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EN 1991 Eurocode 1 – Actions on structures. All parts
EN 1999 Eurocode 9 – Design of aluminium structures
5. Limit state design
EN 1990 gives the partial safety
factor on loads and rules for
combination of loads to give the
different action effects.
EN 1991 gives the characteristic
loads for structures and buildings
such as self weight, live loads,
wind loads, snow loads, traffic
loads etc.
EN 1999 gives the design rules
for aluminium structures.
The ultimate limit state is the
condition where the safety of the
structure is calculated. A structure
shall not collapse and design
in accordance with the ultimate
limit state shall avoid structural
failure.
The partial safety factor for the
resistance (γM) shall take care of
the scattering of the strength
properties and the geometry of
the cross section. For connections
the partial safety factor
shall in addition take care of
uncertainties in the welds and in
the bolts and bolt configuration.
The partial safety factor for the
load effects (γF) shall take care of
the scattering of the determination
of the loads and the probability
in the combination of different
loads. The partial safety
factor is different for the different
types of loads, their certainty
and how they are combined.
Dead loads (i.e. self weight of
structure) have a low partial safety
factor while the live load (i.e.
all forces that are variable during
operation, e.g. weight of goods,
road vibrations etc…) has a higher
partial safety factor.
5.2. What is the ultimate
limit state
62
ALUMINIUM IN COMMERCIAL VEHICULES CHAPTER VI DESIGN AND CALCULATION 62 | 63
The condition to be fulfilled is:
Rk ≥ γF
γ . Ek M
where:
Rk is the characteristic value of
the resistance; it may be axial
tension or compression, bending
moment, shear or a combined
resistance.
Ek is the characteristic value of
the load effects; it may be axial
tension or compression, bending
moment, shear or a combined
load effect on a cross section or a
connection.
γM is the partial safety factor for
the resistance, also often called
material factor.
γF is the partial safety factor for
the load effects, also often called
load factor.
This relation is shown in the
Figure VI.2.
Typical values for the partial safety
factor for the resistance are
1.10 (gM1) for members and 1.25
(γM2 and γMw) for bolt and rivet
connections and welded connections.
These are the material factors
for building and civil engineering
and may also be used in
all structural design because the
material, the geometrical dimensions
and the fabrication of connections
are almost similar in all
aluminium structures.
FIGURE VI.2
Frequency
The serviceability limit state is
the condition where the serviceability
criteria have to be satisfied.
The most used serviceability
criteria are:
• Deflection limits in all directions
• Dynamic effects like vibrations
In serviceability limit states both
the partial safety factor for the
resistance (gM) and the partial
safety factor for the load effects
(γF) are 1.0.
Typical values for the load effect
factors in buildings and civil engineering
are 1.2 for dead loads
and 1.5 for live loads. For design
of components for commercial
vehicles the following load factors
may be used:
Dead load: 1.1
Live load: 1.5
Ek RE k k
. γF <
Rk
γM
5.3. What is the serviceability limit state
63
EUROPEAN ALUMINIUM ASSOCIATION
All calculations in serviceability
limit state are elastic calculations.
Elastic deformations are calculated
and compared with the limits
for deflections. The sizes of vibrations
have to be calculated in the
same manner. If the vibration has
a high number of cycles, the
members and the connection
details have to be checked for
fatigue.
Normally the calculations of elastic
deflections are based on the
moment of inertia for the gross
cross-section of the member. For
members in cross-section class 4
(see section 7.2.4 in EN 1999-1-1)
it is necessary to reduce the
moment of inertia, if the stresses
of the compression part of the
cross section are higher than the
stresses when local buckling
occurs.
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