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Revista ingeniería de construcción

versión On-line ISSN 0718-5073

Rev. ing. constr. vol.29 no.1 Santiago  2014

http://dx.doi.org/10.4067/S0718-50732014000100001 

 

Study of the behavior of composite beams made of concrete and steel by using numerical simulation

 

Hildemar Hernández¹*, Jorge Bonilla*, Gilberto Rodríguez*

* Universidad de Ciego de Ávila, Ciego de Ávila. CUBA


Dirección de Correspondencia


ABSTRACT
The present research develops a preliminary study on the behavior of composite beams made of concrete and steel, which are assembled by bolt-type connectors. The numerical simulation process employed software named ABAQUS, which is based on a Finite Element Method (FEM). In order to model the steel behavior, a bilinear model with failure criterion by Von Mises was employed, as well as concrete damage plasticity model. The results obtained from a numerical simulation on real tests show a quite appropriate relationship with results obtained from trial test, thus validating the use of FEM for the study of these kinds of structures. Besides, some strain-stress phenomena take place, which are produced inside the structure. Variability of diverse physical parameters and their influence on the behavior of the composite structure are also studied, such as the case of friction in the concrete slab–structural steel interfaces, as well as in the spacing areas between connectors.

Keywords: Composite beams, numerical simulation, stud connectors, stress-strain behaviour


1. Introduction

In order to study the behavior of composite structures, specifically the connection area, experimental tests constitute the starting point from which the first calculation methods are based on. Methods were developed from connectors tests [Davies (1969), Larrúa (1992), Rambo-Roddenberry (2002)]. Although, to a small extent, verification tests on bending beams have also been employed as complementary corroboration means.

Nowadays, there is a trend to employ numerical simulation as a tool for the study of the behavior of connectors, using the least possible resources, to achieve an adequate relationship with the physical model (push out test). It is worthwhile mentioning previous research works developed by Lam and Ellobody (2005), Recarey et al. (2005), Ellobody and Young (2006), Bonilla et al. (2007 a) (2007 b) (2007 c) and Bonilla et al. (2010).

In order to study the strain-stress behavior of composite beams in this research, numerical simulation has been used and, also tests such as calibration and validation standards, based on the method of finite elements (FEM) implemented by the software ABAQUS. Non-linearity of steel and concrete are considered. Besides, the procedure to carry out a virtual simulation of composite beam test is proposed, considering aspects related to the geometrical conception of the model, by taking advantage of physical-mechanical symmetry and loads, and also defining the edge and interface conditions between the elements making up the virtual specimen. The whole procedure is approached for calibration, which is related to the selection of finite element type and, the selection of optimal mesh density. Finally, the results of the study of composite concrete-steel beams behavior is released, thus validating the use of numerical simulation. The behavior of the structure is described by considering different values of friction coefficients in the slab-structural steel interface, and other geometrical and mechanical conditions in the model. The influence of spacing area between connectors on the structure ultimate strength capacity is also studied.

2. Description of the specimen

The characteristics of the specimen under study correspond to specimen D4 from Series 2, pertaining to the studies developed by Davies (1969). The specimen is made up of a structural steel I (BSB 5 in x 3 in x 9 lb or UB 127 mm x 76 mm x 13 kg/m), with a typical steel strength of 301 MPa, a concrete slab of 15in (381 mm) width and, 2 ½ in (63.5 mm) thickness, with 35 MPa for steel reinforced concrete resistance. The connection slab-structural steel is achieved by means of bolts with a 450 MPa ultimate tensile resistance, allocated in the beam center and spaced at 1 ½ in (38.1 mm). The beam covers a span of 4 feet (1220 mm). In the experimental study, the beam was covered with a lubricating film on the contact area, between the structural steel and the concrete slab.

Figure 1 shows the composite beam and distribution of connectors, as well as the beam cross section in detail.

Figure 1. Specimen in detail

 

 

3. Virtual modeling test of composite beams exposed to tensile stress

3.1. Modeling geometry
The tri-dimensional modeling of the specimen (3D) has been adopted, thanks to favorable geometrical representation provided by ABAQUS/CAE, which is consistent with the experimental test layout.

3.2. Modeling support, limit or edge conditions

a) Bolt: there are two interaction surfaces in a bolt. One enables the connection bolt-structural steel and the other the linkage bolt-concrete.

