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
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Modular ratio m 31 18.7 13.3 11
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(Rounded-of values)
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.
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