Optimization of parameters for fiber laser-MAG hybrid welding in shipbuilding applications

The Arctic region becoming very active area of the industrial developments since it may contain approximately 15-25% of the hydrocarbon and other valuable natural resources which are in great demand nowadays. Harsh operation conditions make the Arctic region difficult to access due to low temperatures which can drop below -50 °C in winter and various additional loads. As a result, newer and modified metallic materials are implemented which can cause certain problems in welding them properly. Steel is still the most widely used material in the Arctic regions due to high mechanical properties, cheapness and manufacturability. Moreover, with recent steel manufacturing development it is possible to make up to 1100 MPa yield strength microalloyed high strength steel which can be operated at temperatures -60 °C possessing reasonable weldability, ductility and suitable impact toughness which is the most crucial property for the Arctic usability. For many years, the arc welding was the most dominant joining method of the metallic materials. Recently, other joining methods are successfully implemented into welding manufacturing due to growing industrial demands and one of them is the laser-arc hybrid welding. The laser-arc hybrid welding successfully combines the advantages and eliminates the disadvantages of the both joining methods therefore produce less distortions, reduce the need of edge preparation, generates narrower heat-affected zone, and increase welding speed or productivity significantly. Moreover, due to easy implementation of the filler wire, accordingly the mechanical properties of the joints can be manipulated in order to produce suitable quality. Moreover, with laser-arc hybrid welding it is possible to achieve matching weld metal compared to the base material even with the low alloying welding wires without excessive softening of the HAZ in the high strength steels. As a result, the laser-arc welding methods can be the most desired and dominating welding technology nowadays, and which is already operating in automotive and shipbuilding industries with a great success. However, in the future it can be extended to offshore, pipe-laying, and heavy equipment industries for arctic environment. CO2 and Nd:YAG laser sources in combination with gas metal arc source have been used widely in the past two decades. Recently, the fiber laser sources offered high power outputs with excellent beam quality, very high electrical efficiency, low maintenance expenses, and higher mobility due to fiber optics. As a result, fiber laser-arc hybrid process offers even more extended advantages and applications. However, the information about fiber or disk laser-arc hybrid welding is very limited. The objectives of the Master’s thesis are concentrated on the study of fiber laser-MAG hybrid welding parameters in order to understand resulting mechanical properties and quality of the welds. In this work only ferrous materials are reviewed. The qualitative methodological approach has been used to achieve the objectives. This study demonstrates that laser-arc hybrid welding is suitable for welding of many types, thicknesses and strength of steels with acceptable mechanical properties along very high productivity. New developments of the fiber laser-arc hybrid process offers extended capabilities over CO2 laser combined with the arc. This work can be used as guideline in hybrid welding technology with comprehensive study the effect of welding parameter on joint quality.

