Dissertations / Theses on the topic 'Moment-curvature'

There are considerable difficulties in describing the properties of reinforced concrete materials and their interaction. It is therefore necessary to calibrate the mathematical model by accurate testing of laboratory specimens. It can be shown that momentcurvature relationship varies along the length of a member and at beam-column joints. This behaviour depends critically on the geometry of the joint, reinforcement details and the stress-strain characteristics of concrete and steel. Tests have been carried out on model reinforced concrete portal frames and independent specimens making up the frame to predict their non-linear behaviour. The stiffness of the joint plays an important role in the response of the complete frame structure. The behaviour of the corner joints is of particular interest because both the strength and ductility differs for opening and closing joints. The loss of stiffness at joints has a significant effect on the inelastic deformations. The non-linear finite element (FE) program developed takes into account the loss of stiffness at joints and the falling branch behaviour of the material stress-strain relationships. Constant, linear, and parabolic variation in flexural rigidity (EI) and axial rigidity (EA) are taken into consideration along the element length. The combined effect of material and geometric non-linearity is considered. The FE program may use either calculated momentcurvature relationship of different elements or the experimental data obtained from tests. The results show good agreement between the theoretical and experimental beam moment-curvature relationships. Horizontally loaded frame analysis, which involves opening and closing joints, shows that ignoring the joint effect over-estimates the strength. In the case of vertically loaded frames, which involves two closing joints, ignoring the joint effects had little or no influence. The results show good agreement between the theoretical and experimental frame force-displacement relationships throughout the loading range providing the change of stiffness at joints is taken into account for horizontally loaded frames.

To find a relationship between moment versus curvature in a traction-free ovine artery, a pure moment was applied to a radially cut ovine artery (length 50.23 mm). The curvature of the segment opposite the cut was calculated and used to calculate the pre-stresses using a Fung type model. The pre-stresses were then used to calculate the moment. The moment applied during the experiment was calculated by recording the twist applied and the stiffness of the wire applying the moment. The artery was sutured symmetrically with a custom jig, and then sutured to two blocks, one fixed and one subject to the pure moment. The axial strain was assumed unity. The Fung model yielded a linear moment versus curvature relationship, as well as the moment versus curvature relationship for the experiment. Despite both small and large stretches, the strains felt by the artery were not influential enough to display a non-linear correlation for moment vs curvature.

This paper presents results of an experimental investigation to study the structural performance and deformability of a concrete bridge deck reinforced with corrosion resistant reinforcing (CRR) bars, i.e., bars that exhibit improved corrosion resistance when embedded in concrete as compared to traditional black steel. Flexural tests of one-way slabs were conducted to simulate negative transverse flexure over a bridge girder as assumed in the commonly employed strip design method. The bar types studied were Grade 60 (uncoated), epoxy-coated reinforcing (ECR, Grade 60), Enduramet 32 stainless steel, 2304 stainless steel, MMFX2, and glass fiber reinforced polymer (GFRP). The experimental program was designed to evaluate how a one-to-one replacement of the Grade 60 with CRR, a reduction of concrete top clear cover, and a reduction in bar quantities in the bridge deck top mat influences flexural performance at service and ultimate limit states. Moment-curvature predictions from the computer-based sectional analysis program Response 2000 were consistent with the tested results, demonstrating its viability for use with high strength and non-metallic bar without a defined yield plateau.    
    Deformability of the concrete slab-strip specimens was defined with ultimate-to-service level ratios of midspan deflection and curvature. The MMFX2 and Enduramet 32 one-to-one replacement specimens had deformability consistent with the Grade 60 controls, demonstrating that bridge deck slabs employing high strength reinforcement without a defined yield plateau can still provide sufficient ductility at an ultimate limit state. A reduction in bar quantity and cover provided acceptable levels of ductility for the 2304 specimens and MMFX2 reinforced slabs.