The bolt-structural steel connection is treated as a rigid joint, as in the real specimen the connection is achieved by means of a wheel bead around the whole perimeter surrounding the bolt base.

The bolt-concrete interface was treated as a rigid joint, just the same as the previous connection, although it is well known that there is no continuity between both materials. However, there is a great friction stress in some areas of the bolt surface, because some high regular stresses take place, especially around the connector base.

Lam and Ellobody (2005) used a rigid contact for the bolt-concrete interface, disconnecting those nodes that do not participate in the contact effect, as reported by real experimental tests. This predicament has also been considered by Bonilla et al. (2007 b) and Bonilla (2008).

b) Slab: on the surface where the slab and structural steel get in contact, it was assumed that only contact or regular stress took place, since in the experimental model there is no friction area or tangential contact, provided that there is a grease layer between both materials.

c) Structural steel: All types of contact were previously treated for different interactions between bolt and structural steel, as well as for concrete and structural steel. Considering the geometrical simplification applied to the experimental model, it was decided to model an articulated support for the quarter of specimen, where displacement of axes X and Y are restricted but allowing the displacement in the axis Z. Being consistent with the symmetric simplification applied to the specimen, the displacement of Surface I was restricted in X axis direction, because of the cutting off applied by such axis. Similarly, the displacement of Surface 2 is restricted in Z axis direction, in order to simulate the cut off applied to the specimen (see Figure 2).

Figure 2. Virtual specimen. Conditions of support, limit or edge and applied load

3.3. Modeling load
The load is applied and distributed on a surface at the beam mid span, so as to avoid high concentrations of stresses and to simulate the real experimental test. Load increments are applied by the RIKS algorithm at small intervals, where the size of them is automatically selected by the ABAQUS code, which is based on numeric convergence conditions. Such algorithm is based on the Newton-Rahpson method, which is normally employed to predict the collapse of a structure.

3.4. Modeling materials
3.4.1. Modeling steel
In order to model the steel strain-stress behavior, the studies developed by Nie and Cai (2004), Lam and Ellobody (2005), Ellobody and Young (2006), and Bonilla et al. (2007 b) were considered. Such studies deal with composite structures modeling, where a bilinear behavior was adopted for steel, using the breaking criterion developed by Von Mises. These studies show high relationship between experimental tests and the numerical simulation. The outcomes validate the use of such criterion for modeling steel. In order to apply this behavior, *PLASTIC command from ABAQUS code is used.

3.4.2. Modeling concrete
In order to model steel behavior, in its non-linear stage, the Concrete Damage Plasticity model was employed, which is implemented by ABAQUS code. Such model properly reproduces the concrete non-linear behavior and it was selected considering the adequate results obtained from previous studies developed by Bonilla et al. (2007 b), Bonilla (2008) and Bonilla et al. (2010). The model was validated by these authors, because there is a proper relation between the virtual model and the experimental tests. This study does not report details on the calibration of this model, but details can be found on researches previously quoted.

3.5. Study and selection of the type of finite element to be used
ABAQUS owns a program library with solid (3D) elements, with three different typologies: 6-sides binoculars, 5-sides binoculars (wedge) and tetrahedrons (pyramid of triangular base), which may belong to lagrangian or serendipite branches, indistinctly.

For the selection process of the finite element to be employed, a set of models with different configurations were run. The selected configuration was the one having the numerical model behavior closest to the experimental model.

This study indicates that to complete discretization of connector, elements C3D8R shall be employed, which is consistent with previous researches developed by Bonilla et al. (2007 b) and Bonilla (2008), because this connector properly adapts itself to the geometry of such body. For discretization of concrete and the upper wing of the structural steel (structural steel area in contact with concrete) elements C3D6 shall be employed. However, for the rest of structural steel, C3D8R elements shall be used.

3.6. Study and selection of optimal mesh density
Choosing the type of finite element to be used is not enough, it is required to obtain the adequate size of the finite elements to be used for discretization. Therefore, a study is developed to achieve mesh density, where accuracy is considered as the pattern to compare simulation with experimental tests.

Figure 3. Discrete model

Three different mesh densities were analyzed for each element making up the composite beam (concrete slab, structural steel I and bolt), see Figure 3. For the bolt and structural steel, a uniform distribution of the mesh elements size was employed.

The slab shows the progressive increase of density towards the interest zone, where the highest concentration of stresses take place, that is to say the area between the bolt and the slab. Discretization was carried out in accordance with the considerations established by Bonilla et al (2007 b) and Bonilla (2008).

Table 1 shows the mesh density employed by each model in different zones, as well as the achieved loading capacity and errors expressed in percentages, in regards with the calibration experimental test.

Table 1. Model configuration for different mesh densities

Once the model considerations were established, a general layout is obtained that enables the study of different parameters, taking as base a calibrated specimen.

4. Behavior of concrete-steel composite beams

A total of thirty six virtual and full scale tests were developed on composite beams, which have a free span of 4.0 m. The slab cross section length is of 0.20 x 0.14 m, which is constant for all models. Compressive resistance was established at 30 MPa. Connectors kept constant geometrical characteristics, using bolts of 110.0 height and 16.0 mm diameter, thus producing models with three spacing areas between connectors, where the ultimate steel tensile stress is 450 MPa. For structural steel two different heights were used, one of 127.0 mm, corresponding to the structural steel described by UB 127 x 76 x 13, and other of 254.0 mm described by UB 254 x 102 x 22, both in accordance with the British Standard Beam. The steel strength is 300 MPa for structural steels. The results achieved by these models are shown by Table 2.

Table 2. Results achieved by numerical models

4.1. Description of strain-stress behavior of composite beams

The studied composite beam is made of structural steel I and a concrete slab in the structural steel upper wing; both materials are joined together by bolt-type connectors. Generally, in function of the neutral line position, the concrete slab endures the compressive stress applied to the beam due to bending stress. Consequently, structural steel, or part of it, endures the tensile stresses when the structure bends as a whole. Connectors are in charge of joining the concrete slab and the structural steel, trying to avoid displacement and detachment of both materials (steel and concrete), thus ensuring a combined structural performance and taking advantage of both materials properties.

Figure 4 shows a detail of stresses endured by concrete slab, for concentrated load as well as for distributed load. In the front area of the connector base, we can observe that a stress transmission cone or failure cone takes place, provoked due to the stress transmission from concrete to the bolt, which in turn passes the stress to the structural steel. Above proves the statements developed by Bonilla et al (2007 b). There is an increment of stress cone as long as connectors are closer to the beam support area. However, in the beams area enduring concentrated load, it is observed that stress cones in each connection have similar stress values.

By observing the virtual models, the statements developed by Jayas and Hosain (1988), Kitoh and Sonoda (1990), and also by Bonilla et al. (2007 b) are confirmed. These authors state that there is a loss of contact in the back side of the connector, which is opposite to the applied load direction.

Figure 4. Detailed simulation. a) Detail of slab with concentrated load. b) Detail of bolt with concentrated load. c) Detail of slab with distributed load. d) Detail of bolt with distributed load

4.2. Influence of friction on the section loading capacity

The study of the interface employed three friction coefficient values (0.00; 0.15 and 0.30) for each employed structural steel and, for each spacing area between connectors under analysis. The charts on Figure 5 show the results for composite beam simulation.

By analyzing load values for each friction coefficient, it is observed that ultimate loading values increase, as long as the friction coefficient rises, in each case. Such increments are not relevant, as they do not exceed the 5% of ultimate loading capacity.

Figure 5. Friction influence. a) Structural steel of 127mm, concentrated load. b) Structural steel of 127mm, distributed load. c) Structural steel 254mm, concentrated load. d) Structural steel, distributed load

Based on above facts, it is possible to state that friction contribution can be disregarded in the experimental studies, which is consistent with the proposal made by EUROCODE 4 for push out tests; that suggests covering the slab-structural steel interface with a lubricating layer. Other authors, such as Lyons et al. (1994) and Rambo-Roddenberry (2002), highlight the importance that friction produces on the slab-structural steel interface, as they applied a regular stress on the slab during the push out test.

4.3. Spacing between concrete and steel in slab-concrete interface
In order to analyze the spacing area taking place in the slab-concrete interface, samples are taken from a set of twelve models. Five measurements are carried out at points located at the mid-span slab, at three eighths from support, at one quarter from support, one eighths from support and at a point near the support, since at the same support the resulting spacing area is equal to cero, (measurement areas are made to coincide with intermediate points between two connectors). Measurements were carried out for 33.3% (1/3), 66.6% (2/3) and 100% of ultimate load value.

