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Estudo da aderência de concretos ativados alcalinamente à base de cinza da casca de arroz e metacaulim /Guimarães, Paulo Victor Campos. January 2019 (has links)
Orientador: José Luiz Pinheiro Melges / Resumo: A indústria do cimento Portland é responsável direta por uma carga de poluentes de significativo dano ambiental. Os Concretos Ativados Alcalinamente (CAA) são matrizes compostas por um ativador alcalino e um aglomerante alternativo. O material comumente utilizado para a ativação alcalina é o silicato de sódio, cuja fabricação também se mostra como ambientalmente nociva. O silicato de sódio, junto ao cimento Portland, podem ser dispensados, uma vez que a produção do ativador pode se dar através de um composto rico em silício (materiais pozolânicos no geral), sendo a cinza da casca de arroz (CCA) o instrumento de estudo do trabalho apresentado, e a soda cáustica como fornecedora de sódio (meio alcalino). Os concretos CAA foram definidos conforme o parâmetro ξ (CAA-ξ), que representa a relação molar entre SiO2 e Na2O, com as variações ξ = 1,2, ξ = 1,6 e ξ = 2,0, esta última representando o concreto ativado alcalinamente com maior taxa de CCA. Este trabalho tem como intuito a avaliação das propriedades mecânicas dos concretos CAA, comparando-as, em seguida, com duas tipologias de concreto com cimento Portland CPV-ARI, com distintos fatores água cimento (0,45 e 0,55). A variação na relação a/c teve como intuito a análise de duas referências com valores diferentes de fck. Os resultados demonstram que a resistência à compressão axial e diametral (sete dias de cura) para os concretos CAA se encontraram na faixa de 25 a 30 MPa, e de 1,5 a 3,5 MPA, respectivamente. Não foram observados... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The Portland cement industry is directly responsible for a load of pollutants of significant environmental damage. Alkali-Activated Concrete (AAC) is a matrix with prior activation and alternative binder. The catalyst material commonly used for prior activation is the sodium silicate, the manufacture of which is also environmentally harmful. Sodium silicate, together with Portland cement, can also be dispensed with, since the activator can be produced through a silicon-rich compound (pozzolanic materials in general), with the rice husk ash (RHA) being the instrument of study of the work presented, and caustic soda as a supplier of sodium. The AAC concretes were defined according to the parameter ξ (AAC- ξ), which represents the molar ratio of SiO2 and Na2O, with the variations ξ = 1.2, ξ = 1.6 and ξ = 2.0, the latter representing the AAC with higher RHA rate. This work intends to evaluate the mechanical properties of AAC, comparing them to two types of concrete with ordinary Portland cement with high early resistance, with different water cement factors (0.44 and 0.55). The variation in the water/binder mass ratio was intended to analyze two references with different values of compressive strength class. The results demonstrate that the axial and diametric compression strength (seven days cure) for the AAC concretes were in the range of 25 to 30 MPa, and of 1.5 to 3.5 MPA, respectively. There were no significant gains in the transition between the ages of 7 and 28 days, and 2... (Complete abstract click electronic access below) / Mestre
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Bond of glass fibre reinforced polymer bars in high strength concreteSaleh, Najia M. January 2018 (has links)
Very limited research studies have been conducted to examine bond of glass fibre reinforced polymer (GFRP) bars with high concrete strength. The current research project aims to compare between bond measured from a pull-out test and a hinged beam test for GFRP bars embedded in high strength concrete. Different parameters influencing bond such as GFRP bar diameter, embedment length and surface configuration were investigated in both test methods, while the bar position, i.e. top or bottom, was only studied in hinged beams.
Seventy-two pull-out cubes, eight pull-out prisms and twenty-four hinged beams reinforced with GFRP bars were constructed and tested to failure. Twelve pull-out cubes and four hinged beams reinforced with steel bars were also tested for comparison purposes. The results showed that bond stress – slip curves obtained from various testing methods were similar, consisting of high initial stiffness, followed by nonlinear ascending and softening branches. In addition, it was found that the experimental bond strength obtained from hinged beams was higher than both bond strengths measured by the pull-out cube and pull-out prism. However, when a finite element analysis was conducted for hinged beams, it was shown that the tensile force in the reinforcing bar estimated by equilibrium conditions is overestimated as the large deformation of hinged beams at failure was not considered. Therefore, if the tensile force obtained from the finite element analysis is used to calculate the bond strength, it would be similar to that obtained from pull-out cube and prism. Moreover, it was found that the distribution of tensile and bond stresses was nonlinear along the GFRP embedment length and bond stress at the vicinity of the free end increased with increasing the load due to redistribution of bond stresses along the embedment length.
