Many research studies have been carried out on the different parameters affecting the bond strength of tension lap splices in RC beams but limited attention has been given to the effect of using transverse reinforcement along the splice length. The first part of this research is an experimental program which consisted of sixteen reinforced concrete beams tested at the concrete laboratory of the Faculty of Engineering, Cairo University. The parameters under study herein are the diameter of the transverse reinforcement as well as its shape and distribution while using three different types of concrete. The beams were all simply supported with 1800 mm span and 150 250 mm cross section. The tensile steel was spliced in the constant moment zone. The second part of the research consisted of an analytical study to enhance the understanding of the topic of this research. Threedimensional nonlinear finite element analysis was carried with the help of the wellknown finite element software; ABAQUS. The concrete damaged plasticity model is selected at this study because it is capable of representing the complete inelastic behavior of concrete both in tension and in compression including damage characteristics. The analytical and experimental results were compared and contrasted. Good agreement was obtained.
ORIGINAL ARTICLE Behavior of RC beams with tension lap splices confined with transverse reinforcement using different types of concrete under pure bending Rasha T.S Mabrouk *, Ahmed Mounir Faculty of Engineering, Cairo University, Giza, Egypt Received April 2017; revised 27 April 2017; accepted May 2017 Available online June 2017 KEYWORDS Transverse reinforcement; Lap splice; High strength concrete; Self-compacting concrete; Ductility; ABAQUS Abstract Many research studies have been carried out on the different parameters affecting the bond strength of tension lap splices in RC beams but limited attention has been given to the effect of using transverse reinforcement along the splice length The first part of this research is an experimental program which consisted of sixteen reinforced concrete beams tested at the concrete laboratory of the Faculty of Engineering, Cairo University The parameters under study herein are the diameter of the transverse reinforcement as well as its shape and distribution while using three different types of concrete The beams were all simply supported with 1800 mm span and 150 Â 250 mm cross section The tensile steel was spliced in the constant moment zone The second part of the research consisted of an analytical study to enhance the understanding of the topic of this research Three-dimensional nonlinear finite element analysis was carried with the help of the well-known finite element software; ABAQUS The concrete damaged plasticity model is selected at this study because it is capable of representing the complete inelastic behavior of concrete both in tension and in compression including damage characteristics The analytical and experimental results were compared and contrasted Good agreement was obtained Ó 2017 Faculty of Engineering, Alexandria University Production and hosting by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Introduction Splicing of reinforcing bars is one of the common practices used in concrete structures It is quite impossible to have con* Corresponding author at: Concrete Laboratory, Faculty of Engineering, Cairo University, 48 Gezeeret El Arab, El mohandeseen, Giza, Egypt E-mail addresses: yrasha@yahoo.com (R.T.S Mabrouk), ahmedmounir73@gmail.com (A Mounir) Peer review under responsibility of Faculty of Engineering, Alexandria University tinuous reinforcement bars in concrete elements This can be due to many reasons such as; steel fabrication, transportation limitations and steel workshop detailing Lap splicing, which is often achieved by the overlapping of two parallel bars with enough length, has long been considered as an effective and economical splicing method Good bond strength of the lap splice with the surrounding concrete reduces the probability of bar slippage or splitting failure before the yielding of reinforcing steel bars Many parameters affect the bond strength of a lap splice such as: lap length, concrete cover, reinforcement bar diameter, reinforcement ratio, bar relative rib area and transverse reinforcement provided within the lap zone http://dx.doi.org/10.1016/j.aej.2017.05.001 1110-0168 Ó 2017 Faculty of Engineering, Alexandria University Production and hosting by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) 1728 R.T.S Mabrouk, A Mounir other variables were considered He concluded that there is a drastic increase in ductility of beams when transverse reinforcement was used Ghasabeh [7] conducted an experimental program on twelve beam specimens cast with self-compacting concrete He concluded that the ACI 408R-03 [8] descriptive equation for predicting the stress at spliced bars was good just for beams without transverse reinforcement within lap zone, while it was not accurate for beams that contain transverse reinforcement where it under-estimates the role of confinement by stirrups Generally, it can be said that design codes such as ECP 203-2007 [9] and ACI 318-05 [10] not take the effect of transverse reinforcement into consideration Based on the above, it can be seen that the usage of the transverse reinforcement has not yet been fully investigated The main objective of this research is to study the effect of using transverse reinforcement with