Surface characterization of chemically modified fiber, wood and paper

Inorganic-organic sol-gel hybrid coatings can be used for improving and modifying properties of wood-based materials. By selecting a proper precursor, wood can be made water repellent, decay-, moisture- or UV-resistant. However, to control the barrier properties of sol-gel coatings on wood substrates against moisture uptake and weathering, an understanding of the surface morphology and chemistry of the deposited sol-gel coatings on wood substrates is needed. Mechanical pulp is used in production of wood-containing printing papers. The physical and chemical fiber surface characteristics, as created in the chosen mechanical pulp manufacturing process, play a key role in controlling the properties of the end-use product. A detailed understanding of how process parameters influence fiber surfaces can help improving cost-effectiveness of pulp and paper production. The current work focuses on physico-chemical characterization of modified wood-based materials with surface sensitive analytical tools. The overall objectives were, through advanced microscopy and chemical analysis techniques, (i) to collect versatile information about the surface structures of Norway spruce thermomechanical pulp fiber walls and understand how they are influenced by the selected chemical treatments, and (ii) to clarify the effect of various sol-gel coatings on surface structural and chemical properties of wood-based substrates. A special emphasis was on understanding the effect of sol-gel coatings on the water repellency of modified wood and paper surfaces. In the first part of the work, effects of chemical treatment on micro- and nano-scale surface structure of 1st stage TMP latewood fibers from Norway spruce were investigated. The chemicals applied were buffered sodium oxalate and hydrochloric acid. The outer and the inner fiber wall layers of the untreated and chemically treated fibers were separately analyzed by light microscopy, atomic force microscopy and field-emission scanning electron microscopy. The selected characterization methods enabled the demonstration of the effect of different treatments on the fiber surface structure, both visually and quantitatively. The outer fiber wall areas appeared as intact bands surrounding the fiber and they were clearly rougher than areas of exposed inner fiber wall. The roughness of the outer fiber wall areas increased most in the sodium oxalate treatment. The results indicated formation of more surface pores on the exposed inner fiber wall areas than on the corresponding outer fiber wall areas as a result of the chemical treatments. The hydrochloric acid treatment seemed to increase the surface porosity of the inner wall areas. In the second part of the work, three silane-based sol-gel hybrid coatings were selected in order to improve moisture resistance of wood and paper substrates. The coatings differed from each other in terms of having different alkyl (CH3–, CH3-(CH2)7–) and fluorocarbon (CF3–) chains attached to the trialkoxysilane sol-gel precursor. The sol-gel coatings were deposited by a wet coating method, i.e. spraying or spreading by brush. The effect of solgel coatings on surface structural and chemical properties of wood-based substrates was studied by using advanced surface analyzing tools: atomic force microscopy, X-ray photoelectron spectroscopy and time-of-flight secondary ion spectroscopy. The results show that the applied sol-gel coatings, deposited as thin films or particulate coatings, have different effects on surface characteristics of wood and wood-based materials. The coating which has a long hydrocarbon chain (CH3-(CH2)7–) attached to the silane backbone (octyltriethoxysilane) produced the highest hydrophobicity for wood and wood-based materials.

Evaluation of the in vitro glycemic index of a fiber-rich extruded breakfast cereal produced with organic passion fruit fiber and corn flour

The aim of this study was to determine the influence of process parameters and Passion Fruit Fiber (PFF) addition on the Glycemic Index (GI) of an extruded breakfast cereal. A 2³ Central Composite Rotational Design (CCRD) was used, with the following independent variables: raw material moisture content (18-28%), 2nd and 3rd barrel zone temperatures (120-160 ºC), and PFF (0-30%). Raw materials (organic corn flour and organic PFF) were characterized as to their proximate composition, particle size, and in vitro GI. The extrudates were characterized as to their in vitro GI. The Response Surface Methodology (RSM) and Principal Component Analysis (PCA) were used to analyze the results. Corn flour and PFF presented 8.55 and 7.63% protein, 2.61 and 0.60% fat, 0.52 and 6.17% ash, 78.77 and 78.86% carbohydrates (3 and 64% total dietary fiber), respectively. The corn flour particle size distribution was homogeneous, while PFF presented a heterogeneous particle size distribution. Corn flour and PFF presented values of GI of 48 and 45, respectively. When using RSM, no effect of the variables was observed in the GI of the extrudates (average value of 48.41), but PCA showed that the GI tended to be lower when processing at lower temperatures (<128 ºC) and at higher temperatures (>158 ºC). When compared to white bread, the extrudates showed a reduction of the GI of up to 50%, and could be considered an interesting alternative in weight and glycemia control diets.

Effect of Urethane Based Bonding Agent on the Cure Characteristics and Mechanical Properties of Styrene Butadiene Rubber - Whole Tyre Reclaim - Short Nylon Fiber Composite

The cure characteristics and mechanical properties of short nylon fiber- styrene /whole tyre reclaim (SBR/WTR) composites with and without an interfacial bonding agent based on 4,4 diphenyl methane diisocyanate and polyethylene glycol (MDI/PEG) have been studied. An 80:40 blend of SBR/ WTR reinforced with 20 phr of short nylon fiber has been selected and the MDI/ PEG ratio has been changed from 0.67:1 to 2:1. The minimum and maximum torques increased with isocyanate concentration. The scorch time and cure time showed an initial reduction. The cure rate showed an initial improvement. Tensile strength, tear strength and abrasion resistance increased with MDI/PEG ratio, these values were higher in longitudinal direction. Resilience and compression set increased with isocyanate concentration.

