DEVELOPMENT OF SHEAR STRESS EQUATION CONTRIBUTED BY STEEL FIBRE IN REINFORCED CONCRETE

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1 VOL., NO. 8, APRIL 06 ISSN Asian Research Publishing Network (ARPN). All rights reserved. DEVELOPMENT OF SHEAR STRESS EQUATION CONTRIBUTED BY STEEL FIBRE IN REINFORCED CONCRETE N. N. Sarbini, I. S. Ibrahim, A Aziz Saim, M. A. A. Kadir and S. M. Syed Mohsin Department o Structure and Materials, Faculty o Civil Engineering, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia Faculty o Civil Engineering and Earth Resources, Universiti Malaysia Pahang, Gambang, Pahang, Malaysia noornabilah@utm.my ABSTRACT The rise o extensive research and development on the application o steel ibre inside concrete is a tremendous topic in the last ew decades. The obvious beneits o adding steel ibre inside concrete can be seen rom the improvement o the mechanical properties o steel ibre reinorced concrete (SFRC). The improvement o the mechanical properties can be seen easily on the higher value o tensile and lexural strengths or SFRC compared to plain concrete. However, a question arises on to what extent does the steel ibre exerts an additional stress to increase the strength. Currently, this additional stress is called shear stress supplement. In this study, shear supplement model developed by Rilem was quantiied with some statistical modiication to predict the additional shear exerted by the steel ibre when it is placed inside the concrete. To achieve the objective, 5 prism specimens (50 mm 50 mm 750 mm) were prepared and dier in terms o the type o steel ibre and the ibre volume raction, V. Two types o hooked-end steel ibre labeled as SF60 and SF50 were used in this research. Meanwhile, each type o steel ibre was mixed into a plain concrete with respect to the V o 0.5%, 0.50%, 0.75%,.00%,.5%,.50%,.75%, and.00%. Plain concrete prisms were prepared as the control specimens. Ater 8 days o curing period, the prism was then transerred to the test rame to undergo lexural strength test. The results rom the lexural strength test were used to develop the shear stress equation to predict the contribution o steel ibre to increase the shear stress. The modiied equation was then used to predict the value o shear stress supplement. The results showed that, the modiied model well predicted the shear stress supplied by the steel ibres well which was shown by higher coeicient o correlation. Keywords: shear stress supplements, shear stress, steel ibre, steel ibre reinorced concrete. INTRODUCTION Concrete is a composite material, where the matrix is made rom the combination o ine aggregate, coarse aggregate, cement and water (Hibbeler, 0), (Sarbini, 04). However, the combination o those materials in the concrete matrix is not enough to sustain the tensile load. This is due to the strength o the concrete matrix which is good against compressive load. Thereore, other materials are added to the concrete matrix to sustain the tensile load. This includes using steel reinorcement, which is a common material used in building construction. Even so, nowadays people are looking or something that is more cost eective. Hence, it opposes the idea o using ibre instead o steel. The randomly distributed discreet ibres to reinorce plain concrete provide threedimensional resistances against the applied load as compared to the plain concrete (Paine, 997), (Altun et al., 007), (Holschemacher et al., 00), (Ibrahim et al., 0). The extensive use o steel ibre reinorced concrete (SFRC) is due to its perormance in restraining shear stresses induced by the concrete element. Thereore, randomly discreetly distributed steel ibres are added into plain concrete expecting that the shear stress is eectively transerred within the developed cracks. There were a lot o works concentrated on the tensile and lexural resistance o SFRC. Previously, Pierre et al. (999) have studied the dierences in the behavior o steel ibres when it is placed inside concrete and mortar. They ound out that the mechanical properties or both types o composites improved due to the addition o steel ibres. The improvement