different ratios, distribution and shapes on the behavior of reinforced concrete beams loaded under pure tension while using three different types of concrete namely normal strength concrete, self-compacting concrete and high strength concrete [1] In addition, the mechanical properties of concrete have a significant effect on the bond characteristics which makes the type of concrete a worthy parameter in the study of the behavior of the tension lap splices [2] Many advances in the production of concrete led to different concrete types such as SelfCompacting Concrete and High Strength Concrete SelfCompacting Concrete is known for its excellent deformability and high resistance to segregation [3] High Strength Concrete has the advantage of a much higher strength than the usual normal strength concrete Many researches were reported on the bond strength between deformed bars and concrete for each of the above mentioned three types separately El-Azab [4] tested sixteen High Strength Self Compacting beam specimens with two or three spliced bars He studied the effect of reinforcement diameter, and ratio, splice length and casting position He concluded that for improving the splice bond strength, a splice length of 40 times the bar diameter need to be taken as well as using smaller bar diameter for the same reinforcement ratio and avoiding top casting position Twelve full-scale beams were tested in positive bending by Turk [5] with the loading system designed to determine the effect of self-compacting concrete and the diameter of reinforcement on the bond–slip characteristics of tension lap splices The results showed that load transfer within the tension lap spliced bars embedded in selfcompacting concrete was better than that of the spliced bars embedded in normal strength concrete Some research was conducted to study the effect of transverse reinforcement on the behavior of the tension lap splice Seventeen full-scale beam specimens cast with high strength concrete were tested in positive bending by Ahmed [6] He studied the effect of the concrete compressive strength, splice length and the amount of transverse reinforcement within lap splice zone The results showed that providing stirrups within lap splice zone increase the beam’s ultimate load capacity and ductility Diab [1] tested twelve normal strength concrete beam specimens In this study, the type, spacing and shape of spacing and shape of transverse reinforcement in splice region embedded in normal strength concrete among Experimental program 2.1 Test specimens A total of sixteen concrete beams were fabricated and tested at the concrete laboratory of Cairo University, Giza, Egypt [11,12] All the specimens were 2000 Â 250 Â 150 mm with a loaded span 1800 mm The main reinforcement consisted of two high grade (400/600) steel deformed bars with diameter 10 mm The specimens were divided into five groups as shown in Table Group I consisted of three control specimens cast with the three types of concrete used in this research namely Normal Strength Concrete (NC), High Strength Concrete (HC), and Self-Compacting Concrete (SC) In these control specimens, no splices were used Group II consisted of specimens with lap splice in the middle zone to study the effect of the transverse reinforcement in terms of number, diameter and Table Details of the test specimens Group Beam No Specimen notation Concrete type Splice length (mm) Average cube strength (MPa) Transverse reinforcement No Diameter Shape I NC- L00-0T6-V HC- L00-0T6-V SC- L00-0T6-V Normal High strength Self-compacting 0 31.86 92.91 34.30 0 0 0 – – – II NC-L30-0T6-V NC -L30-2T6-V NC -L30-4T6-V NC-L30- 6T6-V NC-L30-2T8-V NC-L30-NT6-V Normal Normal Normal Normal Normal Normal 300 300 300 300 300 300 30.67 30.92 28.60 32.56 30.92 27.80 6 6 6 Vertical Vertical Vertical Vertical Vertical Vertical III 10 11 HC-L30-0T6-V HC-L30-6T6-V High strength High strength 300 300 87.29 89.70 6 Vertical Vertical IV 12 13 SC-L30-0T6-V SC- L30-6T6-V Self-compacting Self-compacting 300 300 33.20 34.51 6 Vertical Vertical V 14 15 16 NC-L30-4T6-S NC-L30-4T6-R NC-L30-4T6-C Normal Normal Normal 300 300 300 28.67 30.50 29.10 4 6 Spiral Rectangular Corrugated Behavior of RC beams with tension lap splices distribution Group III and Group IV studied the HC and SC concrete, respectively Group V studied the effect of the different shapes of stirrup Four different types of stirrups were Fig Different shapes of transverse reinforcement used Fig 1729 investigated namely vertical, rectangular, corrugated and spiral as shown in Fig All the specimens other than the control group were designed to have a lap splice of length 300 mm at mid span This value was selected to develop stresses in steel less than the yield stress in order to ensure a splitting mode of failure [9] Transverse reinforcement with diameter of mm and spacing of 100 mm (Ø @100 mm) was provided outside the splice region of all beams to avoid shear failure Complete details of the different specimens are shown in Fig A four-part notation system was used to indicate the variables of each beam The first part of the notation indicates the type of concrete: NC, HC and SC for Normal strength, High strength and Self Compacting concretes respectively The second part indicates splice length: L00 for no splice and L30 for 300 mm splice The third part indicates details of transverse reinforcement provided and it is represented by two numbers For example; 4T6, the first number indicates existence of four stirrups within lap