Master of Science

In recent earthquakes, structures have not performed as well as expected resulting in a need for better means of retrofitting and improvements in seismic design. Fiber Reinforced Polymers (FRP), as a material with potential to increase strength and ductility of columns in conjunction with capacity design methodology, has promise for seismic design. By investigating the displacement, ductility, and flexural strength properties of FRP confined reinforced concrete circular cross sections, this study analyzes the seismic applications of FRP confinement. The study is performed by incorporating an FRP confined concrete stress-strain model into a developed Moment-Curvature and PM Interaction software. This software conducts a comparison between traditional steel and FRP confined sections while performing parameter studies on the 28-day unconfined concrete compressive strength, longitudinal reinforcing ratio, cross section diameter, FRP confinement jacket thickness-cross section diameter ratio, and FRP confinement system design variables. These studies validate FRP’s performance for seismic applications resulting in several design recommendations to increase displacement capacity, ductility, and flexural strength and, thus, seismic performance.

A model is presented to use normalized multi-linear tension and compression material characteristics of strain-hardening textile reinforced concrete and derive closed form expressions for predicting moment-curvature capacity. A set of design equations are derived and simplified for use in spreadsheet based applications. The model is applicable for both strain-softening and strainhardening materials. The predictability of the simplified model is checked by model calibration and development of design charts for moment capacity and stress developed throughout the cross section of a flexural member. Model is calibrated by predicting the results of Alkali Resistant Glass and Polyethylene fabrics. A case for the flexural design of Glass Fiber Reinforced Concrete (GFRC) specimen as a simply supported beam subjected to distributed load is used to demonstrate the design procedure.

ABSTRACT AN ANALYTICAL STUDY ON THE MINIMUM CONFINEMENT IN SPIRAL COLUMNS Ö
zkaya, Cenan M.S., Department of Civil Engineering Supervisor: Prof. Dr. Gü
ney Ö
zcebe Co-Supervisor: Prof. Dr. Ugur Ersoy July 2005, 135 pages The minimum spiral ratio equation given in the codes is derived by equating the strength at the second peak to the strength at the first peak for spiral columns tested under uniaxial load. In this study, specimen behavior under combined bending and axial load was taken as basis while deriving proposed equations. Analyses were carried out by using a Moment-Curvature program. For normal strength concrete, one regression and one simplified equation giving minimum spiral ratio are proposed. Difference between two equations arises from the number in front of (Ac/Ack). In regression equation, this number is calculated by means of a function. In simplified equation, this number is a constant. For high strength concrete, a different regression equation is proposed which is valid for concrete strengths up to 95 MPa. Simplified equation proposed for normal strength concrete is also proposed for high strength concrete up to concrete strengths of 120 MPa. It was found that
(i) Simplified equation proposed for normal and high strength concrete yielded consistent results in the range of variables studied
(ii) Except some points, regression equations yielded consistent results
(iii) It is recommended to use simplified equation instead of regression and code equations since it yields more consistent results than code and regression equations. Keywords: Confined Concrete, Ductility, Moment-Curvature, Minimum Spiral Volumetric Ratio

