Moisture from concrete has been estimated to be responsible for over $1 billion annually from damages in floor coverings. To prevent damages, flooring manufacturers require installers to test concrete moisture levels to determine if the concrete has dried sufficiently to receive flooring or covering. Two of the main tests used in the United States to determine concrete moisture levels are moisture vapor emissions rate (MVER) tests and relative humidity (RH) tests. Changes in ambient temperature can affect the results of both RH and MVER tests. The goal of this study was to investigate the effects of ambient temperature changes on the RH of concrete, and compare the sensitivity of RH measurements to the results of MVER tests at the same ambient temperature. The RH of concrete was measured at 20%, 40%, 60%, and 80% of depth in each sample and tracked over a period of 24 days to develop drying curves at each depth, and drying profiles of each sample. The changes in concrete RH due to a change in ambient temperature were predicted using the psychrometric process and a model developed during this study. Due to size constraints on the concrete samples, ASTM 1869 had to be altered during the MVER tests. Typical RH change in the concrete samples was under 4% RH after either an increase or decrease in an ambient temperature of 5.5°C (10°F). The psychrometric process predicted that the concrete RH would change between 20% - 40% RH after the ambient temperature changed by 5.5°C. Psychrometric properties were not able to full describe the behavior of air in concrete pores so a new model was created to better predict the change in concrete RH after a change in ambient temperature. The developed model was able to predict concrete RH change within 5% error over the range of tested temperatures. / Master of Science

Thesis (MScEng)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Fibre reinforced concrete (FRC) transforms concrete from a characteristically brittle material to one with a post-crack tensile residual capacity. Its application in industry has varied over the past of which the tensile properties have generally been used in the form of crack mitigation. More recently, the introduction of steel fibres has broadened this scope to structural applications in which the resisting tensile stresses that develop within a steel FRC (SFRC) element can be rather significant. This thesis reviews the existing practices and design models associated with SFRC and the suitability of its implementation as the sole form of reinforcement in in-situ cast flat slab systems. As a material SFRC is dependent on a number of factors which include the fibre type and volume, fibre distributions, element size, as well as the support and applied load conditions. Thus, its performance can be considered rather variable in comparison to conventional concrete should the incorrect practices be implemented. In order to adequately define the material characteristics, it is necessary to use test procedures that accurately reflect on the intended structural application. As a result a number of test procedures have been developed. In addition to this, the post-crack material performance is associated with a non-linear behaviour. This attribute makes the design of structural SFRC elements rather difficult. In an attempt to simplify this, existing design models define stress-strain or stress-crack width relations in which assumptions are made regarding the cross-sectional stress distribution at specified load states. This thesis takes on two parts in defining the suitability of SFRC as the sole form of reinforcement in flat slab systems. The first is a theoretical investigation regarding the micro and macro scale material performance of SFRC, the practices that exist in defining the material properties and its application in structural systems (particularly suspended slab systems), and a breakdown of the existing design models applicable to strain softening deflection hardening SFRC materials. The second part is an experimental program in which the fresh state and hardened state material properties of specified SFRC mix designs defined through flow and beam testing respectively. These properties are then implemented in the design and construction of full scale flexural and punching