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Moment of inertia for calculation
of deflections for cross section
class 4 members:
Iser = Igr -
σgr (Igr - Ieff)
fo
Where:
σgr is maximum compressive
stress in serviceability limit state
in the cross section, based on the
gross cross-section properties
(positive in the formula)
Igr is the moment of inertia for
the gross cross-section
Ieff is the moment of inertia of the
effective cross-section in ultimate
limit state, with allowance for
local buckling
7.1. Cross section classes
Cross-sections are classified in 4
classes. In Table VI.2 the different
classes identify how the
cross-section behaves during
compression and bending. This
is directly linked to the resistance
(load bearing capacity) of the
cross-section.
Thin parts of a cross-section may
buckle at low stresses, and this
will reduce the resistance of the
cross-section. This is taken care
of with the rules for cross-section
classification.
6. Serviceability limit state 7. Ultimate
limit state
64
ALUMINIUM IN COMMERCIAL VEHICULES CHAPTER VI DESIGN AND CALCULATION 64 | 65
Class 1 Class 2 Class 3 Class 4
Cross-sections that can
form a plastic hinge with
the rotation capacity
required for plastic analysis
without reduction of
the resistance.
Cross-section that can
develop their plastic
moment resistance, but
have limited rotation
capacity.
Cross-section where the
calculated stress in the
extreme fibre of the aluminium
member can
reach its proof strength.
Cross-section that will get
local buckling before
attainment of proof stress
in one or more parts of
the cross-section.
The resistance may be
calculated on the basis
of plastic behaviour taking
the material hardening
effect into account.
Rules are given in EN
1999-1-1. Annex F.
The resistance may be
calculated on the basis
of perfectly plastic
behaviour for the material
using the conventional
elastic limit as the
limit value. Rules are
given in EN 1999-1-1.
Annex F. The resistance
is calculated on the
basis of elastic design.
The resistance is calculated
on basis of an effective
cross-section. Rules
for calculating the effective
cross-section are
given in EN 1999-1-1,
6.1.5
EN 1999-1-1, 6.1.4 gives rules
how to classify any cross-section.
A β value (i.e. width to thickness
ratio) is calculated as:
β = η . b
t
where:
b = the width of a cross-section
part
t = the corresponding thickness
η = a value depending on the
stress situation and if the part is
an outstand or an internal crosssection
part
Limits are given for the β value
for the different classes and for
welded or unwelded parts and
for outstand or internal parts.
Most aluminium structures in
commercial vehicles will be optimised
regarding weight. Cross
section classes 1 and 2 will therefore
seldom be used. Elastic
design in cross section class 3 and
4 will be the normal situation.
TABLE VI.2
7.2. Load bearing resistance
The load bearing resistance shall
always be higher than the factored
load effects.
EN 1999-1-1 gives rules for calculating
the load bearing resistances
for different kinds of members
exposed by different load
effects. In the Table VI.3, some of
these rules are listed, and references
are given:
65
EUROPEAN ALUMINIUM ASSOCIATION
Situations Ref. EN 1999-1-1 Resistance
Tension 6.2.3 The smaller of:
No,Rd =
Ag . fo , Nu,Rd =
0,9 . Anet
. fu or Nu,Rd =
Aeff
. fu
γM1 γM2 γM2
No,Rd is the design resistance to general yielding.
Nu,Rd is the design resistance to axial force of the net cross-section
at holes for fasteners or the effective cross-section at welds.
Ag is the gross cross-section.
Anet is the net area of cross-section.
Aeff is the effective area of cross-section taking the HAZ effects
into account.
Compression
(with no
buckling)
6.2.4 The smaller of:
Nu,Rd =
Anet . fu , Nc,Rd =
Aeff
. fo
γM2 γM1
Nu,Rd is the design resistance to axial force of the net cross-section
at holes for fasteners.
Nc,Rd is the design resistance to axial force at each cross-section.
Anet is the net section area with deduction for holes and if required
the effects of HAZ softening at the cross section with holes.
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