Shear-wall dominant multi-story reinforced concrete structures, constructed by using a special tunnel form technique are commonly built in countries facing a substantial seismic risk, such as Chile, Japan, Italy and Turkey. In 1999, two severe urban earthquakes struck Kocaeli and Dü
zce provinces in Turkey with magnitudes (Mw) 7.4 and 7.1, respectively. These catastrophes caused substantial structural damage, casualties and loss of lives. In the aftermath of these destructive earthquakes, neither demolished nor damaged shear-wall dominant buildings constructed by tunnel form techniques were reported. In spite of their high resistance to earthquake excitations, current seismic code provisions including the Uniform Building Code and the Turkish Seismic Code present limited information for their design criteria. This study presents experimental investigation of the panel unit having H-geometry. To investigate the seismic behavior of panel buildings, two prototype test specimens which have H wall design were tested at the Structural Mechanics Laboratory at METU. The experimental work involves the testing of two four-story, 1/5-scale reinforced concrete panel form building test specimens under lateral reversed loading, simulating the seismic forces and free vibration tests. Free vibration tests before and after cracking were done to assess the differences between the dynamic properties of uncracked and cracked test specimens. A moment-curvature program named Waller2002 for shear walls is developed to include the effects of steel strain hardening, confinement of concrete and tension strength of concrete. The moment-curvature relationships of panel form test specimens showed that walls with very low longitudinal steel ratios exhibit a brittle flexural failure with very little energy absorption. Shear walls of panel form test specimens have a reinforcement ratio of 0.0015 in the longitudinal and vertical directions. Under gradually increasing reversed lateral loading, the test specimens reached ultimate strength, as soon as the concrete cracked, followed by yielding and then rupturing of the longitudinal steel. The displacement ductility of the panel form test specimens was found to be very low. Thus, the occurrence of rupture of the longitudinal steel, as also observed in analytical studies, has been experimentally verified. Strength, stiffness, energy dissipation and story drifts of the test specimens were examined by evaluating the test results.

Esta pesquisa apresenta a monitoração de modelos reduzidos para a investigação do comportamento de estruturas. O estudo do comportamento estrutural consistiu basicamente na medição de grandezas físicas de forma experimental, para o qual os modelos físicos reduzidos foram submetidos a múltiplos ensaios em laboratório. Posteriormente, os dados experimentais foram tratados e analisados, para então serem comparados com os resultados dos modelos teóricos, avaliando assim, sua capacidade de simulação. No total foram monitorados três modelos reduzidos, cujas grandezas físicas foram medidas utilizando-se sensores elétricos, tais como: extensômetros, LVDTs e um servoatuador hidráulico, os quais estavam ligados ao sistema de aquisição da National Instrument, controlado por um computador de comando e pelos programas LabView e DynaTester. Um dos modelos construído em alumínio foi utilizado a fim de se estudar o comportamento da ponte do rio Suaçui, assim como calibrar os modelos teóricos em função dos dados experimentais da estrutura real e do modelo reduzido e estabelecer uma relação entre eles. Os outros dois modelos construídos em microconcreto foram utilizados para estudar o comportamento de estruturas na fase não linear e em fratura, para o qual foram submetidos a carregamentos incrementais. A ponte de microconcreto foi ensaiada com o intuito de se verificar a variação da rigidez de sua seção transversal e a construção de uma relação experimental de momento-curvatura. As vigas levemente armadas foram ensaiadas a flexão em três pontos até a ruptura, com a finalidade de se verificar que seu comportamento depende de vários parâmetros tais como: taxa de armadura, tamanho da viga, forma da seção transversal e a aderência aço-concreto. O estudo experimental foi complementado com ensaios de caracterização de materiais, estudos teóricos e o desenvolvimento de aplicativos como o programa PUENFLEX para o cálculo de relações de momento-curvatura de seções e o aplicativo desenvolvido em LabView para monitoração de estruturas que permite visualizar seu comportamento em tempo real.
This research presents the monitoring of scale reduced models for investigation the behavior of structures. The study of structural behavior consisted basically in the measurement of physical quantities on an experimental basis, to which the reduced physical models were subjected to multiple laboratory tests. Then the experimental data were processed and analyzed, so at the finally the results were compared with theoretical models and thereby to evaluate their ability to simulation. In total were monitored three reduced models, whose physical quantities were measured using electrical sensors such as strain gauges, LVDT\'s and a system hydraulics load, which in the same time were connected to the system of acquisition of the National Instrument, controlled by a computer command and DynaTester and LabView programs. One of the models constructed of aluminum was used to study the behavior of Suaçuí river bridge, as well as calibrate the theoretical models on the basis of experimental data of the real structure and the reduced model and to establish a relationship between them. The other two models built in microconcrete were used to study the behavior of structures in the nonlinear phase and fracture, for which they were subjected to incremental loads. The bridge of microconcrete was tested in order to verify the variations the rigidity of their cross section and the construction of an experimental relationship for the moment-curvature. The beams with minimum flexural reinforcement were tested in three-point bending to failure, in order to verify that his behavior depends on various parameters such as reinforcement ratio, the beam size, shape of cross section and steel-concrete adherence. The experimental study was completed with material characterization tests, theoretical studies and the development of applications such as PUENFLEX program for calculating the moment-curvature relationships for cross sections and the program developed in LabView for monitoring structures to visualize their behavior in real time.

