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A NATURAL FIBER-CONCRETE EXPERIMENTALCOMPUTATIONAL DESIGN THROUGH DYNAMICAL TIMOSHENKO THEORY

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This work deals with a gap in the behavior of structural mechanics and design: determination of mechanical properties to allow the employment of natural fibers in concrete composition, resulting in a natural fiber composite. Bamboo and cocoa fibers
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  IV ECCOMAS Thematic Conference on the Mechanical Response of Composites COMPOSITES 2013 F Pietrobon-Costa, R Carvalho Alvim, R A Arleo Alvim, L Pereira da Silva  © IDMEC 2013 A NATURAL FIBER-CONCRETE EXPERIMENTAL-COMPUTATIONAL DESIGN THROUGH DYNAMICAL TIMOSHENKO THEORY Flávio Pietrobon Costa * 1,  , Ricardo de Carvalho Alvim *, †  , Rosana de Albuquerque Arleo    Alvim *2  ,  Lucas Pereira da Silveira #   *1 professor, State University of Santa Cruz, UESC DCET, Rodovia Ilhéus Itabuna, km 16, Ilhéus, Bahia, Brazil pietrobon.costa@pq.cnpq.br  *1 professor, State University of Santa Cruz, UESC rosana.alvim@globo.com  †  professor, State University of Santa Cruz, UESC  in memoriam   # bachelor student at production engineering, scientific beginner lucassilveira_18@hotmail.com  Keywords:  Natural fibers–concrete composites, Experimental-computational modeling, Timoshenko’s Beam Theory. Summary:  This work deals with a gap in the behavior of structural mechanics and design: determination of mechanical properties to allow the employment of natural fibers in concrete composition, resulting in a natural fiber composite. Bamboo and cocoa fibers was used as strength element to concrete beams. Tall structures in reinforced or prestressed concrete need more strength construction elements, as non-slim structures components. For beams, to deal with this problem, was employed the Timoshenko Beams Theory (TBT), at small configuration changes, taking in account the dynamics of concrete-natural fibers beams. In this first work the damping internal mechanisms were not considered, to acquire the behavior of the influence in incorporating the natural fibers to concrete. This research performs correlation analysis between experimental and computing solutions. Numerical formulation considers the shear coefficient introduced by TBT, correcting distortion in the total rotation of beam cross section, not considered in the Classical Euler – Bernoulli Theory. Laboratory essays consider the design and making of proof CPs Timoshenko’s beams. Computational solutions are obtained in a finite element transient semi-discrete model. Numerical and experimental examples were performed, and results present an intrinsic potential to next development. With this approach, the natural fiber content rate to concrete was characterized, acquiring an optimal performance in the structure response. Results show an increment of composite concrete tensile strength in relation to a pure concrete one. Cocoa fiber incorporated to the composite concrete answer to a best performance of elastic modulus with an increment of elastic limit to the material.  Pietrobon-Costa, F.; Carvalho Alvim, R.; ArléoAlvim, R. A.; Siveira, L.P. 1 INTRODUCTION Natural fibers have been touted as an alternative material suitable for use in construction, with the potential for cost reduction, offering quality and durability, incorporation a strength compatible with conventional technologies. The behavior of structures have been extensively studied in the literature, but gaps remain requiring validation of specific theories, especially when considering the construction of tall structures, and in the design of more resistant, flexible, and elastic, constructive elements, as fencing blocks, masonry, covering surfaces, and also floor elements. The use of unconventional materials, such as composites of natural fibers, allows the incorporation of those desired characteristics. The design of composites was obtained with the incorporation of cocoa or bamboo to a concrete matrix. The interest was is project the employment of those composites in more strength structural elements, for use in tall buildings or slenderness structures. This work is a first approach in this target. With those employments in mind, to deal with the requirement for stronger structural, and at the same time more elastic, elements and materials, the Timoshenko’s Beam Theory, TBT, was used to design the proof specimen for laboratorial essays, and for computational simulations. TBT is suitable to project and design beams with those characteristics point below, and has the advantage of consider the occurrence of growth in transversal displacement in relation to Euler-Bernoulli slenderness beams. The focus of this work was to acquire knowledge about (1st) the behavior of composites Timoshenko’s beams elements under loads, at free dynamic behavior to evaluate the influence of natural fibers incorporation on amplitude, or transversal displacement, answer, and (2nd) also about theirs mechanical properties, in special on the longitudinal elastic modulus, on the strength to compressive and shear loads, and about the influence of intrinsic water incorporation to the material, along others mechanical characteristics. The development of new compounds arises from the need to combine the characteristics of two or more materials in order to improve product performance in certain specific applications. In construction, fragile cement based matrices are used, largely on their applications. These matrices mostly derived from mineral binders suffer plastic deformation rupture, and although resistant to compressive forces, do not support requests from large tensile, shear or dynamic