EUROSTEEL 2014, September 10-12, 2014, Naples, Italy
NUMERICAL AND EXPERIMENTAL INVESTIGATIONS ON THE VERTICAL SHEAR RESISTANCE OF BOXED STEEL CROSS-SECTIONS WITH CONCRETE INFILL (DELTABEAMS) Matti V. Leskela, Simo Peltonen, Aristidis Iliopoulos, Panagiotis Kiriakopoulos Peikko Group Corporation, Finland, National Technical University of Athes, Greece
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INTRODUCTION Deltabeams are composite beams of high bearing capacity composed of closed steel cross-sections of trapezoidal shape filled with concrete. Due to the contribution of concrete in the beam's structural behaviour a hybrid strut and tie system is activated which leads to significantly higher vertical shear resistance than is found in the steel member only. In this paper a part of the experimental campaign of Peikko Group Corporation on the shear resistance of Deltabeams is presented. The shear tests took place in the Technical Research Center of Finland (VTT). Loading tests have been carried out for Deltabeams during the development history and for verifying the design models. For looking deeper in the composite interaction, a 3D FEM analysis model was developed in which material non-linearities are taken into account. The authors point out that the confinement effect is present in the critical node of the compressive load path; an ultimate limit state design method developed by Kotsovos M. D., Pavlovits M. N. 1999. 1
GENERAL
1.1 Description of the Deltabeams Deltabeams are welded steel beams of hollow cross-sections (Fig. 1). The bottom flange is larger than the top one and equipped with ledges allowing unpropped support for various floor slabs, such as precast planks, hollow core slabs and composite slabs with steel decking. The web of the Deltabeam has circular openings so that transverse rebars easily pass through and provide continuity for the slab. The concrete filled steel section constitutes a composite slim floor beam of increased stiffness and strength. Deltabeams can be fabricated with any desirable precambering values; thus, large spans with cross-sections of limited total height are feasible. In case of high-rise buildings one or even two additional floors can be constructed. Above the bottom flange longitudinal reinforcement is usually placed, so that the required fire resistance rate is reached. In [9] it has been experimentally proven that Deltabeams can reach a fire resistance rate of 180 mins.
Fig. 1. The Deltabeam
Table 1 gives an overview of the standard Deltabeam dimensions according to [10]. Different dimensions may be feasible as well. Table 1.
Min. in mm Max. in mm
b2 100 330
Standard Dimensions of Deltabeam [10] according to Figure 1
d1 10 40
b 200 600
b1 97.5 130
d2 5 25
h 200 500
t 5 8
Ø 80 150
s 300
Deltabeams have been used with success in numerous building applications and have been established in the European domestic markets as one of the most versatile slim floor solutions. 1.2 Structural behaviour 1.2.1 General The effects of vertical shear force and bending in Deltabeams induce similar crack patterns that are found in RC (reinforced concrete) members, and generally the response to vertical shear force bears resemblance to that in RC members. However, the resistance to vertical shear in Deltabeams is considerably higher than in normal RC members of similar size. This is attributable to the contribution of the steel member both in providing the effect of transverse shear reinforcement (⇔ web plates between the web openings) and in providing confinement for the concrete in compression in the critical sections under the top plate (sagging bending) or above the bottom plate (hogging bending). The detailed behavior is more complex than in similar RC members, but it is possible to explain the typical ULS behaviour of Deltabeams on account of the compressive force path + strut and tie resistance. The concept of the compressive force path for evaluating the behavior of RC members was developed by M.D. Kotsovos and his colleagues [1, 2, 3, 4] and is based on the developments already started by G. Kani in 1964 [5]. 1.2.2 Compressive force path modelling The only way that the concrete can transfer loads efficiently in flexural members is by compression, as the tensile strength cannot contribute primarily to any major stress resultant. However, the important fact that should not be forgotten is that the concrete in compression always fails due to tension in direction transverse to the principal compressive stresses [4]. When it is assumed that concrete can primarily only have compressive stresses for transferring loads, the load bearing system must be based on a compressive force path within the concrete content of the composite member and the failure of the member follows from the failure of the concrete in the most critical section of the force path. As the plastic shear resistance of the bare steel member is smaller than the resistance of the composite member, the failure in the concrete causes an unstable state where the load cannot prevail on its ultimate level, but unloading occurs. Depending on the location of the critical section, the failure may formally be termed either a shear failure or a flexural failure. An important fact should be noted: a shear connection is always required for the development of composite interaction, but it is not essential on what exact vertical position of the cross-section the connection is located. Its function is to take care of the horizontal shear transfer between the steel section and its concrete content when the horizontal equilibrium of forces is considered, and it is analogous to the bond forces between the reinforcement and the surrounding concrete. In the overall composite system of Deltabeams, the web openings and the end plates serve as the primary longitudinal shear connection, the task of which is to balance resultant Cc. It may be noted that there can obviously be also other components which contribute to the horizontal shear connection, e.g. friction, but this is ignored.
