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Aeff is the effective section area based on the reduced thickness
allowing for the effect of local buckling.
Bending
moment
6.2.5
6.2.5.2
6.2.5.1
Bending moment resistance in a net section:
Mu,Rd =
Wnet . fu
γM2
Bending moment resistance in each cross section:
Mc,Rd =
α . Wel . fo
γM1
Wnet is the elastic modulus of the net section allowing for holes
and HAZ softening.
Wel is the elastic modulus of the gross section.
α is the shape factor given in table 6.4 in EN 1999-1-1, 6.2.5.
Shear 6.2.6
6.7.4 6.7.5
6.7.6
The design value for shear resistance for non-slender sections:
VRd=
AV . fo
√ 3 . γM1
Av is the shear area.
For slender webs and stiffened webs the rules for capacity of plate
girder webs have to be used (plate buckling).
TABLE VI.3
66
ALUMINIUM IN COMMERCIAL VEHICULES CHAPTER VI DESIGN AND CALCULATION 66 | 67
Situations Ref. EN 1999-1-1 Resistance
Torsion 6.2.7
6.2.7.2
6.2.7.3
The design St. Venants torsion moment resistance without warping:
TRd=
WT,pl . fo
√ 3 . γM1
WT,pl is the plastic torsion modulus
For torsion with warping the capacity is the sum of two internal
effects. For combined shear force and torsional moment the
capacity is given by a reduced shear capacity.
Bending and
shear
6.2.8 The shear force will reduce the moment resistance. If the shear
force is less than half of the shear force resistance, the effect
of the moment resistance is so small that it can be neglected.
Bending and
axial force
6.2.9
6.2.9.1
6.2.9.2
6.2.9.3
Formulae are given for the combined effect of an axial tension
and bending moments about one or two axis for:
• open cross-sections
• hollow sections and solid cross-sections
• members containing localized welds
Bending, shear
and axial force
6.2.10 The shear force will reduce the combined axial tension and
moment resistance. If the shear force is less than half of the shear
force resistance, the effect of the combined axial tension and
moment resistance is so small that it can be neglected.
Web bearing 6.2.11 This is for design of webs subjected to localized forces caused
by concentrated loads or reactions applied to a beam.
Compression
(buckling
resistance)
6.3 Members subject to axial compression may fail in one of the
three ways listed below:
• flexural
• torsional or flexural torsional
• local squashing
The design buckling resistance of a compression member is:
Nb,Rd =
κ . χ . Aeff
. fo
γ M1
κ is a factor to allow for effect of the HAZ at welds
χ is the reduction factor for the relevant buckling mode
Aeff is the effective area of the cross section. (For cross section class
1, 2 and 3 this is the gross cross-section, for cross section class 4
it is reduced for local buckling effects)
67
EUROPEAN ALUMINIUM ASSOCIATION
Situations Ref. EN 1999-1-1 Resistance
Members
in bending
and axial
compression
6.3.3
6.3.3.1
6.3.3.2
6.3.3.3
6.3.3.4
6.3.3.5
Members subject to bending and axial compression may fail in one of
the two ways listed below:
• flexural buckling
• lateral-torsional buckling
Combination formulas are given for members with axial
compression in combination with bending about one or two axis
and fail for flexural buckling. These formulas are given for:
• open double symmetric cross-section
• solid cross-section
• hollow cross-section and tube
• open mono-symmetrical cross-section
Combination formula for open cross-section symmetrical about
major axis, centrally symmetric or double symmetric cross-section
is given for lateral- torsional buckling.
Formulas are also given for calculation of the following effects:
• members containing localized welds
• members containing localized reduction of cross-section
• unequal end moments and/or transverse loads
Plate girders 6.7
6.7.2 & 6.7.3
6.7.4 & 6.8
6.7.6
6.7.5
6.7.7
6.1.5
6.3.2
A plate girder is a deep beam with a tension flange, a compression
flange and a web plate. The web is usually slender and may be
reinforced by transverse or/and longitudinal stiffeners.
Webs buckle in shear at relatively low applied loads, but considerably amount
of post-buckled strength can be mobilized due to tension field action.
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