Civil Engineering Reference
In-Depth Information
Abeamcross-sectionmustbedesignedsothatitsfactoreddesignmoment
M
Ed
does not exceed the design section moment resistance, so that
M
Ed
≤
M
c
,
Rd
.
(4.63)
Beamsmustalsobedesignedforshear(Section4.7.3)andagainstlateralbuckling
(Section 6.9).The section resistance
M
c
,
Rd
is given by
M
c
,
Rd
=
Wf
y
γ
M
0
(4.64)
inwhich
W
istheappropriatesectionmodulus,
f
y
theyieldstrengthand
γ
M
0
(
=
1
)
the partial section resistance factor. For Class 1 and 2 beam cross-sections
W
=
W
pl
,
(4.65)
where
W
pl
is the plastic section modulus and which allows many beams to be
designed for the full plastic moment
M
p
=
W
pl
f
y
(4.66)
as indicated in Figure 4.28.
For Class 3 beam cross-sections, the effective section modulus is taken as the
minimum elastic section modulus
W
el
,
min
which is that based on the extreme
fibre that reaches yield first. Some I-sections have Class 1 or 2 flanges, but con-
tain a Class 3 web and so based on the EC3 classification they would be Class
3 cross-sections and unsuitable for plastic design. However, the EC3 permits
these sections to be classified as effective Class 2 cross-sections by neglecting
part of the compression portion of the web. This simple procedure for hot-
rolled or welded sections conveniently replaces the compressed portion of the
web by a part of width 20
ε
t
w
adjacent to the compression flange, and with
another part of width 20
ε
t
w
adjacent to the plastic neutral axis of the effective
cross-section.
For a beam with a slender compression flange supported along both edges,
the effective section modulus
W
el
may be determined by calculating the elastic
section modulus of an effective cross-section obtained by using a compres-
sion flange effective width
b
eff
obtained using equation 4.53. The calculation
of
W
el
must incorporate the possibility that the effective section is not sym-
metric, and that the centroids of the gross and effective sections do not
coincide.
Worked examples of classifying the section and checking the section moment
capacity are given in Sections 4.9.2-4.9.4, 5.12.15 and 5.12.17.
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