zone while the second number indicates that the used diameter for the stirrups is Elevation and cross-section of all the specimens under study 1730 R.T.S Mabrouk, A Mounir Table Details of the three concrete mixes used Mix type Mix-proportions per (kg/m3) NC SC HC Dolomite 10 Dolomite 20 Sand Water Cement Silica fume Super plasticizer 620 450 446 620 285 893 640 990 446 200 190 130 300 450 500 – 45 75 – 11 17 mm The fourth part represents the four different shapes of stirrups used V indicates vertical closed stirrups, R indicates rectangular hoop stirrups, C indicates corrugated stirrups and S indicates spiral stirrups 2.2 Materials used Three types of concrete mixes were designed to satisfy the experimental program objectives The first one is normal strength concrete (NC) with a 30 MPa targeted compressive strength after 28 days This concrete did not contain any type of admixtures The second mix is for self-compacting concrete (SC) with the same targeted compressive strength of 30 MPa but requires a high level of fluidity This was achieved by adding mineral and chemical admixtures The last mix was the high strength concrete (HS) which requires a higher cement content and lower water content together with using admixtures to produce a characteristic compressive strength of 90 MPa In the three mixes, ordinary Portland cement CEM I 42.5R was used that complies with ASTM C150 type cement The fine aggregate was natural sand with a specific gravity of 2.63 and fineness modulus of 2.78 was used The coarse aggregate used was well graded crushed dolomite with a nominal maximum size of 20 and 10 mm with specific gravity of 2.61 and water absorption of 0.5% by mass The mineral admixture was light gray locally produced silica fume The chemical admixture was super-plasticizer type GLENIUM C315 which is used to increase the workability of concrete and to reduce the amount of required mixing water The mixes used to cast the specimens were developed by trial batching at the Concrete Research Laboratory of Cairo University Mixture proportions are shown in Table The SC was poured into the mold at once without any vibration while the NC and HC were cast in two layers in each beam specimen and compacted using an electrical vibrator Methods used to determine the fresh self-compacting concrete properties are different than the ones recommended for fresh normal vibrated concrete In addition to the slump, there are several other essential test items for fresh concrete properties of SC based on the guidance given in EFNARC (2005) [3], including the slump flow, T50, V-funnel test, L-box test and segregation sieve test The slump of NC was 68 mm as measured before casting while, a slump flow of 660 mm was obtained for SC as shown in Fig Typically, three 150 Â 150 Â 150 mm cubes were cast with each test beam and used for compression test The beams and cubes were kept under the same curing conditions Compression test on cubes were carried out on the same day of beam testing, and the results were higher than the design compressive strengths of concrete 2.3 Test procedure Fig Slump Flow Test and Slump test for fresh SC and NC respectively (a) Control specimens with no splices Fig A two point loading system was applied to all the beams to ensure an area of pure bending in the mid zone The testing machine consisted of a static hydraulic loading jack with an electrical load cell which was used to apply the concentrated vertical load at increments of 3.5 kN/s The load from the testing machine was transferred through a stiff steel spreader (b) Specimens with lap splices Strain gauges locations for the main longitudinal reinforcement Behavior of RC beams with tension lap splices 1731 sured using 10 mm strain gauges which were attached at the center of the main reinforcement in case of the control specimens with no splices While in case of splices, two strain gauges were used one at the middle and the other one at the end of the splice as shown in Fig In addition to longitudinal reinforcement, strain gauges were also attached to the stirrups Fig shows the general test arrangement and Fig shows a schematic view Results and discussion Fig In this part the experimental results of all the tested beams are discussed in terms of load-deflection relationships, ductility (D) and modes of failure Table shows the output results for all the tested beams The ductility index of the beam is defined as the ratio of mid span deflection at ultimate load to the mid span deflection at the yielding load of the main steel [11] In this research, the ultimate deflection of the tested beams is also compared to the ultimate deflection of the control specimen and is referred to herein as the relative ductility Crack patterns and load strain curves can be referred to in Refs [12,13] General test arrangement 3.1 Stirrups and stirrups spacing Fig Schematic view of test arrangement beam onto the specimens in the form of two equally concentrated loads A digital load indicator with kN accuracy was used to measure the applied load At each load stage, deflection readings were taken at mid span and one-third of the beam span using LVDT instrument gauge of 0.01 mm accuracy Cracks at the faces of the specimens were marked for further analysis Strain in steel was mea- Table The results for group II and the control specimen NC-L000T6-V are discussed in this section All beams in this group were normal concrete Fig shows the comparison between beams NC-L00-0T6-V, NC-L30-0T6-V and NC-L30-6T6-V It can be seen that