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Tension Lap Splice Length of Reinforcing Bars Embedded in Reactive Powder Concrete (RPC)
Structures 19 (2019) 362–368
Contents lists available at ScienceDirect
Structures journal homepage: www.elsevier.com/locate/structures
Tension Lap Splice Length of Reinforcing Bars Embedded in Reactive Powder Concrete (RPC)
T
Hussein Al-Quraishia, Mahdi Al-Farttoosib, , Raad AbdulKhudhura ⁎
a b
Civil Engineering Department, University of Technology, Baghdad, Iraq Faculty of Engineering, Civil Engineering Department, University of Baghdad, Baghdad, Iraq
ARTICLE INFO
ABSTRACT
Keywords: RPC Beam Tension splice bars
Reactive Powder Concrete (RPC) is an emerging cementations construction material which has superior mechanical properties such as high compressive and tensile strength, high density and homogeneous. In this research, the tension splice behaviour of reinforcement bars embedded in RPC was investigated using experimental and numerical studies. Six reinforced RPC beams with four-point loading were tested. The parameters investigated in the experimental program were steel fibre contents, size of reinforcing bar, tension reinforcement splice length, and amount of transverse reinforcement. The experimental findings showed that the increasing of steel fibre content, amount of transverse reinforcement, length of spliced bars, and diameter of spliced bars increased the tension splice strength of steel bras embedded in RPC members. Splitting of concrete is the dominate mode of failure that occurred in RPC beams spliced with tension reinforcement. Finite element method was used in this study to simulate the behaviour of members tested experimentally and a comparison between experimental and numerical results was conducted. The comparisons showed a good agreement between experimental results and numerical results in terms of load deflection curves and splice strengths. The verified finite element model was used then to study the effect of wide range of data for variables affect the splice strength using a parametric study. A proposed design equation of splice strength of tension reinforcing bars embedded in RPC was proposed in this study and verified with numerical results.
1. Introduction RPC is the new advanced concrete material that has excellent mechanical properties compared with the normal concrete. RPC is considered as cementitious material that mainly characterized by them outstanding high tensile properties which improve the bond between the reinforcing bars and concrete. It is difficult to use continuous reinforcing bars in construction long concrete element due to transportation limitations and handling. Splicing short reinforcing bars is one of the common practice methods that can be used to fabricate concrete members. The bond between the splice bars and the surrounding concrete affected the probability of bar slippage which may results in failure of concrete members. The variables that affect the bond of spliced bars are: concrete mechanical properties, rebar rib area, spliced length, diameter of rebar and concrete cover within the spliced zone [2]. Tension lap splice is defined as the peak tension force that can be transferred between the spliced bars through the bond action. Splice length represents the embedment length necessary to develop the full
⁎
tensile strength of those discontinuous bars, controlled by either pullout or splitting. The beam specimen, beam anchorage, and pull-out specimen are the specimen configuration used to represent the tension lap splice. Among these three specimens, beam specimens represents more realistic response of splice strength under flexural stresses and this method of testing was adopted in this study. Orangun et al. [3] tested 116 concrete specimens to investigate the bond strength of reinforcing bars embedded in normal strength concrete. Furthermore, design equation for the maximum steel bar stress was presented:
Abf s/ f c = 0.25 l d (c min + 0.4 db) + 16. 6Ab + l dAtr fy t/41.5 s·n
(1)
Yuan and Graybeal [4] studied the effect of fibre content on the tension lap strength in RPC beams. Various spliced lengths and RPC mixes were tested. They demonstrated that the bond strength is depends on the matrix and post-cracking tensile strength of RPC. Lagier et al. [5] tested 4-point-bending RPC slabs with tension lap splices. Within these tests the lateral reinforcement and splice length in the
Corresponding author. E-mail address: [email protected] (M. Al-Farttoosi).
https://doi.org/10.1016/j.istruc.2018.12.011 Received 25 September 2018; Received in revised form 14 December 2018; Accepted 19 December 2018 Available online 17 January 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
Structures 19 (2019) 362–368
H. Al-Quraishi, et al.
Nomenclature Ab Atr C cmin
yield stress of rebar stress in steel bar compressive strength of concrete development length of steel bar spacing of stirrups number of stirrups
fy fs fc ld S n
area of steel bar transverse reinforcement index constant of statistical analysis minimum concrete cover
splice zone were varied. The test results showed that the length of the lap splice and the presence of any lateral reinforcement affect the failure mechanism, the crack width and crack development in the splice zone. Lagier et al. [6] used direct tension specimens to investigate the effect of fibre concrete in RPC on the bond strength. Three amount of amount steel fibre were used. The experimental findings showed that the bond performance improved and splitting failure was controlled. Furthermore, the bond strength is strongly related maximum tensile strength and strain ductility in RPC. These conducted experimental and numerical investigations provide an increase in our understanding of the bond characteristics of tension lap splice reinforcing bars. The knowledge gained from this study is significant to develop a robust design equation to tension lap splice length of reinforcing embedded in RPC which can be used simply in practice.
