The nominal strength is obtained by applying static equilibrium and
compatibility of stress and strain. The design strength is
calculated by dividing nominal strenght by strength reduction factor φ
(phi).
With reference to the equivalent stress diagram as per
Whitney,
Force of tension due to tension rebar;
T = (area tension rebar) * (stress of
steel)
T = As fy
It is required that tension steel has yielded when failure takes
place. This makes sure that the section is not controlled by
concrete.
Foce of compression (due to concrete);
C_{c}
= (average
compressive stress) * (equivalent area of concrete)
C_{c} =
(0.85f_{C}'
) * (b a)
For equilibrium, the
force of tension equals the force of compression.This gives the
values of "a";
a = (A_{s}
f_{y}
) / (0.85f_{C}'
b)
The depth of neutral axis; x = a/β_{1}
The nominal moment strength of the section is calculated by taking
the moment of compressive force about the centroid of tension steel
area.
M_{n} = C_{c} (d  a/2)
effective depth "d" is the distance from extreme
compression fibre to the centroid of tension rebar.
To learn more about strength of reinforced concrete beam please
visit solved
example 91 ,
example 92,
example 93
Doubly Reinforced Concrete beam
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