loads. In tropical countries, the waste generated by agribusiness plant fiber can be a source of raw material for the production of building components. Depending on the quantities available and the geographical dispersion, as the costs of natural fibers are low, use this as reinforcement of brittle cement based matrices materials has aroused great interest in developing countries, because not only because of its low cost, but cause of it’s availability, energy savings and also as regards environmental issues [27]. However, the increase in tensile strength even greater evidence depends in particular on the fibers and ground natural state. Moreover, the determination of it’s benefic properties is already an research nest. Another aspect of this research is to analyze the resistance of lightweight concrete reinforced with fibers, since its main application is in the manufacture of masonry blocks, tiles and floors. Therefore, the need to seek an adequate and useful cement matrix, requires that the material be light and strength enough for shipping and handling during the construction process. Obtaining new materials for construction in environmentally sustainable conditions is a challenging way. When studying a new composite material, the main objective is to understand the  IV ECCOMAS Thematic Conference on the Mechanical Response of Composites COMPOSITES 2013 F Pietrobon-Costa, R Carvalho Alvim, R A Arleo Alvim, L Pereira da Silva  © IDMEC 2013 potential of it to use in practical applications or to substitute other products that are more expensive or that have environmental disadvantages. This research line so far is developing a standard operating procedure for the fabrication of lightweight composite cement matrix reinforced with fibers of bamboo and coconut, in order to obtain accurate results, optimized and low deviation between samples. For these reasons this design, studied composites are made from lightweight cement mortar, with modifications to the incorporation of cement partly replaced by additions of minerals, and use of bamboo fibers and coconut fibers all fresh, untreated surface. From historical works of [1, 2], studies of the deformation shear effects, had been addressed by several researchers. Sought this theory, TBT, corrects the classical theory of Euler-Bernoulli, which disregards the effect due to shear, getting underestimated values of displacement and deflection of the beam, under external loads. The introduction of a dimensionless correction factor, the shear coefficient, k, attempted to obtain values of displacement and strains compatible with the the real ones. The numeric formulation for the shear deformability evaluation was developed on a semi-discrete finite elements approach, adopting an energy method based on the minimization of a variational formulation. The object of this study correlates the response to dynamic loads of beams, developed with natural fibers, with the study of the efficiency of the Theory of Timoshenko beams for the study of structures of composite materials, simulating a static response to the dynamic response calibration by computational numerical analysis, and using this to develop a dynamic free vibratory model. The study then contributes in an area little explored in the technical literature. The response of Timoshenko beam vibration has already been studied with analysis results concerning to the oscillation of the beam excited by impact load. Composites TBT beams has being a developing research, approached on our computational model. This 1 st  line of this work finds application in vibration control industrial, construction of composite structures with natural fibers in composite materials, and the use of natural materials in structural systems construction. With relation to our 2 nd  guide line, that target to evaluation and determination of mechanical and physical properties of natural fiber –cement based composites; some laboratory experimental essays were performed, to acquire data that answer to what is the composite laboratory specimen, CP, responses to external loads. Those essays gives also elastic and strength properties. The experiments and laboratory analyzes have considered the preparation of fibers from bamboo and coconut, milled in a Wiley mill, achieving high surface of contact with the concrete, oven-dried to determine the moisture content. Analysis of resistance to compression and tension in flexion of the material was carried out with a content of 5% fiber, both parts incorporating bamboo fiber as for the coconut fiber. Body-of-proof, to 28 days of age, where tested: for direct compression and traction in flexion. Laboratory essays shows a little decrease in compressive resistance, detected in consequence of some compactation difficulties of CPs development, meanwhile, for the test results in the bending tensile essays, was detected an increase of 37.97% (coconut fiber) and of 35.95% (bamboo fiber) of the tensile strength when compared to pure cement matrix related CPs performance. The use of vegetable fibers to improve the behavior of building materials has been a recent development, due to its low cost, availability, and energy savings. There is interest in strengthening brittle matrix fiber cement, and seek better structural solutions. This target is linked to increased tensile, flexural, and shear resistance, but also answer to impact and dynamic excitation, preventing or delaying the appearance of cracks and higher material  Pietrobon-Costa, F.; Carvalho Alvim, R.; ArléoAlvim, R. A.; Siveira, L.P. toughness. Cement matrix composites reinforced with continuous fibers from bamboo pulp indicated that the content of refined fibers around 8%, showed remarkable improvements