The mechanical effects of short-circuit currents in - Montefiore

m
(2.47) M = σm
= Z mσ
m
dm
2
J
where M is the inner moment, Jm the second moment of
area with respect to the axis O-O. Jm and Zm can be
found in handbooks for all used profiles.
a)
O
b)
O s
O
O s
c)
O s
O
O s
M m
M m
M m
e s
e s
A m
y
x
A s
y
x
A s
y
x
b m
b
b
S m
S s
S m
S s
S s
S m
S s
d m
d
d
d
d
d
d
O
O s
O
O s
O s
O
O s
σ
z
x
z
x
σ
S m
σ m
σ m
S s
S m
x s S s
Figure 2.12 Stresses in main conductors
a) Single conductor
b) No connection of sub-conductors
c) Rigid connection of sub-conductors
2.2.5.2 Section moduli of main-conductors consisting of
sub-conductors
Different number and type of connecting pieces and
direction of force on the main conductor result in
different values of Jm and Zm. Three possibilities are
dealt with in the following.
1. No connection of sub-conductors and main
conductor force perpendicular to surface:
The sub-conductors are independently displaced by the
outer moment m Mr . Figure 2.12b shows the stresses in
the sub-conductors. The opposite surfaces move axial
against each other. One is subjected to compressive
stress with shortened fibres, the other one is subjected to
tensile stress with elongated fibres. The movement have
their maxima at the supports and are zero at the middle
of the span. The independent displacements are possible
if
– there are no connecting pieces or
– the connecting pieces act as spacers or
– there is one stiffening element in the middle of the
span.
It is assumed that the connecting pieces do not increase
the stiffness. On each sub-conductor the moment Mm/2
z
x
σ
S m
σ m
M m
M m
M m
25
acts and the inner moment M in each sub-conductor
becomes:
J
s
(2.48) M m = 2M = 2 σm
= 2Z
sσ
m = Z mσ
m
dm
2
Js and Zs are to be taken with respect to the axis Os-Os of
the sub-conductors. Therefore the section modulus Zm of
the main conductor with respect to the axis O-O is the
sum of section moduli Zs.
n sub-conductors in a main conductor in Figure 2.13a
leads to
(2.49)
Z = nZ
m
2. Rigid connection of sub-conductors and main
conductor force perpendicular to surface:
With rigid connection, the sub-conductors are not able
to move towards each other; the upper conductor is
compressed, the lower one elongated, see Figure 2.12c.
This can be obtained using two or more stiffening
elements. The distribution of the stress is similar to the
single conductor in Figure 2.12a. The second moment of
area with respect to the axis O-O is to be calculated by
Steiner’s law:
(2.50) 2
= ( J + e )
J m 2 s s As
and equation (2.47) holds. For n sub-conductors in
Figure 2.13a, Jm becomes
(2.51)
2
2
( J + e A ) + 2(
J + e A )
J = 2
+ L
m
s
+ 2
1
s
s
s
n 2
2 ( Js
+ en
2 As
) = nJ s + 2As
∑
i=
1
2
s
e
2
i