Bond strengths were compared against the prediction methods provided in ACI-440.1R, CSA-S806, CSA-S6 and JSCE 1997. In general, all design codes showed conservative results for all specimens tested and ACI predictions gave a good agreement with experimental data compared to other codes.
Artificial neural network models were developed to predict bond strength of GFRP bars in concrete. These models used bar diameter, embedment length, concrete compressive strength and concrete cover as input variables. The developed ANN models showed to be able to predict bond strength of GFRP bars in concrete and, therefore, were used to conduct a parametric study. / Higher Education Institute, Government of Libya
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Estudo da influência do uso de fibras de aço e de estribos no comportamento da ancoragem de barras / Study of the influence of steel fibers and stirrups on the behavior of the anchorage of barsCorreia, Vinicius Costa 01 June 2012 (has links)
O comportamento estrutural do concreto armado depende da união entre o concreto e a armadura. Esta união se estabelece por meio da aderência, que funciona como um mecanismo de transferência de tensões e garante a compatibilidade de deformações entre a armadura e o concreto. Este trabalho tem como objetivo investigar os efeitos da adição de fibras de aço e armadura transversal no comportamento da ancoragem. A investigação experimental foi feita por meio de dois tipos de ensaio de arrancamento de barras, sendo eles o modelo-padrão do RILEM-CEB-FIP e modelo proposto pelo autor, este considerando barras de pontas retas e com ganchos de 90º. Todos os modelos utilizaram comprimento aderente igual a cinco vezes o diâmetro da barra. As armaduras longitudinais eram compostas por barras de 10 mm e 16 mm e a resistência à compressão média do concreto era igual a 50 MPa no dia do ensaio. Foram utilizadas fibras de aço com ganchos nas extremidades, com relação de aspecto igual a 65, comprimento igual a 35 mm e fração volumétrica de 2% (157 Kg/m³). Também foram realizadas comparações com modelos teóricos, analisados através do estudo de bibliografias existentes e das normas NBR 6118:2003 e ACI-318-08. Os resultados experimentais mostraram que os estribos e as fibras exercem influência significativa na resistência ao fendilhamento do concreto. Observou-se ainda que, para os corpos de prova com barras de aço de 10 mm e 16 mm com pontas retas, as fibras estudadas exerceram pequena influência na resistência ao arrancamento. / The structural behavior of reinforced concrete depends on connection behavior of concrete and steel. This union is established by means of bond, which serves as a mechanism to transfer forces and ensure the compatibility of deformation between the reinforcement and the concrete. This research aims investigating the effects of the use of steel fibers and stirrups on the behavior of the anchorage. An experimental investigation was carried out by means of pull-out tests according to the RILEM-CEB-FIP standard model and pull-out tests of straight and with 90º hooked bars, with a bonded length of five times the bar diameter. The longitudinal reinforcement bars were of 10 mm and 16 mm and concrete compressive strength was 50 MPa at the day of test. Steel fibers with hooked ends, aspect ratio of 65, and length of 35 mm and volumetric fraction of 2% (157 kg /m³) were used. Comparisons with theoretical models, analyzed through the literature review and recommendations of NBR 6118:2003 and ACI-318-08 were also performed. The experimental results showed that the stirrups and the fibers have significant influence on the cracking of the concrete. It was also observed that, for the specimens with steel bars of 10 mm and 16 mm with straight anchorage, the fibers had small influence on the pull-out resistance.
