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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
81

Long term and short term deflection of GFRP prestressed concrete slabs

Singh, Mahendra 25 June 2014 (has links)
This thesis investigates the performance of GFRP pretensioned concrete slabs and compares their flexural behaviour with GFRP reinforced and steel prestressed concrete slabs. A total of 12 slabs were cast in this program. The slab mid-span deflections are theoretically predicted and the results indicate that the short-term response of GFRP prestressed concrete slabs can be predicted well by the existing methods. Long-term deflection behaviour has been estimated using the Age Adjusted Effective Modulus Method by incorporating three creep and shrinkage models. A large influence of creep and shrinkage models on the theoretical determination is observed and the use of long term multipliers is not suitable for GFRP prestressed concrete members. The slabs were instrumented for long-term monitoring using strain gauges and fibre-optic sensors. It was concluded that the electrical strain gauges can be successfully used for long-term strain monitoring.
82

Cost-benefit Analysis For Various Rehabilitation Strategies

Cetinceli, Serkan 01 February 2005 (has links) (PDF)
Over the last decade, six major earthquakes that occurred in Turkey dramatically demonstrated the poor performance of the buildings that were designed and constructed far from Turkish seismic code&rsquo / s requirements. The Marmara region, where most of the population and industry is located, is in the active seismic zone. With the rising cost of damages due to earthquakes, the necessity of the cost-benefit analysis for various rehabilitation strategies used in existing buildings has become a major concern for the decision makers who are in the position of making decisions on the building rehabilitation This study evaluates the performance of two different rehabilitation strategies applied to two five-story reinforced concrete buildings and assesses their cost-benefit analyses. These buildings were chosen to be representative of the typical residential To carry out the structural analysis of the buildings, three-dimensional models of the buildings were developed using SAP2000 [6]. Two alternative strengthening methods, insertion of reinforced concrete shear walls and application of Carbon Fiber Reinforced Polymers (CFRP) on hallow clay tile infill walls, were used for both of the buildings. While modeling infill walls strengthened with CFRP, two specific modeling attempts proposed by the researchers at Middle East Technical University were used. Pushover analyses were performed to evaluate seismic performance of the buildings. The Life Safety criterion was chosen as the rehabilitation objective. The global and component response acceptability limits were checked and the cost-benefit analysis was performed in order to determine the most attractive rehabilitation alternative. The results and comparisons given here illustrated that strengthening with shear wall had the most significant improvement on the seismic performance and cost effectiveness of the case study buildings. Outcomes of this study are only applicable to the buildings employed here and are bound by the assumptions made, approximations used and parameters considered in this study. The findings cannot be generalized for the buildings rehabilitated with CFRP due to lack of the consistent models for CFRP application. More research needs to be conducted to provide solid guidelines and reliable models applicable to the CFRP rehabilitated infill walls.
83

[en] EXPERIMENTAL STUDY OF REINFORCED CONCRETE SHORT CORBELS WITH CARBON FIBER COMPOSITES / [pt] ESTUDO EXPERIMENTAL DOS CONSOLES CURTOS DE CONCRETO ARMADO REFORÇADOS COM COMPÓSITOS DE FIBRAS DE CARBONO