is seen by the higher strength o steel ibre concrete and steel ibre mortar, compared to the plain ones. On the other hand, Gao et al. (997) reported the dierences in the behaviour o the steel ibres reinorced high strength and lightweight concrete. Though, both types o concrete show improvement due to the addition o steel ibres, the improvement by lightweight concrete is less. This is due to the lightweight aggregate which act as a weak component and lessen the strength improvement compared to other type. Other studies have shown that SFRC improved the properties o toughness and modulus o elasticity even with small dosage o ibre volume raction (example 0.5%) and even at a ibre aspect ratio less than 40 (Song and Hwang, 004), (Teng et al., 004), (Altun et al., 007), (Thomas and Ramaswamy, 007), (Yazici et al., 007), (Xu and Shi, 009), (Ramli and Dawood, 00), (Pawade et al., 0), (Soulioti et al., 0). Unortunately, their works mostly reported on the strength values and the specimen behaviour. To the concern o the study on shear stress restrained by steel ibres inside the concrete element, it is a great step to ocus on the additional stress contributed by steel ibres. This special attention on shear supplement by steel ibres is somehow a study that is rarely ocused by any researcher, while other usually studies on the tensile and lexural perormances. It is well-known that the ailure o SFRC due to the applied lexural load is associated with the de-bonding 5445

2 VOL., NO. 8, APRIL 06 ISSN Asian Research Publishing Network (ARPN). All rights reserved. process o steel ibres rom the surrounding concrete. During the early stage o the de-bonding process, the cracks initiated are slow due to the ability o bridging ibres. At some stage where the element is no longer capable o sustaining the lexural load, the de-bonding process occurred rapidly. Due to the unstable cracks propagation at the point o where the steel ibres are pulled out rom the specimen, ailure will occur. This is also associated with exceeding the maximum limit o ultimate bond strength between the steel ibres and surrounding concrete (Gao et al., 997). This shows why the prediction o additional shear stress contributed by steel ibres is important; it is to determine the capacity o such ibres when restraining concrete. Sand Table-. Mix composition. Gravel Water, Cement, Admixture RESEARCH METHODOLOGY Material preparation Two types o hooked-end steel ibre were used in this study labeled as SF60 and SF50. The details o the steel ibres are given in Table-, while Figure- shows the illustration o the hooked-end steel ibre. Table-. Properties o steel ibres. Properties SF60 SF50 Length, mm Diameter, mm Aspect ratio, L/D Tensile strength, MPa Figure-. Prism specimens (illustration beore being de-mould). Testing procedures The schematic diagram o the lexural strength test is shown in Figure-3. Three units o linear variable dierential transormer (LVDT) were positioned at the mid-span and at both supports. LVDT was used to measure the delection and deormation throughout the test. The load was applied incrementally at every kn until the irst crack line appeared. Ater the irst crack had been observed, the additional load was controlled by the delection at every 0.0 mm until the specimen ails. During the test, data were recorded or the irst peak, peak and residual strengths at speciied delections. Figure-. Schematic diagram o lexural strength test. Eight (8) dierent ibre volume ractions, V are used or each type o steel ibre. The V were 0.5%, 0.50%, 0.75%,.00%,.5%,.50%,.75%, and.00%. At the same time, one plain concrete (without any ibre addition) was prepared as the control batch. The specimen was a prism specimen with a cross-section o 50 mm 50 mm, and length o 750 mm. The concrete batch was prepared or grade 40 N/mm and the mix proportion is given in Table-. For each type o steel ibre and ibre volume raction, three (3) prism specimens were prepared (Figure-). Figure-3. Schematic diagram o lexural strength test. Analytical works The additional shear rom steel ibres, v d is the parameter introduced by Rilem to determine the shear strength enhancement due to the addition o steel ibres in plain concrete (Rilem, 00). The general equation or the additional shear rom steel ibres is given as: v d () Ak k d A = 0.7 (bond and orientation actors) k =.0 (or rectangular section) k = + (00/d), with d in mm 5446

