Civil Engineering Reference
In-Depth Information
and
K
1
,
K
2
and
MM
are defined by Eqns 10.21a, 10.21b and 10.21e
respectively. Therefore, at any point on a moment-deflection curve for a
specified value of
e
cu
and the neutral axis depth
ratio
x/h
are related by Eqn 10.23. If the concrete strain ratio, say [
a
, the concrete strain ratio
e
c
/
e
cu
]
1
, at
a certain point on a moment-deflection curve for a particular value of
e
c
/
can
somehow be found, then the corresponding neutral axis depth ratio, say [
x/
h
]
1
, can be found by solving Eqn 10.23. Hence, the values of ¦ and at
that point on the moment-deflection curve can be calculated by substituting
the pair {[
e
C
/
e
cu
]
1
, [
x/h
]
1
} into Eqns 10.20 and 10.16 respectively.
It is now clear that, for a given value of
a
, a complete curve can be
constructed by the appropriate solution of Eqn 10.23 for different
e
c
/
e
cu
ratios (see Section 10.4.3.3 later). Before the detailed procedure for
preparing the whole family of
a
curves is given, it is necessary to
examine some of their properties.
10.4.3.2.
Some properties of
curves
constructing the
curve may be summarised as follows (Kong and
Wong, 1987):
i)
On a curve for a given value of
a
(Figure 10.14), the neutral
axis depth ratio
x/h
decreases with while the concrete strain
ratio
e
c
/
e
cu
increases with until
e
c
/
e
cu
=1, when the curve
terminates (see point
D
in Figure 10.14).
ii)
Consider again a typical curve for a given value of
a
, as
shown in Figure 10.14. The figure is divided into two regions by the
Figure 10.14
Variation of
x/h
and
e
c
/
e
cu
along a typical
curve