5. Experimental program
2. Objective of this study
6. Test setup and instrumentation
A total of six RPC beams were constructed and tested in the laboratories of Civil Engineering Department-University of TechnologyIraq. To provide area of constant moment at the location of spliced bars, all beams were tested under four point loading. The influence of transverse reinforcement ratio in the lap splice zone was studied using two beams (TS1-Ref and TS2-trans). The concrete cover was investigated by testing beams (TS1-Ref and TS3-cover). Beams (TS1-Ref and TS4-dia) were used to study the effect of size of spliced bars. The effect of steel fibre content was investigated by comparing the results of beams (TS1-Ref and TS5-fiber), and finally the length of spliced bars was studied using beams (TS1-Ref and TS6-Splice). The characteristics of the tested beams are summarized in Table 2.
The deflection at the mid-span of the beams was measured using LVTD mounted at the top of the specimens. Two electrical resistance strain gauges were used to measure the strains in splice bars in order to estimate the tension strength in the middle of spliced bars. The hydraulic machine of 2500 kN capacity was used to test specimens. The load-control at a rate of 10 kN/min was used to test the specimen till failure. At each of load stage, the cracks propagation was drawn. Fig. 3 shows the beam specimen under testing using the heavy test machine.
The main goals of this study are investigation the following:
• The tension lap splice strength and modes of failure of reinforcing • •
bars embedded in RPC member through an experimental and numerical programs. The effect of a number of variables on tension splice strength in RPC members such, steel fibre content, amount of transverse reinforcement, length of spliced bars, and diameter of spliced bars. Proposing a design equation to predict the tension splice strength in RPC members.
7. Test results 7.1. The variables effect on the tension lap-splice strength
3. Materials
Table 3 shows the comparisons of the results of reference beam (TS1-Ref) with that of beams (TS2-trans, TS3-cover, TS4-dia, TS5-fiber, TS6-length). It can be notes from the table of comparisons the following:
The compositions of the RPC are: Portland cement – type I; quartz sand with specific gravity of 2.57; silica fume with the bulk density of 650 kg/m3; high range water reducing admixture (Sika Viscocrete 2810) with the relative density of 1.07 as shown in Table 1. The steel fibres have a length of 15 mm, diameter of 0.2 mm, aspect ratio of 70 and ultimate tensile strength of 2000 MPa that were used to fabricate the specimens. The spliced reinforcing bars used to reinforce RCP samples were 12 mm in diameter. The bars have an elastic modulus of elasticity of 200 GPa, yield strength of 420 MPa, and ultimate tensile strength of 620 MPa.
• Increase the amount of transverse reinforcement in the lap splice •
4. Tested specimens
•
The experimental program included testing six RC beams with splice tensile reinforcement at mid-span. The beam specimens were 1500 mm long and had a rectangular cross section of 130 mm wide and 180 mm depth. The tested beams were simply supported and loaded with two equal point loads at the middle-third of the span, see Fig. 1. Two 12 mm diameter longitudinal bars were used in tension face and spliced in the mid-span of the beam. In compression region of the beam, two 12 mm bar diameter were placed. Fig. 2 shows the specimens after casting. The splice lengths for the reference beams were designed according to the provisions of ACI 318-14 [7] of NSC to get the yielding stress in reinforcing bars. The beams in region out of splice zone were reinforced with 10 mm diameter stirrups spaced at 100 mm to prevent shear failure. End anchorage hooked 90° was used at the ends of longitudinal bars.
region from 2-ϕ10 to 5-ϕ10, increases the tension lap-splice strength by 9.5%. This is due to major confinement role of transverse reinforcement along the splice length. Increase the concrete cover in the region of lap splice from 20 mm to 40 mm results in an increase in tension lap-splice strength by 8%. The radial tensile stresses induced by bar ribs balanced by the concrete cover and consequently the tension splice strength was increased. The tension splice strength increased by 9% when the diameter of
Table 1 Mix proportion of RPC.
363
Compositions
Weight (kg/m3)
Water Cement Fine aggregate Silica fume HRWRA Steel fibre (0.25/20)
231 1100 858 253 49.5 0.28 for 0.75% fibre content 0.56 for 1.5% fibre content
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H. Al-Quraishi, et al.
Fig. 1. Geometry of tested beam.
Fig. 3. Test machine.
bars and concrete compression stress after cracking of beam in tension zone. Third; after yielding, the deflection increased rapidly until failure of beams by concrete crushing in compression zone after longitudinal splitting in splice zone. The TS5-fib specimen shows high elastic and ductile behaviour before failure due to the effect of steel fibre which restricted the opening of flexural cracking and increased the tensile strength of concrete. All beams in this investigation showed flexural mode of failure. They failed by splitting occurred along the tension longitudinal bar. The longitudinal cracks initiated at the free ends of spliced bars (stresses concentrated points), then extended along the longitudinal reinforcing bars. Fig. 2. Tested specimen after casting.
