Scholarly article on topic 'Ultra-high performance steel fibers concrete corbels: Experimental investigation'

Ultra-high performance steel fibers concrete corbels: Experimental investigation Academic research paper on "Civil engineering"

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Abstract of research paper on Civil engineering, author of scientific article — Maha M.S. Ridha, Nagham T.H. Al-Shafi’i, Milad M. Hasan

Abstract In the present paper, results of testing eleven ultra-high performance steel fibers concrete (UHPSFC) corbels with concrete compressive strength 150MPa and under vertical loading are reported. The main test variables were shear span-to depth ratio, main tension reinforcement ratio and the provision of secondary reinforcement (closed stirrups). In all corbels, except one, the main steel bars yielded before failure and corbels failed in a consistent manner. Whereas the validity from provision the secondary reinforcement in the UHPSFC corbels represents by a significant increase in the corbels stiffness with taking into consideration the corbels failure modes. The test results in terms of load versus deflection curves, stiffness, ductility and crack patterns show the effectiveness of using ultra high performance steel fibers concrete to ensure a superior strength and deformation capacity in reinforced concrete corbels. Experimental results have been compared with diverse prediction methods. The truss model can provide accurate strength predictions in comparison with the ACI 318-14 cod’s procedure.

Academic research paper on topic "Ultra-high performance steel fibers concrete corbels: Experimental investigation"

Accepted Manuscript

Title: Ultra-high performance steel fibers concrete corbels: experimental investigation

Authors: MahaM.S. Ridha, NaghamT.H. Al-Shafi'i, Milad M. Hasan

PII: DOI:

Reference:

S2214-5095(17)30052-9

http://dx.doi.org/doi:10.1016/j.cscm.2017.07.004 CSCM 107

To appear in:

Received date: 13-3-2017

Revised date: 23-6-2017

Accepted date: 12-7-2017

Please cite this article as: Ridha Maha MS, Al-Shafi'i Nagham TH,

Hasan Milad M.Ultra-high performance steel fibers concrete corbels:

experimental investigation. Case Studies in Construction Materials http://dx.doi.org/10.10167j.cscm.2017.07.004

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Ultra-high performance steel fibers concrete corbels: experimental investigation

Maha M. S. Ridha*, Nagham T. H. Al-Shafi'i**, & MiladM. Hasan***

*Building and Constructional Engineering Department, University of Technology, Baghdad, Iraq. Email: Dr.mahams@yahoo.com

**Civil Engineering Department, University of Al-Mustansiriyah, Baghdad, Iraq. Email: naghamtariq95@gmail.com *** Department of Civil Engineering, Wasit University, Wasit, Iraq. Email: mhasan@uowasit.edu.iq

Abstract: In the present paper, results of testing eleven ultra-high performance steel fibers concrete (UHPSFC) corbels with concrete compressive strength 150 MPa and under vertical loading are reported. The main test variables were shear span-to depth ratio, main tension reinforcement ratio and the provision of secondary reinforcement (closed stirrups). In all corbels, except one, the main steel bars yielded before failure and corbels failed in a consistent manner. Whereas the validity from provision the secondary reinforcement in the UHPSFC corbels represents by a significant increase in the corbels stiffness with taking into consideration the corbels failure modes. The test results in terms of load versus deflection curves, stiffness, ductility and crack patterns show the effectiveness of using ultra high performance steel fibers concrete to ensure a superior strength and deformation capacity in reinforced concrete corbels. Experimental results have been compared with diverse prediction methods. The truss model can provide accurate strength predictions in comparison with the ACI 318-14 cod's procedure.

Keywords: Corbels; Steel fibers; Vertical loads; Ultra-high performance concrete.

1. Introduction:

Corbels are structural members commonly used to transfer vertical and horizontal forces from beams to walls or columns in precast structures and reinforced concrete structures. A corbel is typically characterized by a shear span-to-depth ratio lower than unity and by a complex flow of

internal stresses. The previous studies in the literature addressed investigating the structural behavior of corbels experimentally and analytically and highlighting the parameters role that influence the performance of corbels such as strength of concrete, shear span-to-depth ratio, amount of main and secondary reinforcement bars, type and amount of fibers, and shape and dimensions of corbels (Campione 2005; Fattuhi 1990, 1994; Foster et al. 1996;).

