Civil Engineering Reference
In-Depth Information
Eqns 10.12 and 10.13 can also be applied to a cracked section where, of
course,
x/h
<1 (
Figure 10.11
)
; note, however, that for a cracked section, the
limit of integration
Ó
c
in Eqn 10.12 becomes zero. Therefore, for a cracked
section, Eqn 10.12 becomes
e
(10.15)
10.4.2.4
Calculation of
a
, ¦
and
For any values assigned to
e
c
and x, i.e.
assigned to the pair [
e
c
/
e
cu
,
x/h
], Eqn 10.12 or 10.15 can be used to calculate
a
c
.
a
is then calculated from Eqn 10.13 and ¦ from Eqn 10.14. It can be
shown (Kong et al., 1986b; Kong and Evans, 1987) that the additional
eccentricity
where
n
2
is the numerical constant which depends on the curvature
distribution and
Therefore the lateral deflection parameter
of Eqn 10.3 can be written as
(10.16)
10.4.2.5
Preparation of
curves
The procedure for preparing the
moment-deflection curves
can be summarised as follows:
Step 1:
With reference to
Figure 10.9
a
, select a convenient value for the
concrete strain ratio
cu.
Step 2(a):
With reference to
Figures 10.10
b
and c (and
Figures 10.11
b
and
c) select a convenient
x/h
value, and calculate the area
A
under
the stress-strain curve and the centroidal strain
e
c
/
e
cu
, say
e
c,1
/
e
e
g
from Eqns 10.5
and 10.6 respectively, noting that
e
Ó
c
=
e
c
[1-1/(
x/h
)] for
x/h
‡
1 (i.e.
uncracked section; Figure 10.10), and
e
Ó
c
=
0 for
x/h
<1 (i.e.
cracked section; Figure 10.11).
Step 2(b):
Calculate
a
, ¦ and
from Eqns 10.13, 10.14 and 10.16
respectively.
Step 3:
Repeat Step 2 with other
x/h
values until a sufficient number of
points is obtained for plotting curve Ia in
Figure 10.12
a, curve Ib
in Figure 10.12b and curve Ic in Figure 10.12c.
