Civil Engineering Reference
In-Depth Information
in Figures 5.30a and 5.31a.Aworked example of the plastic collapse analysis of
a non-uniform beam is given in Section 5.12.14.
ThelimitationsontheuseofthemethodofplasticanalysisintheEC3strength
design of beams are discussed in Section 5.6.2.
The application of the methods of plastic analysis to rigid-jointed frames is
discussedinSection8.3.5.5.Thisapplicationcanonlybemadeprovidedtheeffects
of any axial forces in the members are small enough to preclude any instability
effects and provided any significant decreases in the full plastic moments due to
axial forces are accounted for (see Section 7.2.2).
Q
2
Q
M
1
M
2
M
3
M
4
1
2
2
3
3
4
1
2
3
4
M
2
M
1
-
L/
3
M
3
M
2
-
L/
3
M
4
M
3
-
L/
3
L /
3
L/
3
L/
3
( a ) B u i lt- in b e a m
( b ) Beam segments
2
Q
Q
2
Q
Q
1
4
M
p
M
p
M
p
M
p
2
2δ
δ
(c ) Fi r st mec han i sm and virtual displacements
Q
Q
2
Q
2
Q
1
4
M
p
M
p
M
p
M
p
2δ
3
δ
(d ) Co r r ec t mec h a n i sm and virtual displacements
Figure 5.30
Plastic analysis of a built-in beam.
q
M
p
L
0.5
L
(a) Propped cantilever
(c) First mechanism
M
p
M
p
0.583
L
0.586
L
(b) Correct mechanism
(d) Second mechanism
Figure 5.31
Plastic analysis of a propped cantilever.
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