In measurements developed at load intervals of 33.3% and 66.6%, there is no significant spacing difference between the two materials in the interface slab-structural steel interface, being values close to 0.01 mm. When specimens achieved 100% of ultimate load, a higher spacing area was observed, which is greater at the points located between one quarter of the beam span and the support; while at the beam mid-span spacing area was almost null.

In models with a 127mm-structural steel, a higher spacing area than in models with 254mm-structural steel was observed, which is explained by stiffness variations. As long as spacing area between connectors was increased, the slab spacing area also increased, yielding higher values among connectors of 450 mm. Besides, it was observed that in models where concentrated load was applied, spacing area was also higher than in those models were load was distributed alongside of the span.

Figura 6

There is a spacing area in the slab-structural steel interface for all analyzed models. The most critical cases achieved values close to 0.08 mm.

Finally, it can be concluded that provided a spacing area in the slab-structural steel interface, there is a bonding loss in the interfaces, which evidences a reduction of physical contact between two materials, thus wasting any contribution provided by friction. This fact proves the statement posed in EUROCODE 4 and is consistent with experimental tests.

4.4. Influence of spacing area between connectors
In the thirty six analyzed numerical models, three spacing areas between connectors were used (150, 300 and 450 mm). Charts (Figure 7) show the influence on the ultimate loading capacity at different spacing areas between studied connectors.

It is quite clear that when increasing the spacing area among connectors, the ultimate loading capacity decreases, and a failure takes place in each model. This occurs in models with structural steel I of 127 mm height, as well as in models with structural steel I of 254 mm height, independently from the friction coefficient value employed by the model. This is explained by the detachment produced between the slab and the structural steel, which increases as long as spacing area between connectors rises, thus provoking bonding loss between materials (steel and concrete). This aspect was observed and proven during the whole experimental test developed prior to the push out test.

Therefore, using a spacing area quite wide, that makes concrete slab and reinforced steel beam work independently from each other, becomes disadvantageous for the composite beam. Placing fewer connectors in this section would make that the stress transmitted by the concrete to the connector (as well as other stresses produced by horizontal displacement in the slab-structural steel interface) would be distributed among fewer connectors, therefore, stress to be endured would be higher in terms of horizontal shear.

Figure 7. a) Concentrate load, 127mm height; b) Distributed load 127mm height; c) Concentrated load 254mm height; d) Distributed load 254mm

For analyzed models with concentrated load, while the spacing area between connectors increases, the load decreases in a value ranging from 15% and 20%. However, in models with distributed load, while the spacing area between connectors increases, load decreases near 30% and, in some cases almost 40%.

The analysis developed by this research allows us to reconfirm that any contribution to friction in the strength capacity of a composite beam can be disregarded, even in different spacing areas between connectors. Undoubtedly, it is necessary to determine a proper spacing area between connectors in order to enable a joint work leading to a favorable structural behavior of a composite beam.

 

5. Conclusions

• The feasibility of studying composite structures has been proven, particularly the composite beams structural behavior, by employing previously calibrated numerical simulation previously calibrated. An adequate consistency was observed between numerical and experimental results. Consequently, the use of FEM is validated. Modeling considerations for the study of composite beams have been validated as well.

• It was possible to prove that friction stress in the slab-structural concrete does not significantly contribute in the connection area´s strength capacity and, therefore, in the ultimate strength capacity of the composite beam. The later is in accordance with EUROCODE 4, which recommends covering the slab-structural steel interface with a grease layer, when specimens are prepared for the push-out test.

• In all analyzed cases, there is a detachment in the slab-structural steel interface, which is increased as long as spacing area between connectors is also increased, thus provoking a loss of physical contact between the two surfaces. Therefore, the contribution to the strength capacity that might be provided by friction strength is lower.

• As a result of this study, it can be concluded that numerical modeling and experimental tests are complementary research tools. Numerical methods deliver approximate solutions for engineering problems. These methods are not exempt from errors; therefore, potential errors might be controlled by means of calibration based on experimental results

 

6. References

 

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E-mail: hildemar@ingenieria.unica.cu

Fecha de Recepción: 05/10/2013 Fecha de Aceptación: 04/03/2014