LARISSA AZEVEDO CURTY 29 January 2018 (has links)
[pt] Este trabalho é uma pesquisa experimental realizada no Laboratório de Estruturas e Materiais da PUC–Rio, utilizando–se a técnica de aplicação do compósito de fibras de carbono (CFC) colados externamente em consoles curtos de concreto armado. Foram ensaiados seis consoles curtos, sendo: um de referência, três com reforço de CFC na horizontal e dois com reforço de CFC na diagonal. A resistência média do concreto aos 28 dias foi de 30 MPa. A seção transversal do pilar foi de 25 cm × 50 cm e a seção do transversal console foi de 25 cm × 37,5 cm. O diâmetro da armadura tracionada em laço era de 10 mm e o diâmetro da armadura de costura era de 6,3 mm. Os consoles foram instrumentados com extensômetros elétricos de resistência na armadura tracionada, no estribo, no concreto e no CFC. Os ensaios comprovaram um razoável desempenho dessa técnica de reforço. Os resultados experimentais foram comparados com os resultados obtidos no modelo de Bielas e Tirantes e no modelo cinemático da Teoria da Plasticidade, visando a comparação das forças verticais últimas teóricas e experimentais. Foi avaliado o ângulo de inclinação das bielas e o fator de efetividade da deformação específica no reforço de CFC. / [en] This work is an experimental research of concrete short corbels wrapped with Carbon Fiber Reinforced Polymer (CFRP) strips. Different strengthening configurations were used. Was carried out on six corbels strengthened by CFRP. One control specimen without CFRP, three corbels with horizontal CFRP strips and two corbels with diagonal CFRP strips. The concrete had a 28 day compressive strength of 30 MPa. The column cross-section dimensions were 25 cm x 50 cm and the corbel cross-section dimensions were 25 cm x 37,5 cm. The flexural reinforcement consisted of four deformed bars each of diameter 10 mm with four transverse bars of diameter 6,3 mm. The corbels were instrumented with strain gages in flexural reinforcement, stirrup, concrete surface and CFRP strips. The analytical models based on Strut-and-Tie model and in the kinematic model of the Theory of Plasticity, allows one to determine the bearing capacity of corbels. The experimental values are then compared with the analytical results, showing good agreement. The strut angle and the strengthening effectiveness were evaluated.
84

Development and structural testing of new basalt fiber-reinforced-polymer (BFRP) bars in RC beams and bridge-deck slabs / Étude du comportement structural de poutres et de dalles de ponts en béton armé d'une nouvelle armature à base de fibre de basalte sous charge statique