Reinforced concrete corbels with a low percentage of longitudinal reinforcement bars typically fail by yielding of the main tension reinforcement bars with a ductile manner, while corbels with a high percentage of bars fail with a brittle manner by crushing of the concrete strut or shortly after yielding of the main tension reinforcement bars (Campione 2009; El-Maaddawy and Sherif 2014; Fattuhi 1994). Researchers found increasing the amount of the secondary reinforcement bars (closed stirrups) leads to increase the corbel strength capacity and makes the failure less calamitous, but also weakens the quality and strength of concrete because of the overcrowding of reinforcement, honeycombs, and/or voids. Where it was recorded a significant loss in load capacity shortly after reaching the peak load in case of increasing the amount of the secondary reinforcement bars. As a solution, using steel fibers instead of the conventional secondary reinforcement have been recommended by several researchers, where reinforcing corbels with steel fibers can improve the structural behavior of concrete corbels through increasing the corbel strength capacity, decreasing the cracks width and enhancing the failure mode to be in a gradual and controlled manner (Campione 2005, 2007; Fattuhi and Hughes 1989; Fattuhi 1994).

In recent years, ultra-high performance steel fibers concrete (UHPSFC) has provided an attractive use of composite materials in several structural applications such as, bridges, high rise structures, nuclear power plants.. .etc. The exceptional properties of UHPSFC are achieved due to low water to cement ratio, eliminating the coarse aggregate and presence of micro steel fibers which results to higher concrete compressive strength up to five times that of ordinary concrete, higher concrete tensile strength up to ten times that of ordinary concrete as well as greater ductility and durability than ordinary concrete (Graybeal 2008). Based on the fact that corbel behavior is predominantly controlled by shear, it is very interesting to use UHPSFC in the corbel manufacturing.

Previous research papers on corbels have addressed the behavior of high strength concrete corbels with or without the presence of steel fiber up to 132 MPa concrete compressive strength (Bourget et al. 2001; Campione et al. 2007; Foster et al. 1996; Yang et al. 2012; Yong 1994). No research

data has been published in regards to the behavior of ultra-high performance steel fibers concrete corbels. To this end, the present research aims to investigate the structural response of ultra-high performance steel fiber concrete corbels. The experimental results are compared with the predictable results of using various models that proposed by Fattuhi (1994), Foster et al. (1996), Russo et al. (2006), and the ACI 318-14 code recommendations.

2. Experimental investigation:

2.1. Test specimens

In this study, a total of eleven UHPSFC corbels specimens, except one corbel without reinforcement bars, were tested in order to investigate the structural behavior characteristics, the ultimate load and the crack patterns, ductility and failure modes of UHPC corbels. The considered variables were main reinforcement ratio, shear span-to-depth ratio (a/h), and the provision of secondary reinforcement as shown in Table 1.

The column with cross section dimensions of 150mm by 150 mm and length of 450 mm supporting two trapezoidal corbels cantilevering on each sides with a cantilever projection length of 250mm, with thickness of 250 and 125 mm at the face of the column and at the free end, respectively. All UHSFPC corbels are similar in the size and in the testing method by using a three point flexural loading, as shown in Fig. 1.

The longitudinal steel bars used in the UHPSFC corbels are of different diameters of 6, 8, 12 and16 mm. The main tension reinforcement bars for UHPSFC corbels consisted of two deformed steel bars of N8, N12 or N16 welded to transverse bars according to the anchorage provision of the ACI-14 code. One additional of N8 hoop at a space 70 mm (closed stirrups), were placed over a depth less than 2/3 of the height of five corbels according to the crack-control requirements of ACI 318-14 (Clause 11.8.4). The shear reinforcement consisted of 6 mm diameter plain bars ties spaced at 100 mm on center for each corbel's column. The clear concrete cover was 40 mm.

The specimens were labelled as CXGY, for the UHPSFC corbel, where X represents the number of corbel and Y represents the number of group that the corbel belong to.