• •
8. Finite elements analysis A finite element method FEM was used to simulate the behaviour of beams tested experimentally. LUSAS [8] software package was used to conduct the numerical modelling and analyses.
lap splice bars were increased from 12 to 16 mm. This is due to increasing in surface area between steel bars and concrete when big bar size is used and that increase the bonding between them. Increase the steel fibre content in tested specimens from 0.75% to 1.5% increases the tension splice strength by 2.2%. This, due to, the presence of steel fibres improve the bond strength and delays the formation and propagation of cracks. Increase the length of tension splice from 216 to 432 leads to increase the splice strength by 53.2% due to increase the bonding surface area between concrete and steel bars.
8.1. Materials modelling Multi-crack concrete materials model was used to model the RPC beams. The material model considers the loss of tensile strength with compressive crushing, non-linear behaviour in compression, crack opening and closing with both shear and normal crack surface movements and softening in tension leading to the formation of fully formed stress free cracks [8]. The pre- and post-peak nonlinear behaviour was included using the friction hardening and softening model. The crack opening and closing are modelled using the directional damage with plasticity.
7.2. Load-deformation behaviour The load-deflection curves as recorded from the test setup data are shown in Fig. 4 for all tested specimens. From Fig. 4, it can be noted that failure of specimens caused mainly by ductile cracking and the specimens show different stage of behaviour till failure: first; linear behaviour under low applied load (elastic stage). Second; yielding point which represent steadily increasing in both tension stress of reinforcing
8.2. Model geometry Fig. 5 illustrates the geometry of the FE model of the RPC beams. 3D isoperimetric element with 16 nodes was used to simulate the beams.
Table 2 Characteristics of tested specimens. Specimen
Steel fibre content (%)
fc (MPa)
No. of transverse reinf. in the spliced region
Concrete cover (mm)
Bar diameter (mm)
Splice length (mm)
TS1-Ref TS2-trans TS3-cover TS4-dia TS5-fiber TS6-length
0.75 0.75 0.75 0.75 1.5 0.75
153 153 153 153 162 153
2-ϕ10 5-ϕ10 2-ϕ10 2-ϕ10 2-ϕ10 2-ϕ10
20 20 40 20 20 20
12 12 12 16 12 12
216 216 216 216 216 432
364
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Table 3 Tension lap-splice strength of tested specimen. Specimen Tension lap splice strength (MPa)
TS1-Ref
TS2-trans
TS3-cover
TS4-dia
TS5-fiber
TS6-length
274
300
296
298
280
420
TS2-trans
used to simulate crack opening; A fictitious crack model based on a crack-opening law and fracture energy. Fig. 7 describes the softening models used for the fibre-reinforced concrete with the crack width formulation according to:
TS3-cover
Wc = 5.14
20
TS4-dia
10
TS5-fib
where; w is the crack opening at the complete release of stresses, Gf is the fracture energy (area under the stress-crack width relation) and ft is the tensile strength of concrete. Discrete crack model at element nodes with fixed direction was adopted to model the crack opening.
60 TS1-Ref
Load (kN)
50 40 30
0
TS6-length
0
2
4
6
8
10
Deflection (mm)
Gf ft
8.5. FEA results and discussion
Fig. 4. Load-deflection curve of tested specimen.
To verify ability of the constitutive adopted FE model to simulate the behaviour of RPC beams, the numerical load deflection curves were compared with that of experimental tests for all specimens as shown in Fig. 8. The comparisons showed a good agreement between numerical and experimental load-deflection curves. The numerical ultimate loads were slightly higher than that of experimental results by about 8%. The comparisons confirm a good prediction of adopted FE model and it can be used for further studies.
Each node has three degrees of freedom translate in x, y and z directions. Hexahedral element of 1 × 2 × 2 mm size was used in the region of splice bars and 2 × 4 × 4 mm size in the outer zone in order to increase the accuracy of the results and fine mesh was used in the area of concentrated forces (support and applied load). Due to symmetry, half of the beam was analysed to reduce the computation time. Newton Raphson iterative nonlinear solver was used with load steps of 0.1 kN.
8.6. Parametric analysis
8.3. Reinforcement bond models
In experimental work, a little values of variables that affect the splice strength were examined due to high cost of RPC material. To study a wide range of these variables, the verified FE model was used through parametric study. This parametric analysis was important to obtain more data which is essential to propose required design equation to find the strength of splice strength of bars embedded in RPC beams. In the conducted parameter study, 38 samples tested numerically and the values of variables used in FE model were ranged as following: 216 mm (18 db) to 580 mm (48.3 db) for splice length, 10 to 25 mm for bar diameter, 10.4 to 17.4 the transverse reinforcement index Ktr, and
The reinforcement bond-slip relationship depends on the value of current slip between reinforcement and surrounding concrete. In this study, the CEB-FIB model code 1990 shown in Fig. 6 was adopted and the defined parameters values are presented in Table 4. 8.4. Tension before cracking The behaviour of concrete in tension before cracking is assumed to be a linear elastic as shown in Fig. 7. After Cracking, two models are
Fig. 5. Geometry of the FE beam model.