when a splice is applied without any transverse reinforcement as in case of beam NC-L30-0T6-V, the ultimate load is reduced by 21.5% compared to the beam without splice and the ductility is much reduced as represented by the area under the load deflection curve as well as the ductility index shown in Table However, in case of beam NC-L306T6-V where six stirrups are added in the splice zone, the behavior is much improved The value of the ultimate load Ultimate loads and ductility measures for the tested beams Group Specimen notation Deflection at yield (mm) Deflection at ultimate load (mm) Ultimate load (kN) Ductility index Relative ductility Mode of failure I NC-L00-0T6-V HC-L00-0T6-V SC-L00-0T6-V 7.9 2.74 4.02 32.49 40.43 29.46 104 132 106 4.11 14.76 7.33 1 Flexure Flexure Flexure II NC-L30-0T6-V NC-L30-2T6-V NC-L30-4T6-V NC-L30-6T6-V NC-L30-2T8-V NC-L30-NT6-V 3.92 3.56 2.74 3.68 3.78 3.26 6.66 6.10 5.80 30.10 5.91 22.71 84.6 99 98 102 93 95.5 1.70 1.71 2.12 8.18 1.56 6.97 0.20 0.19 0.18 0.93 0.18 0.70 Splitting Splitting Flexure Flexure Splitting Splitting III HC-L30-0T6-V HC-L30-6T6-V NAa 5.89 NAa 40.08 96 130 NAa 6.80 NAa 1.23 Splitting Flexure IV SC-L30-0T6-V SC-L30-6T6-V 3.88 3.78 10.10 22.30 101 122 2.60 5.90 0.31 0.69 Splitting Flexure V NC-L30-4T6-S NC-L30-4T6-R NC-L30-4T6 C b 6.48 5.41 5.58 75.6 101 81 b 0.20 0.17 0.17 Splitting Flexure Flexure a b 4.57 3.13 An error occurred with the data reading during the experiment Steel did not yield 1.18 1.78 R.T.S Mabrouk, A Mounir 120 120 100 100 Total verƟcal load (KN) Total verƟcal load (KN) 1732 80 60 40 NC-L00-0T6-V NC-L30-0T6-V NC-L30-6T6-V 20 0 20 40 NC-L30-4T6-V 80 60 40 20 60 DeflecƟon (mm) Fig NC-L30-2T8-V Effect of stirrups capacity became 98% of that of the beam with no splice and the relative ductility reached a value of 0.93 In addition, the mode failure changed from splitting to flexure failure This can be attributed to the fact that the use of transverse reinforcement eliminated the formation of splitting cracks at tension splice zone and minimized the width of cracks Compared to NC-L30-0T6-V, it can be seen from Fig 8, that there is a slight increase in the ultimate load capacity of the beams by 17%, 17% and 21% when two, four, and six stirrups were used, respectively However, the ductility was significantly improved as the spacing between the stirrups decreased, where the ductility index reached a value of 8.18 in case of using six stirrups In addition, relative ductility values increased from 0.19 for beam NC-L30-2T6-V to 0.93 in case of NC-L30-6T6-V 3.2 Stirrups diameter For group II, comparing beams NC-L30-4T6-V and NC-L302T8-V, both beams had the same transverse reinforcement area but the first beam a larger number of stirrups (4) were used with smaller bar diameter (6 mm) and the second one a bigger diameter (8 mm) and only two stirrups were used Fig shows the results for the two beams The ductility index 30 40 Effect of stirrups diameter was higher in case of NC-L30-4T6-V and the ultimate load slightly increased by 5.4% However, the major advantage of using four stirrups with smaller bar diameter was in the mode of failure where it changed from splitting failure in case of specimen NC-L30-2T8-V to flexure failure in case of specimen NC-L30-4T6-V 3.3 Stirrups distribution Some codes for example Eurocode 1992-1 [14], recommend that the transverse reinforcement be positioned at the outer sections of the lap splice Nonuniform distribution of splice transverse reinforcement was clearly represented in specimen NC-L30-NT6-V, while specimen NC-L30-6T6-V, had the same amount of transverse reinforcement but with a uniform distribution of stirrups Fig 10 shows the results of the two specimens where it can be seen that the ultimate load capacity was only 6% higher in case of uniform distribution However, it can be seen that uniform distribution resulted in a flexural mode of failure and a deformation very close to the control beam with no splice (relative ductility = 0.93) compared to a splitting mode of failure in specimen NC-L30-NT6-V with relative ductility of 0.70 That can be attributed to the role of uni- 120 120 100 Total verƟcal load (KN) Total verƟcal load (KN) 20 DeflecƟon (mm) Fig 80 60 40 NC-L30-2T6-V NC-L30-4T6-V NC-L30-6T6-V 20 10 100 80 60 40 0 20 40 60 NC-L30-NT6-V 20 NC-L30-6T6-V DeflecƟon (mm) Fig Effect of stirrups spacing 20 40 DeflecƟon (mm) Fig 10 Effect of stirrups distribution 60 Behavior of RC beams with tension lap splices 1733 120 Total verƟcal load (KN) form distribution of stirrups along the splice length, which allows more bar lugs to share in the stress transfer mechanism This causes the stress distribution to be very close to uniform distribution as well as increasing the compatibility between steel and the surrounding concrete Fig 11 shows the load strain curves for the readings obtained at the middle of the splice and the end of the splice which can be correlated to steel stresses It can be seen that the gap between the readings of the two strain gauges was reduced in case of specimen NC-L306T6-V with uniform distribution of stirrups compared to the beam with no uniform distribution 60 40 Four different shapes of stirrups were studied namely vertical, rectangular, corrugated and spiral as shown previously in Fig As can be noted from Table 3, the change in relative ductility when using the four types of stirrups was not remarkable where it ranged from 0.17 to 0.2 Fig 12 shows the load deflection curves for the four beams It can be seen