Studies on Acrylonitrile Butadiene Rubber - Short Nylon Fiber Composites

Acrylonitrile butadiene rubber (NBR) matrix was reinforced with different levels of short nylon fiber loading. Cure characteristics and mechanical properties of composites in longitudinal and transverse directions have been studied. Cure time was reduced while processability, as indicated by the minimum torque, was marginally reduced with increase in fiber loading. Tensile and tear properties improved with fiber concentration and the values were higher in longitudinal direction of fiber orientation. Abrasion resistance, resilience and compression set were increased in presence of fibers. Elongation at break values showed a drastic drop on introduction of fibers. Heat build up was higher for composites.

Modification of Polypropylene/Glass Fiber Composites with Nanosilica

Poly(propylene) (PP) reinforced with short glass fiber was modified with precipitated nanosilica (pnS) by melt mixing. The weight of the glass fiber was varied by keeping the pnS at optimum level. The properties of the composites were studied using universal testing machine, dynamic mechanic analyser (DMA), differential Scanning calorimetry (DSC) and thermo gravimetric analyser (TGA). The amount of the glass fiber required for a particular modulus could be reduced by the addition of nanosilica.

Studies on short nylon fiber - reclaimed rubber/elastomer composites

The thesis deals with the development of short nylon fiber-reclaimed rubber/elastomer composites. Three rubbers viz, natural rubber, acrylonitrile butadiene rubber and styrene butadiene rubber were selected and were partially replaced with reclaimed rubber. The blend ratio was optimized with respect to cure characteristics and mechanical properties. Reclaimed rubber replaced 40 parts of NR and SBR and 20 parts of NBR without much affecting the properties. These blends were then reinforced with short nylon fibers. The mechanical properties of the composites were studied in detail. In all the cases the tensile strength, tear strength and the abrasion resistance increased with increase in fiber content. In the case of NRlreclaimed rubber blends, the tensile strength-fiberloading relationship was non-linear where as in the case of NBRlreclaimed rubber blends and SBRlreclaimed rubber blends the tensile strength-fiber loading relationship was linear. All the composites showed anisotropy in mechanical properties. The effect of bonding system on the composite properties was also studied with respect to cure characteristics and mechanical properties. For this, a 20 phr fiber loaded reclaimed rubber/elastomer composites were selected and the effect of MDI/PEG resin system was studied. The resin used was 5 phr and the resin ratios used were 0.67: I, 1:1, 1.5:1 and 2:1. The bonding system improved the tensile strength, tear strength and abrasion resistance. The best results are with SBRlreclaimed rubber-short nylon fiber composites. The optimized resin ratio was 1:1 MDI/PEG for all the composites.

Recyclable Short Fibre Reinforced Plastics PP/Nylon and HDPE/Nylon composites

The study shows that standard plastics like polypropylene and high density polyethylene can be reinforced by adding nylon short fibres. Compared to the conventional glass reinforced thermoplastics this novel class of reinforced thermoplastics has the major advantage of recyclability. Hence such composites represent a new spectrum of recyclable polymer composites. The fibre length and fibre diameter used for reinforcement are critical parameters While there is a critical fibre length below which no effective reinforcement takes place, the reinforcement improves when the fibre diameter decreases due to increased surface area.While the fibres alone give moderate reinforcement, chemical modification of the matrix can further improve the strength and modulus of the composites. Maleic anhydride grafting in presence of styrene was found to be the most efficient chemical modification. While the fibre addition enhances the viscosity of the melt at lower shear rates, the enhancement at higher shear rate is only marginal. This shows that processing of the composite can be done in a similar way to that of the matrix polymer in high shear operations such as injection moulding. Another significant observation is the decrease in melt viscosity of the composite upon grafting. Thus chemical modification of matrix makes processing of the composite easier in addition to improving the mechanical load bearing capacity.For the development of a useful short fibre composite, selection of proper materials, optimum design with regard to the particular product and choosing proper processing parameters are most essential. Since there is a co-influence of many parameters, analytical solutions are difficult. Hence for selecting proper processing parameters 'rnold flow' software was utilized. The orientation of the fibres, mechanical properties, temperature profile, shrinkage, fill time etc. were determined using the software.Another interesting feature of the nylon fibre/PP and nylon fibre/HDPE composites is their thermal behaviour. Both nylon and PP degrade at the same temperature in single steps and hence the thermal degradation behaviour of the composites is also being predictable. It is observed that the thermal behaviour of the matrix or reinforcement does not affect each other. Almost similar behaviour is observed in the case of nylon fibre/HDPE composites. Another equally significant factor is the nucleating effect of nylon fibre when the composite melt cools down. In the presence of the fibre the onset of crystallization occurs at slightly higher temperature.When the matrix is modified by grafting, the onset of crystallization occurs at still higher temperature. Hence it may be calculated that one reason for the improvement in mechanical behaviour of the composite is the difference in crystallization behaviour of the matrix in presence of the fibre.As mentioned earlier, a major advantage of these composites is their recyclability. Two basic approaches may be employed for recycling namely, low temperature recycling and high temperature recycling. In the low temperature recycling, the recycling is done at a temperature above the melting point of the matrix, but below that of the fibres while in the high temperature route. the recycling is done at a temperature above the melting points of both matrix and fibre. The former is particularly interesting in that the recycled material has equal or even better mechanical properties compared to the initial product. This is possible because the orientation of the fibre can improve with successive recycling. Hence such recycled composites can be used for the same applications for which the original composite was developed. In high temperature recycling, the composite is converted into a blend and hence the properties will be inferior to that of the original composite, but will be higher than that of the matrix material alone.