São descritas as recomendações da Norma Brasileira NBR-6118/1978 e do Código Modelo do Comité Euro-internacional du Béton CEB-1990 para a verificação da estabilidade de pilares esbeltos de concreto armado com seção variável submetidos à flexão normal composta, empregando-se a teoria do método geral. Para a obtenção dos momentos de segunda ordem são descritos os métodos de Engesser-Vianello e da integração numérica das curvaturas das seções transversais ao longo do pilar. Para a determinação do momento fletor absorvido pelas seções em função da curvatura proveniente da flexão do pilar sob a ação de uma força normal, desenvolvem-se as expressões para seções retangulares e circulares (cheias e vazadas) com base nas relações de tensão-deformação dos materiais segundo a norma e o código supracitados. Apresenta-se também um programa para microcomputador, elaborado em linguagem PASCAL, destinado à verificação da estabilidade de pilares com opção de adoção dos critérios da NBR-6118/1978 ou do CEB-1190. Não foram abordados os efeitos decorrentes de vibrações, fazendo-se apenas a descrição dos métodos de consideração dos efeitos decorrentes da deformação lenta.
The recommendations of Brazilian Code NBR-6118/1978 and Comité Euro-Internacional du Béton Model Code CEB-1990 are described, for stability verification of concrete slender columns with variable cross sections, subjected to axial load and bending moment, using the exact method. To obtain the second order bending moments, the Engesser-Vianello method and the numeric integration of the cross section curvatures along the longitudinal axial of column method are described. To obtain of bending moment supported by the cross sections due to curvature resultant of the column flexure under axialload, expressions for rectangular and circular (full and hollow) cross sections are developed, using stress-strain relations for materials proposed by model codes above mentioned. It\'s also presented a software written in PASCAL language for microcomputer and destined to column stability verification, with option to adopt the NBR-6118/1978 or CEB-1990 model code recommendations. Effects due to vibrations were nor included. Methods to take in account creep effects were described.

Orientador: Francisco Antonio Menezes
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo
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Resumo: Neste trabalho são apresentadas as expressões matemáticas necessárias para determinar o momento de inércia em função da curvatura para seções retangulares de concreto armado solicitadas a flexo-compressão reta. As expressões são determinadas através da integração analítica da curva tensão-deformação do concreto. Com base nestas expressões foi desenvolvido um programa de computador para calcular o momento de inércia em função da curvatura. O objetivo é obter o momento de inércia real da seção para ser utilizado na verificação das deformações. Para o programa é necessário conhecer: a geometria, a disposição das armaduras, as características dos materiais e as solicitações atuantes na seção. Na entrada de dados é possível controlar os coeficientes de ponderação dos materiais e das solicitações. Para o módulo de elasticidade, podem ser adotados os valores prescritos na NBR6118, ou outro valor que deve ser informado. A resistência à tração do concreto foi desprezada. Para validação dois modelos estruturais são analisados. A análise estrutural é feita de várias formas, sendo que uma delas é a análise considerando a não linearidade fisica (NLF) através da curvatura. Neste caso os elementos estruturais têm uma discretização maior, visando considerar a não linearidade ao longo do comprimento das peças. O objetivo é avaliar a possibilidade de implementar um processo de análise estrutural onde a consideração dos efeitos de segunda ordem seja relevante, que considere um. momento de inércia que aproxime o modelo matemático do modelo fisico real
Abstract: In this work, are presented the mathematic expressions necessary for determinate the moment of inertia in function of the curvature for rectangular cross-section the reinforced concrete submitted to mono-axial eccentricity. The expressions are determinate by the integration of analytic parabola rectangle stress strain diagram of concrete. Based in these expressions a computer system was developed to calculate the inertia of moment curvature. The objective is to get the moment of real inertia to be used in the verification of the deformations. It is necessary that the computer system know: geometry, the disposal of the bars, the characteristics of the materiaIs and operating requests in the section. When the database is imputed it is possible to have a control over the method of partial factors of materiaIs and solicitations. For the elasticity model may be adopt the NBR6118's values, or another value that must be informed. The resistance tension of concrete was rejected. To make the validation two structural models are analyzed. The structural analysis is made of severa! forms, one of them is the analysis considering no-linearity physical (NLP) through the curvature. In this case the structural elements have the biggest discretization, aiming to consider no-linearity along the length of the parts. The objective is to evaluate the possibility to implement a process of structural analysis where the effects of second order are relevant, that considers an inertia moment that can make the mathematical model dose to the real physical one
Mestrado
Estruturas
Mestre em Engenharia Civil