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H. Al-Quraishi, et al.
Fig. 6. Bond-slip law by CEB-FIP model code 1990.
9. Proposed design equation
Table 4 CEB-FIP model parameters values. Value
S1 S2 S3 τmax τf
The conducted parametric study provided a wide range bank of data which helps to propose a design equation of tension lap-splice length of reinforcing bar embedded in RPC member. Based on the simple formula adopted by ACI 318-14 [7], the general expression of the tension lap-splice strength has the following form:
Bond condition Good
Other cases
0.6 0.6 1 2√fc
0.6 0.6 2.5 1.0√fc
0.15τmax
f sp = C
(fy K1/f c K2)
(2)
where; fps is the tension splice strength; C is the constant of statistical analysis chosen with the purpose of making the average numerical to propose splice strength ratios approximately equal to 1.0; fy is the yield strength of reinforcing bars; factors k1 = 1 and k2 = 0.33 are constant provided by the influence function of each variables according to parametric analysis. So, the final form of the tension splice strength has the form of:
350 to 800 MPa for yield stress of rebar. Figs. 9a, b, c and 7d show the effect of these variables on the splice strength of reinforcement bars. It can be noted from figures that the tension splice strength increases linearly with these variables. The values ranged from 150 to 250 MPa were used to study the effect of concrete compressive strength on the tension lap-splice strength. The splice strength can be described approximately by a 0.33 power function of the compressive strength of concrete (see Fig. 9e).
f sp = 3.34 (f y /fc0.33)
(3)
Fig. 10 shows the ratio between the numerical splice strength of 38 samples tested numerically (Section 8.4) and proposed splice strength (Eq. (3)). The Figure shows a satisfactory agreement between proposed
Fig. 7. Tension softening model. 366
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H. Al-Quraishi, et al.
Fig. 8. Variables effect on tension splice strength.
Fig. 9. Variables effect on tension splice strength.
• Splitting of concrete is the type of failure that occurred in RPC beams spliced with tension reinforcement. • The FE model is capable to simulate the experimental behaviour of
equation and numerical splice strength with the mean value of 1.03 and coefficient of Coefficient of Variation (CoV) is 0.11. 10. Conclusion The following conclusions can be drawn from conducted experimental and numerical studies:
•
• Increase the steel fibre content, amount of transverse reinforcement, length of spliced bars, and diameter of spliced bars increase the tension lap-splice strength of steel bras embedded in RPC member.
367
RPC beams reinforced with splice bars under flexure. Good agreements were found between the FEA results and that of experimental results in terms of load deflection curve and ultimate load. New design equation for tension splice strength of RPC member is proposed and verified with the results of 38 samples tested numerically in this study. This equation can be used with wide range of parametric variations; ranged between 216 mm (18 db) to 580 mm (48.3 db) for splice length, 10 to 25 mm for bar diameter, 10.4 to
Structures 19 (2019) 362–368
H. Al-Quraishi, et al.
agreement with numerical results obtained from this study with the mean value of 1.01 and CoV = 0.11. References [2] Lagier F, Massicotte B, Charron J-P. Bond splitting of lap splice embedded in ultra high fibre reinforced concrete under direct tension. Proceeding of the 4th Conference on Bond in Concrete, Brescia, Italy. 2012. p. 351–8. [3] Orangun C, Jirsa J, Breen J. Revaluation of test data on development length and splices. ACI J Proc 1977;74(3):114–22. [4] Yuan J, Graybeal B. Bond behavior of reinforcing steel in ultra-high performance concrete, FHWA-HRT-14-090. US Department of Transportation, Federal Highway Administration; 2014. p. 78. [5] Lagier Fabien, Massicotte Bruno, Charron Jean-Philippe. Experimental investigation of bond stress distribution and bond strength in unconfined UHPFRC lap splices under direct tension. Cem Concr Compos 2016;74:26–38. [6] Lagier F, Massicotte B, Charron J-P. Bond strength of tension lap splice specimens in UHPFRC. Construct Build Mater 2015;93:84–94. [7] ACI Committee 318. Building code requirements for structural concrete (ACI 318011) and commentary. Farmington Hills: American Concrete Institute; March 2011. p. 233. [8] Nilson A, Darwin D, Dolan C. Design of concrete structures. forteenth edition in si unit Mc Graw Hill Eductaion; 2009.
Fig. 10. Ratio between numerical and proposed splice strength.