Fabrication and Characterization of Chalcogenide nano composite based materials for Photonic device applications

In this context,in search of new materials based on chalcogenide glasses,we have developed a novel technique for fabrication of chalcogenide nano composites which are presented in this theis.The techniques includes the dissolution of bulk chalcogenide glasses in amine solvent.This solution casting method allows to retain the attractive optical properties of chalcogenide glasses enabling new fabrication routes for realization of large area thick-thin films with less cost. Chalcogenide glass fiber geometry opens new possibilities for a large number of applications in optics,like remote temperature measurements ,CO2 laser power delivery, and optical sensing and single mode propagation of IR light.We have fabricated new optical polymer fibers doped with chalcogenide glasses which can be used for many optical applications.The present thesis also describes the structural,thermal and optical characterization of certain chalocogenide based materials prepared for different methods and its applications.

Performance of Gabion Faced Reinforced Earth Retaining Walls

Gabion faced re.taining walls are essentially semi rigid structures that can generally accommodate large lateral and vertical movements without excessive structural distress. Because of this inherent feature, they offer technical and economical advantage over the conventional concrete gravity retaining walls. Although they can be constructed either as gravity type or reinforced soil type, this work mainly deals with gabion faced reinforced earth walls as they are more suitable to larger heights. The main focus of the present investigation was the development of a viable plane strain two dimensional non linear finite element analysis code which can predict the stress - strain behaviour of gabion faced retaining walls - both gravity type and reinforced soil type. The gabion facing, backfill soil, In - situ soil and foundation soil were modelled using 20 four noded isoparametric quadrilateral elements. The confinement provided by the gabion boxes was converted into an induced apparent cohesion as per the membrane correction theory proposed by Henkel and Gilbert (1952). The mesh reinforcement was modelled using 20 two noded linear truss elements. The interactions between the soil and the mesh reinforcement as well as the facing and backfill were modelled using 20 four noded zero thickness line interface elements (Desai et al., 1974) by incorporating the nonlinear hyperbolic formulation for the tangential shear stiffness. The well known hyperbolic formulation by Ouncan and Chang (1970) was used for modelling the non - linearity of the soil matrix. The failure of soil matrix, gabion facing and the interfaces were modelled using Mohr - Coulomb failure criterion. The construction stages were also modelled.Experimental investigations were conducted on small scale model walls (both in field as well as in laboratory) to suggest an alternative fill material for the gabion faced retaining walls. The same were also used to validate the finite element programme developed as a part of the study. The studies were conducted using different types of gabion fill materials. The variation was achieved by placing coarse aggregate and quarry dust in different proportions as layers one above the other or they were mixed together in the required proportions. The deformation of the wall face was measured and the behaviour of the walls with the variation of fill materials was analysed. It was seen that 25% of the fill material in gabions can be replaced by a soft material (any locally available material) without affecting the deformation behaviour to large extents. In circumstances where deformation can be allowed to some extents, even up to 50% replacement with soft material can be possible.The developed finite element code was validated using experimental test results and other published results. Encouraged by the close comparison between the theory and experiments, an extensive and systematic parametric study was conducted, in order to gain a closer understanding of the behaviour of the system. Geometric parameters as well as material parameters were varied to understand their effect on the behaviour of the walls. The final phase of the study consisted of developing a simplified method for the design of gabion faced retaining walls. The design was based on the limit state method considering both the stability and deformation criteria. The design parameters were selected for the system and converted to dimensionless parameters. Thus the procedure for fixing the dimensions of the wall was simplified by eliminating the conventional trial and error procedure. Handy design charts were developed which would prove as a hands - on - tool to the design engineers at site. Economic studies were also conducted to prove the cost effectiveness of the structures with respect to the conventional RCC gravity walls and cost prediction models and cost breakdown ratios were proposed. The studies as a whole are expected to contribute substantially to understand the actual behaviour of gabion faced retaining wall systems with particular reference to the lateral deformations.