shear test slabs in an attempt to verify the theory applied. The investigation reveals that the use of SFRC significantly improves the ductility of concrete systems in the post-crack state through fibre crack bridging. This ductility can result in deflection hardening of flat slab systems in which the redistribution of stresses increases the load carrying capacity once cracking has taken place. However, the performance of large scale test specimens is significantly influenced by the construction practices implemented in which the material variability increases as a result of non-uniform fibre distributions. The results indicate that the load prediction models applied have potential to adequately predict the ultimate failure loads of SFRC flat slab systems but however cannot account for possible non-uniform fibre distributions which could result in premature failure of the system. / AFRIKAANSE OPSOMMING: Vesel versterkte beton (VVB) verander beton van die kenmerkende uiters bros material na ‘n material met ‘n residuele post-kraak trekkapasiteit. Die toepassing daarvan in die bedryf het in die verlede gewissel en die trek eienskappe is oor die algemeen gebruik vir kraak vermindering. Meer onlangs het die bekenstelling van staal vesel hierdie omvang verbreed na die strukturele toepassings waar trekspannings wat ‘n VVB element kan weerstaan noemenswaardig kan wees. Hierdie tesis ondersoek bestaande praktyke en ontwerpmodelle met die oog op staalvesel versterkte beton (SVVB) en die geskiktheid van die implementering daarvan as die enigste vorm van bekisting in in-situ gegiete plat blad stelsels. As ‘n materiaal, is SVVB afhanklik van ‘n aantal faktore wat die tipe vesel en volume, vesel verspreiding, element grootte, sowel as die randvoorwaardes tipe aangewende las insluit. As gevolg hiervan, kan die gedrag van SVVB, wat korrek geïmplimenteer word, as redelik varieerbaar beskou word wanneer dit met konvensionele beton vergelyk word. Ten einde die materiaaleienskappe voldoende te definieer, is dit noodsaaklik dat prosedures wat die strukturele toepassing akuraat voorstel, getoets word en daarom is ‘n aantal toets prosedures ontwikkel. Verder het die post-kraak materiaalgedrag ‘n nie-lineêre verband wat struktuurontwerp met SVVB redelik moeilik maak. Om dit te vereenvoudig, definieer bestaande ontwerpmodelle spanning-vervorming of spanning-kraakwydte verhoudings waarin aannames gemaak word ten opsigte van die spanningsverdeling oor ‘n snit, gegewe sekere lastoestande. Hierdie studie bestaan uit twee dele wat die geskiktheid van SVVB as die enigste vorm van bikisting in plat blad stelsels definieer. Die eerste deel bestaan uit ‘n teoretiese ondersoek wat handel oor die mikro- en makro-skaal materiaalgedrag van SVVB, die praktyke wat bestaan om die materiaaleienskappe en toepassing in strukturele sisteme (spesifiek opgelegde blad stelsels) te definieer, en ‘n uiteensetting van die bestaande ontwerpmodelle wat van toepassing is vir defleksie as gevolg van vervormingsversagting wat SVVB material verhard. Die tweede deel bestaan uit ‘n eksperimentele program waarin die materiaaleienskappe van gespesifiseerde SVVB meng-ontwerpe in die vars toestand en in die verharde toestand gedefinieer word deur middel van vloei- en balktoetse onderskeidelik. Hierdie eienskappe word dan toegepas vir die ontwerp en konstruksie van volskaalse buig- en ponsskuif toetsblaaie ten einde die modelle en teorie wat toegepas is, te bevestig. Die ondersoek toon dat die gebruik van SVVB die duktiliteit van beton sisteme noemenswaardig verbeter in die post-kraak toestand deur kraak oorbrugging. Hierdie duktiliteit kan defleksie verharding van plat blad stelsels veroorsaak waarin die herverdeling van spannings, nadat kraking plaasgevind het, die lasdraende kapasiteit verhoog. Die gedrag van die grootskaalse toetsmonsters word egter noemenswaardig beïnvloed deur die konstruksiemetodes wat geïmplementeer word waarin die materialveranderlikheid toeneem as ‘n gevolg van nie-uniforme vesel verdelings. Die resultate dui daarop dat die modelle wat toegepas is om die laste te voorspel, die potensiaal het om die grens falingslas van SVVB plat blad stelsel voldoende te voorspel, maar neem nie moontlike nie-uniforme veselverdelings wat kan lei tot vroeë faling van die stelsel in ag nie.