av s
compressive force path
inactive concrete
Ca
σRd.1
σRd.2
Cc
Sect.1 R H.ep
Rv.f
Ts R H.f
R
Principal inclined crack
Ta
Section2
Fig. 2. Compressive force path in the concrete inside the steel member shown as hatched It is sometimes argued that longitudinal shear connection cannot reside in the tensile zone of the concrete, which is cracked. This argument is not based on reality, as the concrete in the cracked tensile zone does not vanish into rubbles, but is working between the cracks and can transfer shear loads, as illustrated in Fig. 2. This, however, requires that the horizontal shear is resisted by the web openings in a ductile manner, i.e. the force can be maintained while the slip increases. In fact, it has been shown experimentally that the concrete dowels in the web holes have ample slip capacity, which is satisfactory for the span range of Deltabeams for classifying the longitudinal shear behavior as ductile [7]. Within the length s the inclined part of the force path ends to the end plate and reaction RH.ep takes care of the horizontal equilibrium of forces. Another force, RH.f may also be considered, but its value depends on the effective coefficient of friction, the reliable value of which may not be easily predicted. Referring to EN 1992-1-1 [6], the node in section 1 may conservatively be defined as a compression node with tie and the maximum stress developed in the node concrete from the side of the strut is σRd.2. Where the horizontal force path meets the node, the maximum concrete stress is taken as σRd.1. The failure of the member is classified as due to vertical shear, when the vertical shear force causes the node failure in section 1 before the failure in section 2 takes place, otherwise the failure is due to flexure. 2
EXPERIMENTAL AND NUMERICAL INVESTIGATIONS
2.1 The test arrangement A number of loading tests have been carried out in VTT (Technical Research Centre of Finland) for the investigation of the Deltabeams' behaviour against vertical shear, e.g. those referred to in [11]. One of the main test configurations is illustrated in Figure 3. A simply supported beam with a total length of 5605 mm is equipped with a pinned support at its start and a roller one at a distance of 4365 mm; thus, leaving a cantilever with a length of 1235 mm. In the first 3600 mm the core of the beam is filled with concrete and the other part is pure steel. The aim of the partial concreting of the beam is to clarify the shear resistance of the Deltabeam both during erection phase before concrete hardening (section C-C) and in later stages after the concrete has hardened (sections A-A and B-B). A point load P is applied at the top flange of the beam leaving a shear span equal to 900 mm. The specimens were made of steel S355J2G3 and concrete grade is C20/25.
Fig. 3. Shear test arrangement 2.2 The finite element model The model consists of two different parts (Fig. 4a): the steel beam and the concrete. The steel and concrete parts were meshed using hexahedral elements (solid) of type C3D8. The software used is Abaqus [14] and the total number of elements is 12374. The Concrete Damage Plasticity model was used to define the non-linear behaviour of concrete, which is based on the Drucker-Prager strength hypothesis [12]. It takes into account the stiffness degradation due to tensile cracking and allows the computation of the post-failure response due to the confinement effect. The stress-strain relationship for the structural steel S355 was taken from the samples tested in the laboratory and was inserted in the software as a non-linear one taking into account the hardening of the material. A similar procedure was followed for the concrete material as well. The post-crack tensile behaviour of concrete was taken into account by introducing a bi-linear tension-stiffening model with a tensile strength equal to 2.2 MPa and a maximum strain equal to 0.1%. This concrete strain softening model is the simplest one; it is widely used due to its positive effect on the numerical stability of the FE-model and was proposed by Bazant and Oh in [13]. The contact between concrete and steel parts was modelled using a surface-to-surface interaction. The surfaces were able to separate from each other, but no penetration was allowed. After many trials a coulomb friction coefficient equal to 0.3 was chosen as the most appropriate one for calibration. A constant friction value was chosen since it guarantees a more stable numerical path. 2.3 The results The first cracks in the concrete were observed for a vertical shear force equal to 95 kN. However, the shear cracks penetrating the whole web thickness became visible at 974 kN. At 1065 kN the beam looked damaged but it could still carry the applied load (Fig. 4c). Higher loads could not be applied due to equipments' restrictions. The response of the Deltabeam against shear is graphically demonstrated by the shear force - displacement curve of Figure 4b. The first observation is associated with a ductile failure mode with a ductility factor greater than 4. Moreover, the maximum shear resistance is 167% higher than that of an identical test arrangement and no concrete infill. This proves the significant enhancement of the shear resistance due to the concrete infill and the activation of the strut and tie path of Figure 2. The design shear resistance of the composite beam calculated with the Kotsovos method [3] is 766.1 kN; 28% less than the maximum shear force
measured during the test (Fig.4b). The characteristic shear resistance of the composite beam calculated with the same analytical method is 957.6 kN; 10% less than the maximum shear force measured during the test. The shear resistances were calculated with the nominal values of the material strengths. The partial safety factors were equal to 1.5 for concrete and 1.1 for structural steel for the design situation and both equal to unity for the characteristic one. The numerical model represented the structural response of the system quite satisfactory with practically zero deviations in the elastic branch and acceptable ones in the inelastic one; always smaller than 7.7%. In Fig. 4b the development of the shear force maxV is depicted, devided by the design value VRd calculated according to [3].
