The use of Plain Concrete in structural works is limited by the fact that the tensile strength of concrete is only about 1/10th its compressive strength. Hence, a Beam of plain concrete will fail in the bottom when top portion can still take ten time the stress. By inserting steel bars in the bottom of the Beam to take the tensile stress, the beam is made ten times as strong as a plain beam. Volume for volume steel cost about 60 times as much as concrete and for the same cross-section steel resists about 280 times as much in tension and 28 times as much in compression as concrete. Therefore, a combination of concrete and steel makes for economy.
Two methods of design for reinforced concrete structures are used, the working stress or elastic method and the load factor or ultimate load method. In the working stress method, the design is based on the working loads and the criterion for the strength of the structure is its capacity to sustain the loads and forces imposed on it. The load factor method of design is based on a determination of the load at which a structure fails, and a certain factor of safety is adopted. The working stress method of design, which is the older and by far the steel most commonly used, is adopted here. (Both the methods give somewhat different results.)
Factor of safety, which is the relation between the ultimate strength at failure and the permissible stress, generally adopted is 3 for concrete based on cube crushing strength, and 2 for steel based on the ratio of yield stress of permissible stress.
Modulus of elasticity is a measure of the elastic property of a material and is the ratio between the stress caused by an applied load and the resulting strain or deformation, which disappears on removal of the load. In other words,
Modular Ratio. The relation between the modulus of elasticity of reinforcing steel and the modulus of elasticity of concrete is called the modular ratio. It is represented by nation “m” here.
As there is no relative movement between concrete and steel in a reinforced concrete unit, the elongation or contraction of both concrete and steel is equal. As such modular ratio m is proportional to the permissible stresses in steel and concrete which work together. In other words, the value of modular ratio varies with the modulus of elasticity of steel and concrete respectively.
The modular ratios of various grades of concrete will be as follows:
Grades of concrete M100 M150 M200 M250
1:3:6 1:2:4 1:1.5:3 1:1:2
Modular ratio m 31 18.7 13.3 11
When a steel bar is embedded in the bottom of a concrete beam and the beam if stressed the concrete and the steel is extend and compress equally together provided there is no slip of the bar in the concrete, the deformation in both the materials will be equal. Since stresses are proportional to the respective elastic moduli, the stress in the steel will be “m” times the stress in the concrete. Similarly if a steel bar is embedded in concrete column, then under load the steel and the concrete both must shorten by an equal amount, and since the steel takes “m” times more stress than the concrete when strained equally, the steel will carry “m” times more load per unit area than the concrete.
The tensile stress (in the bottom portion of a beam under load) is in design assumed to be carried wholly by the steel, the strength of the concrete in tension being neglected as it will have failed before the steel is fully stressed under the working load; the concrete on the tensile side will always crack (though the crack may not be visible to the naked eye).
Due to inequalities of workmanship and materials and variable conditions during placing and other reasons, strength of the concrete will be found to differ considerably even in adjacent parts of the same structure. Many assumptions are made in reinforced concrete design, therefore, fictitious accuracies is merely a waste of time.
Grades of concrete. Concrete is of two grades – ordinary concrete and “controlled concrete”. Ordinary concrete in which the proportions of cement, sand and aggregate are arbitrarily specified (like 1:2:4, 1:3:6). Controlled concrete is in which the proportions of cement, sand and aggregate and also water are determined by tests in a laboratory, and the exact proportions depend upon the gradings and size of the aggregate. Controlled concrete give higher strengths by about 25 percent for the same proportions of ingredients. ( The ingredients in controlled concrete are slightly different from the arbitrary proportions of ordinary concretes.) Concrete consolidated by vibrations give still higher strengths by about 10 percent than when consolidated by hand.