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.

<p> A research programme is presented for assessing the capability of Hollow Structural Sections in Plastic Design. This investigation attempts to relate the flange slenderness and yield stress to the rotation capacity of Hollow Structural Sections subjected to both constant moment regions and to moment gradients. </p> <p> An experimental programme was performed on 31 different cross sections to evaluate the moment-curvature relationship which is of fundamental importance in Plastic Methods. The occurrence of local buckling for some sections in the compression flange and the consequent reduction in moment resistance is the critical factor which separates members into compact and non compact categories. </p> <p> The moment-curvature relations from tests are compared with analytical predictions. The plastic hinge rotations delivered by the present test sections are compared with the maximum practical requirements for plastically designed continuous beams. Theoretical elastic and inelastic buckling solutions of plate elements are also presented to relate to possible local buckling of the flats of square and rectangular hollow structural sections. </p> <p> Plate ratios of compression flanges are then selected for use in plastic design of hollow structural sections. Such a separation permits segregation into compact and non compact categories and can be used in working stress or elastic design methods. </p> / Thesis / Master of Engineering (ME)

ABSTRACT AN ANALYTICAL STUDY ON THE MINIMUM CONFINEMENT IN SPIRAL COLUMNS &Ouml / zkaya, Cenan M.S., Department of Civil Engineering Supervisor: Prof. Dr. G&uuml / ney &Ouml / 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

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.

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.

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 D&uuml / 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.

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.