2.2. Material properties:

UHPSFC with 150 MPa compressive strength at 28 days of age was used in this research. The mix design involved the following materials:

1000 kg/m3 of Tasloja ordinary portland cement (ASTM Type I), 500 kg/m3 of fine silica sand which is produced in Al-Ramadi Glass factory (average size 50 p,m), 500 kg/m3 of fine silica sand which is produced in Al-Ramadi Glass factory (average size 400 p,m)250 kg/m3 of densified silica fume with a specific surface of (21 m2/g), 164 kg/m3 micro steel fibers (13mm length and 0.2mm diameter) with a volume fraction (Vf) of 2.3 %, 25kg/m3 high-range water-reducing admixture Sika Viscocrete PC20, and 0.2 water to cement ratio (w/c) were used in this research.

The dry constituents of the UHPSFC were batched by an electronic balance and mixed in a horizontal pan concrete mixer for about 5 minutes. Superplasticizer and water mixed together and added to the dry materials. The mixing process had to continue for 15 minutes. Then steel fibers were distributed uniformly for 2 minutes. Finally, continue the mixing process for an additional 5 minutes, as shown in Fig. 2-a. The flow of UHPSFC was 220 mm in environment with 15 degree. The corbels were cast horizontally with two corbel specimens cast for each batch. To prevent fiber segregation, the UHPSFC was compacted using a vibrating table. After casting process, all of the UHPSFC corbels and control specimens were covered with a plastic sheet for 24 hours. All specimens were then cured in the water bath under a certain temperature (20o) until age of 28 days.

By using cylinders with dimensions of 100-mm by 200-mm, the standard compressive tests and split tests were carried out to determine the values of the UHPSFC compressive strength, f'c, the corresponding peak strain, e'c as shown in Fig. 2-c , and the splitting tensile strength, fp. The flexural strength, fr, of 100*100*400 mm UHPSFC prisms tested under four-points loading was obtained as well. Table 2 provides the results of ancillary testing for constituent material properties that used in the construction of the UHPSFC corbels. Fig.2 shows side of the experimental work procedures and the ancillary testing.

2.3. Test set- up and instrumentation:

All the corbels specimens were tested by using a 5000 kN-capacity Avery testing machine. Vertical loading was applied to the UHPSFC corbels through steel roller supports centered at 100, 150 or 200mm from the face of the column. Loading was applied at a constant rate of 0.5 mm/min.

For all the specimens, two strain gauges with a gauge length of 6 mm were placed on the main tension reinforcement bars in the middle near column-corbel junction. A mechanical dial gage was used to measure the deflection in the center of corbels' columns, as shown in Fig.1. The readings were recorded for each load increment until the failure occurred. A high definition portable microscope (X 40 magnification crack detection) was used to determine the first crack load and the crack pattern for each corbel.

A variety of additional tests were carried out on the constituent materials of corbels as shown in Table 2, including: (a) compression tests, split tensile tests, and flexural tensile tests on UHSFPC, (b) tensile tests on steel bars, and (c) Steel fibers properties.

3. Experimental results

In this section, cracking and failure modes, strain in main tension reinforcement bars, and load-deflection behavior for UHPSFC corbels are presented and discussed. Variables considered in this investigation are shear ^pan-to-depth ratio (a/h), the percentage of main tension reinforcement ratio, and the provision of secondary reinforcement. Table (1) lists tests results, modes of failure, stiffness and ductility for the UHPSFC corbels.

3.1. Cracking and failure modes:

Fig. 3 shows the crack patterns at the peak load for the UHPSFC corbels. In this research, a portable microscope was used to determine the load at first cracking for each UHPSFC corbel. In generally, flexural cracks appeared firstly in all UHPSFC corbels at or vicinity the junction of the face of the column and the tension face of the corbel. Then propagated and became clearer and deeper with the subsequent stages of loading. Cracks observed from the cracks patterns for UHPSFC corbels of this research were finer and less numerous in comparison with the cracks patterns of high strength steel fibers corbels available in the literature (Campione et al. 2007; Yang et al. 2012), which leads to improvement in the aspects of durability, service life and sustainability for corbels based on the authors view. Although all the tested specimens contained steel fibers with 2.3 % volume of fraction (Vf), specimens containing secondary steel reinforcement predominantly contained finer and more irregular cracks. Table 1 shows that in groups G1 and G2, the loads of first cracking featured to decrease with an increase in shear span-to-depth ratio and the modes of