Thesis (MScEng (Civil Engineering))--University of Stellenbosch, 2010. / ENGLISH SUMMARY: It is found that the serviceability limit state often governs the design of slender reinforced concrete members. Slender flexural members often have a percentage tension reinforcement less than 1.0% and an applied bending moment just above the point of first cracking. For such members, the available methods to evaluate the serviceability conditions produce inadequate and unrealistic results. The evaluation of the serviceability of a slender member includes the calculation of the predicted deflection, either by empirical hand-calculation or analysing a finite element model, and the verification using the span-to-effective-depth ratio. The focus of the study is on flat slab structures. It investigates the different deflection prediction methods and the span-to-effective-depth ratio verifications from various design standards. These design standards include the ACI 318 (2002), the SABS 0100-1 (2000), the EC2 (2004) and the BS 8110 (1997). The background to the methods, as well as the parameters which influences the deflection development for lightly reinforced members, are investigated in order to define the limitations of the methods. As a result of the investigation of the deflection calculation methods, an Alternative Approach is suggested and included in the comparisons of the various methods. The deflection prediction methods and the span/effective depth verification procedures are accurately formulated to predict the serviceability behaviour of beams. Additional approaches had to be used to apply these methods to a two-dimensional plane such as that of a flat slab structure. The different deflection prediction methods and the span/effective depth verification methods are calculated and compared to the recorded data of seven experimental flat slab specimens as performed by others. A study by Gilbert and Guo (2005) accurately recorded the flexural behaviour of flat slab specimens under uniformly distributed loads for test periods up to 750 days. The methods to evaluate the serviceability of a slender member were also applied to slab examples designed using South African standards. The study concludes by suggesting a suitable deflection prediction method for different parameter (limitation) categories with which a slender member can comply to. The typical span/effective depth ratio trend is also presented as the percentage tension reinforcement for a slender member changes. It is observed that the empirical hand-calculation methods present more reliable results than those of the finite element models. The empirical hand-calculation methods are accurate depending on the precision to which the slab was constructed relative to the actual slab design. The comparison of the deflection methods with South African case studies identified the role played by construction procedures, material parameters and loading history on slab behaviour. / AFRIKAANSE OPSOMMING: Die diensbaarheidstoestand is in baie gevalle die bepalende faktor vir die ontwerp van slank gewapende beton elemente bepaal. Slank elemente, soos lig bewapende buigbare beton elemente, het gewoonlik ‘n persentasie trekbewapening van minder as 1.0% en ‘n aangewende buigmoment net wat net groter is as die punt waar kraking voorkom. Die metodes beskikbaar om die diensbaarheid van sulke elemente te evalueer gee onvoldoende en onrealistiese resultate. Die evaluering van die elemente in die diensbaarheidstoestand sluit in die bepaling van defleksies deur berekening of die analise van ‘n eindige element model, en die gebruik van die span/effektiewe diepte metode. Die fokus van die studie is platbladstrukture. Die doel van die studie is om die verskillende metodes vir die bereking van defleksie asook die verifikasie volgens span/effektiewe diepte metodes van die verskillende ontwerp standaarde te ondersoek. Die ontwerp standaarde sluit die ACI 318 (2002), SABS 0100-1 (2000), EC2 (2004) en die BS 8110 (1997) in. Die agtergrond van hierdie metodes is ondersoek asook die parameters wat ‘n rol speel, sodat die beperkings van die metodes geidentifiseer kan word. As ‘n gevolg van die ondersoek na die beperkings van die metodes, is ‘n Alternatiewe Benadering voorgestel. Die Alternatiewe Benadering is saam met die metodes van die ontwerpstandaarde gebruik om die verskille tussen die metodes te evalueer. Die defleksievoorspelling en die span/effektiewe diepte verifikasie metodes is korrek geformuleer om die diensbaarheid van balke te evalueer. Ander benaderings was nodig om die diensbaarheid van blad blaaie te toets. Die onderskeie defleksievoorspelling en span/effektiewe diepte metodes is bereken vir sewe eksperimentele plat blaaie soos uitgevoer deur ander navorsers. Gilbert and Guo (2005) het ‘n studie uitgevoer waar die buigingsgedrag van die sewe plat blaaie, met ‘n uniforme verspreide las vir ‘n toetsperiode van tot 750 dae, akkuraat genoteer is. Die metodes om die diensbaarheid van ‘n slank element te toets, was ook op Suid-Afrikaanse blad voorbeelde getoets. Dit was gedoen om die Suid- Afrikaanse ontwerp van ligte bewapende beton elemente te evalueer. Die gevolgetrekkings stel ‘n gepaste defleksie metode vir ‘n slank element vir verskillende beperking kategorië voor. Dit is ook verduidelik hoe die tipiese span/effektiewe diepte verhouding met die persentasie trek bewapening vir ‘n slank element verander. Dit is bevind dat die imperiese handmetodes om defleksies te bereken, meer betroubaar as die eindige element modelle se resultate is. Die imperiese handberekening metodes is akkuraat relatief tot hoe akkuraat die blad konstruksie tot die blad ontwerp voltooi is. ‘n Vergelyking van defleksieberekening met Suid-Afrikaanse gevallestudies het die belangrikheid van konstruksieprosedures, materiallparamteres and belastingsgeskiedenis geïdentifiseer.

