SHEAR RESISTANCE BETWEEN CONCRETE-CONCRETE SURFACES

Transcription

1 , DOI: /sjce M. KOVAČOVIC SHEAR RESISTANCE BETWEEN CONCRETE-CONCRETE SURFACES Marek KOVAČOVIC Research field: composite structures Address: Department of Concrete Structures and Bridges, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, Bratislava, Slovak Republic Abstract key words The application of precast beams and cast-in-situ structural members cast at different times has been typical of bridges and buildings for many years. A load-bearing frame consists of a set of prestressed precast beams supported by columns and diaphragms joined with an additionally cast slab deck. This article is focused on the theoretical and experimental analyses of the shear resistance at an interface. The first part of the paper deals with the state-of-art knowledge of the composite behaviour of concrete-concrete structures and a comparison of the numerical methods introduced in the relevant standards. In the experimental part, a set of specimens with different interface treatments was tested until failure in order to predict the composite behaviour of coupled beams. The experimental part was compared to the numerical analysis performed by means of FEM basis nonlinear software. Surface modification, interface, coupling, nonlinear analysis, effect of shear reinforcement. 1 Introduction The start of prefabrication in the early years of the 20th century had significant meaning due to rapid and economically efficient construction. The technology of prefabrication is associated with coupling technology. A comprehensive proposal for calculating shear resistance involves several factors, and it is difficult to calculate. The technology of coupling has a simple, but very effective basis, when by avoiding mutual slippage at the interface level, the moment of inertia is greatly increased; consequently, the entire resistance of an element is also enhanced without any need to change the geometry of the element, thereby increasing or strengthening the quality of the materials. The main goal of the research was to verify the theoretical and experimental shear resistance of the interface performed on the beams with different interface modifications as well as the use of the shear reinforcement effect. Thus, the results obtained by the experimental investigation were compared with one another and also verified by the FEM numerical analysis. 2 MATERIALS AND METHODS The load-bearing capacity of a coupling cross-section is significantly increased only when the mutual slipping at the interface is avoided. For comparison, two basic types of composite beams are illustrated. 2.1 Uncoupled members If the structural elements are freely placed on each other, it is possible for any slippage to occur at the interface level and the bending moment is distributed to the particular parts of the whole structure according bending stiffness of the elements (Fig.1). Elements without any interface interaction seem to be an unsuitable solution, because the total possible bearing capacity of the crosssection is not used. 25

2 Fig. 1 Action of uncoupled member σ, ε. Fig. 2 Action of coupled members σ, ε. 2.2 Coupled members Due to coupling, a shear stress is induced at the contact area. This leads to the transmission of internal forces from one element to another. Thus the created element behaves as a monolithic cast at the same time. If we consider two elements of the same cross section and their parameters, the moment of inertia would be four times greater than in the case of uncoupled elements (Fig. 2). (1) act on the cross-section, the tensile force component Ft in the axis of the steel reinforcement, and the compressive force component F c in the centre of the concrete s compressed zone, due to the influence of the bending moment. On the opposite side of the fragment, the same forces act, but in an opposite direction, which also stresses the effect of the additional bending moment ΔM = V. Δx. The whole element must be balanced by the vertical and horizontal forces, and also the balance of the bending moment associated with any point must also be maintained. In both the compressed and tensioned zones, the unbalanced forces due to the bending moment are transmitted by the shear strength of the concrete to the point of contact with the coupling factors. From the equilibrium of the forces in the longitudinal reinforcement it is known that: (3) (2) where: z lever of internal forces, Δx length of the selected fragment of the beam The longitudinal shear stress in the concrete cross section is caused by the difference in the bending moment over the length of the element, as is shown in Fig. 3. At each level of the cross-section, the stress is transmitted by the monolithic behaviour of the concrete only at the interface level, this stress must be transferred by the factors involved in the shear resistance of the coupling. The pair of forces The shear resistance at the interface is calculated as: (4) 26