failure were shear and become inclined shear in corbels C3G1 and C6G2, where shear span-to-depth ratio is 0.8. For UHPSFC corbels reinforced with main tension reinforcement only in group G3 or with secondary steel bars as well in group G4, the loads of first cracking appeared to increase with an increase in the main tension reinforcement ratio and the mode of failure were flexural-tension failure in C7G3, as shown in Fig. 3-b, and flexural-shear failure in C9G4 with main tension reinforcement ratio 0.33% and shear failure in others corbels of groups G3 and G4. As expected, the most ductile failures observed in this research were tension failures. In addition, C11G3 which was reinforced with only steel fibers and without main or secondary rebar failed with shear failure and maximum load capacity was approximately three times higher than the specimen cracking load.

3.2. Strain in main reinforcement:

Fig.4 shows the load versus the average of the measured strains for the two strain -gages located on the main tension reinforcement bar on either side of the cantilever beam for each specimen. The following observations can be made relating to the main tension reinforcement strain variation. The curves have four stages similar to those reported by some researchers in literature (Foster et al. 1996, 1996; Khadraoui 1998). The first stage is the steepest and ends when the first crack occurs. The second stage is not linear because of starting the development of the cracks at or near the corbel-column junction. The third stage is linear but with some discontinuities due to the cracking development. The fourth stage starts when the stress in the main tension reinforcement bars reaches the yield strength of the steel. For all the tested corbels in this research, except specimen C11G3 where it was produced without containing on main or secondary reinforcement bar, the main reinforcement yielded before reaching the maximum load capacity in spite of the fact that all of those corbels contained steel fibers with volume fraction (Vf =2.3%) that is supposed to cause reduction in the main reinforcement strains. For instance, the evolutions of the main reinforcement strain versus the load show that for specimen C7G3 the main reinforcement yielding was speedily reached and the failure occurred after the main reinforcement was cut off, as shown in Fig. 3, where the specimen failed with flexural tension mode.

Generally, in all tested specimens the main tension reinforcement ratios were much lower than or close to the ACI 318-14 limitations, where a minimum amount of reinforcement required for the

concrete corbel design is ps-min. = 0.04 (fc' /fy) as in (Clause 11.8.5). The main tension reinforcement ratios used in this research were 0.74% for specimens C1G1-C6G2, 0.33% for specimens C7G3 and C9G4, and 1.32% for specimens C8G3 and C10G4, which should be according to the ACI 318-14 requirements not less than 1.43%, 1.98% and 1.19%, respectively. The authors view that for the purposes of design, the ACI 318-14 reinforcement requirements is not recommended to use with UHPSFC corbels and more research should be achieved in order to establish the limits for the main tension reinforcement ratio, to prevent the possibility of sudden failure of the corbel under the action of flexural moment, and for the secondary reinforcement ratio to prevent a premature diagonal tension failure or diagonal splitting failure of the corbel.

3.3. Load-deflection behavior:

Flexural tests on UHPSFC corbels are presented and discussed though load (P) versus deflection (A) curves in Fig.5 and through stiffness, ductility, and loads with correspondent center deflection at first cracking (Acr), first yielding (Ay), and the peak loads (Au), in Table 1. As expected, corbels of group G1 and group G2 show higher peak load, Pu, stiffness and ductility as the shear span- to-depth ratio decreasing from 0.8 to 0.6 and 0.4. Specimens C1G1 and C4G2 with shear span- to-depth ratio 0.4 reached the maximum load capacities at 1626 kN and 1658.5 kN, respectively, which represent 78% and 75% increasing higher than the maximum load capacities of specimens C3G1 and C6G2 with shear span- to-depth ratio 0.8, respectively. In addition, the deflection ductility, which is taken as the ratio of the deflection at the peak load to deflection at first yielding of the main reinforcement, increased significantly in specimens C1G1 and C4G2 by 57% and 48% higher than the ductility of specimens C3G1 and C6G2, respectively. The stiffness of specimens C1G1 and C4G2, which is taken as the slope of the straight line at the first stages of loading until the point of first yielding of the main tension reinforcement, increased just slightly by 14.5% and 13.3% higher than the stiffness of specimens C3G1 and C6G2, respectively.