that using the rectangular stirrups gave a value of ultimate load capacity (101 kN) even slightly higher than the case of vertical stirrups (98 kN) The spiral and corrugated stirrups gave a lower value of 75.6 kN and 81 kN, respectively The mode of failure was flexure except in case of spiral stirrups where it was splitting failure It can be concluded that using rectangular stirrups around the spliced bars in the tested specimens gave the best improvement on the beam behavior causing it to act very close to the beams provided with vertical stirrups along the splice length compared to using corrugated or spiral stirrups 10 20 Total verƟcal load (KN) 140 120 100 80 60 40 NC-L30-6T6-V 20 SC-L30-6T6-V HC-L30-6T6-V 20 40 Fig 13 Load deflection curves for high strength concrete ing the ultimate load capacity for the two cases of no splice and when six stirrups were provided within the splice zone, there was not much difference for NC and HC However, for SC concrete the ultimate load of the beam with transverse reinforcement surpassed the beam with no splice with about 15% 100 100 80 80 Load (kN) 120 60 40 end strain gauge 20 end strain gauge 20 mid strain gauge mid strain gauge 0 0.001 0.002 0.003 0.004 Strain 0.001 0.002 0.003 0.004 Strain (a) Beam NC-L30-6T6-V Fig 11 0.005 60 DeflecƟon (mm) 120 40 30 Effect of stirrups shape Fig 12 60 DeflecƟon (mm) 3.5 Concrete type Load (kN) 80 20 3.4 Stirrups shape Figs and 14 show the load deflection curves for the beams using the three types of concrete NC, SC and HC Regardless of concrete type, all beams without stirrups along splice length (NC-L30-0T6-V, SC-L30-0T6-V and HC-L30-0T6-V) had a sudden splitting mode of failure Similar increase of transverse reinforcement resulted in an increase in the beams ductility over beams with no stirrups along the splice length and a change in the mode of failure to flexural one as seen for beams NC-L30-6T6-V, SC-L30-6T6-V and HC-L30-6T6-V Compar- NC-L30-4T6-V NC-L30-4T6-R NC-L30-4T6-C NC-L30-4T6-S 100 (b) Beam NC-L30-NT6-V Load – strain curves at mid and end of splice 0.005 R.T.S Mabrouk, A Mounir 140 140 120 120 Total verƟcal load (KN) Total verƟcal load (KN) 1734 100 80 60 40 SC-L00-0T6-V 20 SC-L30-6T6-V SC-L30-0T6-V 20 40 80 60 40 HC-L00-0T6-V HC-L30-6T6-V 20 60 DeflecƟon (mm) (a) Self-compacting concrete Fig 14 100 0 20 40 60 DeflecƟon (mm) (b) High strength concrete Load deflection curves for different types of concrete Fig 13 shows a comparison between the three types of concrete in case of using six stirrups within the lap splice It can be seen that the beam with HC had an ultimate load capacity 30% higher than that of NC while the beam with SC had an ultimate load 22% higher than NC despite the fact that the SC mix was designed with the same compressive characteristic strength as the NC This can be attributed to the fact that selfcompacting concrete has good bonding characteristics that resulted in improving the beam behavior more than the normal vibrated concrete with the same compressive strength [2,5] It can be said that self-compacting concrete can give optimum compatibility between concrete, main reinforcement and transverse reinforcement at splice zone Comparing the ductility of the three beams in Fig 13, it can be seen that normal concrete had the highest ductility index of 8.18 followed by high strength concrete (6.8) and finally the self-compacting concrete with 5.9 Numerical simulation In order to support the experimental results, a threedimensional nonlinear finite element analysis was undertaken with the help of the commercial finite element software; ABAQUS version 6.13 ABAQUS is a very complex finite element analysis program introduced with huge material characteristics (a) Concrete model (C3D8) Fig 15 and parameters to reproduce high accuracy in calculations and provide comprehensive outputs concerning stress analysis Fully integration scheme was chosen to integrate the element’s internal forces and stiffness The materials nonlinearity due to cracking, crushing of concrete, and yielding of reinforcement were taken into consideration during the analysis [15] ABAQUS has an advanced and extensive library for elements and materials [15] As shown in Fig 15a, concrete was modeled using 3-dimensional, 8-node solid elements; C3D8, with three degrees of freedom for each node; translations u, v, and w in the three orthogonal directions; x, y and z, respectively Steel reinforcement was modeled as 2-node truss elements also with three degrees of freedom per each node The bonding between reinforcement and concrete was achieved in ABAQUS using the ‘‘embedded” technique as shown in Fig 15b, where, steel reinforcement was used as the embedded element and the concrete was designated as the host element Supporting and loading plates that transfer the reactions from and to the concrete elements are modeled as rigid solid parts Similar to concrete beam, the three dimensional solid element C3D8 was chosen to model the steel plates on both loading and supporting positions Figs 16 and 17 show the different model components To avoid stress concentrations within the concrete beam, the reaction forces were transferred to the beam through plates (b) Embedded technique Elements used in FEM analysis Behavior of RC beams with tension lap splices 1735 4.1 Concrete model Fig 16 Model for solid components Reinforced concrete is a complicated material to be modeled within finite element packages A proper material model in FEM should be able to simulate both the elastic