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Financiadora de Estudos e Projetos
In this paper, a free analysis program is presented for the verification of ultimate and serviceability limit states of reinforced or prestressed concrete sections with polygonal shape submitted to axial forces and biaxial bending. In addition, the program also calculates the bending-axial force-curvature relation (M, N, 1 / r) of the sections, which can be used in further analysis, for example, the general method for calculating pillars. For this is used the object-oriented programming, so that this work can be resumed and amended, providing technical material for future work in the same line, therefore provides that the calculation routines along with the program. The programming lines and routines includes explanations of its operation to encourage its further use as part of other programs. The data entry is presented as a form and the program enables the exchange of data, both input and output via text type files. The criteria adopted follows the brazilian standard ABNT NBR 6118: 2014, which compared to the previous version features suggestions for concrete with superior characteristic strength higher than 50 MPa. The structure of the routines is presented so that criteria of other standards, or updates of the same Brazilian standard referenced, can be easily implemented. Some validation examples for the program are presented in different situations and finally commented and listed some other extensions which can be made.
No presente trabalho, apresenta-se um programa livre e gratuito de análises e verificações de estados-limite último e de serviço de seções de concreto armado e protendido com forma poligonal submetidas à flexão composta oblíqua. Além disso, o programa calcula também a relação momento-normal-curvatura (M, N, 1/r) das seções, que pode ser usada em outras análises, como por exemplo, o método geral para o cálculo de pilares. Para isso se usa a programação orientada ao objeto, a fim de que o presente trabalho possa ser retomado e alterado, dando subsídio técnico para trabalhos futuros da mesma linha, por esse motivo fornece-se as rotinas de cálculo juntamente ao programa. As linhas e rotinas de cálculo constam com explicações de seu funcionamento para incentivar seu uso posterior como parte de outros programas. A entrada dos dados é feita de forma de formulário e o programa permite a troca de dados, tanto de entrada como de saída através de arquivos do tipo texto. Os critérios adotados seguem a norma brasileira ABNT NBR 6118:2014, que em relação à versão anterior apresenta sugestões para concretos com resistência superior a 50 MPa. A estrutura das rotinas é apresentada de maneira que critérios de outras normas, ou ainda atualizações da mesma norma brasileira referenciada, possam ser facilmente implementadas. Apresenta-se vários exemplos de validação do programa em diversas situações e finalmente comentadas e listadas as ampliações que podem ser feitas.