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Estudo da influência do uso de fibras de aço e de estribos no comportamento da ancoragem de barras / Study of the influence of steel fibers and stirrups on the behavior of the anchorage of barsVinicius Costa Correia 01 June 2012 (has links)
O comportamento estrutural do concreto armado depende da união entre o concreto e a armadura. Esta união se estabelece por meio da aderência, que funciona como um mecanismo de transferência de tensões e garante a compatibilidade de deformações entre a armadura e o concreto. Este trabalho tem como objetivo investigar os efeitos da adição de fibras de aço e armadura transversal no comportamento da ancoragem. A investigação experimental foi feita por meio de dois tipos de ensaio de arrancamento de barras, sendo eles o modelo-padrão do RILEM-CEB-FIP e modelo proposto pelo autor, este considerando barras de pontas retas e com ganchos de 90º. Todos os modelos utilizaram comprimento aderente igual a cinco vezes o diâmetro da barra. As armaduras longitudinais eram compostas por barras de 10 mm e 16 mm e a resistência à compressão média do concreto era igual a 50 MPa no dia do ensaio. Foram utilizadas fibras de aço com ganchos nas extremidades, com relação de aspecto igual a 65, comprimento igual a 35 mm e fração volumétrica de 2% (157 Kg/m³). Também foram realizadas comparações com modelos teóricos, analisados através do estudo de bibliografias existentes e das normas NBR 6118:2003 e ACI-318-08. Os resultados experimentais mostraram que os estribos e as fibras exercem influência significativa na resistência ao fendilhamento do concreto. Observou-se ainda que, para os corpos de prova com barras de aço de 10 mm e 16 mm com pontas retas, as fibras estudadas exerceram pequena influência na resistência ao arrancamento. / The structural behavior of reinforced concrete depends on connection behavior of concrete and steel. This union is established by means of bond, which serves as a mechanism to transfer forces and ensure the compatibility of deformation between the reinforcement and the concrete. This research aims investigating the effects of the use of steel fibers and stirrups on the behavior of the anchorage. An experimental investigation was carried out by means of pull-out tests according to the RILEM-CEB-FIP standard model and pull-out tests of straight and with 90º hooked bars, with a bonded length of five times the bar diameter. The longitudinal reinforcement bars were of 10 mm and 16 mm and concrete compressive strength was 50 MPa at the day of test. Steel fibers with hooked ends, aspect ratio of 65, and length of 35 mm and volumetric fraction of 2% (157 kg /m³) were used. Comparisons with theoretical models, analyzed through the literature review and recommendations of NBR 6118:2003 and ACI-318-08 were also performed. The experimental results showed that the stirrups and the fibers have significant influence on the cracking of the concrete. It was also observed that, for the specimens with steel bars of 10 mm and 16 mm with straight anchorage, the fibers had small influence on the pull-out resistance.
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Relationship Between Compressive Strength of Different Shape and Thickness Specimens of Type S MortarMoffett, Theodore James 01 December 2018 (has links)
Mortar is the cementitious binding material placed between masonry blocks to create a composite system. The American Society of Testing and Materials (ASTM), along with other organizations, have established the testing of prismatic mortar specimens for evaluating mechanical properties, like compressive strength. Mortar joints, however, possess vastly different characteristics compared to prismatic specimens, especially in terms of geometry and water content. These differences prevent a direct comparison of compressive strength between prismatic specimens and actual mortar joints in the assembly. The objective of this study was to analyze Type S mortar joints, with particular emphasis on specimen shape and water content, to draw accurate comparisons of compressive strength to ASTM prescribed mortar prismatic specimens.To examine the effect of water on mortar compressive strength, three different water contents were evaluated across nearly all testing series. Cubic (2-in) and cylindrical (2 by 4-in) mortar specimens were prepared and tested according to ASTM guidelines to verify the compressive strength relationship described by ASTM and to be used as comparative data. In addition, a small masonry wall was assembled and cured in a laboratory to simulate true properties of mortar joints. Mortar joints subjected to testing were a combination of thin slices cut from prismatic specimens as well as in-place bed joints cured between concrete masonry units (CMU). Two unorthodox test methods, the double punch test (DPT) and helix pull-out test (HPT), were selected as methods for assessing mortar joints. In addition, confining effects from neighboring material common to DPT were evaluated as a function of specimen face dimensions. The compressive strength ratio obtained through testing of 2-in cubic and 2 by 4-in cylindrical specimens was lower than ASTM recommendations. This may have been in part due to testing cylindrical specimens with rough surfaces and no capping material. DPT confinement on 2-in square and 2-in diameter circular specimens was found to be equivalent. Thinly sliced specimens tested in DPT showed increases in compressive strength as water content and specimen thickness decreased. As a whole, DPT results on thin mortar slices showed promise for accurate comparison to prismatic mortar specimens. In-place mortar joints tested in HPT showed moderate to high scatter. In addition, evaluation via HPT was determined to be more appropriate for qualitative rather than quantitative assessments of in-situ mortar.