and plastic behavior of concrete in compression and tension Using ABAQUS, damage can be simulated with either of the three crack models for reinforced concrete elements; namely Smeared crack concrete model, Brittle crack concrete model, and Concrete damaged plasticity model [15] In this study, the concrete damaged plasticity model was utilized as it is capable of representing the complete inelastic behavior of concrete both in tension and in compression including damage characteristics The concrete damaged plasticity model assumes that the two main failure mechanisms in concrete are the tensile cracking and the compressive crushing A typical stress-strain curve of concrete and steel modeled in this study is shown in Fig 18a and b, respectively From Fig 18a, it can be seen that concrete in compression is described with an initial linear-elastic range up to 30–40% of its compressive strength after which it is represented by a plastic behavior Concrete compressive behavior was input to the ABAQUS by applying a numerical expression that was developed by Hognestad [16] as shown using the following equations: r e e For ð0 < e < e0 ị 1ị ẳ2 rcu e0 2e0 r e À e0 ¼ À 0:15 rcu ecu À e0 Fig 17 Model for truss components having the same dimension of the spreading girder used on the loading frame experimentally and were defined as rigid bodies having a very high modulus of elasticity in order to be undeformable Plates transfer reactions from and to concrete are connected to the concrete beam solid element using the ‘‘tie” option, which means that parts cannot be disconnected during loading Fig 18 For ðe0 < e < ecu Þ ð2Þ where rcu is the maximum concrete compressive strength, e is the strain corresponding to each stress r value, e0 is the strain corresponding to peak stress usually around 0.002 and ecu is the ultimate strain usually around 0.0035 The behavior was plotted on a characteristic stress-strain curve for normal strength concrete of 30 MPa as shown in Fig 19 applying both Eqs (1) and (2) The uniaxial compressive strength of concrete was designed to be 30 MPa for NC and 90 MPa for HC but the input values used in ABAQUS models were the actual values taken from test cubes at casting time for each beam separately to perform Typical stress-strain curves for both concrete and steel 1736 R.T.S Mabrouk, A Mounir a fair comparative study between FEM and experimental results When subjected to tension, the concrete stress is assumed to increase linearly till its tensile strength is reached Concrete tensile behavior is input to the ABAQUS by applying the standard equation in Eurocode 1992-1 [14] as shown in Eqs (3) and (4) The elastic part of the curve describing tensile behavior can be represented by Eq (5) instead of the original model adopted by the ABAQUS manual as shown in Fig 20 Plasticity is generally defined as the unrecoverable deformation after all loads have been removed Damage is generally characterized by the reduction in elastic stiffness ABAQUS specify five parameters as inputs to completely describe the plastic behavior of concrete; K, €, rb/rc and W The default values according to ABAQUS manual [15] were used as the following 2/3, 0.1, 1.16 and 36° respectively K: The ratio of the second stress invariant on the tensile for any given value of the pressure invariant P such that the maximum principle stress in negative €: Plastic potential eccentricity It is a small positive value which expresses the rate of approach of the plastic potential hyperbola to its asymptote It can be calculated as a ratio of tensile strength to compressive strength rb/rc: The ratio of the strength in the biaxial state to the strength in the uniaxial state W: Dilation angle It is interpreted as a concrete internal friction angle The effect of the damage is different in tension and compression, and the degraded response of concrete is taken into account by introducing two independent scalar damage variables for tension and compression respectively The damage variables can take values from zero, representing the undamaged material, to one, which represents total loss of strength Eqs (6) and (7) show the damage index for compression and tension, respectively fctm ¼ 0:3 f2=3 ck 3ị rc ẳ dc ị Â E Â ðec À ee Þ ð6Þ ð4Þ rt ¼ ð1 À dt Þ Â E Â ðet À ee Þ ð7Þ ð5Þ The damage parameter value (dc) is defined as the ratio of the inelastic strain to the total strain, E is modulus of elasticity and ee is the elastic strain 35 Stress (MPa) 30 25 20 15 10 0 0.001 0.002 0.003 0.004 Strain Fig 19 Equivalent uniaxial stress-strain curve for 30 MPa concrete C50=C60 fctm ẳ 2:12 log1 ỵ fcm =10ịị ee ¼ fctm E > C50=C60 where fctm is the tensile strength of concrete, fck is the characteristic cylinder strength, fcm is the target mean cylinder strength, E is the modulus of elasticity and ee is the elastic strain C50/C60 represents the strength class equivalent to fcu = 60 N/mm2 After the crack is initiated, the tensile stress starts to decrease by means of a softening response [15] In order to simulate the complete tensile behavior of reinforced concrete in ABAQUS, a simplified post failure stress-strain relationship for tension according to Nayal and Rasheed [17] is adopted Fig 20 4.2 Steel reinforcement model The reinforcing steel is assumed to be elastic-perfectly plastic material in both tension and compression The steel input data for all beams were taken as follows: in elastic zone; the elastic behavior was modeled as linear and isotropic The modulus of elasticity and Poisson’s ratio of