(a)
(b)
(c) Fig. 4. (a)The finite element model (b) The shear ratio - deflection curve (c) Test specimen after unloading The maximum principal steel stresses for the maximum value of the applied point load are shown in Figure 5a. The highest values are observed around the first two web holes indicating a local overloading due to excessive shear. In Figure 5b one can see that excessive concrete stresses (higher than 20 MPa, black colour) are located at the position of the applied load at the top flange and the intersection area between the flanges and the 15 mm endplate (Fig. 3). This indicates the activation of the confinement effect due to the considerable contact stresses developed between the concrete infill and the steel plates, especially at the edges of the cross-section. In Fig. 5b the existence of the inactive concrete area of Fig. 2 is verified.
(a) (b) Fig. 5. (a) Maximum principle steel stresses (b) Minimum principle concrete stresses 3
SUMMARY
The design model for the vertical shear resistance of composite Deltabeams based on the Kotsovos compressive force path concept and the due strut and tie mechanism derived from it is in agreement with the 3D FEM model presented, but slightly conservative; while the FEM model predicts the shear resistance quite accurately (maxVR,FEM / maxVR,test = 92.3%), the ratio between the design model and the test result is VRk,calc / maxVR,test = 89.9%. It is important to note that the failure of Deltabeams in vertical shear is very ductile and the strut resistance can be maintained until the effective tie action by the steel webs between the openings has developed (Fig. 4c). REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
[13] [14]
Kotsovos, M.D. and Pavlovic, M.N., “Ultimate limit-state design of concrete structures - A new approach”, Thomas Telford, 1999. Kotsovos, M.D. and Michelis, P., “Behaviour of Structural Concrete Elements Designed to the Concept of the Compressive Force Path”, ACI Structural Journal, Vol. 93, No. 4, pp. 428-436, July-August 1996. Kotsovos, M.D. and Lefas, I.D., “Behavior of Reinforced Beams Designed in Compliance with the Concept of Compressive Force Path”, ACI Structural Journal, Vol. 87, No. 2, pp. 127-139, March-April 1990. Kotsovos, M.D., “Compressive Force Path Concept: Basis for Reinforced Concrete Ultimate Limit State Design”, ACI Structural Journal, Vol. 85, No 1, pp. 68-75, January-February 1988. Kani, G.J., “The Riddle of Shear Failure and Its Solution”, ACI Journal V. 61, No. 4, pp. 441-467, April 1964. EN 1992-1-1, “Eurocode 2, Design of concrete structures. Part 1-1: General rules and rules for buildings”, CEN 2005. Peltonen, S. and Leskelä, M. Connection, “Behaviour of a Concrete Dowel in a Circular Web Hole of a Steel Beam”, Composite Construction in Steel and Concrete V, pp. 544-552, 2006. Kotsovos, M.D., “Concepts Underlying Reinforced Concrete Design: Time for Reappraisal”, ACI Structural Journal, V. 104, No 6, pp. 675-684, November-December 2007. Plum, C. M., Peltonen, S., “Fire resistance of hollow-core slabs supported on non-fire protected Deltabeams”, Betonwerk und Fertigteiltechnik, pp. 10-17, March 2010. www.peikko.com, “Deltabeam. Composite Beam”, Peikko Group Corporation, Technical Manual. VTT Research Report No. RTE2318/05. Load Tests on Deltabeams, 2005 (Confidential). Kmiecik, P., Kaminski, M.: “Modelling of reinforced concrete structures and composite structures with concrete strength degradation taken into consideration”. Archives of civil and mechanical engineering, Vol. XI, No. 3, pp. 623-636, 2011. Bazant, Z.P. and Oh, B.H., "Crack Band Theory for Fracture of Concrete". Materials and Structures, RILEM, Paris, Vol. 16, pp. 155-176, 1983. ABAQUS: Abaqus analysis user's manual, Version 6.9, 2009, Dassault Systèmes.