3 VOL., NO. 8, APRIL 06 ISSN Asian Research Publishing Network (ARPN). All rights reserved. τ d = Design value o the increase in shear strength due to steel ibres, N/mm To determine the design value or the increase in shear strength due to steel ibres, τ d, Rilem proposed two calculation methods (Rilem, 00). Both calculation methods diered in terms o the test procedure. In the irst method, the test procedure ollowed was as recommended in BS EN 465:005, whereby, the second method procedure was as recommended by JCI-SF (BS EN 465, 005), (JCI-SF, 984). In both test procedures, the lexural test was carried out or prism specimen. However, during the test they diered in terms o the measured variables. The irst procedure measured the CMOD (crack mouth opening displacement) when the prism specimen was applied under lexural load, whereas in the second procedure, the mid-span delection o the prism specimen was measured. In the irst procedure, the residual strength, Rk4 was calculated based on the measured CMOD until a crack width up to 3.5 mm. Meanwhile, or the second procedure, the equivalent lexural ratio was measured rom the midspan delection up to 3.0 mm. Ater the residual strength rom the irst procedure and the equivalent lexural ratio rom the second procedure were determined, the design value o the increase in shear strength due to steel ibres can be determined. These are accomplished using either equation () or the irst procedure or equation (3) or the second procedure. () d 0. Rk4 (3) d 0.Re, 3 p Rk4 = Residual lexural strength measured in BS EN 465: 005 R e,3 = Equivalent lexural ratio in JCI-SF: 984 p = Characteristic peak strength o plain concrete RESULTS AND DISCUSSIONS The lexural strength test carried out in this research work is related closely to the one that is assigned in JCI-SF test procedure. Thereore, equation (3) was used to determine the design value o the increase o shear strength due to steel ibres. Theoretically, the equation indicates that the shear strength due to steel ibre is the enhancement on lexural/peak strength o plain concrete, when steel ibre is added into the mix. Rilem suggested that the enhancement can be determined using the multiplication rom the equivalent lexural ratio at a maximum delection o 3 mm with the characteristic peak strength o plain concrete (Rilem, 00). The equivalent lexural ratio was determined as the ratio between the residual strength at net delection o L/50, 50D, to the peak strength o SFRC, p,sfrc. The equivalent lexural ratio is given as, p D 50, SFRC Analytical works using SPSS sotware was used to determine the peak strength o SFRC (Carver and Nash, 009). The proposed undamental relationship is given in equation (4) and it is also complied with ACI 38-08, ACI-363R-9 and Eurocode or the prediction o lexural strengths o plain concrete (ACI-38, 008), (ACI-363R, 99), (BS EN 99--, 004). x A cu (4) A = Material coeicient x = Flexural/peak strength o plain concrete, N/mm cu = Compressive strength o plain concrete, N/mm In the work by Thomas and Ramaswamy (007), they suggested that the lexural strength can be predicted using an additive method as given in equation (5). The irst term in the equation is the concrete compression contribution, whereas the second term is the contribution rom steel ibres to the matrix strength. L x V L x A V D cu D (5) In this research, the second term was modiied. The modiication was related to the eects o the peak strength and ibre volume raction in a quadratic relationship o the second degree. Thereore, the new analytical equation is given in equation (6). x A BV CV A, B, C = Regression coeicients (6) The peak strength rom the experimental results was assigned as the dependent variable, whereas the independent variables were cu, V cu and V cu. Next, the proposed models are given as in equation (7) and equation (8). The coeicient o determination, R were 0.84 and 0.87 or SF60 and SF50, respectively. A higher value o R (greater than 0.80) or both proposed models indicated the suitability o the test results. The correlation between the test results and the proposed models with : line is shown in Figure-4 and Figure-5. p p First term V 0.03V (7) Second term V 0.07V (8). 5447