3 Fig. 3 Effect of the load coupled member with a shear crack. Fig. 4 Action of shear reinforcement at an interface. 1. Cohesion c is the ability of two contact surfaces to resist shear loading without any compressive force up to the point of mutual slippage. Its value ranges from 0.25 for a smooth surface to 0.5 for an indented surface according to the type of interface modification (EN ). 2. Friction depends on the contact force F N acting perpendicular to the surface area and the coefficient of friction µ. The amount of friction force is calculated according to the well-known formula F T = µ.f N. The value of µ ranges from 0.5 to 0.9 according to the type of surface modification (EN ). 3. Shear reinforcement is the most important shear resistance factor. The action of the transverse reinforcement is based on the self-prestressing effect (Fig. 4). As a result of mutual slippage, the contact gap is widened. Consequently, the force induced in the shear reinforcement acts against the contact area and closes the gap area. Shear resistance is based upon friction resistance. If the reinforcement is fully stressed, the value of the friction force can be calculated as V = µ.f y.a s, where f y is the yield strength of steel and A s is the cross-sectional area of the steel in one row. 2.3 EXPERIMENTAL OBSERVATION A total of eight composite beams were tested in order to verify the theory. The first part of the test was performed at the Central Laboratory of Slovak University of Technology (SUT) (Fig. 5a) and focused on the shear resistance using beams with stirrups. For this purpose, two composite beams were tested. The second part of the test (Fig. 5b), which focused on the shear resistance with regard to the effect of the different interface modifications, was performed at Slovak Academy of Sciences (SAS), Department of Construction and Architecture, where six test beams were made. Both series of beams were loaded with force increments till failure occurred. The six beams (Fig. 6b) were made at the Central laboratory of SAS: two beams with indented surfaces, two beams with rough surfaces and the last two beams with the contact areas reinforced by stirrups, respectively. These beams were tested in two phases: In the first phase, the unstrengthened beam was loaded at a level of 70 % (350 kn) of its flexural resistance; in the second phase, these beams were strengthened by over-concreting and consequently loaded until failure. 27

4 a) b) Fig. 5.a Beams with shear reinforcement, CL-SUT. Fig. 5.b Beams without shear reinforcement, CL-SAS. a) b) Fig. 6.a Loading arrangement: Beams with shear reinforcement. Fig. 6.b Loading arrangement: Beams without shear reinforcement. 28

5 Fig. 7 Shear failure at the interface of the beam N The failure due to the exhaustion of the shear resistance of the couplings was accompanied by a sudden fracture of the contact joint without any warning. Tab. 1 Material characteristics of concrete (f cc cube strength, f ctf flexural strength, E c Young s modulus of elasticity), St stirrups, In indented, R rough. Member Beam Deck f cc [MPa] f ctf [MPa] E c [GPa] f cc [MPa] f ctf [MPa] E c [GPa] N SUT N St St In SAS In R R In Tab.1, the basic working parameters of the concrete are introduced. All the tests were performed on specimens aged 28 days (three 150 mm cubes in order to test the cube strength, and six 150 x 150 x 300 mm prisms in order to test their flexural strength and modulus of elasticity). An ordinary ribbed steel with a tensile yield strength of 575 MPa was embedded for all the beams. During the experimental measurement of the beams with the transverse reinforcement, we reached a shear resistance in the case of Beam No.2 with 175 mm stirrups spaced under a load of 460 kn (Fig. 7). This value was almost 13 % higher than the calculated value of the shear resistance. In the three other cases, the flexural failure occurred under a load of kn, which was about 8-17 % higher than the originally calculated value of the shear resistance. It is most likely if the beams had a higher flexural strength shear failure could be expected. In the second phase of the experiment we aimed at verifying the shear resistance with different interface modifications; a total of six samples were tested. The full shear failure at the interface level only occurred in two cases (both rough contact modifications); in the other two cases a particular failure occurred (the interface crack changed into an incline crack crossing the beam wall). The flexural and transverse shear resistance was reached in the last two reference beams reinforced by the coupling reinforcement. The maximum achieved value of the loading force was from 650 to 700 kn in relation to the value of the shear loading from 325 to 350 kn. The theoretically calculated values of the shear resistance were lower than the experimentally acquired values; thus, the standard regulations for the calculations provide conservative values of the shear resistance. In the case of the rough interface modifications, the experimentally and numerically acquired shear resistance was 16 % higher than the value calculated according to the standard recommendation. Fig. 8.a Shear failure of beams Indented interface - In1. Fig. 8.b Shear failure of beams Rough interface - R2. 29