reinforcing steel are input to ABAQUS for elastic behavior simulation However, once the stress in the steel exceeds the yield stress, permanent plastic Tension stiffening model according to (a) ABAQUS manual and (b) Nayal and Rasheed simplified model Behavior of RC beams with tension lap splices 1737 deformation begins to occur The stiffness of the steel decreases once the material yields The material model used for reinforcing steel follows the standard stress-strain diagram in Eurocode 1992-1 [14] as shown in Fig 21 analysis using ABAQUS are presented The goal of this comparison is to assess the behavior of the lap splices in the beams under study and to assure that the elements, material properties, real constants and convergence criteria are adequate to model the behavior of reinforced concrete beams containing 4.3 Experimental verification 120 Total verƟcal load (KN) In this section, a comparison between the results obtained from both the experimental program and the finite element 100 80 60 NC-L30-0T6-V 40 Experiment 20 ABAQUS 10 DeflecƟon (mm) Fig 21 Design stress-strain diagram of reinforcing steel Fig 24 120 Total verƟcal load (KN) Total verƟcal load (KN) 120 100 80 60 40 Experiment 20 Load deflection curve for NC-L30-0T6-V 100 80 60 10 20 30 Experiment 20 ABAQUS NC-L30-2T6-V 40 40 ABAQUS DeflecƟon (mm) Load deflection curve for NC-L00-0T6-V Fig 22 Fig 25 Total verƟcal load (KN) Total verƟcal load (KN) 120 100 80 60 HC-L00-0T6-V 40 Experiment 20 10 Load deflection curve for NC-L30-2T6-V ABAQUS 20 40 60 100 80 60 Load deflection curve for HC-L00-0T6-V NC-L30-4T6-V 40 Experiment 20 DeflecƟon (mm) Fig 23 120 140 DeflecƟon (mm) ABAQUS 10 DeflecƟon (mm) Fig 26 Load deflection curve for NC-L30-4T6-V 1738 R.T.S Mabrouk, A Mounir tensile reinforcement lap splice with or without transverse reinforcement within the splice zone Currently, there are no specific models incorporated in the design codes to simulate the behavior of self-compacting concrete instead of normal concrete in terms of material mod- elling Therefore, the three beams cast using self-compacting concrete were not studied using ABAQUS Further study and investigations are needed in this area Figs 22–34 show the comparison between experimental data and results obtained using ABAQUS regarding the load 120 100 Total verƟcal load (KN) Total verƟcal load (KN) 120 80 60 NC-L30-6T6-V 40 Experiment 20 ABAQUS 10 20 30 100 80 60 40 DeflecƟon (mm) Load deflection curve for NC-L30-6T6-V Fig 30 120 140 100 120 80 60 40 NC-L30-2T8-V Experiment 20 10 80 60 HC-L30-6T6-V 40 Experiment ABAQUS 10 Load deflection curve for NC-L30-2T8-V Fig 31 30 40 50 Load deflection curve for HC-L30-6T6-V 120 Total verƟcal load (KN) Total verƟcal load (KN) 20 DeflecƟon (mm) 100 80 60 NC-L30-NT6-V 40 Experiment 20 ABAQUS 10 15 20 25 100 80 60 Load deflection curve for NC-L30-NT6-V NC-L30-4T6-S 40 Experiment 20 DeflecƟon (mm) Fig 29 40 100 10 120 30 Load deflection curve for HC-L30-0T6-V DeflecƟon (mm) Fig 28 20 20 ABAQUS ABAQUS DeflecƟon (mm) Total verƟcal load (KN) Total verƟcal load (KN) Fig 27 Experiment 20 40 HC-L30-0T6-V ABAQUS 10 DeflecƟon (mm) Fig 32 Load deflection curve for NC-L30-4T6-S Behavior of RC beams with tension lap splices 1739 Total verƟcal load (KN) 120 100 80 60 NC-L30-4T6-R 40 Experiment 20 ABAQUS 10 DeflecƟon (mm) Total verƟcal load (KN) Fig 33 Load deflection curve for NC-L30-4T6-R deflection curves for the studied beams The curves are shown up to the failure point as the post failure part is not well represented using ABAQUS Regarding the values of the ultimate deflection, there is a rather big difference in the values obtained from experiment and those estimated using finite element One reason for that can be that the post cracking stiffness and simulation of the reinforced concrete elements are not well represented which is another point that requires further investigation Overall, the general load – deflection curves estimated using ABAQUS followed the same trend compared to the ones obtained from experiment Table summarizes the output results It can be seen that the differences in case of ultimate load capacity did not exceed 20% except for three cases It can be said that the results obtained from the finite element analysis in terms of the ultimate load gave a reasonable agreement when compared with the experimental data 120 Conclusions 100 Sixteen concrete beams containing an overlapping splice of two bars at the tension side of the beam were studied under constant bending moment Comparison with FEM program ABAQUS was conducted Based on the analysis and comparison of ultimate load capacity, modes of failure, loaddeflection relationship and ductility of the beams studied in this research, the following conclusions were made: 80 60 40 NC-L30-4T6-C Experiment 20 ABAQUS 10 DeflecƟon (mm) Fig 34 Load deflection curve for NC-L30-4T6-C Table a Regardless of concrete type, the failure of beams with lap splices at mid span without transverse reinforcement was violent and occurred along the entire length of the splice Adding stirrups along the splice zone improved the behavior as transverse reinforcement eliminated the formation of splitting cracks at tension splice zone Experimental data vs ABAQUS output results % represents ratio of values estimated by ABAQUS to values from Experimental results 1740 It is highly recommended to increase number of stirrups inside splice zone to be spaced at about 60 mm which gave the best results within the beams in this study Increasing number of