Civil Engineering Reference
In-Depth Information
Figure 7.1
Stress (c) and strain (b) distributions in a fully cracked reinforced concrete
section (a) (state 2) subjected to
M
and
N
. Convention for positive
M
,
N
,
y
,
y
n
and
y
s
.
7.4 Instantaneous stress and strain
Consider a concrete section reinforced by a number of layers of steel and
subjected to a bending moment
M
and a normal force
N
at an arbitrarily
chosen reference point O (Fig. 7.1(a) ). The values of
M
and
N
are such
that the top
bre is in compression and the bottom is in tension, producing
cracking at the bottom face.
The equations, graphs and tables presented in this section and subsections
7.4.1 and 7.4.2 are based on the assumption that the top
fi
bre is in compres-
sion and the bottom part of the section is cracked due to tension. When the
bottom part of the section is in compression and the tension zone and crack-
ing are at the top, the equations apply if the direction of the
y
-axis is reversed
and all reference to the top
fi
fi
bre will be considered to mean the bottom
fi
bre.
In this case, the
ange of a T section will be at the tension zone; the graphs
and tables for a rectangular section (of width equal to the width of the web)
will apply as long as the compression zone is a rectangle.
Not included here are the situations when the stresses over all the section
are of the same sign. When all the stresses are compressive, the equations for
uncracked sections presented in Chapter 2 apply. When all the stresses are
tensile, the concrete is assumed to be ine
fl
ective in the fully cracked state 2
and the internal forces are resisted only by the steel. In this case, creep and
shrinkage have no e
ff
ect on the stress and strain distribution over the section.
The stress and strain distributions shown in Fig. 7.1(b) and (c) are assumed
to be produced by the combined e
ff
ect of
M
and
N
as shown in Fig. 7.1(a).
The resultant of
M
and
N
is located at eccentricity
e
given by
ff
e
=
M
/
N
(7.1)
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