in mechanical properties of the composites compared to the homogeneous matrix [22]. Other studies showed that tiles made from fiber-reinforced composite residual sisal "baler wine" topper, eucalyptus pulp, mauve and banana, and combination of coconut fibers and eucalyptus pulp, acquires a higher resistance to bending loads. This solution is unique, in relation to the systems without the addition of fibers. [23] demonstrated the efficiency of mass determination in the lower order of higher frequency energy beams and concrete floors, of major concern in the analysis of dynamic structures. The mass reduction system, allowed by adding natural fibers to concrete, is of great interest for practical purposes, for project and design of composites. Those results indicated the potential of its use in the reinforcement of brittle matrices, based on Portland cement, with the increase of its ductility [24]. Researches developed in UESC, State univertity of Santa Cruz, show the better performance of cement – natural fibers composites, in relation to solely cement matrix structures. Similar research, with the use of composite materials have been developed in UEFS, using natural sisal fiber [26], and long steel fibers, with successful results, also with consideration of the theory of Timoshenko beams, and slender beam [25]. Section 2 deal with the computational model performed to analyze the structural dynamic behavior of those composites, and section 3 shows the laboratory essays methodology. Section 4 presents some experimental (at computational or laboratory) results with comments. 2 COMPUTATIONAL MODEL 2.1 Conceptual model As being previously developed [10, 14] the computational application model is a prismatic beam of symmetrical section related to the plan defined by longitudinal axis, x, and transversal axis, z. The Cartesian axis are oriented as a direct tried, resulting in transversal axis, y, oriented in normal direction of symmetric plan determined by x and z-axis. Models to compute simulation are non-damped free vibratory beams with length of 0,24 m, with 0,04 m in height and 0,04 m in width. This gives a aspect radius of 0.167, inside the TBT requirement for a Timoshenko’s beam. Load pattern is computed as a double uniformly distributed load of 100 kN/m and a midspan point shock load of 1,0 kN, for instantaneous impact, inducing free vibrations of beam models. This computational analysis is focused on determining composite cement – to – natural fibers dynamical performance, in relation to pure cement CPs beam, at TBT assumptions. Taking in account symmetrical bending of beams with little configurations change, and also considering a corrected rotation of transversal section in coupled bending and shear effect analysis. Arnold, Madureira and Zhang [28] studied the range of applicability of Reissner-Mindlin [3 to 9] and Kirchhoff-Love theories in 3D thin plate elastic models showing that Reissner-Mindlin has a convergent solution while Kirchhoff-Love fails for shear effect. [10] is one of the few works in the literature that effort to determine limit of validity to Timoshenko’s Beams models to deal with structural shear effects, at concrete material in an effort to support carbon nanotubes, CNT, design. In an first analogous way, Harik [17] and Pietrobon-Costa [14] proposed ranges of validity of the continuum beam model for CNT in a way to realize the extreme properties and benefits of CNT in stiffness and strength – to -  IV ECCOMAS Thematic Conference on the Mechanical Response of Composites COMPOSITES 2013 F Pietrobon-Costa, R Carvalho Alvim, R A Arleo Alvim, L Pereira da Silva  © IDMEC 2013 weight high ratios. One dimensional beam models were used and response was plotted in transversal displacement ratio versus aspect ratio, h/L. Transversal displacement ratio was posed between displacement, in relation to shear effect consideration: with, w(G0), a TBT approach, and without, w(G4), and Euler – Bernoulli Theory approach. The variational formulation is developed to support the semi-discrete finite element formulation. A finite differences approach was used to deal with acceleration terms. Results were obtained taking in account a dynamic equilibrium condition for the structural system. Small configuration changes induce linear geometric behavior, without the effect of damping in the dynamic answer. In this way some assumptions were posed to solve the problem: (1) loads acts transversally, time independent, in the plan of symmetry xz; (2) material is homogeneous, isotropic and linearly elastic; (3) normal tensions σ y  and σ z  are small when compared to the normal tension σ x ; (4) displacements w act transversally to longitudinal axis of the beam; (5) transversal sections are plane and normal to the beam longitudinal axis, in the not deformed configuration, but comes plane and non-warped, even not normal to the axis, after the bending. 2.2 Variational formulation A displacement field, u , is defined, based in assumption 5, considering that traverse sections suffer only an rotation angle ψ  , different from the declivity ∂ w/  ∂ x of longitudinal axis. In the scope of the Linear Theory of the Elasticity, it’s posed a deformation-displacement relationship between differential operator B  and displacement field, εεεε   = Bu . Hooke’s Law derives from this last relation, to the tension-deformation relationship, where D  is the elasticity matrix, in the form σσσσ  = D εεεε , or σσσσ  = DBu . Displacement field, differential operator, and elasticity matrix are given respectively by:  −=  = )t,x(w 0)t,x(z wvu  ψ  u  (1)  ∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂= yzxzxyz000y000x B  (2)
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