Thesis (MScEng)-- Stellenbosch University, 2013. / ENGLISH ABSTRACT: Macro synthetic fibre reinforced concrete (SynFRC) is a relatively new concrete for the purpose of being used in structural elements which only require minimum reinforcement and are supported continuously by sub-layers. One structural element that is of particular interest is slabs-on-grade which is supported by a subgrade/sub-base and requires minimum reinforcement to control the shrinkage strains which may result in cracking. The aim of this project is to investigate the potential use of macro SynFRC in the application of controlling drying shrinkage cracking (DSC) in concrete slabs-on-grade. The focus is on the use of concrete slabs-on-grade that is intended for industrial floors. The SynFRC material parameters of interest were characterised first with the aid of various experimental tests. These are: flexural tests, compression tests, friction tests between the SynFRC and wooden surfaces used for full scale testing, and the shrinkage of the concrete. Next the post-cracking tensile behaviour of the SynFRC was determined by way of an inverse analysis. These tensile responses were subsequently used to perform a series of different finite element analyses. These analyses were performed on specific slabs-on-grade to determine the effects of the added tensile behaviour of the SynFRC on the DSC. The results obtained concerned: the spacing of cracks, the maximum and average crack width, and the difference in crack width between the normal concrete (NC) and the SynFRC. These changes take place in accordance to the concrete age. From the analyses it was determined that the addition of fibres gives the concrete a ductility that allows the concrete to crack more than NC, yet does not allow the cracks to propagate. This applies to low fibre contents of less than 0.4% by volume and a slab thickness of 200mm, as well as to fibre contents that have Re,3 values of 0.51 and higher. Moreover, it results in improvements seen when adding fibres if the friction is sticky, meaning when the maximum friction between the slab and the subgrade is reached with a very small amount of movement. With a stickier friction though smaller crack widths occur within both the NC and the SynFRC. / AFRIKAANSE OPSOMMING: Makro sintetiese vesel versterkte beton (SynFRC) is 'n relatiewe nuwe beton. Dit het ten doel om gebruik te word in strukturele elemente wat minimale versterking benodig en wat deurlopend deur sublae ondersteun word. Een spesifieke strukturele element van belang is grondvloere wat deur 'n sublaag ondersteun word en wat minimale ondersteuning benodig om die krimping vervorming te beheer wat moontlike krake kan veroorsaak. Die doel van die projek was om die potensiële gebruik van makro sintetiese vesels te ondersoek tydens die beheer van die uitdroog krimp kraking van 'n beton grondvloer. Die fokus was op die gebruik van betonvloere vir fabrieksdoeleindes. Die eienskappe van SynFRC materiale is vooraf vasgestel vir die doel van verskeie eksperimentele toetse. Hierdie toetse sluit in buigbaarheidstoetse, druktoetse, krimping van beton en toets van wrywing tussen die SynFRC en hout oppervlaktes wat gebruik is vir volskaalse toets. Die trek gedrag van SynFRC na kraking is vasgestel deur inverse analise. Hierdie trek gedrag is dan gebruik om 'n reeks eindige element analises uit te voer. Hierdie analises is uitgevoer op spesifieke grondvloere om die effek te bepaal van verhoogde trek gedrag van SynFRC op die uitdroog krimp kraking. Volgens die uitslae sodoende verkry was die kraakspasiëring, die maksimum en gemiddelde kraakwydte en die verskil in die kraakwydte tussen normale beton en die SynFRC as ‘n funksie van beton oudedom. Vanuit die analises het dit duidelik geblyk dat die byvoeging van vesels die beton se smeebaarheid verhoog het en dit het tot gevolg gehad dat die beton meer krake vorm, maar dat die krake nie vergroot nie. Dit is waargeneem by 'n lae vesel inhoud van minder as 0.4% per volume en 'n betonblad met 'n dikte van 200mm. Dit is ook waargeneem by 'n hoër vesel volume wat Re,3 waardes van 0.51 en hoër het. Kleiner kraakwydte is waargeneem waar vesel volume verhoog is indien die wrywing hoër is, bedoelende dat die maksimum wrywing tussen die betonblad en die sublaag bereik is met baie min beweging. Daar het wel kleiner kraakwydtes in beide die normale beton en die SynFRC voorgekom waar daar hoër wrywing was.

