Civil Engineering Reference
In-Depth Information
y
f
then the integration
coefficient 0.14 is reduced to 0.11, the coefficient 0.07 is reduced to 0.055 while the coefficient
0.2 is reduced to 0.188. The problem of choosing a sufficiently large number of integration points
is illustrated in Fig. 7.7, where the normalised joint acceptance function
ˆ
n
J
for an arbitrary force
component whose influence function is linear and with a maximum of 0.5 at midspan is plotted
versus
N
for three different values of the ratio between
This solution has been based on
L
==
LL
and
N
=
5
. If
N
=
40
exp
u
and the relevant length scale
x
L
L
,
exp
j
uw
or
x
y
=
(and
=
). It is seen that the necessary number of integration points is in general
f
j
uw
or
considerable. The reason for this is that
) is a rapidly decaying function.
Similarly, in Fig. 7.8 the joint acceptance function has been plotted versus the ratio between the
length of the span (
ρ
(
=
jj
) and the relevant integral length scale
x
L
=
L
L
,
j
=
uw
or
. The case
exp
(
)
x
lim
LL
→
/
0
is identical to the situation with an evenly distributed load along the entire
j
span. As can be seen,
ˆ
nn
x
J
is a rapidly decreasing function with increasing values of
L
L
. At a
j
x
large value of
L
L
it is close to 0.05.
j
Fig. 7.7
The joint acceptance function
ˆ
nn
J
vs. number of integration points
