Civil Engineering Reference
In-Depth Information
4.7.3 Members in compression and bending
Forcross-sectionssubjectedtoadesigncompressiveforce
N
Ed
andadesignmajor
axis bending moment
M
y
,
Ed
, EC3 requires the interaction equation
N
Ed
N
Rd
+
M
y
,
Ed
M
y
,
Rd
≤
1
(4.67)
tobesatisfied,where
N
Rd
isthecompressionresistanceofthecross-sectiondeter-
minedfromequation4.49and
M
y
,
Rd
isthebendingresistanceofthecross-section
determined according to equation 4.63. Generally, the provision of equation 4.67
is overly conservative and is of use only for preliminary member sizing, and so
EC3 provides less conservative and more detailed member checks depending on
the section classification.
If the cross-section is Class 1 or 2, EC3 reduces the design bending resistance
M
y
,
Rd
to a value
M
y
,
N
,
Rd
, dependent on the coincident axial force
N
Ed
. Provided
that
N
Ed
≤
0.25
N
pl
,
Rd
and
(4.68)
N
Ed
≤
0.5
h
w
t
w
f
y
γ
M
0
(4.69)
where
N
pl
,
Rd
is the resistance based on yielding given by equation 4.49 and
γ
M
0
(
=
1
)
isthepartialsectionresistancefactor,noreductionintheplasticmoment
capacity
M
y
,
Rd
=
M
pl
,
y
,
Rd
is needed since for small axial loads the theoretical
reductionintheplasticmomentisoffsetbystrainhardening.Ifeitherofequations
4.68 or 4.69 is not satisfied, EC3 requires that
1
−
n
1
−
0.5
a
M
N
,
y
,
Rd
=
M
pl
,
y
,
Rd
(4.70)
where
n
=
N
Ed
/
N
pl
,
Rd
(4.71)
is the ratio of the applied compression load to the plastic compression resistance
of the cross-section, and
a
=
(
A
−
2
b
f
t
f
)/
A
≤
0.5
(4.72)
is the ratio of the area of the web to the total area of the cross-section.
For Class 3 cross-sections, EC3 allows only a linear interaction of the stresses
arisingfromthecombinedbendingmomentandaxialforce,sothatthemaximum
longitudinal stress is limited to the yield stress, that is
σ
x
,
Ed
≤
f
y
/γ
M
0
.
(4.73)
As for Class 3 cross-sections, the longitudinal stress in Class 4 sections sub-
jected to combined compression and bending is calculated based on the effective
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