is diffiult to assure the orret plaement of reinforement even in pre-ast onditions. 2. Steel fiber addition improves RC shells flexural behavior. Bending tests on SFRC shell speimens show a good adjustment when using the flexural tensile strength (residual tensile strength) values obtained from standard tests. This values are higher than those provided by the manufaturer. 3. Fiber addition improves the results uniformity, beause their influene does not depend on the plaement. 4. The proposed analytial model adjusts to the experimental results. It inludes the effet of fibers as a tensile stress blok extended to the lower setion edge. Fiber tensile ontribution is, thus, onsidered below reinforement depth (unlike the model proposed in ref. [3]). 5. Test should be arried on in order to verify the effets of dispersion of results in the neessary seurity fators. Future tests should onsider new variables, as fiber ontents, and should analyze the evolution of raking. Referenes [1] ACI 544.1R-82, State of the Art Report on Fiber Reinfored Conrete, Conrete International, (May. 1982) [2] A.Domingo,C.Lázaro,P.Serna,Design of a thin shell steel fiber reinfored onrete hypar roof, in R. Astudillo, A.J. Madrid (eds.), Shell and Spatial Strutures: from reent past to the next millenium, CEDEX, (1999) A 169-A 179. [3] Dramix Guideline, Steel fiber reinfored onrete strutures with or without ordinary reinforement, Infrastrutuur in het Leefmilieu, 4, (1995), [4] ACI 506.1R-98, ACI Committee Report on Fiber Reinfored Shotrete, (Apr. 1998) [5] P. Serna, Método para la formulaión de hormigones de fibras metálias, Materiales de Construión, 34, (1984), in spanish [6] V. Gopalaratnam, R. Gettu, On the haraterization on flexural toughness in FRC, Proeedings of Workshop on Fiber Reinfored Cement and Conrete, Sheffield, (1994). [7] ACI 544.4R-88, Design Considerations for Steel Fiber Reinfored Conrete, (1988, reapproved 1994) [8] J. Ortiz Herrera, A. Del Río Bueno, Estudio rítio del álulo de flehas en vigas de hormigón armado según la instruión EH-88, Hormigón y Aero, 173, (1990), 9-26, in spanish 17

18 Prof. A. Domingo, Ass. Prof. C. Lázaro, Prof. P. Serna [9] R. Park, T. Paulay, Estruturas de Conreto Reforzado, Limusa, (1975) [10] Félix Candela Arquiteto (Catálogo de la exposiión organizada en 1994), Ministerio de Obras Públias, Transportes y Medio Ambiente,