4 VOL., NO. 8, APRIL 06 ISSN Asian Research Publishing Network (ARPN). All rights reserved. Figure-4. Relationship o peak strength between test results and proposed model or SF60 steel ibre. Figure-6. Relationship between the residual strength at net delection o L/50 and volume raction. D V p, SFRC.875 (9) D V p, SFRC.47V p, SFRC (0) On the other hand, Figure-7 and Figure-8 presents the correlation between the test results and the proposed models with : line. Figure-5. Relationship o peak strength between test results and proposed model or SF50 steel ibre. Then, the residual strength at net delection o L/50 was derived using regression analysis. The proposed models to derive the residual strength at net delection o L/50 using the SPSS sotware is shown in Figure-6. From the igure, the relationship between residual strength at net delection o L/50 and ibre volume raction or SF60 is linear, while or SF50 the relationship is quadratical relationship. These relationships were taken into account during the regression analysis. Equation 9 and equation 0 are the proposed models or SF60 and SF50, respectively. From the results, it was ound that higher coeicient o determination, R o 0.89 and 0.86 were obtained or SF60 and SF50, respectively. These showed that the proposed models are suitable to represent the test results o the residual strength at net delection o L/50. Figure-7. Relationship o residual strength between test results and proposed model or SF60 type o steel ibre. Figure-8. Relationship o residual strength between test results and proposed model or SF50 type o steel ibre. 5448

5 VOL., NO. 8, APRIL 06 ISSN Asian Research Publishing Network (ARPN). All rights reserved. The newly proposed models on the residual strength at net delection o L/50 were then applied to equation (3). The new equations on the prediction o the design value o the increase in shear strength due to the steel ibres are given in equation () and equation () or SF60 and SF50, respectively. clearly or both types o steel ibre. Through the Figure-9, it can be seen that all calculated values are closely mapped to the trendline. Thereore, the additional shear calculated rom the proposed equation is suitable or predicting the contribution rom steel ibres inside concrete..875 d V p p, SFRC () c V.47V p p, SFRC () In order to calculate the additional shear rom steel ibre, equation () and equation () are applied to equation. The calculated values are plotted in Figure-9, while the values are tabulated in Table-3. The additional shear supplement was plotted with respect to the ibre reinorcing index, RI. The ibre reinorcing index is the multiplication between ibre volume raction, V and ibre aspect ratio, L/D. The purpose o plotting the values using the ibre reinorcing index is to illustrate the overall view Figure-9. Relationship between additional shear rom steel ibres and ibre reinorcing index. Prism V (%) Table-3. Shear supplement values. SF60 SF50 p,sfrc τd vd p,sfrc τd vd

6 VOL., NO. 8, APRIL 06 ISSN Asian Research Publishing Network (ARPN). All rights reserved. CONCLUSIONS In this study, an analytical model was developed to propose an equation in predicting the shear stress supplement due to the existence o steel ibre in reinorced concrete. Rilem guideline has proposed an equation (as given in equation () to predict the shear supplement. However, there is a restriction on the model as its consideration is very general and applies to all types o steel ibre. In consideration o the current type o hookedend steel ibre, some modiications were made so that it can be applied to this speciic type o ibre. Besides, the modiication also considered a wide range o ibre reinorcing index, RI rom 67 and up to 80. This is believed to be able