Polypropylene/metal oxide nanocomposites: fiber spinning and evaluation”

PP has been getting much attention over the years because it is a very durable polymer commonly used in aggressive environments including automotive battery casings, fuel containers etc. They are used to make bottles, fibers for clothing, components in cars etc. However, it has some shortcomings such as low dimensional and thermal stability. Materials such as metal oxides with sizes of the order 1–50 nm have received a great deal of attention because of their versatile applications in polymer/ inorganic nanocomposites, optoelectronic devices, biomedical materials, and other areas. They are stable under harsh process conditions and also regarded as safe materials to human beings and animals. In the present investigation, PP is modified by incorporating metal oxide nanoparticles such as ZnO and TiO2 by simple melt mixing method. Melt spinning method was used to prepare PP/metal oxide nanocomposite fibers. Various studies have been carried out on these composites and fibers. In the first part of the study, ZnO nanoparticles were prepared from ZnCl2 and NaOH in presence of chitosan, PVA, ethanol and starch. This is a simple and inexpensive method compared to other methods. Change in morphology and particle size of ZnO were studied. Least particle size was obtained in chitosan medium. The particles were characterized by using XRD, SEM, TEM, TGA and EDAX. Antibacterial properties of ZnO prepared in chitosan medium (NZO) and commercial zinc oxide (CZO) were evaluated using a gram positive and a gram negative bacteria

High-Speed Semiconductor Lasers based on Low-Dimensional Active Materials for Optical Telecommunication

The scope of this work is the fundamental growth, tailoring and characterization of self-organized indium arsenide quantum dots (QDs) and their exploitation as active region for diode lasers emitting in the 1.55 µm range. This wavelength regime is especially interesting for long-haul telecommunications as optical fibers made from silica glass have the lowest optical absorption. Molecular Beam Epitaxy is utilized as fabrication technique for the quantum dots and laser structures. The results presented in this thesis depict the first experimental work for which this reactor was used at the University of Kassel. Most research in the field of self-organized quantum dots has been conducted in the InAs/GaAs material system. It can be seen as the model system of self-organized quantum dots, but is not suitable for the targeted emission wavelength. Light emission from this system at 1.55 µm is hard to accomplish. To stay as close as possible to existing processing technology, the In(AlGa)As/InP (100) material system is deployed. Depending on the epitaxial growth technique and growth parameters this system has the drawback of producing a wide range of nano species besides quantum dots. Best known are the elongated quantum dashes (QDash). Such structures are preferentially formed, if InAs is deposited on InP. This is related to the low lattice-mismatch of 3.2 %, which is less than half of the value in the InAs/GaAs system. The task of creating round-shaped and uniform QDs is rendered more complex considering exchange effects of arsenic and phosphorus as well as anisotropic effects on the surface that do not need to be dealt with in the InAs/GaAs case. While QDash structures haven been studied fundamentally as well as in laser structures, they do not represent the theoretical ideal case of a zero-dimensional material. Creating round-shaped quantum dots on the InP(100) substrate remains a challenging task. Details of the self-organization process are still unknown and the formation of the QDs is not fully understood yet. In the course of the experimental work a novel growth concept was discovered and analyzed that eases the fabrication of QDs. It is based on different crystal growth and ad-atom diffusion processes under supply of different modifications of the arsenic atmosphere in the MBE reactor. The reactor is equipped with special valved cracking effusion cells for arsenic and phosphorus. It represents an all-solid source configuration that does not rely on toxic gas supply. The cracking effusion cell are able to create different species of arsenic and phosphorus. This constitutes the basis of the growth concept. With this method round-shaped QD ensembles with superior optical properties and record-low photoluminescence linewidth were achieved. By systematically varying the growth parameters and working out a detailed analysis of the experimental data a range of parameter values, for which the formation of QDs is favored, was found. A qualitative explanation of the formation characteristics based on the surface migration of In ad-atoms is developed. Such tailored QDs are finally implemented as active region in a self-designed diode laser structure. A basic characterization of the static and temperature-dependent properties was carried out. The QD lasers exceed a reference quantum well laser in terms of inversion conditions and temperature-dependent characteristics. Pulsed output powers of several hundred milli watt were measured at room temperature. In particular, the lasers feature a high modal gain that even allowed cw-emission at room temperature of a processed ridge wave guide device as short as 340 µm with output powers of 17 mW. Modulation experiments performed at the Israel Institute of Technology (Technion) showed a complex behavior of the QDs in the laser cavity. Despite the fact that the laser structure is not fully optimized for a high-speed device, data transmission capabilities of 15 Gb/s combined with low noise were achieved. To the best of the author`s knowledge, this renders the lasers the fastest QD devices operating at 1.55 µm. The thesis starts with an introductory chapter that pronounces the advantages of optical fiber communication in general. Chapter 2 will introduce the fundamental knowledge that is necessary to understand the importance of the active region`s dimensions for the performance of a diode laser. The novel growth concept and its experimental analysis are presented in chapter 3. Chapter 4 finally contains the work on diode lasers.