Elgabbas, Fareed Mahmoud January 2016 (has links)
L'avancée de la technologie des PRF a suscité l'intérêt de l'introduction de nouvelles fibres, comme la fibre de basalte, qui a un potentiel d'offrir une solution efficace, lorsqu’utilisée dans les structures en béton, soit sur la résistance à la corrosion, la durabilité et la rentabilité. En outre, les codes et les guides disponibles, ne fournissent pas de recommandations pour l'utilisation de barres en PRFB puisque les recherches passées dans ce domaine sont limitées. Donc, des travaux de recherche sont nécessaires pour caractériser et comprendre le comportement des barres de PRFB dans les éléments en béton armé. En conséquence, les objectifs principaux sont d'évaluer les caractéristiques à court et long terme des barres de PRFB nouvellement développées, ainsi que d'évaluer les performances structurales de ces nouvelles barres comme renforcement interne dans les poutres et les dalles de pont et d'introduire ce nouveau renforcement dans les codes et les guides de dimensionnement. Les tests expérimentaux ont été faits en trois parties. La première partie porte sur le développement de trois nouvelles barres et tendons en PRFB pour déterminer leurs propriétés physiques et mécaniques. Les performances à long terme et de durabilité ont été réalisées en conditionnant les barres de PRFB dans une solution alcaline simulant les conditions humides dans le béton pour déterminer la compatibilité comme renforcement interne dans les éléments en béton. Par la suite, les propriétés ont été déterminées et comparées avec des spécimens non conditionnés (référence). La seconde partie a porté sur sept dalles de pont en béton armé grandeur réelle avec les bords restreints, simulant les tabliers de pont les plus utilisés en Amérique du Nord, pour évaluer la performance des dalles renforcées de PRFB et d'acier. Les dalles mesurent 3000 mm de long × 2500 mm de large × 200 mm d'épaisseur. Les dalles ont été testées jusqu'à la rupture sous une charge concentrée au centre de celles-ci simulant l'empreinte d'une roue d'un camion. Les capacités en poinçonnement sont prédites en utilisant les exigences réglementaires disponibles, et sont comparées aux résultats expérimentaux. La troisième partie de cette étude portait sur les essais de 14 poutres en béton de 3100 mm de long × 200 mm de large × 300 mm de profond pour examiner le comportement en flexion et les performances en service des barres de PRFB avec deux états de surfaces: fini sablé et crénelé. Les poutres ont été testées en flexion en quatre points avec une portée libre de 2700 mm jusqu'à la rupture. Les résultats sont introduits et discutés en terme : du comportement de la fissuration, des flèches, de la capacité en flexion et des modes de ruptures. De plus, le coefficient d'adhérence (kb) des barres de PRFB est déterminé et comparé avec les recommandations des codes et guides actuels. Les résultats sont introduits et discutés en terme : du comportement de la fissuration, des flèches, de la capacité en flexion et des modes de ruptures. De plus, le coefficient d'adhérence des barres de PRFB est déterminé et comparé avec les recommandations des codes et guides actuels. Les résultats de l'étude concluent sur la viables pour la production des barres de PRFB pour respecter les exigences des codes actuelles. Également, les résultats d'essai indiquent que les barres de PRFB ont de bonnes propriétés mécaniques et peuvent être placées dans la même catégorie que les barres de PRFV, soit grade III. De plus, le comportement des poutres et des dalles de pont renforcées de PRFB est similaire que pour un renforcement en PRFV et PRFC et les exigences réglementaires sont applicables pour les barres de PRFB. / Abstract: The advances in fiber-reinforced-polymer (FRP) technology have spurred interest in introducing new fibers, such as basalt FRP (BFRP), which has the potential to offer an efficient solution when implemented in concrete structure, such as corrosion resistant, durable and cost-effective. Furthermore, the available design codes and guides do not provide any recommendations for the use of BFRP bars since fundamental studies and relevant applications are still limited. Therefore, investigations are needed to characterize and understand the behavior of BFRP bars in concrete members. Consequently, the main objectives of this experimental investigation are to evaluate the short- and long-term characteristics of newly developed BFRP bars, as well as evaluate the structural performance of these new bars as internal reinforcement for concrete beams and bridge-deck slabs to introduce these new reinforcing bars to the design codes and guides. The experimental tests were completed through three parts. The first part was conducted on three newly developed BFRP bars and tendons to investigate their physical and mechanical properties. Durability and long-term performance were assessed by conditioning the BFRP bars in an alkaline solution simulating the moist concrete environment to determine their suitability as internal reinforcement for concrete elements. Thereafter, the properties were assessed and compared with the unconditioned (reference) values. The second part of this study was conducted on seven full-scale edge-restrained concrete bridge-deck slabs simulating actual slab-on-girder bridge-deck that is commonly used in North America to evaluate the performance of concrete bridge-deck slabs reinforced with BFRP and steel bars. The deck slabs measured 3000 mm long × 2500 mm wide × 200 mm deep. The slabs were tested up to failure under single concentrated load acting on the center of each slab simulating the footprint of sustained truck wheel load. The punching shear capacities were predicted using the available provisions, and compared with the experimental results. The third part of this study included testing of fourteen concrete beams of 3100 mm long × 200 mm wide × 300 mm deep to investigate the flexural behavior and serviceability performance of sand-coated and ribbed BFRP bars in concrete beams. The beams were tested under four-point bending over a clear span of 2700 mm until failure. The results are introduced and discussed in terms of cracking behavior, deflection, flexure capacity, and failure modes. In addition, the bond-dependent coefficient (kb) of the BFRP bars was determined and compared with the recommendations of the current FRP design codes and guides. The findings of this study concluded the feasibility of producing BFRP bars meet the requirements of the current FRP standards. Also, the test results revealed that the BFRP bars had good mechanical behavior and could be placed in the same category as grade II and grade III GFRP bars. Moreover, the behavior of the concrete bridge-deck slabs and beams reinforced with BFRP bars was quite similar to the counterparts reinforced with glass- and carbon-FRP bars and the available FRP provisions are applicable for BFRP bars. The beam test results yielded an average bond-dependent coefficient (kb) of 0.76±0.03 and 0.83±0.03 for the sand-coated and ribbed BFRP bars, respectively.
85

Définition des indicateurs clés de performance et évaluation multicritère de filières durables de recyclage des polymères renforcés de fibres de carbone issus de l’industrie aéronautique / Definition of key sustainability performance indicators and multicriteria evaluation of recycling sector for carbon fiber reinforced polymers from the aerospace industry