Both group G3 corbels and group G4 corbels show higher peak load and stiffness as the main tension reinforcement ratio increasing from 0.33% to 0.74% and 1.32%. Specimens C8G3 and C10G4 with main tension reinforcement ratio 1.32% reached the maximum load capacities at 1403.3 kN and 1454.9 kN, respectively, which represent 38.6% and 39.3% increasing higher than the maximum load capacities of specimens C7G3 and C9G4 with main tension reinforcement ratio

0.33%, respectively. In addition, the stiffness of specimens C8G3 and C10G4 increased by 29.6% and 70.7% higher than the stiffness of specimens C7G3, and C9G4, respectively. In the other side, the ductility decreased significantly in specimens C8G3 and C10G4 by 71.8% and 28.2% lower than the ductility of specimens C7G3 and C9G4, respectively, because the failure modes changed from ductile flexural tension failure in specimen C7G3 and ductile flexural-shear failure in specimen C9G4 to the brittle shear failure in specimens C8G3 and C9G4. However the main tension reinforcement ratio in specimen C7G3 does not meet the ACI-14 Code requirement for the minimum reinforcement, the maximum load capacity and stiffness of specimen C7G3 was higher than specimen C11G3 by 29.9% and 40%, respectively

Table 1 also shows the provision of secondary reinforcement in the G2 corbels and G4 corbels led to increase the maximum load capacity very slightly by average 3.7% and 4.1% higher than G1 corbels and G3 corbels, respectively. While the provision of secondary reinforcement led to increase the stiffness of specimens G2 and G4 significantly by average 36.9% and 34.1% more than specimens G1 and G3. In all tested corbels, the provision of secondary reinforcement did not affect significantly the ductility of similar corbel that manufactured with just main tension reinforcement except in specimen C9G4, where the ductility decreased by 25.9% lower than specimen C7G3 because the failure mode changed from the flexural tension failure in specimen C7G4, which is highly ductile failure, to the flexural-shear failure in specimen C9G3.

4.Existing analytical models:

For comparison purpose, the following shear strength formulas are used in this research. 4.1. Fattuhi model:

The truss model presented by Fattuhi (Foster 1994) to use for steel fiber concrete corbels will be applied in the present investigation to predict the ultimate shear capacity of UHPSFC corbels. The model can be written with three equations:

lsinC = Asfys+fyiAsi+k°fctbh m

P 0.85f'b+kofct b .......( )

where fyS is the yield strength of the main tension reinforcement, As is the area of the main tension reinforcement, fyi is the yield strength of the secondary reinforcement, Asi is the area of the

secondary reinforcement, fct is the split tensile strength of concrete, and ko represents the contribution of fibrous concrete in tension. ko=1 and $=1 are assumed in this research.

0.425 ft b(l sinfix)2 cot2 fi + 0.85 ft a b (I sin fi) cotfi - fyAs [d - - fyiAsi [dt -

V^-0.5 k0fct bh [h-(lsinfi)] = 0 .......(2)

By using the corbel's properties, the value of (l sin^P) can be calculated from equation (3). Then from equation (4) cot P can be obtained. The shear capacity can be obtained as:

_ fyAs^-^^YfyiAs^d-^^Yo.5 kpfct bh [h-(l sin P)]

4.2. Foster model:

a+0.5 (l sin P) cotfi

The plastic truss model presented by Foster (Foster et al. 1996) in conjunction with the efficiency factor proposed by Warwick and Foster (1993) to use for high strength concrete corbels up to 105 MPa, will be applied in the present investigation to predict the ultimate shear capacity of UHPSFC corbels. The model can be written with the following equations:

(f —

Ps Tsy a <min.(0 2 f'c ) ft w/d V 5 5 J

H = d — ^d2 — 2aw + w2

where w is the bearing plate width, ft is the effective strength of the concrete compression strut, and Q is the effective anchorage depth. • For corbels with a/d < 2.0:

. i[1.25—^ — 0.72- + 0.18(-)2]ft

ft = min.y 500 d ydJ iJC

0.85 ft;

• For corbels with a/d > 2.0:

ft; = [°-53—éà'ft;

4.3. Russo model:

Russo et al. (2006) proposed a formula to determine the shear strength for reinforced concrete corbels (10 <f'c <105MPa), based on composing the shear strength contribution of the strut-and-

tie mechanism due to the cracked concrete and main tension reinforcement, and the strength contribution due to secondary reinforcement (stirrups). The model can be given with the equations below:

Vu =0.8(k x f'c cos9 + 0.65phfyh cotQ)......(8)

X=0.74({^)3 — 1.28({^)2 + 0.22({^) + 0.87 .......(9)

k= J(npf)2 + 2npf — npf ........(10)

0 = 2arctan

yydJ y 4

a k d 2

n = 4j6 .......(12)

Pfmin. =~s......(13)

where, 0 is the angle between the compressed concrete strut and the vertical direction, ph = Ah/bd is the second reinforcement ratio at the column-corbel interface, fyh is the secondary reinforcement yielding strength, n is the ratio of the elastic moduli of steel and concrete, and pf is the flexural reinforcement ratio. 4.4. ACI Code 318-14 model:

For UHPSFC corbels tested in the present investigation, the analytical expressions for the shear strength prediction of normal and high strength concrete corbels recommended by ACI 318-14 will be applied for comparison purpose.

• For corbels with a/d < 1.0, the shear capacity according to ACI 318-14 code can be written as: Pvf fy M

Vu=mm. -

Ps fys jd/a[l + a (h — d)]

< min. 2 ......(14)

where pf = (pf + ph) is the frictional reinforcement ratio, fy is the yield strength of the friction reinforcement, p, is the coefficient of friction (taken as 1.4 for monolithic construction), f'c is the concrete compressive strength, p^ is the main tension reinforcement ratio, a is the horizontal-to-vertical loads ratio, and jd is the lever arm, given by formula:

jd = d- 0.5(Afys - N„)/(0.85/c b)......(15)

• For corbels with 1.0 < a/d < 2.0, the shear capacity according to Appendix A of ACI 318-14 is calculated using the strut-and-tie modeling procedure. 4.5. Comparison of Experimental and Analytical Results

Existing research, so far, does not contain any UHPSFC corbels, that can be applied to this work. Therefore, in Table 3, Fig 6 and Fig 7, the experimental results are compared with predictions made on the basis of different models proposed by Fattuhi (1994), Foster et al. (1996), Russo et al. (2006), and the ACI 318-14 code recommendations.

The predictions of ultimate shear capacity for UHPSFC corbels by using the truss method proposed by Fattuhi (1994) give best convergence with the experimental results (the coefficient of variation is 0.037) in comparison with the other models in Table 3. In this model Fattuhi modified the earlier work of Hagberg (1983) by considering in the analysis the influence of the steel fibers on the concrete strength in tension through using the indirect tensile splitting strength of concrete. The truss model also takes into account the presence of main and secondary reinforcement. Ideally, the truss model can be used to estimate the ultimate shear capacity of corbels for all failure modes. However, it has been recommended by Hagberg (1983) to use the truss model for predicting the strength of corbels that fail in flexure only for more accurate results, where based on the view of Hagberg, the truss model underestimates the predicted strengths of corbels failing in other modes. In this research and as shown in Figs 6 and 7, using the modified truss model of Fattuhi shows satisfactory predictions for all UHPSFC corbels despite that the failure modes were various in those specimens as shown in Table 2.