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Bond strength between corroded steel and recycled aggregate concrete incorporating nano silicaAlhawat, Musab M., Ashour, Ashraf 08 November 2019 (has links)
Yes / Limited information related to the application of nano silica in recycled aggregate concretes has been available in the literature. However, investigations on the effect of nano silica on the bond performance of reinforcement embedment length in recycled aggregate concrete have not been conducted yet. Therefore, the present study aimed at investigating the bond strength for recycled aggregate concretes incorporating nano silica under different levels of corrosive environments. The experimental work consisted of testing 180 pull-out specimens prepared from different mixtures. The main parameters studied were the amount of recycled aggregate (i.e. 0%, 25%, 50% and 100%), nano silica (1.5% and 3%), embedment length (5 and 13Ø) as well as reinforcement diameter (12 and 20mm). Different levels of corrosion were electrochemically induced by applying impressed voltage technique for 2, 5, 10 and 15 days. Finally, the experimental results were compared with the existing models.
Experimental results showed that the bond performance between un-corroded steel and RCA concrete slightly reduced, while a significant degradation was observed after being exposed to corrosive conditions, in comparison to normal concrete. On the other hand, the use of a small quantity of NS (1.5%) showed between 8 and 21% bond enhancement with both normal and RCA concretes under normal conditions. However, much better influence was observed with the increase of corrosion periods, reflecting the improvement in corrosion resistance. NS particles showed a more effective role with RCA concretes rather than conventional concretes in terms of enhancing bond and corrosion resistance. Therefore, it was superbly effective in recovering the poor performance in bond for RCA concretes. By doubling the content of NS (3%), the bond resistance slightly enhanced for non-corroded samples, while its influence becomes more pronounced with increasing RCA content as well as exposure time to corrosion.
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Bond strength between corroded steel reinforcement and recycled aggregate concreteAlhawat, Musab M., Ashour, Ashraf 05 February 2019 (has links)
Yes / This paper investigates the bond performance of recycled coarse aggregate (RCA) concrete with un-corroded/corroded reinforcing steel bars, with the main parameters being RCA content, corrosion level, bar diameter and embedment length. For this purpose, 60 pull-out specimens containing different percentages of RCA (i.e. 0%, 25%, 50% and 100%) and steel bars of two diameters (12 and 20 mm) and different embedment lengths were tested. In order to establish various levels of corrosion, specimens were exposed to an electrochemical corrosion for 2, 5, 10 and 15 days. The bond strength between RAC concrete and un-corroded/corroded steel are compared to current codes and equations proposed by other researchers.
Experimental results showed that larger corrosion rate of steel bars was observed with the increase of the replacement level of RCA due to its high porosity and water absorption. The use of RCA had a slight influence on bond strength for un-corroded specimens compared to that obtained from conventional concrete. Furthermore, the bond strength of RCA concrete was strongly affected by corrosion products; bond strength slightly enhanced for up to about 2% corrosion rate, and then significantly decreased as the corrosion time further increased, similar to that of conventional concrete. However, the rate of bond degradation between RCA concrete and corroded steel bars was much faster than that observed in corroded conventional concrete.
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A computer-based justification for using the simple bend test as the basis for predicting the performance of steel hooked-end fibres in reinforced concreteBam, T.J. January 2019 (has links)
The classical test to confirm the performance of a given fibre design for use in reinforced concrete is the pull-out test. While attempts have been made to simulate the performance of such pull-out tests, in practice it has been found that there is a significant disparity between prediction and real-life performance.
The high strength of steel reinforcing fibres is a consequence of the cold wire drawing process and subsequent fabrication. Residual stresses exist in cold drawn wire as a consequence of the elastic response to a non-uniform distribution of plastic strain. This also introduces a yield strength profile where yield strength varies radially through the wire. The question arises as to whether fibre design should use a starting material model that considers these properties.
This thesis examines whether the tensile test, simple bend test and pull-out test provide enough information to define a starting material model that may be used for further design and simulation of such fibres.