Compared to the knowledge base for ordinary portland cement concrete (OPCC), relatively little information exists for calcium aluminate cement concrete (CACC), despite its existence for over 100 years. There is particularly a lack of knowledge related to early-age behavior of CACC, specifically volume change and cracking potential. To assess these early-age properties, two unique pieces of equipment were developed and employed: a rigid cracking frame and free deformation frame which enabled quantification of restrained stress generation and unrestrained autogenous deformation, respectively. These two pieces of equipment employed active temperature control and allowed a wide range of isothermal and realistic temperature conditions to be imposed upon hydrating cementitious samples. Match-cured samples (i.e. identical temperature curing to that in the frames) enabled the quantification of mechanical property development. Samples cured at discrete isothermal temperatures up to 30 °C developed tensile forces in the rigid cracking frame and exhibited shrinkage phenomena in the free deformation frame. At temperatures above 30 °C, the converse was true and significant compressive forces developed in restrained testing and expansion was observed in unrestrained testing. It was found that this was a direct result of microstructural development related to the formation of metastable phases (associated with shrinkage) and stable phases (expansion as a result of conversion from metastable to stable phases). Proper use of this material must take into account behavior associated with both types of hydrate assemblages, metastable and stable. Realistic time-temperature histories were also investigated based on field-scale concrete cast as part of this research project. It was found that volume change at earlyage was dominantly controlled by thermal history. Furthermore, it was not simply the maximum temperature reached, but the rate of temperature rise during hydration and the resulting duration of time spent at high temperature that profoundly influenced volume change and property development. The research described in this dissertation represents a significant advancement of the state-of-knowledge of this unique material and has further elucidated the role of temperature during hydration of CACC. / text

Unbonded post-tensioned (UPT) flat plate concrete slabs have seen widespread use in multi-storey office and condominium buildings since the 1960s. The popularity of these systems can be attributed to various economic and structural benefits, including reductions in slab thickness, storey height, building mass, and excellent deflection control over large spans. The “inherent fire resistance” of these systems is often quoted as a key additional benefit as compared with competing structural systems. Such statements are apparently based largely on satisfactory results from large scale standard fire resistance tests performed on UPT slabs during the 1960s and on experience from real fires in UPT buildings. However, much remains unknown about the true structural behaviour of continuous multiple bay UPT slabs in real building fires. For instance, relatively little data exist on the effects of elevated temperature on cold drawn prestressing steel under realistic, sustained service stress levels. The primary objective of this thesis is to provide a greater understanding of the high-temperature performance (predominantly related to prestress relaxation) of prestressing steel used in UPT flat plate slabs. A computational model is developed, extending previous research by others, to predict transient high temperature stress relaxation (i.e., prestress loss) for a tendon in a typical UPT multiple span flat plate concrete slab under transient heating and cooling. The computational model is validated by comparison against a series of novel high temperature experiments on locally-heated, stressed, and restrained prestressing tendons with realistic as-built configurations. Reasonable agreement between measured and predicted prestress losses is observed, although some refinement of the model’s input parameters may be required. Test data also indicate that the most crucial fire scenario on a UPT concrete slab may be localized heating rather than a global, fully developed fire. The model is subsequently used to predict the capacity in flexure and punching shear of a UPT flat plate structure under various spatial and temporal heating regimes. The results highlight the need for particular care in the construction of UPT slabs to ensure adequate, robust concrete cover for structural fire safety. / Thesis (Master, Civil Engineering) -- Queen's University, 2009-09-24 18:27:25.559

Please read the abstract in the section 00front of this document / Dissertation (M Eng (Structural Engineering))--University of Pretoria, 2006. / Civil Engineering / unrestricted