17.44 the range of transverse reinforcement index Ktr, 350 to 800 MPa for yield stress of rebar and 150 to 250 MPa for compressive strength of concrete. This equation shows a satisfactory
368
Contents lists available at ScienceDirect
Structures journal homepage: www.elsevier.com/locate/structures
Tension Lap Splice Length of Reinforcing Bars Embedded in Reactive Powder Concrete (RPC)
T
Hussein Al-Quraishia, Mahdi Al-Farttoosib, , Raad AbdulKhudhura ⁎
a b
Civil Engineering Department, University of Technology, Baghdad, Iraq Faculty of Engineering, Civil Engineering Department, University of Baghdad, Baghdad, Iraq
ARTICLE INFO
ABSTRACT
Keywords: RPC Beam Tension splice bars
Reactive Powder Concrete (RPC) is an emerging cementations construction material which has superior mechanical properties such as high compressive and tensile strength, high density and homogeneous. In this research, the tension splice behaviour of reinforcement bars embedded in RPC was investigated using experimental and numerical studies. Six reinforced RPC beams with four-point loading were tested. The parameters investigated in the experimental program were steel fibre contents, size of reinforcing bar, tension reinforcement splice length, and amount of transverse reinforcement. The experimental findings showed that the increasing of steel fibre content, amount of transverse reinforcement, length of spliced bars, and diameter of spliced bars increased the tension splice strength of steel bras embedded in RPC members. Splitting of concrete is the dominate mode of failure that occurred in RPC beams spliced with tension reinforcement. Finite element method was used in this study to simulate the behaviour of members tested experimentally and a comparison between experimental and numerical results was conducted. The comparisons showed a good agreement between experimental results and numerical results in terms of load deflection curves and splice strengths. The verified finite element model was used then to study the effect of wide range of data for variables affect the splice strength using a parametric study. A proposed design equation of splice strength of tension reinforcing bars embedded in RPC was proposed in this study and verified with numerical results.
1. Introduction RPC is the new advanced concrete material that has excellent mechanical properties compared with the normal concrete. RPC is considered as cementitious material that mainly characterized by them outstanding high tensile properties which improve the bond between the reinforcing bars and concrete. It is difficult to use continuous reinforcing bars in construction long concrete element due to transportation limitations and handling. Splicing short reinforcing bars is one of the common practice methods that can be used to fabricate concrete members. The bond between the splice bars and the surrounding concrete affected the probability of bar slippage which may results in failure of concrete members. The variables that affect the bond of spliced bars are: concrete mechanical properties, rebar rib area, spliced length, diameter of rebar and concrete cover within the spliced zone [2]. Tension lap splice is defined as the peak tension force that can be transferred between the spliced bars through the bond action. Splice length represents the embedment length necessary to develop the full
⁎
tensile strength of those discontinuous bars, controlled by either pullout or splitting. The beam specimen, beam anchorage, and pull-out specimen are the specimen configuration used to represent the tension lap splice. Among these three specimens, beam specimens represents more realistic response of splice strength under flexural stresses and this method of testing was adopted in this study. Orangun et al. [3] tested 116 concrete specimens to investigate the bond strength of reinforcing bars embedded in normal strength concrete. Furthermore, design equation for the maximum steel bar stress was presented:
Abf s/ f c = 0.25 l d (c min + 0.4 db) + 16. 6Ab + l dAtr fy t/41.5 s·n
(1)
Yuan and Graybeal [4] studied the effect of fibre content on the tension lap strength in RPC beams. Various spliced lengths and RPC mixes were tested. They demonstrated that the bond strength is depends on the matrix and post-cracking tensile strength of RPC. Lagier et al. [5] tested 4-point-bending RPC slabs with tension lap splices. Within these tests the lateral reinforcement and splice length in the
Corresponding author. E-mail address: [email protected] (M. Al-Farttoosi).
https://doi.org/10.1016/j.istruc.2018.12.011 Received 25 September 2018; Received in revised form 14 December 2018; Accepted 19 December 2018 Available online 17 January 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
Structures 19 (2019) 362–368
H. Al-Quraishi, et al.
Nomenclature Ab Atr C cmin
yield stress of rebar stress in steel bar compressive strength of concrete development length of steel bar spacing of stirrups number of stirrups
fy fs fc ld S n
area of steel bar transverse reinforcement index constant of statistical analysis minimum concrete cover
splice zone were varied. The test results showed that the length of the lap splice and the presence of any lateral reinforcement affect the failure mechanism, the crack width and crack development in the splice zone. Lagier et al. [6] used direct tension specimens to investigate the effect of fibre concrete in RPC on the bond strength. Three amount of amount steel fibre were used. The experimental findings showed that the bond performance improved and splitting failure was controlled. Furthermore, the bond strength is strongly related maximum tensile strength and strain ductility in RPC. These conducted experimental and numerical investigations provide an increase in our understanding of the bond characteristics of tension lap splice reinforcing bars. The knowledge gained from this study is significant to develop a robust design equation to tension lap splice length of reinforcing embedded in RPC which can be used simply in practice.