Since the details of the wire drawing process and material specification are proprietary and therefore unknown, a sensitivity study was conducted to determine which aspects of the wire drawing process have the greatest effect on the pull-out curve and the following were established as being significant:
• Plastic strain due to wire drawing was shown to be the most important factor.
• The bilinear curve was shown to be a suitable approximation for the stress-strain curve.
• Replacing the plastic strain profile with a single value of average equivalent plastic strain is practical.
The following were established as having negligible effect:
• The consequences of the hooked-end forming process.
• The residual stress profiles due to wire drawing provided that the above was also excluded.
• The hardening law
While inverse analysis demonstrated that all tests provide sufficient information to determine the required properties for this bilinear material model, the pull-out test was shown to provide more accurate approximations of the maximum pull-out force at the first and second peaks and the bend test was shown to produce more accurate approximations of the energy associated with pull-out. Good correlation with the baseline pull-out curve was found for both the isotropic and the kinematic hardening laws and it is concluded that behaviour during pull-out is insensitive to the hardening law.
Sensitivity analysis and characterisation of the material model using an experimental pull-out curve demonstrated the importance of the coefficient of friction. Full characterisation using the pull-out curve therefore requires the solution to a three-variable problem: yield strength, tangent modulus and coefficient of friction. This was a suggested topic for further study. / Dissertation (MEng)--University of Pretoria, 2019. / Mechanical and Aeronautical Engineering / MEng (Mech) / Unrestricted
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Numerical investigation to determine the development of tensile strength in the early age of concrete using experimental data from anchor pull-out testsPan, Zengrui 18 October 2023 (has links)
This study investigates the tensile behavior of anchor pull-out tests from super early
age concrete(less than 12h) by finite element(FE) software ANSYS Workbench. In
previous experiment, several series of pull-out tests were finished and analyzed. In
each per hour, different speeds(1mm/s, 0.2mm/s, 0.1mm/s and 0.833mm/s) were
evaluated, getting the results about correlation of pull-out force and displacement(F-D
curve). It is difficult to evaluate the specific development of tensile strength in super
young concrete, due to the super plasticity that makes itself soft and unstable. The
first step of this study is to collect relevant empirical formula, theoretical varying
material properties with time and pull-out force of experimental applied anchors.
Comparison of simulation analysis results and empirical formulas determines whether
the establishment of the finite element model and adapted constitutive model of
known natural hardened concrete(NHC) are valid or not. The second procedure is that
the material properties of NHC are replaced by different age values and modified until
getting the same simulation results as experiment outcome. The propose of this paper
is to investigate a more accurate modified formula to describe the development of
tensile behavior in super early age concrete:1. Introduction
2. Background
2.1 Modes of failure
2.2 A new failure mode
2.3 Finite Element Numerical Simulation
3. Research Questions
4. Aims/Objectives of the Research
5. Proposed Research Method
5.1 Previous Empirical theory
5.1.1 Cubic Compressive strength of Early Age Concrete
5.1.2 Tensile Strength of Early Age Concrete
5.1.3 Modulus of Elasticity in Early Age Concrete
5.1.4 Prediction of pull-out maximum force to headed studs from concrete
5.2 Pervious Experiment
5.3 Numerical Simulation
6. Significance/Contribution to the Discipline
7. Experiment Program
7.1 Experiment Setup
7.2 Experiment Result
8. Numerical simulation and analysis
8.1 Material Properties
8.2 Modelling Setup
8.3 The first pull-out test
8.4 Comparison Results at different stages
9. Discussion and Results
10. Summary and Conclusion
11. Recommendation for future studies
12. References
13. Appendix
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Estudo da interface bloco/graute em elementos de alvenaria estrutural / Study of the block/grout interface in concrete and clay block masonry structuresSoto Izquierdo, Orieta 08 April 2015 (has links)