An investigation on the application of basalt fibre reinforced polymer (BFRP) and carbon fibre reinforced polymer (CFRP) bars as longitudinal reinforcement for simple and continuous concrete slabs is presented. Eight continuously and four simply concrete slabs were constructed and tested to failure. Two continuously supported steel reinforced concrete slabs were also tested for comparison purposes. The slabs were classified into two groups according to the type of FRP bars. All slabs tested were 500 mm in width and 150 mm in depth. The simply supported slabs had a span of 2000 mm, whereas the continuous slabs had two equal spans, each of 2000 mm. Different combinations of under and over FRP (BFRP/CFRP) reinforcement at the top and bottom layers of slabs were investigated. The continuously supported BFRP and CFRP reinforced concrete slabs exhibited larger deflections and wider cracks than the counterpart reinforced with steel. The experimental results showed that increasing the bottom mid-span FRP reinforcement of continuous slabs is more effective than the top over middle support FRP reinforcement in improving the load capacity and reducing mid-span deflections. Design guidelines have been validated against experimental results of FRP reinforced concrete slabs tested. ISIS¿M03¿07 and CSA S806-06 equations reasonably predicted the deflections of the slabs tested. However, ACI 440¿1R-06 underestimated the deflections, overestimated the moment capacities at mid-span and over support sections, and reasonably predicted the load capacity of the continuous slabs tested. On the analytical side, a numerical technique consisting of sectional and longitudinal analyses has been developed to predict the moment¿curvature relationship, moment capacity and load-deflection of FRP reinforced concrete members. The numerical technique has been validated against the experimental test results obtained from the current research and those reported in the literature. A parametric study using the numerical technique developed has also been conducted to examine the influence of FRP reinforcement ratio, concrete compressive strength and type of reinforcement on the performance of continuous FRP reinforced concrete slabs. Increasing the concrete compressive strength decreased the curvature of the reinforced section with FRP bars. Moreover, in the simple and continuous FRP reinforced concrete slabs, increasing the FRP reinforcement at the bottom layer fairly reduced and controlled deflections.

Submitted by Luis Ricardo Andrade da Silva (lrasilva@uefs.br) on 2017-11-28T23:42:31Z No. of bitstreams: 1 Dissertacao - Mercurie Janeai Mateus Araujo Rocha.pdf: 2758370 bytes, checksum: 944f4fc5f24c7c08b8ca7abcf999414a (MD5) / Made available in DSpace on 2017-11-28T23:42:31Z (GMT). No. of bitstreams: 1 Dissertacao - Mercurie Janeai Mateus Araujo Rocha.pdf: 2758370 bytes, checksum: 944f4fc5f24c7c08b8ca7abcf999414a (MD5) Previous issue date: 2017-09-04 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - CAPES / In this work the influence of the shear strength of the concrete in the bending of reinforced concrete slabs was studied through two models of analysis. The first model (proposed model 1) combines an isotropic damage model for concrete, proposed by Oliver et al., and the perfect elastoplastic model for steel reinforcement. The second model (proposed model 2), which is in fact a modification of the previous model, introduces a unique damaging to the concrete transverse modulus of elasticity, based on a proposal by Matzenbacher. The behavior of slabs was simulated through the Classical Theory of Laminates and the variational formulation of the problem was developed through the Principle of Virtual Works. The numerical treatment of the problem was based on the Finite Element Method, using a finite rectangular element with 24 degrees of freedom, incorporating Newton-Raphson's incremental-iterative process with load control and displacement control. The validation of the two models was based on the simulation of four rectangular slabs under bending, whose analysis revealed that it is essential to damage the concrete modulus of elasticity when using the damage mechanics. / Neste trabalho foi estudada a influ?ncia da resist?ncia ao cisalhamento do concreto na flex?o de lajes de concreto armado, atrav?s de dois modelos de an?lise. O primeiro modelo (modelo proposto 1) combina um modelo de dano isotr?pico para o concreto, proposto por Oliver e colaboradores, e o modelo elastopl?stico perfeito para o a?o das armaduras. O segundo modelo (modelo proposto 2), que na verdade ? uma modifica??o do modelo anterior, introduz uma danifica??o exclusiva para o m?dulo de elasticidade transversal do concreto, baseado em uma proposta de Matzenbacher. O comportamento das lajes foi simulado atrav?s da Teoria Cl?ssica de Laminados sendo desenvolvida a formula??o variacional do problema por meio do Princ?pio dos Trabalhos Virtuais. O tratamento num?rico do problema foi baseado no M?todo dos Elementos Finitos, utilizando um elemento finito retangular com 24 graus de liberdade, incorporando o processo incremental-iterativo de Newton-Raphson com controle de carga e controle de deslocamento. A valida??o dos dois modelos se deu a partir da simula??o de quatro lajes retangulares sob flex?o, cujas an?lises revelaram ser imprescind?vel a danifica??o do m?dulo de elasticidade transversal do concreto ao se usar a mec?nica do dano.

Abstract not available