Pillain, Baptiste 30 June 2017 (has links)
La consommation globale de plastique renforcé de fibres de carbone (PRFC) est en constante augmentation, ce qui induit la nécessité de créer un secteur de recyclage capable de traiter l’ensemble des fibres de carbone actuellement consommées et qui représente la quantité de déchets à traiter en devenir. Cette thèse porte sur le développement et l'application d’une méthodologie d’évaluation multicritère du développement durable pour la création d’une filière de recyclage des plastiques renforcés de fibres de carbone (PRFC) issus du secteur aéronautique, mais aussi des autres secteurs consommateurs de fibres de carbone tels que l’automobile et l’éolien. Cette méthodologie a pour but d’identifier les indicateurs les plus pertinents ainsi que les méthodes qui leurs sont associés, c'est-à-dire qu’elle vise à la création et l’adaptation d’indicateurs clé de performance du développement durable pour caractériser au mieux les impacts environnementaux et sociaux-économique de cette filière de recyclage. Le résultat final de ce travail est la création d’une méthodologie d’évaluation du développement durable dédiée à la filière de recyclage des fibres de carbone par la considération des différents aspects de celui-ci. Cette méthodologie, aidant à l’identification et la définition des indicateurs clé de performances du développement durable peut être aussi appliquée à d’autres secteurs souhaitant s’implanter en suivant les principes de ce développement. / The global consumption of carbon-fiber reinforced plastic (CFRP) is constantly growing since the last decade, leading to the need to create a recycling sector able to manage the amount of carbon fibers currently consumed and representing the amount of waste to be treated in the future. This thesis focus on the creation of a methodology for evaluating the sustainability potential for the implementation of a carbon fiber reinforced plastics recycling (CFRP) sector. CFRP coming from the aeronautics sector as well as other sectors such as the automobile and wind-energy industries. This methodology aims at identifying the most relevant indicators and associated methods, but also aims at the creation and adaptation of indicators to best assess the environmental and socioeconomic impacts of this recycling sector. The final result of this work, is the creation of a sustainability assessment methodology dedicated to the carbon fiber recycling sector, considering the different sustainability pillars. However this methodology also define more widely a tool that helps to identify sustainability performance indicators and that can be applied to other sectors if necessary.
86

Fatigue Damage Characterization Of Carbon/Epoxy Laminates Under Spectrum Loading

Sudha, J 01 1900 (has links) (PDF)
Fibre Reinforced Polymer Composites are extensively used in aircraft structures because of its high specific stiffness, high specific strength and tailorability. Though Fibre Reinforced Polymers offer many advantages, they are not free from problems. The damage of different nature, e.g., service mechanical damages, fatigue damage or environmental damage can be observed during operating conditions. Among all the damages, manufacturing or service induced, delamination related damage is the most important failure mechanisms of aircraft-composite structures and can be detrimental for safety. Delamination growth under fatigue loading may take place due to local buckling, growth from free edges and notches such as holes, growth from ply-drops and impact damaged composites containing considerable delamination. Delamination growth can also occur due to interlaminar stresses, which can arise in complex structures due to unanticipated loading. The complex nature of composite failure, involving different failure modes and their interactions, makes it necessary to characterize/identify the relevant parameters for fatigue damage resistance, accumulation and life prediction. An effort has been made in this thesis to understand the fatigue behavior of carbon fibre reinforced epoxy laminates under aircraft wing service loading conditions. The study was made on laminates with different lay-up sequences (quasi-isotropic and fibre dominated) and different geometries (plain specimen, specimen with a hole and ply-drop specimen). The fatigue behaviour of the composite was analyzed by following methods: . Ultrasonic C-Scan was used to characterize the delamination growth. . Dynamic Mechanical Analysis (DMA) was done to study the interfacial degradation due to fatigue loading. In this analysis, the interfacial strength indicator and interfacial damping were calculated. The DMA also provides the storage modulus degradation under fatigue loading. . Scanning electron microscope examination was carried out to understand the fatigue damage mechanisms. . A semi-empirical phenomenological model was also used to estimate the residual fatigue life. This research work reveals that the Carbon Fibre Reinforced Polymer laminates are in the safe limit under service loading conditions, except the specimen with a hole. The specimen with a hole showed delaminations around the hole due to stress concentration and higher interlaminar stresses at the hole edges and this delamination is found to be associated with fibre breakage and fibre pullout. The quasi-isotropic laminate is found to show poorer fatigue behaviour when compared to fibre dominated laminate and ply-drop also shows poor performance due to high stress concentration in the ply-drop region.
87