Esta investigación aborda la real influencia que tiene el agrietamiento de los elementos estructurales en la reducción de rigidez cuando se produce un evento sísmico. Para ello, en primer lugar, describió la realidad problemática, los antecedentes y generalidades previos acerca del tema para determinar qué tipo de edificación utilizar. En segundo lugar, el marco teórico expuso un conjunto de conceptos fundamentales necesarios para entender el agrietamiento del concreto, la obtención de la inercia efectiva, la irregularidad de edificaciones y se dio un repaso sobre las consideraciones de normas extranjeras. En tercer lugar, se determinó trabajar con 6 planos de viviendas multifamiliares, de los cuales 3 fueron estructuras regulares y 3 fueron irregulares. Asimismo, se subdividió las estructuras en alturas de 5, 10 y 15 pisos, ya que son el tipo de edificación que más se construyen en Lima. Después se halló los parámetros geográficos, de uso y geométricos a partir de la Norma E-030, para luego realizar el análisis sísmico lineal (estático y dinámico). Luego, se realizó los diagramas de momento – curvatura (vigas, columnas y placas), para que, a partir de ellos, obtener un factor de reducción de la inercia bruta y realizar un nuevo análisis sísmico considerando este valor como efecto del agrietamiento. Finalmente, se realizó un análisis comparativo entre los resultados obtenidos de acuerdo a la altura en edificaciones regulares e irregulares.
This research addresses the real influence of the cracking of structural elements in the reduction of rigidity when a seismic event occurs. To do this, first, he described the problematic reality, the background and previous generalities about the topic to determine what type of building to use. Secondly, the theoretical framework exposed a set of fundamental concepts necessary to understand the cracking of concrete, the obtaining of effective inertia, the irregularity of buildings and a review of the considerations of foreign standards. In the third place, it was determined to work with 6 multifamily housing plans, of which 3 were regular structures and 3 were irregular. Likewise, the structures were subdivided into heights of 5, 10 and 15 floors, since they are the type of building that is most constructed in Lima. Afterwards, the geographic, use and geometrical parameters were found from the E-030 standard, to then perform the linear seismic analysis (static and dynamic). Then, the moment diagrams - curvature (beams, columns and plates) were made, so that from them, obtain a reduction factor of the gross inertia and perform a new seismic analysis considering this value as an effect of cracking. Finally, a comparative analysis was made between the results obtained according to the height in regular and irregular buildings.
Tesis

Este trabalho tem a finalidade de estudar a influência da parede de concreto na análise de estabilidade de contenções atirantadas bem como discutir sobre segurança nestas análises. Para isto foram elaborados modelos em estado plano de deformação por meio do método dos elementos finitos, MEF, para análise. A parede de concreto foi modelada com variações de rigidez e modelos reológico, com o fim de se entender sua influência no fator de segurança. Por fim foi realizado um breve estudo sobre a utilização dos métodos estatísticos na análise de estabilidade de contenções.
This work has the purpose of study the influence of the concrete wall in the stability analysis of tieback retaining walls and to discuss these safety analysis. Models were developed using plane strain state via the finite element method, FEM, for analysis. The concrete wall was modeled with variations of stiffness and rheological models, in order to bore its influence on the safety factor. Finally a brief study was conducted on the use of statistical methods in stability analysis of retaining walls.

abstract: A simplified bilinear moment-curvature model are derived based on the moment-curvature response generated from a parameterized stress-strain response of strain softening and or strain-hardening material by Dr. Barzin Mobasher and Dr. Chote Soranakom. Closed form solutions are developed for deflection calculations of determinate beams subjected to usual loading patterns at any load stage. The solutions are based on a bilinear moment curvature response characterized by the flexural crack initiation and ultimate capacity based on a deflection hardening behavior. Closed form equations for deflection calculation are presented for simply supported beams under three point bending, four point bending, uniform load, concentrated moment at the middle, pure bending, and for cantilever beam under a point load at the end, a point load with an arbitrary distance from the fixed end, and uniform load. These expressions are derived for pre-cracked and post cracked regions. A parametric study is conducted to examine the effects of moment and curvature at the ultimate stage to moment and curvature at the first crack ratios on the deflection. The effectiveness of the simplified closed form solution is demonstrated by comparing the analytical load deflection response and the experimental results for three point and four point bending. The simplified bilinear moment-curvature model is modified by imposing the deflection softening behavior so that it can be widely implemented in the analysis of 2-D panels. The derivations of elastic solutions and yield line approach of 2-D panels are presented. Effectiveness of the proposed moment-curvature model with various types of panels is verified by comparing the simulated data with the experimental data of panel test.
Dissertation/Thesis
Masters Thesis Civil and Environmental Engineering 2015