Plastic truss method to predict the ultimate strength of corbels with using a concrete efficiency factor model proposed previously by Warwick and Foster (1993) was examined by using 30 high strength concrete corbels of Foster et al. (1996), where the corbels compressive strengths were from 45 MPa to 105 MPa without the presence of steel fibers. The concrete efficiency factor model involves the influence of shear span-to-effective depth ratio (a/d) and concrete compressive strength. However, Table 3 shows that using this method to determine the ultimate shear capacity of UHPSFC corbels gives a reasonably low coefficient of variation of 0.12, modification on this model can be achieved in the future taking into consideration the effect of the intensive presence

of steel fibers in concrete to get a more reliable model for predicting the ultimate strength of UHPSFC corbels.

Russo et al. (2006) proposed a formula to determine the shear strength for reinforced concrete corbels based on composing the shear strength contribution of the strut-and-tie mechanism due to the cracked concrete and main tension reinforcement, and the strength contribution due to secondary reinforcement (stirrups). Table 3 shows that the predictions of this model can be described as conservative with a coefficient of variation 0.27 for UHPSFC corbels. The reason might be that the contribution of steel fibers in resisting tensile forces is neglected in this model and the concrete compressive strength is limited by: 20 < fc < 100 MPa.

Recommendations of the ACI 318-14 for corbels design with a/d < 1.0, based on the shear friction theory, are used and compared with the experimental results of this research as shown in Table 3, Fig 6 and Fig.7. The contribution of steel fibers in resisting tensile forces is neglected in the shear strength formulas of ACI 318-14 code, therefore, the results are very conservative in comparison with the other presented models.

5. Conclusions:

In this investigation, eleven UHPSFC corbels were prepared and tested under only vertical loading. The main test variables were shear span-to depth ratio, the main tension reinforcement ratio and the provision of secondary reinforcement.

The following conclusions can be deduced based on the test results:

1. The first cracks are flexural cracks appeared at or vicinity the corbel-column intersection, and the first cracking load increases either with decreasing the shear span-to-depth ratio or with increasing the main tension reinforcement ratio.

2. Providing secondary reinforcement reduces crack widths, improves corbel stiffness, and enhances ductility slightly.

3. For the purposes of design, the ACI 318-14 reinforcement requirements is not recommended to use with UHPSFC corbels and more research should achieve in order to establish new limits for the main and secondary reinforcement ratios taking into account the massive presence of steel fibers in the UHPSFC.

4. The analytical expressions recommended by ACI 318-14 gives very conservative predictions for the shear capacity of UHPSFC corbels.

5. The truss model proposed by Fattuhi provides good tool for designing UHPSFC corbels for all columns failure modes. While the plastic truss model in conjunction with the efficiency factor proposed by Warwick and Foster needs more modification taking into consideration the effect of the presence of steel fibers in concrete.

The authors declare that they have no conflict of interest. A cknowledgements:

The authors would like to thank, and acknowledge the University of Technology (www.uotechnology.edu.iq) and AL-Mustansiriyah University (www.uomustansiriyah.edu.iq) for supporting the present work through conducting all the experimental works at their concrete and structural laboratories. The authors are grateful to Dr. Maan S Hassan for his support and the technical assistance of staff from the Building and Constructional Engineering Department at the University of Technology and from the Civil Engineering Department at AL-Mustansiriyah University. The views and findings presented here are those of the writers alone and not necessarily those of the University of Technology or AL-Mustansiriyah University.

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Warwick, W. B., and Foster, S. J., (1993). "Investigation into the efficiency factor used in non flexural reinforced concrete members design." UNICIV Rep. No. R-320, School of Civil Engineering, Univ. of New South Wales, Kensington, Sydney, Australia.

Fig.1: Load scheme of corbels and specimens geometry and steel arrangements.

Fig.2: (a) Side of the experimental work procedures, (b) The ancillary testing, and (c) UHPSFC stress-strain curve.

Fig.3 Failure pattern: (a) crack patterns at the peak load for the UHPSFC corbels (b) flexural-tension failure of specimen C7G3.

Fig. 4: Load- tensile strain curves for main steel bars: (a) effect of a/h ratios; (b) effect of main tension reinforcement ratios.

Fig. 5: Load - deflection curves: (a) for UHPSFC corbels without secondary steel (2*8); (b) for UHPSFC corbels with secondary steel (2*8).

Fig. 6: comparison between experimental data and calculated.

100 200 300 400 500

Fig. 7: Comparison of various equations with experimental data.