Feasibility Analysis of a Fiber Reinforced Polymer Bridge

Murphy, Neil January 2013 (has links)
When implementing a bridge design proposal, it is common that several alternatives be considered, each with a different material of construction. Traditional building materials used for the construction of bridges have mainly been concrete, steel, timber or aluminium. With all these materials options, maintenance and replacement costs throughout the lifespan of a bridge make up for a large proportion of their total life cycle costs. Fiber Reinforced Polymer (FRP) provides a new viable construction material, which can be implemented in bridge construction. This plastic based material has favourable material properties such a very high strength to weight ratio, high corrosion resistance and durability, as well as very low maintenance costs over its lifetime. In the feasibility analysis, a case study of an existing FRP deck bridge was taken and examined in three aspects: structural, economic and environmental. The bridge was also redesigned with a concrete deck solution, to provide a comparison to a conventional construction material. The results were found, in general to be favourable towards the FRP solution. From the structural analysis savings on deflection, support reactions and superstructure stresses were outputted. Economically, the composite material was found to have a substantial higher initial cost but much lower periodic maintenance costs than the concrete option. Finally the FRP bridge option displayed a lower construction time for the superstructure, at one third of that of concrete and an overall lower environmental impact, based on material production and the overall bridge construction process.
88

Widening of The Nockeby Bridge : Methods for strengthening the torsional resistance

Andersson, Jenny January 2016 (has links)
i Abstract The Nockeby Bridge, in the western part of Stockholm, is a prestressed concrete bridge with an openable swing span of steel. The bridge was built during 1970 and should now be widened with 0.5 meters on each side. The concrete bridge deck is supported by two main-beams and cross-beams are located at the position of all supports. Previous studies of the bridge show that the torsional resistance is too low and the bridge needs strengthening while widened. The aim of this master  thesis  was  to  study  and  compare  different  strengthening  methods  for  The  Nockeby Bridge.  Eight  different  bridges  in  Sweden  and  China  were  reviewed  to  find  possible  strengthening  methods  for  The  Nockeby  Bridge.  External  prestressing  tendons  and  additional  cross-beams between  the  two  main-beams  were  seen  to  have  good  influence  on  the  resistance.  The  effect from strengthening with carbon-fiber reinforced polymer was questioned during small loads and was not seen as a suitable strengthening method for The Nockeby Bridge.  Four different FE-models were generated to be able to compare two strengthening methods. The compared strengthening methods were a method with additional cross-beams between the main-beams and a method with external prestressing tendons. All FE-models were built up by solid- and  truss  elements  where  the  concrete  was  modelled  with  solid  elements  and  the  prestressed reinforcement was modelled with truss elements.  Only a few load-cases were included to limit the scope of the study. The included load-cases were deadweight,  prestressing  forces  and  vehicle  load  from  standard  vehicle  F,  G,  H  and  I.  Two influence lines were created to be able to place the vehicle loads in an unfavorable way. From the FE-models, shear  stresses were  extracted  along two  lines, one  on  each  side  of the main-beam. The torsional part of the shear stresses was calculated from these two results and compared with the torsional resistance of the bridge. While calculating the torsional resistance, the normal force in the cross-section from prestress was extracted with the function “free body cut”. The results showed that none of the tested strengthening methods were enough to  strengthen The  Nockeby  Bridge.  However, the  method  with additional  cross-beams  was  seen  as  a  better method than external prestressing tendons. A combination of the two methods might be suitable but  was  not  tested.  Adding  four  cross-beams  in  each  span  might  also  increase  the  resistance enough, but this was neither tested. It was also seen that a reduction of the torsional stiffness had a large influence on the result. Such a reduction is allowed in some cases and should be utilized if possible. Furthermore,  it  was  seen  that  solid-models  were  extremely  time  consuming  and  there  is  not  a  good alternative to design a bridge with only a solid model. / Nockebybron i västra Stockholm är en förspänd betongbro med ett öppningsbart svängspann av stål. Bron byggdes 1970 och ska nu breddas med 0.5 meter på varje sida. Betongplattan stöds upp av två huvudbalkar och tvärbalkar är placerade vid samtliga stöd. Tidigare studier av bron visar att brons vridstyvhet är låg och bron behöver förstärkas i samband med breddningen. Syftet med detta examensarbete är att undersöka och jämföra olika förstärkningsmetoder för Nockebybron. Åtta olika  broar  i  Sverige  och  Kina  undersöktes  för  att  hitta möjliga  förstärkningsåtgärder  för Nockebybron. Extern spännarmering och extra tvärbalkar mellan de två huvudbalkarna hade en bra inverkan på kapaciteten. Kapacitetsökningen fån förstärkning med kolfiberförstärkt plast är ifrågasatt vid låga laster och uppfattas inte som en bra metod för att förstärka Nockebybron.  Fyra     olika     FE-modeller     skapades     för     att     jämföra     två     förstärkningsmetoder. Förstärkningsmetoderna som jämfördes var metoden med extra tvärbalkar mellan huvudbalkarna samt   en   metod   extern   spännarmering.   Alla   FE-modeller   byggdes  upp   med  solid-  och stångelement  där  betongen  modellerades  med  solidelement  och  den  förspända  armeringen modellerades med stångelement.  Enbart ett fåtal lastfall inkluderades i studien för att minska studiens omfattning. De inkluderade lastfallen  var  egenvikt,  förspänningskrafter  samt  trafiklast  från  typfordon  F,  G,  H  och  I.  Två influenslinjer  skapades  för  att  placera  trafiklasten  på  ett  ogynnsamt  sätt.  Från  FE-modellerna extraherades   skjuvspänningar   från   bägge   sidor   av   en   av   huduvbalkarna.   Från   dessa skjuvspänningar   beräknades   vrid-delen   av   skjuvspänningarna   som   jämfördes   med   brons vridkapacitet.  När  vridkapaciteten  beräknades  togs  tryckkraften  från  tvärsnittet  fram  genom funktionen ”free body cut”.  Resultatet visade att ingen av de testade förstärkningsmetoderna var tillräckliga för att  förstärka Nockebybron.  Hur  som  helst,  metoden  med  extra  tvärbalkar  ansågs  som  en  bättre  metod  än extern  spännarmering.  En  kombination  av  de  bägge  förstärkningsmetoderna  kan  vara  lämplig men detta testades inte. Att lägga in fyra tvärbalkar i varje spann kan också leda till en tillräcklig ökning av kapaciteten, men detta fall testades inte heller. En reduktion av vridstyvheten sågs ha en stor påverkan på resultatet. En sådan reduktion är tillåten i vissa fall och borde utnyttjas om möjligt. Vidare  upptäcktes  att  en  solidmodell  är  väldigt  tidskrävande  varför  det  inte  är  lämpligt  att  dimensionera en bro enbart med hjälp av en solidmodell.
89