Analysis and Simulation of Transverse Random Fracture of Long Fibre Reinforced Composites

La present tesi proposa una metodología per a la simulació probabilística de la fallada de la matriu en materials compòsits reforçats amb fibres de carboni, basant-se en l'anàlisi de la distribució aleatòria de les fibres. En els primers capítols es revisa l'estat de l'art sobre modelització matemàtica de materials aleatoris, càlcul de propietats efectives i criteris de fallada transversal en materials compòsits. El primer pas en la metodologia proposada és la definició de la determinació del tamany mínim d'un Element de Volum Representatiu Estadístic (SRVE) . Aquesta determinació es du a terme analitzant el volum de fibra, les propietats elàstiques efectives, la condició de Hill, els estadístics de les components de tensió i defromació, la funció de densitat de probabilitat i les funcions estadístiques de distància entre fibres de models d'elements de la microestructura, de diferent tamany. Un cop s'ha determinat aquest tamany mínim, es comparen un model periòdic i un model aleatori, per constatar la magnitud de les diferències que s'hi observen. Es defineix, també, una metodologia per a l'anàlisi estadístic de la distribució de la fibra en el compòsit, a partir d'imatges digitals de la secció transversal. Aquest anàlisi s'aplica a quatre materials diferents. Finalment, es proposa un mètode computacional de dues escales per a simular la fallada transversal de làmines unidireccionals, que permet obtenir funcions de densitat de probabilitat per a les variables mecàniques. Es descriuen algunes aplicacions i possibilitats d'aquest mètode i es comparen els resultats obtinguts de la simulació amb valors experimentals.

Serviceability behaviour of fibre reinforced polymer reinforced concrete beams

El uso de materiales compuestos de matriz polimérica (FRP) emerge como alternativa al hormigón convencionalmente armado con acero debido a la mayor resistencia a la corrosión de dichos materiales. El presente estudio investiga el comportamiento en servicio de vigas de hormigón armadas con barras de FRP mediante un análisis teórico y experimental. Se presentan los resultados experimentales de veintiséis vigas de hormigón armadas con barras de material compuesto de fibra de vidrio (GFRP) y una armada con acero, todas ellas ensayadas a flexión de cuatro puntos. Los resultados experimentales son analizados y comparados con algunos de los modelos de predicción más significativos de flechas y fisuración, observándose, en general, una predicción adecuada del comportamiento experimental hasta cargas de servicio. El análisis de sección fisurada (CSA) estima la carga última con precisión, aunque se registra un incremento de la flecha experimental para cargas superiores a las de servicio. Esta diferencia se atribuye a la influencia de las deformaciones por esfuerzo cortante y se calcula experimentalmente. Se presentan los aspectos principales que influyen en los estados límites de servicio: tensiones de los materiales, ancho máximo de fisura y flecha máxima permitida. Se presenta una metodología para el diseño de dichos elementos bajo las condiciones de servicio. El procedimiento presentado permite optimizar las dimensiones de la sección respecto a metodologías más generales.