stirrups provided inside splice zone with smaller bar diameter instead of larger bar diameter with the same reinforcement ratio crossing the potential plane of failure resulted in a drastic change in the mode of failure but a slight change in ultimate capacity Uniform distribution of stirrups along splice length has an important role on improving beam ductility and mode of failure as compared to nonuniform distribution Using special shapes of stirrups around spliced bars affect the beam behavior Based on this study, using rectangular stirrups within lap splice caused the beam to behave closest to that provided with normal vertical stirrups with the advantage of rectangular stirrups consuming less amount of steel Rectangular confining stirrups around spliced bar can be an economical and practical method to improve the behavior of tension lap splices in beams Ductility and behavior improvement due to increasing stirrups along splice length not have the same rate for all types of concrete indicating that concrete type is an important parameter on the response of beam to the contribution of stirrups in stress transfer mechanism For high strength concrete, good confinement using transverse reinforcement in the form of stirrups improved the behavior of the beam with lap splice 10 For the same concrete compressive strength and for well confined concrete, bond strength in self-compacting concrete is found to be higher than normal vibrated concrete indicating that this method of concrete production and placement can be an adequate replacement to normal vibrated concrete in case of tension spliced bars in beams 11 The results from the finite element simulation agree reasonably well with the experimental observations with regard to load-deflection response This indicates that the constitutive models used for concrete and reinforcing steel are able to capture both elastic and plastic behavior reasonably well 12 Consequently, it can be said that ABAQUS represents a promising tool to be used for the nonlinear analysis and design of such elements Acknowledgment Deep gratitude and special thanks are given to Prof Dr Akram M Torkey for his continuous support and help throughout this research R.T.S Mabrouk, A Mounir References [1] A.M Diab, Lap Splices in Reinforced Concrete Beams Subjected to Bending Master Thesis, University of Alexandria, Egypt, 2008 [2] K Pandurangan, A study on the bond strength of tension lap splices in self-compacting concrete, Mater Struct 43 (2009) [3] EFNARC, European Guidelines for Self-compacting Concrete, Specification and Production and Use, Association House, UK, 2005 (www.EFNARC.Org) [4] M.A El-Azab, Effect of Tension Lap Splice on the Behavior of High Strength Self-Compacted Concrete Beams Master Thesis, Cairo University, 2013 [5] K Turk, B Ahmet, Bond strength of tension lap-splices in full scale self-compacting concrete beams, Turkish J Eng Environ Sci 32 (2008) [6] H Ahmed, A Hala, Effect of Transverse Reinforcement on the Behavior of Tension Lap Splice in High Strength Reinforced Concrete Beams, Int J Civ Arch Struct Constr Eng (12) (2013) [7] M Ghasabeh, E Canbay, Lap splice behavior in selfcompacting concrete, in: 10th International Congress on Advances in Civil Engineering, Middle East Technical University, Ankara, Turkey, October 2012 [8] ACI Committee 408, ‘‘Bond and development of straight reinforcing bars in tension”, ACI408R-03, Farmington Hills, MI, 2003, p 49 [9] ECP 203-2007, Egyptian Building Code for Structural Concrete Design and Construction, Ministry of Housing, 2007 [10] ACI 318-05, Building Code Requirements for Structural Concrete and Commentary, American Concrete Institute, Michigan, 2005 [11] A Maghsoudia, H kbarzadeh Bengar, Acceptable lower bound of the ductility index and serviceability state of RC continuous beams strengthened with CFRP sheets, Scientia Iranica 18 (1) (2011) 36–44 [12] A Mounir, Behavior of Tension Lap Splices Confined by Transverse Reinforcement on Different Types of Reinforced Concrete Beams, Faculty of Engineering, Cairo University, 2017 [13] A Mounir, R Mabrouk, A Torkey, An experimental study on the behavior of tension lap splices confined by transverse reinforcement in RC beams, AICSGE9, 2016 [14] Eurocode 1992-1, Design of Concrete Structures-Part, General Rules and Rules for Buildings, European Standard, European Committee for Standardization, October 2001 [15] ABAQUS Standard Version 6.13-4 and ABAQUS standard users’ manual The Abaqus software is a product of Dassault Systems Simulia Corp., Hibbitt Karlsson & Sorensen Inc., 2014 [16] Hognestad Eivind, A Study of Combined Bending and Axial Load in Reinforced Concrete Members, Engineering Experiment Station, University of Illinois, Urbana, Bulletin Series No: 399 A, vol 49, No 22, November 1951 [17] R Nayal, H.A Rasheed, Tension stiffening model for concrete beams reinforced with steel and FRP Bars, J Mater Civ Eng 18 (6) (2006) 831–841 ... steel spreader (b) Specimens with lap splices Strain gauges locations for the main longitudinal reinforcement Behavior of RC beams with tension lap splices 1731 sured using 10 mm strain gauges... research is to study the effect of using transverse reinforcement with different ratios, distribution and shapes on the behavior of reinforced concrete beams loaded under pure tension while using. .. good just for beams without transverse reinforcement within lap zone, while it was not accurate for beams that contain transverse reinforcement where it under-estimates the role of confinement