EXPERIMENTAL INVESTIGATION OF REPAIR TECHNIQUES FOR DETERIORATED END REGIONS OF PRESTRESSED CONCRETE BRIDGE GIRDERS

William Rich (10713612) 06 May 2021 (has links)
<div> <p>Due to harsh environmental conditions, the deterioration of prestressed concrete bridge girders is a commonly observed phenomenon in Indiana and much of the Midwest. Concordantly, one widely observed damage scenario is deteriorated end regions of prestressed concrete girders. Damaged or failed expansion joints expose prestressed concrete girder end regions to chloride-laden water, resulting in a corrosive environment in which reinforcement section loss and concrete spalling can occur. For bridges experiencing this type of deterioration, action is needed to ensure the structure remains safe and serviceable. As such, an experimental program was developed to investigate the effectiveness of three repair techniques in restoring the structural behavior of prestressed concrete bridge girders with end region deterioration. The three examined repair techniques are (i) an externally bonded fiber reinforced polymer (FRP) system, (ii) a near-surface-mounted (NSM) FRP system, and (iii) a concrete supplemental diaphragm. Additionally, installation procedures for the three end region repair techniques were developed. Results, conclusions, and recommendations from the experimental program are presented to help advise best practices for implementing end region repair techniques in the field. </p> </div> <br>
90

Incorporation of Bio Based Flax Fiber Reinforced Polymer Skins for Packaging Enhancements

Sukhyani, Sufia 12 1900 (has links)
Indiana University-Purdue University Indianapolis (IUPUI) / This thesis provides an approach to incorporate natural composites like Flax Fiber using a resin with 30% bio-content to enhance the packaging boxes made of corrugated cardboard. The objective of introducing natural composite skins is to reduce/eliminate the compressive loading subjected to the boxes while stacking in warehouses.

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