碩士
國立交通大學
土木工程系所
97
In this research, analytical model was established by using fiber element method to study the behavior of steel reinforced concrete (SRC) beams under pure bending moment. The flexural strength and the ductility contributed by each component in the section of the SRC beams could be investigated according to the moment-curvature relationship. Analytical model was based on the compatibility of deformations and equilibrium of forces to predict moments and curvatures. Programming was followed by analytical model using MATLAB software to establish the relationship between the moment and the curvature and to plot the relations. Analytical results were compared with experimental data to investigate the influence of the amount of tensile reinforcing bars, the hoop spacing, the depth of the structural steel sections, and the stiffeners. The results indicated the experimental results could be predicted accurately by analytical model. The confinement was not the main factor to raise the ultimate moment strength of SRC beams, but the ductility could be improved along with the increase of highly confined concrete area. Increasing the amount of tensile reinforcing bars and the depth of structural steel could raise the ultimate moment strength effectively.

yes
The main purpose of this paper is to assess moment redistribution in continuous concrete beams reinforced with fibre reinforced polymer (FRP) bars. A numerical technique based on equilibrium of forces and full compatibility of strains has been developed to evaluate the moment–curvature relationships and moment capacities of FRP and steel reinforced concrete sections. Moment redistribution has then been assessed by comparing elastic and experimental moments at failure, and moment capacity at critical sections of continuous FRP reinforced concrete beams reported on the literature. The curvature of under reinforced FRP sections was large at FRP rupture but failure was sudden, that would not allow any moment redistribution. On the other hand, FRP over reinforced sections experienced higher curvature at failure than steel over reinforced sections owing to the lower FRP modulus of elasticity. Although the experimental and elastic bending moment distributions at failure are significantly different for many beams tested elsewhere, in particular CFRP reinforced concrete beams, the experimental bending moment over the middle support at failure was far lower than the corresponding moment capacity owing to the de-bonding of FRP bars from concrete in the middle support region. Furthermore, the hogging moment redistribution over the middle support is always larger than that at mid-span by around 66%. It was also shown that the load capacity prediction of continuous FRP reinforced concrete beams using the de-bonding moment at the middle support section was the closest to the experimental failure load.

Stress-strain relations for unconfined and confined concrete are proposed to overcome some shortcomings of existing commonly used models. Specifically, existing models are neither easy to invert nor integrate to obtain equivalent rectangular stress-block parameters for hand analysis and design purposes. The stress?strain relations proposed are validated for a whole range of concrete strengths and confining stresses. Then, closed form expressions are derived for the equivalent rectangular stress-block parameters. The efficacy of the results is demonstrated for hand analysis applied for deriving the moment-curvature performance of a confined concrete column. Results are compared with those obtained from a computational fiber-element using the proposed stress-strain model and another widely used model; good agreement between the two is observed. The model is then utilized in the development of a new structural system that utilizes the positive attributes of timber and concrete to form a parallel. Timber has the advantage of being a light weight construction material, easy to handle, is environmentally friendly. However, large creep deflections and significant issues with sound transmission (the footfall problem) generally limit timber use to small spans and low rise buildings. Concrete topping on timber sub-floors mitigate some of these issues, but even with well engineered wood systems, the spans are relatively short. In this study, a new structural system called structural boxed-concrete, which utilizes the positive attributes of both timber and reinforced concrete to form a parallel system (different from timber-concrete composite system) is explored. A stress-block approach is developed to calculate strength and deformation. An analytical stress-block based moment-curvature analysis is performed on the timber-boxed concrete structural elements. Results show that the structural timber-boxed concrete members may have better strength and ductility capacities when compared to an equivalent ordinary reinforced concrete member.