5. Experimental program
2. Objective of this study
6. Test setup and instrumentation
A total of six RPC beams were constructed and tested in the laboratories of Civil Engineering Department-University of TechnologyIraq. To provide area of constant moment at the location of spliced bars, all beams were tested under four point loading. The influence of transverse reinforcement ratio in the lap splice zone was studied using two beams (TS1-Ref and TS2-trans). The concrete cover was investigated by testing beams (TS1-Ref and TS3-cover). Beams (TS1-Ref and TS4-dia) were used to study the effect of size of spliced bars. The effect of steel fibre content was investigated by comparing the results of beams (TS1-Ref and TS5-fiber), and finally the length of spliced bars was studied using beams (TS1-Ref and TS6-Splice). The characteristics of the tested beams are summarized in Table 2.
The deflection at the mid-span of the beams was measured using LVTD mounted at the top of the specimens. Two electrical resistance strain gauges were used to measure the strains in splice bars in order to estimate the tension strength in the middle of spliced bars. The hydraulic machine of 2500 kN capacity was used to test specimens. The load-control at a rate of 10 kN/min was used to test the specimen till failure. At each of load stage, the cracks propagation was drawn. Fig. 3 shows the beam specimen under testing using the heavy test machine.
The main goals of this study are investigation the following:
• The tension lap splice strength and modes of failure of reinforcing • •
bars embedded in RPC member through an experimental and numerical programs. The effect of a number of variables on tension splice strength in RPC members such, steel fibre content, amount of transverse reinforcement, length of spliced bars, and diameter of spliced bars. Proposing a design equation to predict the tension splice strength in RPC members.
7. Test results 7.1. The variables effect on the tension lap-splice strength
3. Materials
Table 3 shows the comparisons of the results of reference beam (TS1-Ref) with that of beams (TS2-trans, TS3-cover, TS4-dia, TS5-fiber, TS6-length). It can be notes from the table of comparisons the following:
The compositions of the RPC are: Portland cement – type I; quartz sand with specific gravity of 2.57; silica fume with the bulk density of 650 kg/m3; high range water reducing admixture (Sika Viscocrete 2810) with the relative density of 1.07 as shown in Table 1. The steel fibres have a length of 15 mm, diameter of 0.2 mm, aspect ratio of 70 and ultimate tensile strength of 2000 MPa that were used to fabricate the specimens. The spliced reinforcing bars used to reinforce RCP samples were 12 mm in diameter. The bars have an elastic modulus of elasticity of 200 GPa, yield strength of 420 MPa, and ultimate tensile strength of 620 MPa.
• Increase the amount of transverse reinforcement in the lap splice •
4. Tested specimens
•
The experimental program included testing six RC beams with splice tensile reinforcement at mid-span. The beam specimens were 1500 mm long and had a rectangular cross section of 130 mm wide and 180 mm depth. The tested beams were simply supported and loaded with two equal point loads at the middle-third of the span, see Fig. 1. Two 12 mm diameter longitudinal bars were used in tension face and spliced in the mid-span of the beam. In compression region of the beam, two 12 mm bar diameter were placed. Fig. 2 shows the specimens after casting. The splice lengths for the reference beams were designed according to the provisions of ACI 318-14 [7] of NSC to get the yielding stress in reinforcing bars. The beams in region out of splice zone were reinforced with 10 mm diameter stirrups spaced at 100 mm to prevent shear failure. End anchorage hooked 90° was used at the ends of longitudinal bars.
region from 2-ϕ10 to 5-ϕ10, increases the tension lap-splice strength by 9.5%. This is due to major confinement role of transverse reinforcement along the splice length. Increase the concrete cover in the region of lap splice from 20 mm to 40 mm results in an increase in tension lap-splice strength by 8%. The radial tensile stresses induced by bar ribs balanced by the concrete cover and consequently the tension splice strength was increased. The tension splice strength increased by 9% when the diameter of
Table 1 Mix proportion of RPC.
363
Compositions
Weight (kg/m3)
Water Cement Fine aggregate Silica fume HRWRA Steel fibre (0.25/20)
231 1100 858 253 49.5 0.28 for 0.75% fibre content 0.56 for 1.5% fibre content
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H. Al-Quraishi, et al.
Fig. 1. Geometry of tested beam.
Fig. 3. Test machine.
bars and concrete compression stress after cracking of beam in tension zone. Third; after yielding, the deflection increased rapidly until failure of beams by concrete crushing in compression zone after longitudinal splitting in splice zone. The TS5-fib specimen shows high elastic and ductile behaviour before failure due to the effect of steel fibre which restricted the opening of flexural cracking and increased the tensile strength of concrete. All beams in this investigation showed flexural mode of failure. They failed by splitting occurred along the tension longitudinal bar. The longitudinal cracks initiated at the free ends of spliced bars (stresses concentrated points), then extended along the longitudinal reinforcing bars. Fig. 2. Tested specimen after casting.
