EQUIVALENT VISCOUS DAMPING OF METALLIC FIBER-REINFORCED CONCRETE (MFRC).
ABSTRACT: In this paper, results of an experimental study to investigate the equivalent viscous damping (EVD) of the concrete reinforced with metallic fibers in mono and hybrid form have been presented. Two types of metallic fibers were investigated: Fibra Flex and Dramix fibers. FibraFlex fibers develop strong bond with concrete due to their rough surface. On the contrary, Dramix fibers develop weak bond with concrete due to their smooth surface. Maximum dosage of fibers was kept equal to 40 kg/m3. The findings of this study showed that EVD of concrete is improved with the addition of metallic fibers. Comparison of the effectiveness of two metallic fibers investigated in this study on EVD revealed that increase in the EVD was greater with Fibra Flex fibers up to 4 mm deflection in beam and after that Dramix fibers were found to be more effective to enhance EVD of concrete.
Keywords: Concrete; metallic fibers; equivalent viscous damping; reverse cyclic loading
The dynamic response of structure under free or forced vibration depends, among others factors, on its damping properties. The dynamics effects are particularly aggravated when the load has a harmonic vibration with a frequency close to the structure resonance condition. Experiments in structural dynamics have shown that the presence of damping accessories can effectively bound the dynamic response. The control of the dynamic response in a structure can be achieved with discrete damping elements. In civil engineering, damping properties of reinforced concrete are very important in earthquake engineering once damping provides structure energy dissipation during moderate or strong earthquakes (Carneiro et al. 2006).
Viscous damping is another means of describing the element's capacity in dissipating earthquake energy. For a structure, damping mechanisms can be represented by a viscous damping ratio (Abdelsamine and Tom,2010). The process by which free vibration steadily diminishes in amplitude is called damping. In damping, the energy of the vibrating system is dissipated by various mechanisms, and often more than one mechanism may be present at the same time. In a vibrating reinforced concrete building, these different mechanisms include cracking, reinforcement yielding, and friction between concrete and steel bar during slippage (Chopra, 2006). In reinforced fibrous concrete, friction between fiber and matrix, yielding of fiber, breaking or pulling out of fibers from matrix are also additional mechanisms. The damping in actual structures is usually represented in a highly idealized manner.
The damping coefficient is selected so that the vibrational energy it dissipates is equivalent to the energy dissipated in all the damping mechanisms, combined, present in the actual structure. This idealisation is therefore called equivalent viscous damping. The equivalent viscous damping is accepted as a satisfactory approximation if it is used in the conditions of quasi-static testing because the natural frequency of the specimen is not equal to the exciting frequency (Chopra, 2006).
According to the displacement based design method it is feasible to select a desirable damage performance criteria for a given structural member or structure under a given hazard level (Priestley, 2000). This is an attractive feature of the displacement based design method, as engineers can select the desired structural performance criteria before the design of any structural member (Binggeng and Pedro, 2006). Selection of performance goals can be related directly to displacement ductility levels, which in turn can be associated with the equivalent viscous damping (Hose et al. 2000) and it is one of the crucial parameters in applying the displacement based design method. In seismic design, the EVD for individual reinforced concrete members is estimated from their hysteretic response under fully reversed cyclic loading (Daniel and Loukili, 2002; Binggeng and Pedro, 2006; Clough and Penzien, 1993).
The research reported herein is concerned with the behaviour of reinforced fibrous concrete beams subjected to reverse cyclic bending. The basic purpose of this paper is to examine experimentally the influence of metallic fibers on the EVD of reinforced concrete beam.
MATERIAL AND METHODS
Concrete Composition: Four different concrete mixes, one control and three mixes containing metallic fibers were studied. For all the concrete mixes, CEM I 52.5 R type cement has been used. Local natural sand with maximum particle size of 4 mm was used. Round gravels with size range of 4 -10mm were used as coarse aggregate. A Super-plasticizer has been used as an admixture to improve the workability of the mix in the presence of metallic fibers. Table 1 show the mix proportion of control concrete.
Table 1: Control concrete mix proportion
Table 2: Fibres investigated in this study
###Dimension (mm)###Tensile strength
Fiber###Fiber Type###Geometry###E, GPa
Type of fibres used: Two types of macro-metallic fibres, 30 mm in length were used: 1) Fibra Flex fibres (named in this study as FF fibers) are amorphous metallic fibers produced by Saint-Gobain Seva, France. They are composed of (Fe, Cr) 80% and (P, C, Si) 20% by mass (Saint-Gobain Seva, 2012). Due to their rough surface and large specific surface area, these fibres are characterised by high bond with concrete matrix (Hameed et al. 2010). 2) Dramix fibers produced by Bekaert, Belgium (named in this study as DF fibers) are made using carbon steel wires, and are characterised by a weak bond with the matrix compared to FF fibres due to smooth surface and less specific surface area. They have circular cross-section and hooked-ends.
The characteristics of these two types of metallic fibres are given in Table 2, where L, W, T, D and E are length, width, thickness, diameter and modulus of elasticity respectively.
Displacement controlled reverse cyclic bending tests were performed. Numbers of loading cycles on the specimens for each amplitude value of the imposed displacement were three. The amplitude of imposed displacement was gradually increased from 1 mm to 10 mm. The loading rate of imposed deflection was kept as 0.2 mm/second.