6 2.4 FEM Numerical analysis For verification of the behaviour of the composite beams, a numerical analysis was performed using FEM-based ATENA 3D software. The whole beam was assembled from solid tetrahedron elements. Each element contains 20 nodes with 3 degrees of freedom. The precast beam and strengthening deck had their material characteristics obtained from laboratory tests. 3D nonlinear cementitious material for the concrete modelling and the reinforcement entity was chosen for the modelling of the discrete steel bars, which allow to use of bilinear working diagrams with descending branches. In order to model the contact area, a GAP entity with various parameters (cohesion, coefficient of friction, normal and tangential stiffness of contact) based upon the producer s recommendations was chosen. 3 RESULTS As can be seen in Figs. 9c-d, the failure loads of beams without any shear reinforcement are almost similar. Once the cohesion force at the interface is exceeded, only a residual cohesion remains. Such beams behave as partially coupled. Shear resistance according to the theoretical recommendations is lower by about 20 % than the shear resistance obtained from the experimental analysis. In Figs. 9c-d, it can be seen that the resistance without any transverse reinforcement is not significantly affected by the interface modification; however, this is not true. It is possible to assume that concrete achieves a cohesion above the recommended standard value. For the roughened interface modification of Beam No. 2 (Fig. 8b), the failure of the contact area occurred over almost the whole length of the element when the contact crack changed into an incline. The experimentally acquired shear resistance was just under 350 kn (700 kn in the jack). Fig. 9 Comparison Loading force vs. a) displacements ATENA b) displacements shear reinforcement c) displacements indented interface d) displacements rough interface. 30

7 Fig. 10.a Composite beams STU- N1. Fig. 10.b Stress in direction x -N1 125: F= 200 kn and failure stage. In Fig. 10.a, the beams reinforced with the coupling reinforcement, which were made and tested at CL SUT, are evaluated. The experimentally acquired results are compared with the theoretical and numerical results. The two models of beams with coupling reinforcements with 125 and 175 mm spacing were modeled. As a result of the premature flexural failure of the major part of the beams cast at the STU laboratory, the shear resistance at the interface could not be achieved. It is good to know that even now, the flexural peak load was about 20 % greater than the theoretical value of the shear resistance. The shear resistance shown in Tab.2 is represented by two values, directly by the vertical force V shmax, indirectly by the loading force F jackmax, the value of which corresponds to about 1.25 times the vertical force. As can be seen in Tab. 3, the results of the numerical analysis were similar to the experimental analysis, mainly in case of the reference beams with stirrups at the interface. In the case of the other interface modifications the variance was within 5-20 %. This is caused by the fact that the values of cohesion and friction are predicted with a relatively large scatter and these depend on the Tab. 2 Theoretical, numerical and experimental values of the resistance of the composite beams SUT. Interface modification Theor. - EN Flexural Shear Coupling F flmax [kn] V shmax [kn] F jackmax [kn] c µ ρ sl [ %] V rmax [kn] F jackmax [kn] N N N N Interface modification ATENA 3D Experiment F num [kn] F num /F exp [ % ] Mode of failure F exp [kn] F teor /F exp [ % ] Mode of failure N Flexural Flexural N Flexural Flexural N Contact Contact N Flexural Flexural 31

8 Tab. 3 Theoretical, numerical and experimental values of the shear resistance at the interface - SAS. Interface modification Flexural Theor. - EN Coupling F flmax [kn] c µ ρ sl [ %] V rmax [kn] F shmax [kn] Stirrups Stirrups Indented Indented Rough Rough Interface modification ATENA 3D Experimental F num [kn] F num /F exp [ % ] Mode of failure F exp [kn] F teor /F exp [ % ] Mode of failure Stirrups Trans. shear Trans. shear Stirrups Trans. shear Trans. shear Indented Shear/ Contact Shear/ Contact Indented Shear/ Contact Shear/ Contact Rough Contact Shear/ Contact Rough Contact Contact Fig. 11 Beam failures a) Indented interface - In2 b) Rough interface - R1 c) fragment of rough interface. manufacturing technology in contrast to the reinforcement, which has stable work characteristics. Even in the case of Beam No.1 with the rough interface, the crack did not occur at the level of the contact joint, but just cm below the contact joint (Fig. 11b). Thus, the development of cohesion between the concrete surfaces was very high (Fig. 11c). 4 Summary In the case of linear elements, such as a beam, etc., attention is mainly paid to the correct design of the flexural and shear resistance. Where this structural element is interrupted by discontinuity at the interface area due to technological or other compelling reasons, except for the above-described stresses, the phenomenon of shear resistance at the interface area should be considered. 32

