Civil Engineering Reference
In-Depth Information
(c)
From the
x/h
ratios calculated in Step 6b above, select those
within the range [
x/h
=0;
x/h
=1]. Then arrange the selected
x/h
ratios in ascending order. For example,
Where
P, Q, R
and so on are the selected
x/h
ratios.
(d)
Choose an interval from Step 6c, say interval No.1: [0, P].
Calculate
K
1
,
K
2
and
MM
from Eqns 10.21a, b and e and the
coefficients
b
and c of Eqn 10.23 from Eqn 10.24b and c.
Then determine the positive real root from Eqn 10.25.
(e)
If the root obtained in Step 6d is within the interval of
x/h
chosen in Step 6d, the condition of compatibility is satisfied
and proceed to Step 6f; otherwise, return to Step 6d for other
intervals of
x/h.
(f)
Calculate the force parameter, say
a
Ó
1
by substituting the pair
[
e
cu
is chosen in Step 6a
and the
x/h
is determined and checked in Step 6d and Step 6e,
respectively. The condition of equilibrium is considered
satisfied if |
e
c
/
e
cu
,
x/h
] into Eqn 10.19 where
e
c
/
a
1
is the axial force ratio
chosen in Step 2 and TOL is a small number, say 1.0ċ10
-4
. If
the equilibrium condition is not satisfied, return to Step 6d for
other intervals of
x/h.
a
Ó
1
-
a
1
|<TOL, where
(g)
For the
e
cu
chosen in Step 6a, and the
x/h
determined in Step
6d and checked in Steps 6e and 6f, calculate
K
3
,
K
4
, and
NN
from Eqns 10.21c, d and f. Then calculate the corresponding
values of ¦ and
e
c
/
from Eqn 10.20 and 10.16.
(h)
Repeat Steps 6aÎ6g for other concrete strain ratios
e
c
/
e
cu
until
sufficient pairs of [¦, ] are obtained for plotting the second
portion of the moment-deflection curve (i.e. the portion
BCD
of
Figure 10.14
).
Step 7:
Repeat Steps 2Î6 for other a values. Then plot the moment-
deflection curves (
Details of the authorsÓ computer program and worked examples for the
method are given elsewhere (Kong and Wong, 1987; Wong, 1987a).
10.4.4
Stability analysis of columns: analytical method
The two methods described in Sections 10.4.2 and 10.4.3 require manual
manipulation of machine-generated curves, which would be a disadvantage
when graphical facilities are not readily available or when substantial