A construção de edifícios em alvenaria estrutural tem evoluído de maneira significativa no Brasil. Os edifícios têm se tornado cada vez mais altos, atingindo a marca de 20 pavimentos. Quanto mais altos os edifícios, maiores se tornam os níveis de compressão provenientes dos carregamentos verticais e a sua composição com as ações devidas ao vento e ao desaprumo, obrigando a um maior emprego da alvenaria estrutural armada. A aderência bloco/graute como fator limitante à capacidade do conjunto armadura/graute/bloco na absorção da compressão e tração simples ou da tração oriunda da flexão não é especificada nas normas tanto nacionais como internacionais. Este trabalho tem como objetivo principal estudar o comportamento da interface bloco/graute, tanto para blocos de concreto como cerâmicos e com a presença ou não de armadura, submetidos a solicitações que provocam tração e compressão. Recursos experimentais e numéricos foram realizados para o desenvolvimento da presente pesquisa. Foram feitos ensaios de caracterização dos materiais, dos componentes e da alvenaria, além de ensaios de \"push-out\" (empurramento) para determinar a resistência de aderência na interface graute/bloco e ensaios de \"pull-out\" (arrancamento) considerando-se a presença de barras de armadura para o estudo do comportamento do conjunto graute/bloco/armadura utilizados. Posteriormente foram realizadas modelagens computacionais no programa DIANA, que é baseado no método dos elementos finitos, para prever o comportamento estrutural dos modelos. A partir dos resultados experimentais e numéricos pôde-se concluir que existe uma boa aderência entre as paredes dos blocos de concreto e o graute, suficiente para evitar o escorregamento, sendo possível mobilizar toda a resistência de tração das barras de armadura de diâmetros usuais, desde que devidamente ancoradas. Já com os blocos cerâmicos observa-se uma menor aderência entre as paredes dos blocos e o graute, podendo ocorrer o escorregamento do material de enchimento, antes que a armadura alcance sua tensão de escoamento. O graute de maior resistência à compressão e menor fator água cimento (graute G30) apresentou maior resistência de aderência em relação ao graute mais fraco (graute G14) e de maior fator água/cimento. Quanto aos limites estabelecidos para a tensão de escoamento das armaduras, observa-se que, no caso de blocos de concreto, não deve haver restrição. Em contraposição, quanto aos blocos cerâmicos, o problema é mais complexo, cabendo a realização de mais ensaios para a confirmação de limites, com a variação de blocos e grautes. Os resultados do estudo paramétrico apontam limites que devem ser adotados no caso de diâmetro superior a 10 mm. De maneira simplificada, como ponto para futuras verificações pode-se propor: 75% para Ø 12,5 mm, 50% para Ø 16 mm e 25% para Ø 20 mm. As análises numéricas realizadas nos modelos ensaiados a push-out e pull-out representaram adequadamente o comportamentos observado em laboratório, permitindo a realização da análise paramétrica. / The construction of structural masonry buildings has evolved significantly in Brazil. The buildings have become ever higher, reaching the level of 20 floors. Higher buildings lead to lager compression levels, coming from the vertical loads combined to the horizontal actions due to wind and lack of verticality, obliging a greater use of reinforced structural masonry. The block/grout adherence is not specified in both national and international standards. This work aims to study the behavior of the block/grout interface, for both concrete and clay blocks, with and without reinforcement, submitted to tensile and compressive forces. Experimental and numerical resources were used to development of this study. The experimental program studied the masonry behavior using push-out specimens to determine the bond strength between the grout and the concrete unit, and pull-out specimens to study the behavior of the interface of the grout/block/reinforcement. Computational modelling was carried out using the FEM software Diana, which has a library with constitutive models suitable for civil engineering application, to complete the study and understand the structural behavior of the block/grout interface. The experimental results showed that there is a good bond between the concrete blocks internal faces and the grout, enough to prevent infill-slippage, and that the whole tensile strength of the usual reinforcement rebars is achieved provided they are properly anchored. Nevertheless, for clay blocks there is a low bond between the clay blocks internal faces and the grout, allowing the infill-slippage before the reinforcement bars reach their yield stress. The higher strength grout with lower water/cement ratio (grout G30) presented higher bond strength compared to the lower strength grout and higher water/cement ratio (grout G14). In the case of concrete blocks there should be no restriction limits on the yield stress of reinforcement, in a practical sense and considering other prescribed limits. In contradiction, in the case of clay blocks, additional tests should be carried out for establishing limits, with varying blocks and grouts. The parametric analysis indicates limits that should be adopted for a diameter larger than 10 mm. The authors of this research suggest 75% for Ø 12.5 mm, 50% for Ø 16 mm and 25% for Ø 20 mm as a reference point for future investigations. The numerical analysis showed that the computer models of the push-out and pull-out specimens represented adequately the behavior of the physical models, and thus can be used in parametric analysis.
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