ABSTRACTReinforced important to understand the behavior of reinforced concrete

ABSTRACTReinforced concrete is a highly resilient composite material used in the construction of structures that takes advantage of the contrasting mechanical properties of steel and concrete. Due to its prevalent use, it is important to understand the behavior of reinforced concrete under different configurations and conditions and what affects its performance as a material.The Moment-Curvature graph is a method of graphically describing the behavior of reinforced concrete beam sections by plotting the curvature of the section at against its flexural load at a given instance. This document aims to explore the relationship between the curvature of a concrete section and the moment. This is accomplished by investigating the curvature-moment capacity diagram of a given section to set up a control, and then proceed to manipulate different parameters of the concrete section such as the overall beam dimensions, number of tensile and compression reinforcement and strength of steel and concrete. The values of the depth of compression block, the flexural capacity and the curvature at the points before the onset of initial cracking, immediately after the onset of initial cracking, at the yielding of the tensile steel and finally at the crushing of concrete. These points define the different phases of the behavior of concrete under flexural loading.Figure 1 graphically illustrates the results of the first seven cases, using the Hognestad Model for stress-strain I concrete and using the Priestley et al model for Grade 60 steel to generate the moment-curvature graph. Figure 1.?INTRODUCTIONReinforced concrete is a highly resilient composite material used in the construction of structures, that takes advantage of the contrasting mechanical properties of steel and concrete, whose interplay of properties allows for the construction of highly complex structures that are both structurally sound and economical. Concrete as a material takes advantage of its high compressive strength, low coefficient of thermal expansion, resistance to weather and fire, its workability in its fluid state and its relatively low cost is paired with steel’s properties of high tensile stress, ductility and toughness to compensate for concrete’s low tensile strength and brittle nature.Due to the non-homogenous nature of concrete, the behavior of concrete is typically described in phase or stages, each phase defined by a separate function, rather than defining its behavior using a single function. Therefore, a considerable amount of effort has been exerted to define the behavior of its individual components and how they behave under stress as well as the relationships between the different properties of steel and concrete to simulate and understand the behavior of reinforced concrete as a seemingly homogenous material.Concrete is mainly regarded for its compressive strength, however, it has a very small resistance to tensile stress which significantly affects how reinforce concrete behaves. Thus, it is important to also study the stress-strain relationship of concrete under tension as well as that in compression.Figure 2: Stress Strain Curve for unreinforced ConcreteThe behavior of steel is different from that of concrete and is evident in the stress –strain curve of steel. The curve is defined by three regions, all of which occur at all grades of steel. The three regions or phases of steel are the elastic phase which is the region defined by a linear function, the yielding phase defined by the plateau, hardening phase defined by the positive parabolic arc and necking, defined by the negative parabolic arc. Figure 3. Illustrates these phases against the stress-strain curve for reinforcing steel.The primary focus of the dicussions will be the behavior of concrete under flexural loading. As such, concessions and basic assumptions need to be made in order to set the working parameters for the analysis. The basic assumptions of flexure area. Plane sections remain plain before and after bendingb. The strain in reinforcement and the concrete is directly proportional to its distance from the neutral axis. c. Using a given stress-strain curve model for steel and concrete, the stresses for each material for a given strain can be computed.Reinforced concrete has three principal points of interest that will be investigated. The firs is the point on onset of initial cracking determined by the rupture of concrete under tension.?Initial Onset of Cracking Cracking occurs when the stresses in the bottom most fiber of the concrete reaches the modulus of rupture of concrete, fr,  that is, the strain due to tension is equalt to the tension rupture strain of concrete. Having obtained this value, the critical moment of rupture can be computed using the equation: This gives us the first critical point in our moment-curvature model. At this stage, the concrete loses its ability to resist tension and the tension force it was resisting prior to rupture will now be loaded unto the tension steel.  As this occurs, the section undergoes increased strain without significant increase in the flexural load,