to represent the actual condition o shear supplement o hooked-end steel ibre when it is inside concrete. This gave many beneits as the hookedend type o steel ibre is the most used ibre in research and construction industry. The proposed equations were ound suitable to be used to predict the shear supplement due to steel ibres as it gives gave close estimation to the actual test results. REFERENCES Altun, F., Haktanir, T. and Ari, K Eects o Steel Fiber Addition on Mechanical Properties o Concrete and RC Beams. Journal o Construction and Building Materials, (3), pp American Concrete Institute ACI Building Code Requirements or Structural Concrete. United States: ACI Committee 544. American Concrete Institute. 99. ACI 363R-9-State o the Art Report on High Strength Concrete. United States: ACI Committee 544. British Standard Institute BS EN 99--:004- Eurocode: Design o Concrete Structures-Part -: General Rules and Rules or Building. United Kingdom: BSi. British Standard Institute BS EN A- 007-Test Method or Metallic Fibre Concrete-Measuring the Flexural Tensile Strength. United Kingdom: BSi. Carver, R. H. and Nash, J. G Doing Data Analysis with SPSS Version 6, Canada: Brooks/Cole-Cengage Learning. Gao, J., Suqa, W. and Morino, K Mechanical Properties o Steel Fiber-Reinorced High-Strength, Lightweight Concrete. Journal o Cement and Concrete Composites, 9, pp Hibbeler, R. C. 0. Mechanics o Materials. 8th. Ed. Singapore: Pearson Education South Asia Pte Ltd. Holschemacher, K., Mueller, T. and Ribakov, Y. 00. Eect o Steel Fibres on Mechanical Properties o High- Strength Concrete. Journal o Materials and Design, 3, pp Ibrahim, I. S., Che Bakar, M. B., Sarbini, N. N. and Mohamed, R. N. 0. Shear Capacity o Composite Slab Reinorced with Steel Fibre Concrete Topping. Malaysian Journal o Civil Engineering, 3(), pp. -3. Japan Concrete Institute JCI Standards or Test Methods o Fiber Reinorced Concrete. Japan: Japan Concrete Institute. Kevin Andrew Paine Steel Fibre Reinorced Concrete or Prestressed Hollow Core Slab. Doctor Philosophy, University o Nottingham, Nottingham. Pawade, P. Y., Pande, A. M. and Nagarnaik, P. B. 0. Eects o Steel Fibers on Modulus o Elasticity o Concrete. International Journal o Advance Engineering Sciences and Technologies, 7(), pp Pierre, P., Pleau, R. and Pigeon, M Mechanical Properties o Steel Microiber Reinorced Cement Pastes and Mortar. Journal o Materials in Civil Engineering,, pp Ramli, M. and Dawood, E. T. 00. Perormance o High Strength Flowing Concrete Containing Steel Fibre. Malaysian Construction Research Journal, 6, pp Rilem TC 6-TDF-Test and Design Methods or Steel Fibre Reinorced Concrete. 00. Design o Steel Fibre Reinorced Concrete Using the σ-ε Method: Principles and Applications. Journal o Materials and Structures (RILEM), 35, pp Sarbini, N. N. 04. Optimization on Steel Fibre Reinorced Concrete as Concrete Topping in Composite Slab Construction. Doctor Philosophy, Universiti Teknologi Malaysia, Malaysia. Song, P. and Hwang, S Mechanical Properties o High-Strength Steel Fiber-Reinorced Concrete. Journal o Construction and Building Materials, 8(9), pp Soulioti, D. V., Barkoula, N. M., Paipeties, A. and Matikas, T. E. 0. Eects o Fibre Geometry and Volume Fraction on the Flexural Behaviour o Steel-Fibre Reinorced Concrete. An International Journal or Experimental Mechanics, 47, pp. e535-e54. Teng, T. L., Chu, Y. A., Chang, F. A. and Chin, H. S Calculating the Elastic Moduli o Steel-Fiber Reinorced Concrete using a Dedicated Empirical Formula. Journal o Computational Materials Science, 3, pp Thomas, J. and Ramaswamy, A Mechanical Properties o Steel Fiber-Reinorced Concrete. Journal o Materials in Civil Engineering, 9(5), pp

7 VOL., NO. 8, APRIL 06 ISSN Asian Research Publishing Network (ARPN). All rights reserved. Xu, B. W. and Shi, H. S Correlations among Mechanical Properties o Steel Fiber Reinorced Concrete. Journal o Construction and Building Materials, 3(), pp Yazici, S., Inan, G. and Tabak, V Eect o Aspect Ratio and Volume Fraction o Steel Fiber on the Mechanical Properties o SFRC. Journal o Construction and Building Materials, (6), pp