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Relating Stress strain to reinforced concrete

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Theory

Casting of Reinforced Concrete Beams:Reinforced concrete is an amalgamated material in which the comparatively low tensile strength and ductility of concrete are counteracted by the inclusion of a form of reinforcement having higher tensile strength and in most cases higher degrees of ductility also. The reinforcement is commonly steel reinforcing bars and is customarily embedded in the concrete before the concrete sets. In such a case of composing a reinforced concrete beam, the steel bar is placed and the concrete mix is added just after mixing to contain within its structure, the steel.The concrete used in reinforced concrete consists of inert aggregate particles bounded together by a paste made from Portland cement and water. The paste fills the voids between aggregate particles and after the fresh concrete is placed, it hardens as a result of exothermic reactions between cement and water to form the solid and durable structural material. The size of aggregate has a significant impact on the amount of cement and water required to produce a given unit of concrete with a particular consistency. In addition the quantity of water in relative to quantity of cement is the most decisive factor in determining the strength of concrete. During consolidation, the densification and subsequent volume shrinkage of the fresh concrete forces entrapped air voids and excess water out of the cement mix. The water tends to migrate upward due to a density differential and become bleed water. The air bubbles, however, seek the nearest route to reach pressure equilibrium

Testing of Reinforced Concrete Beams:The purpose of reinforcement in concrete beams is to hold and support the areas that are weak in tension. Concrete is strong in compression and weak in tension whereas steel is strong in tension and compression, therefore steel is an ideal form of reinforcement. The concept of design in a reinforced concrete beam is for all the compression in the member to be taken by the concrete and the tension to be taken by the steel. When the beam is subjected to tensile loading, the first sign of a crack in the concrete specifies that the concrete has failed. The fact that the beam has not collapsed indicates that the steel is functioning as intended and is holding the beam together by supporting the load.The ultimate moment of resistance will be calculated in accordance to the ACI 318-89 design codes for reinforced concrete. According to the ACI 318 89 Standards:

Where:Mn Ultimate Moment of Resistance (Moment Capacity)As Area of Steel (mm2)dt effective depth (mm)a depth of stress block (mm) = 0.9 (tension controlled factor)Fy yield strength (N/mm2)

The theoretical maximum moment is calculated as follows: