The mechanical effects of short-circuit currents in - Montefiore

)
a)
σF σ0,2 σ0,01 σ
ε 0,01 ε 0,2
c)
Figure 2.1 Stress-strain diagram and stress distribution in a
rectangular cross-section
a) Stress-strain;
1 copper, aluminium;
2 ideal elastic-plastic
b) Stress in the elastic range
c) Stress in the elastic-plastic range
d) Stress in the full plastic range
2
1
ε
d)
14
The rectangular beam is loaded by a force Fm per unit
length. In the elastic range the stress increases linearly
from the neutral axis to the outer fibre, Figure 2.1b. The
inner moment is
(2.25)
M
el
2
( x,
y)
d b
= σ
6
m
m
m
d/
2
= ∫σydA= ∫
A
= Z
σ
−d/
2
σ
m
y
d / 2
yb d y
An outer moment acts in opposite direction, e.g. Fl/8 in
the case of a beam with both ends supported. The outer
moment is now increased until the yielding point σF is
reached. Because all other fibres are in the elastic range,
the outer fibre is prevented from yielding, and high
deformations are not allowed to occur. For better usage,
a further propagation of the flow stress over the cross
section is permitted, Figure 2.1c. The areas y < d / 2
are not fully stretched and are able to take part in the
weight-carrying. During partial plasticity the inner
moment becomes
Table 2.1: Factors β and α for different supports
Maximum moment Mpl,max with plastic hinges at the fixing points in the case of single span beams or at the inner supports of continuous
beams, maximum moment Mel,max in the elastic range
type of beam and support Mpl,max Mel,max β α
single span
beam
A and B:
supported
A: fixed
B: supported
A and B:
fixed
two spans
continuous
beam with
equidistant
supports 3 or
more spans
–
m
11
l F
m
16
l F
m
11
l F
m
11
l F
m
8
l F 1,0
A: 0,5
B: 0,5
m
8
l F 8 A: 0,625
= 0,
73
11 B: 0,375
m
12
l F 8 A: 0,5
= 0,
5
16 B: 0,5
m
8
l F 8 A: 0375
= 0,
73
11 B: 1,25
m
8
l F 8 A: 0,4
= 0,
73
11 B: 1,1