200 300 400 soo

too eoo soc

Table 1: Details and results of the corbel tests.

Corbels a/h Main bars, Secondary Pcr Py Pu Acr Ay Au Stiffness Ductility Failure

label mm, (%) bars, mm kN kN kN mm mm mm kN/mm ( Au/ Ay) modes

C1G1 0.4 2$12, (0.74) --- 620 850 1626 1.3 1.72 3.4 477 1.98 Shear

C2G1,3 0.6 2$12, (0.74) --- 450 650 1223.2 0.95 1.4 2.3 473.7 1.64 Shear

C3G1 0.8 2$12, (0.74) --- 250 525 912.9 0.6 1.7 2.3 416.7 1.26 Inclined

C4G2 0.4 2$12, (0.74) 2$8, 650 1050 1658.5 1 1.9 3.8 650 2 Shear

C5G2,4 0.6 2$12, (0.74) 2$8, 550 900 1290 0.88 1.85 3.1 625 1.7 Shear

C6G2 0.8 2$12, (0.74) 2$8, 350 720 946.65 0.61 2 2.7 573.8 1.35 Inclined

C7G3 0.6 2$8, (0.33) --- 300 450 1012.6 0.7 1.3 3.8 428.6 2.92 Flexure

C8G3 0.6 2$16, (1.32) --- 500 1025 1403.3 0.9 2 3.4 555.6 1.7 Shear

C9G4 0.6 2$8, (0.33) 2$8, 500 700 1044.3 1 1.7 3.9 500 2.32 Flexure-

C10G4 0.6 2$16, (1.32) 2$8, 700 1200 1454.9 0.82 2.1 3.8 853.7 1.81 Shear

C11G3 0.6 --- --- 150 525 0.49 - 1.9 306.1 - Shear

Table 2: Results of ancillary testing for constituent material properties.

Material Property Average #of tests

a) UHPSFC 28-day compressive strength (MPa) 150 3

Peak strain (%) 0.45 2

Split tensile strength (MPa) 15 3

Flexural tensile strength (MPa) 18.3 3

b) Rebar Yield strength (MPa)of $8, $12 and $16, Ultimate strength (MPa)of $8, $12 and $16 Elastic modulus (GPa) 302 , 419 and 502 422, 590 and 642 200 3

c) Steel Fibers* Tensile strength (MPa) Density (kg/m3) Aspect ratio, Lf/Df 2600 7800 13/0.2=65

*The results were provided by the manufacturer.

Table (3): Comparison of corbels test results and predicted results

Specimens Vtest (kN) Fattuhi (kN) Fostar et al. (kN) Russo et al. (kN) ACI 318-14 (kN)

C1G1 813 789.3 (1.03) 718.9 (1.1) 338.2 (2.40) 215.1 (3.78)

C2G1,3 611.6 556.1 (1.1) 580.8 (1.105) 460.9 (1.33) 143.4 (4.27)

C3G1 456.45 426.6 (1.07) 467.3 (0.98) 390.9 (1.17) 107.5 (4.24)

C4G2 829.25 813.3 (1.02) 718.9 (1.15) 338.2 (2.45) 215.1 (3.86)

C5G2,4 645 575.9 (1.12) 580.8 (1.11) 460.9 (1.40) 143.4 (4.5)

C6G2 473.3 442.4 (1.07) 467.3 (1.01) 390.9 (1.21) 107.5 (4.4)

C7G3 506.3 501.3 (1.01) 580.8 (0.87) 264.7 (1.91) 42.1 (12.01)

C8G3 701.65 694.7 (1.01) 580.8 (1.21) 397.1 (1.77) 300.2 (2.34)

C9G4 522.15 492.6 (1.06) 580.8 (0.9) 264.7 (1.97) 46.4 (11.26)

C10G4 727.45 713.2 (1.02) 580.8 (1.25) 397.1 (1.83) 300.2 (2.42)

Mean (105) (107) (174) (5.31)

Standard (0.039) (0.13) (0.46) (3.43)

Coefficient (0.037) (0.12) (0.27) (0.645)

Note: Vtest/Vpred is given in parentheses.