9 In order to study shear behaviour at the interface level of composite structures, a set of composite beams with different interface modifications was prepared within our resources. A total of 8 beams were subjected to the experimental testing, 4 of which were reinforced by transverse reinforcement, while the other 4 beams were used only for cohesion and friction effects, which ensure shear resistance at the interface. Also, a numerical analysis using FEM ATENA 3D software was carried out. The experimental measurements confirmed the accuracy of the theoretical calculation procedures implemented in the standards and models for calculating the shear resistance at an interface. The standard procedures, which divide interfaces and the resulting coefficients of cohesion and friction into 4 categories when calculating resistance, may slightly vary within a category because the values of cohesion and friction are taken into consideration. The recommended cohesion factors have a high degree of safety, especially when the indented and rough surfaces are considered. Generally, the numerical and experimental results have shown a good coincidence of the resistance and failure modes. In contrast to the numerical and experimental analyses, the standardized calculating procedures to determine shear resistance provide conservative results that underestimate the actual shear resistance of the interface area. The calculated values are therefore important in the area of safety and provide a reliable design. Time dependent factors are also very important when shear resistance is investigated, but this effect was not involved in this study due to cost and time-saving reasons. In the case of composite beams without any transverse reinforcement, the sudden loss of shear resistance at the interface area without any warning has been observed; thus, we can speak about brittle failure. It is recommended to reinforce the interface area at least at the level of a minimum steel reinforcement, even if the calculations demonstrate a degree of resistance which does not require its usage. When modelling an indented interface modification, a planar interface area should be used, and each contact tooth should be exactly modelled by taking the actual behaviour of the interface into account. This approach is more suitable than the standard recommendations. 33

10 References Kovačovic, M. (2010) Shear resistance between concrete surfaces cast at different times. In Concrete Days 2010: Bratislava, SR, Slovak University of Technology in Bratislava, Bratislava, Slovak Republic, pp , ISBN Petržala, J. Križma, M. Pišťanská, Ľ. Kovačovic, M. (2012) On the relevant mechanical properties of cement composites with dispersed steel reinforcements. In Examinition and quality in civil engineering 2012: Proceedings, Brno, ČR, Faculty of Civil Engineering, Brno University of Technology, Brno, Czech Republik, pp , ISBN Križma, M. - Petržala, J. - Kovačovic, M. (2012) Rheological deformations of concrete floor slabs with content of plastic aggregate. In New Trends in Statics and Dynamics of Buildings: proceedings of 10th international conference. Edited by N. Jendželovský, M. Nagyová. Slovak University of Technology in Bratislava, Bratislava, Slovak Republic, pp , ISBN Kovačovic, M. Križma, M. (2012) Shear resistance between concrete surfaces cast at different times. In Concrete Days 2012: Proceedings. Bratislava, SR, Bratislava, Slovak Republic, pp , ISBN Kovačovic, M. Križma, M. Petržala, J. (2012) Shear resistance between concrete surface cast at different times. In 19th Czech Concrete Days 2012: Proceedings. Hradec Králové, ČR, , Hradec Králové, Czech Republic, pp , ISBN Bilčík, J. - Fillo, Ľ. - Benko, V. - Halvoník, J. (2008) Concrete structures Design according to STN EN , Bratislava, 374 pp., ISBN Harris, J.W. - Stocker, H. (1998) Handbook of Mathematics and Computational Science, Springer, New York, 1028 pp., ISBN MacGregor, J.G. et al. (2000) Reinforced Concrete: Mechanics and Design, Prentice-Hall Canada Inc., Scarborough, Ontario, ISBN Park, R. Pauley, T. (1975) Reinforced Concrete Structures, New York. Wiley, 769 pp. ISBN Kochaník, J. Kormaníková, E. (1994) Final element method I., Košice. Valente, I. - Cruz, P.J.S. (2004) Experimental analysis of Perfobond shear connection between steel and lightweight concrete, Portugal. ČSN (1986) Design of concrete structures, pp EN Eurocode 2 (2004) Design of concrete structures, part 1-1: General rules and building rules, CEN 12. ACI 318M-89 (1989) Building Code Requirements for Reinforced Concrete. AASHTO - LRFD (1998) Bridge Design Specifications, American Association of State Highway and ransportation Officials, Washington DC. Červenka, V. - Červenka, J. (2009) User s Manual for ATENA 3D, Prague. Kabele, P. - Červenka, V. - Červenka, J. (2005) Example Manual ATENA Engineering, Prague. 34