• •
8. Finite elements analysis A finite element method FEM was used to simulate the behaviour of beams tested experimentally. LUSAS [8] software package was used to conduct the numerical modelling and analyses.
lap splice bars were increased from 12 to 16 mm. This is due to increasing in surface area between steel bars and concrete when big bar size is used and that increase the bonding between them. Increase the steel fibre content in tested specimens from 0.75% to 1.5% increases the tension splice strength by 2.2%. This, due to, the presence of steel fibres improve the bond strength and delays the formation and propagation of cracks. Increase the length of tension splice from 216 to 432 leads to increase the splice strength by 53.2% due to increase the bonding surface area between concrete and steel bars.
8.1. Materials modelling Multi-crack concrete materials model was used to model the RPC beams. The material model considers the loss of tensile strength with compressive crushing, non-linear behaviour in compression, crack opening and closing with both shear and normal crack surface movements and softening in tension leading to the formation of fully formed stress free cracks [8]. The pre- and post-peak nonlinear behaviour was included using the friction hardening and softening model. The crack opening and closing are modelled using the directional damage with plasticity.
7.2. Load-deformation behaviour The load-deflection curves as recorded from the test setup data are shown in Fig. 4 for all tested specimens. From Fig. 4, it can be noted that failure of specimens caused mainly by ductile cracking and the specimens show different stage of behaviour till failure: first; linear behaviour under low applied load (elastic stage). Second; yielding point which represent steadily increasing in both tension stress of reinforcing
8.2. Model geometry Fig. 5 illustrates the geometry of the FE model of the RPC beams. 3D isoperimetric element with 16 nodes was used to simulate the beams.
Table 2 Characteristics of tested specimens. Specimen
Steel fibre content (%)
fc (MPa)
No. of transverse reinf. in the spliced region
Concrete cover (mm)
Bar diameter (mm)
Splice length (mm)
TS1-Ref TS2-trans TS3-cover TS4-dia TS5-fiber TS6-length
0.75 0.75 0.75 0.75 1.5 0.75
153 153 153 153 162 153
2-ϕ10 5-ϕ10 2-ϕ10 2-ϕ10 2-ϕ10 2-ϕ10
20 20 40 20 20 20
12 12 12 16 12 12
216 216 216 216 216 432
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Table 3 Tension lap-splice strength of tested specimen. Specimen Tension lap splice strength (MPa)
TS1-Ref
TS2-trans
TS3-cover
TS4-dia
TS5-fiber
TS6-length
274
300
296
298
280
420
TS2-trans
used to simulate crack opening; A fictitious crack model based on a crack-opening law and fracture energy. Fig. 7 describes the softening models used for the fibre-reinforced concrete with the crack width formulation according to:
TS3-cover
Wc = 5.14
20
TS4-dia
10
TS5-fib
where; w is the crack opening at the complete release of stresses, Gf is the fracture energy (area under the stress-crack width relation) and ft is the tensile strength of concrete. Discrete crack model at element nodes with fixed direction was adopted to model the crack opening.
60 TS1-Ref
Load (kN)
50 40 30
0
TS6-length
0
2
4
6
8
10
Deflection (mm)
Gf ft
8.5. FEA results and discussion
Fig. 4. Load-deflection curve of tested specimen.
To verify ability of the constitutive adopted FE model to simulate the behaviour of RPC beams, the numerical load deflection curves were compared with that of experimental tests for all specimens as shown in Fig. 8. The comparisons showed a good agreement between numerical and experimental load-deflection curves. The numerical ultimate loads were slightly higher than that of experimental results by about 8%. The comparisons confirm a good prediction of adopted FE model and it can be used for further studies.
Each node has three degrees of freedom translate in x, y and z directions. Hexahedral element of 1 × 2 × 2 mm size was used in the region of splice bars and 2 × 4 × 4 mm size in the outer zone in order to increase the accuracy of the results and fine mesh was used in the area of concentrated forces (support and applied load). Due to symmetry, half of the beam was analysed to reduce the computation time. Newton Raphson iterative nonlinear solver was used with load steps of 0.1 kN.
8.6. Parametric analysis
8.3. Reinforcement bond models
In experimental work, a little values of variables that affect the splice strength were examined due to high cost of RPC material. To study a wide range of these variables, the verified FE model was used through parametric study. This parametric analysis was important to obtain more data which is essential to propose required design equation to find the strength of splice strength of bars embedded in RPC beams. In the conducted parameter study, 38 samples tested numerically and the values of variables used in FE model were ranged as following: 216 mm (18 db) to 580 mm (48.3 db) for splice length, 10 to 25 mm for bar diameter, 10.4 to 17.4 the transverse reinforcement index Ktr, and
The reinforcement bond-slip relationship depends on the value of current slip between reinforcement and surrounding concrete. In this study, the CEB-FIB model code 1990 shown in Fig. 6 was adopted and the defined parameters values are presented in Table 4. 8.4. Tension before cracking The behaviour of concrete in tension before cracking is assumed to be a linear elastic as shown in Fig. 7. After Cracking, two models are
Fig. 5. Geometry of the FE beam model.