Nomenclature of Tested Beams: Regarding the nomenclature of tested beam, for RCB-cont, RCB stands for reinforced concrete beam and "cont" stands for control (without fibers), for RCB-FF20, FF stands for FibraFlex fibers and 20 is quantity of fibers in kg/m3, similarly RCB-DF20, where DF stands for Dramix fibers. The beam containing fibers in hybrid form is designated by RCB-40HyF, where 40 is total quantity of two fibers in kg/m3 (20 kg/m3 of each fiber) and HyF stands for hybrid fiber reinforced concrete.
Equivalent Viscous Damping: The most common method of defining equivalent viscous damping is to equate the energy dissipated in a vibration cycle of the actual structure and an equivalent viscous system. For an actual structure the load-displacement curve obtained from experiment under cyclic loading is determined; such a curve of arbitrary shape is shown in Fig. 2. For any cycle i, the equivalent viscous damping zeq can be calculated using the following relation (Abdelsamine and Tom, 2010): Where: the area within the inelastic force- displacement response curve denoted by ED, is a measure of the hysteretic damping or energy dissipation capacity of the member and ES depicts the recoverable elastic energy stored in an equivalent linear elastic system. Both ED and ES are defined in Fig.2.
The calculation of the equivalent viscous damping for a loading cycle was divided into two parts as shown in Fig.3. The EVD was calculated for each part separately and then average of two was obtained. The average value for each cycle was considered to represent the equivalent viscous damping of the beam. The zeq was calculated up to maximum displacement of 10 mm for each tested beam and a comparative study was carried out to investigate the effect of each type of fiber used in this study on EVD.
RESULTS AND DISCUSSION
Comparison of zeq of RC beams containing Fibra Flex fibers (RCB-FF20 and RCB-FF40) and control RC beam (RCB-cont) is shown in Fig. 4, where increase in EVD can be observed by the addition of Fibra Flex fibers. Regarding the effect of fiber dosage of Fibra Flex fiber, it is difficult to conclude that zeq increases with increase of fiber dosage because values of EVD of RCB- FF20 and RCB-FF40 varied significantly with respect to each other at different displacement amplitude. The EVD of RCB-FF20 and RCB-FF40 was dropped to value lower than RCB-cont after displacement amplitude of 4 and 5 mm, respectively. This was due to the breaking of fibers at wider crack openings at 4 and /or 5 mm deflection of beam.
In Fig.5, comparison between control beam and beams containing Dramix fibers in terms of EVD is presented. It is observed from this comparison that similar to Fibra Flex fibers, Dramix fibers also contribute to improve zeq. With the increase of Dramix fibers content, generally EVD was also increased.
Comparison of EVD of beams containing Fibra Flex and Dramix fibers at 20 kg/m3 in mono form is shown in Fig.6 along with values of control beam. Up to displacement of 5 mm, the value of zeq was greater with RCB-FF20 with the exception of 2 mm displacement. After 5 mm, it was RCB-DF20 beam which exhibited greater values of EVD. Similarly in Fig.7, comparison of RC beams containing FibraFlex and Dramix fibers at 40 kg/m3 in mono form in terms of zeq is shown along with values of control beam. It is observed in this figure that up to displacement amplitude of 3 mm, the value of EVD was greater with RCB-FF40. After 3 mm, it was RCB-DF40 beam which exhibited greater values of EVD.
While comparing the results of equivalent viscous damping for the beam containing both fibers in hybrid form at content of each fiber equal to 20 kg/m3 (RCB-40HyF) and the beam containing only Fibra Flex
Flex and Dramix fibers in hybrid form (RCB-40HyF) shows that replacing 50% of Dramix fibers by Fibra Flex fibers is not advantageous, since the values of EVD of RCB-40HyF were lower than that of RCB-DF40 at all displacement amplitude up to 10 mm.
Conclusions: The influence of metallic fiber addition on the equivalent viscous damping of the RC beams has been examined. From the analysis of the results and discussion, it is possible to draw the following conclusions;
* For all the tested beams, the value of the EVD through the first cycle was significantly higher than the value through the third cycle at the same displacement amplitude. This was mainly due to decrease in ED in subsequent cycles at the same displacement amplitude.
* Equivalent viscous damping of RC beams is improved with addition of metallic fibers investigated in this study. This improvement is limited up to certain level of displacement amplitude for Fibra Flex fibers which depends on the content of fibers. However, effectiveness of Dramix fibers is noticed at each level of displacement amplitude.
* Equivalent viscous damping is improved over wide range of displacement amplitude by the use of Fibra Flex and Dramix fibers in hybrid form.
Acknowledgement: The financial support for this study from HEC Pakistan is highly acknowledged.
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Hameed R., A. Turatsinze, F. Duprat and A. Sellier.Study on the Flexural Properties of Metallic Hybrid Fiber-Reinforced Concrete. Maejo Int. J. Sci. Tech., 4: 169-184 (2010)
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Saint-Gobain Seva, FibraFlex Department, France, Flexible non-oxidising metallic fibre for concrete reinforcement, www.fibraflex.com (retrieval date: December 2012).
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|Publication:||Pakistan Journal of Science|
|Date:||Jun 30, 2013|
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