The mechanical effects of short-circuit currents in - Montefiore

a) b)
F m
c)
F m
O
d d d d d
O
OT O
d d d D d d
O T
O
O T
O T
d
d
b
Figure 2.13 Stresses in main conductors
The connecting pieces are black
a) Force perpendicular to surface
b) Force in direction of surface
c) Four connecting pieces, two and two
connected
where n is an even number and ei is the distance
between the centre of sub-conductor i and axis O-O. If
the spacings of the sub-conductors are equal to the
thickness d, the sum can be written:
b
F m
n 2
2 2 2 2
∑ ei
= d + ( 3d
) + ( 3d
) + L
i=
1
(2.52)
2
⎛⎛
n ⎞ ⎞ n
+ ⎜⎜
2 −1⎟d
⎟ =
⎝⎝
2 ⎠ ⎠
O
d
O
b
b
b
b
b
b
2 ( n −1)
2
If n is an odd number, the result is the same as the one
given by the equation (2.52). Hence for all n:
n(
n −1)
2 2
(2.53) J m = nJ s + 2As d = n(
4n
− 3)
J s
6
The distance of the outer fibre from axis O-O is (2n –
1)d/2. Zm becomes:
(2.54)
where
Z
m
=
J
m
( 2n
−1)
2 ( 4n
− 3)
n
=
2n
−1
3
2
Z
s
2 ( 4n
− 3)
n
=
d 2 2n
−1
d b
d b
(2.55) J s = Zs
=
12
6
In Figure 2.13c there are four sub-conductors, two by
two connected with stiffening elements. The pairs are
2
d
J
6
s
2
d
26
not connected, therefore Zm follows from equation
(2.48); the section modulus of each pair is to be taken
with respect to the axis OT- OT according to equation
(2.54) and n = 2:
Z = 2Z 26
= 2 ⋅ Z
3
52
= Z
3
It is independent from the spacing of the pairs.
(2.56) m sT
s s
U- and I-profiles can be treated in similar manner.
In equations (2.54) and (2.56) it is assumed an ideal
rigid connection between the sub-conductors. However,
the stiffening elements are mounted at discrete spots and
no continuous stiffening is reached. Therefore the actual
section modulus are lower. [Ref 32] reports about tests
with two sub-conductors Al 80 mm × 10 mm with
spacing of the thickness. The results can be summarised
as follows:
– one stiffening element practically does not increase
the stiffness;
– with two or three stiffening elements, the actual
section modulus is about 60 % of the value
according to equation (2.54);
– with four elements, the actual value is about 80 %.
Tests concerning U- and I-profiles are not known.
Section 2.2.2.3 and Table 5 of the standard recommend
the following section moduli for main conductors:
– with rectangular profiles 60 %
– with U- and I-profiles 50 %
of the value of ideal rigid connection.
3. Main conductor force in the direction of the surface
If the electromagnetic force Fm is as shown in Figure
2.13b, the connecting pieces have non-essential
influence on the stiffness; they may be spacers or
stiffening elements. However, the sum of the lengths of
the elements has to be much smaller than the span
length. The main conductor axis O-O coincides with the
sub-conductor axis Os-Os. In each sub-conductor the
outer moment Mm/n results in the inner moment M:
J
d 2
s
(2.57) M m = nM = n σm
= nZsσ
m = Z mσ
m
The section modulus Zm of the main conductor is the
sum of the section moduli Zs:
(2.58)
Z m = nZs
2.2.5.3 Section modulus of sub-conductors
Besides the force Fm between the main conductors, on
each sub-conductor the force Fs according to equation
(2.4) which gives the outer moment Ms, Figure 2.14.
The sub-conductors move towards each other and they
behave like single conductors fixed at both ends. Js and
Zs of a sub-conductor is equal to the correspondent
values of a single conductor having the same
dimensions and bending axis. For the rectangular