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Fig. 6. Bond-slip law by CEB-FIP model code 1990.
9. Proposed design equation
Table 4 CEB-FIP model parameters values. Value
S1 S2 S3 τmax τf
The conducted parametric study provided a wide range bank of data which helps to propose a design equation of tension lap-splice length of reinforcing bar embedded in RPC member. Based on the simple formula adopted by ACI 318-14 [7], the general expression of the tension lap-splice strength has the following form:
Bond condition Good
Other cases
0.6 0.6 1 2√fc
0.6 0.6 2.5 1.0√fc
0.15τmax
f sp = C
(fy K1/f c K2)
(2)
where; fps is the tension splice strength; C is the constant of statistical analysis chosen with the purpose of making the average numerical to propose splice strength ratios approximately equal to 1.0; fy is the yield strength of reinforcing bars; factors k1 = 1 and k2 = 0.33 are constant provided by the influence function of each variables according to parametric analysis. So, the final form of the tension splice strength has the form of:
350 to 800 MPa for yield stress of rebar. Figs. 9a, b, c and 7d show the effect of these variables on the splice strength of reinforcement bars. It can be noted from figures that the tension splice strength increases linearly with these variables. The values ranged from 150 to 250 MPa were used to study the effect of concrete compressive strength on the tension lap-splice strength. The splice strength can be described approximately by a 0.33 power function of the compressive strength of concrete (see Fig. 9e).
f sp = 3.34 (f y /fc0.33)
(3)
Fig. 10 shows the ratio between the numerical splice strength of 38 samples tested numerically (Section 8.4) and proposed splice strength (Eq. (3)). The Figure shows a satisfactory agreement between proposed
Fig. 7. Tension softening model. 366
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Fig. 8. Variables effect on tension splice strength.
Fig. 9. Variables effect on tension splice strength.
• Splitting of concrete is the type of failure that occurred in RPC beams spliced with tension reinforcement. • The FE model is capable to simulate the experimental behaviour of
equation and numerical splice strength with the mean value of 1.03 and coefficient of Coefficient of Variation (CoV) is 0.11. 10. Conclusion The following conclusions can be drawn from conducted experimental and numerical studies:
•
• Increase the steel fibre content, amount of transverse reinforcement, length of spliced bars, and diameter of spliced bars increase the tension lap-splice strength of steel bras embedded in RPC member.
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RPC beams reinforced with splice bars under flexure. Good agreements were found between the FEA results and that of experimental results in terms of load deflection curve and ultimate load. New design equation for tension splice strength of RPC member is proposed and verified with the results of 38 samples tested numerically in this study. This equation can be used with wide range of parametric variations; ranged between 216 mm (18 db) to 580 mm (48.3 db) for splice length, 10 to 25 mm for bar diameter, 10.4 to
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agreement with numerical results obtained from this study with the mean value of 1.01 and CoV = 0.11. References [2] Lagier F, Massicotte B, Charron J-P. Bond splitting of lap splice embedded in ultra high fibre reinforced concrete under direct tension. Proceeding of the 4th Conference on Bond in Concrete, Brescia, Italy. 2012. p. 351–8. [3] Orangun C, Jirsa J, Breen J. Revaluation of test data on development length and splices. ACI J Proc 1977;74(3):114–22. [4] Yuan J, Graybeal B. Bond behavior of reinforcing steel in ultra-high performance concrete, FHWA-HRT-14-090. US Department of Transportation, Federal Highway Administration; 2014. p. 78. [5] Lagier Fabien, Massicotte Bruno, Charron Jean-Philippe. Experimental investigation of bond stress distribution and bond strength in unconfined UHPFRC lap splices under direct tension. Cem Concr Compos 2016;74:26–38. [6] Lagier F, Massicotte B, Charron J-P. Bond strength of tension lap splice specimens in UHPFRC. Construct Build Mater 2015;93:84–94. [7] ACI Committee 318. Building code requirements for structural concrete (ACI 318011) and commentary. Farmington Hills: American Concrete Institute; March 2011. p. 233. [8] Nilson A, Darwin D, Dolan C. Design of concrete structures. forteenth edition in si unit Mc Graw Hill Eductaion; 2009.
Fig. 10. Ratio between numerical and proposed splice strength.
17.44 the range of transverse reinforcement index Ktr, 350 to 800 MPa for yield stress of rebar and 150 to 250 MPa for compressive strength of concrete. This equation shows a satisfactory
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