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Design of Aluminium Structures 2 For reducing this gap, a continuous comparison between the two metallic materials, aluminium and steel, is necessary in order to emphasise the specific characteristics and the advantages, as well as sometimes the disadvantages, of aluminium alloys as structural material.



Design of Aluminium Structures
For reducing this gap a continuous comparison between the two metallic materials
aluminium and steel is necessary in order to emphasise the specific characteristics and the
advantages as well as sometimes the disadvantages of aluminium alloys as structural
This comparison can lead to identify the design criteria which must be followed in order to
make the use of aluminium alloys friendly and actually competitive with steel in the range of
structural design
The main scope of this paper is to briefly present the innovative aspects which characterize
the Eurocode 9 on Aluminium Structures with respect to other existing codes Mazzolani
1998a b 1999a Starting from the methodology which has been set up within the range of
activity of ECCS Mazzolani Frey 1983 Mazzolani Valtinat 1987 Mazzolani 1995b
during the seventies new calculation methods have been set up during the nineties
First of all the design rules for the evaluation of internal actions have been given by
considering the actual behaviour of the material by means of different degree of refinement in
the model of stress strain relationship related also to the type of alloy The analysis of the
global performance can be done at different levels from the simplest linear elastic to the
most sophisticated generically inelastic with strain hardening giving rise to different
degrees of reliability
For the inelastic analysis a new approximated method has been worked out for practical
purposes being based on the generalization of the well known plastic hinge method
The behaviour of members has been characterized according to four classes whose definition
required the execution of wide range of experimental tests This classification is still based on
b t ratios as in EC3 for steel but the class boundaries have been chosen on the experimental
evidence considering the actual response of aluminium alloys
New calculation methods have been also set up for the verification of local buckling for the
evaluation of rotation capacity and for the design of connections based on a generalized
classification system
Cold formed and shell structures have been introduced during the conversion phase as
autonomous documents
2 Range of structural applications
The success of aluminium alloys as constructional material and the possibility of a
competition with steel are based on some prerequisites which are connected to the physical
properties the production process and the technological features Summing up the following
statements can be considered Mazzolani 1995b 1998c 1999b 2003a 2004
a Aluminium alloys represent a wide family of constructional materials whose mechanical
properties cover the range offered by the common mild steels see Section 3
b Corrosion resistance normally makes it unnecessary to protect aluminium structures even
in aggressive environments
c The lightness of the material gives advantages in weight reduction but it can be partially
offset by the necessity to reduce deformability due to the low elastic modulus which gives
a high susceptibility to instability
d The material itself is not prone to brittle fracture but particular attention should be paid to
those problems in which high ductility is required
e The extrusion fabrication process allows individually tailored shapes to be designed
f As connection solution either bolting riveting and welding techniques are available
Federico M Mazzolani
After these preliminary remarks it is possible to state that aluminium alloys can be
economical and therefore competitive in those applications where full advantage is taken of
their above prerequisites In particular
A Lightness makes it possible to
simplify the erection phases
transport fully prefabricated components
reduce the loads transmitted to foundations
economize energy either during erection and or in service
reduce the physical labour
B Corrosion resistance makes it possible to
reduce the maintenance expenses
provide good performance in corrosive environments
C Functionality of structural shapes due to the extrusion process makes it possible to
improve the geometrical properties of the cross section by designing a shape which
simultaneously gives the minimum weight and the highest structural efficiency
obtain stiffened shapes without using built up sections thus avoiding welding or
simplify connecting systems among different component thus improving joint details
combine different functions of the structural component thus achieving a more
economical and rational profile
The best fit from the application side can be obtained in some typical cases which are
characterised in getting profit at least of one of the main basic properties lightness corrosion
resistance and functionality
The structural applications which best fit these properties in the field of so called civil
engineering are the following
a Long span roof systems in which live loads are small compared with dead loads as in the
case of reticular space structures and geodetic domes covering large span areas like halls
auditoriums Figure 2
b Structures located in inaccessible places far from the fabrication shop for which transport
economy and ease of erection are of extreme importance like for instance the electrical
transmission towers which can be carried by helicopter completed assembled Figure 3
c Structures situated in corrosive or humid environments such as swimming pool roofs river
bridges Mazzolani Mele 1997 Mazzolani 2001b hydraulic structures and offshore
super structures Figure 4
d Structures having moving parts such as sewage plant crane bridges Mazzolani 1985a
and moving bridges where lightness means economy of power under service Figure 5
e Structures for special purposes for which maintenance operations are particularly difficult
and must be limited as in case of masts lighting towers antennas tower Mazzolani 1991
sign motorway portals and so on Figure 6
The above groups mainly belong to the range of the so called civil engineering
A wider overview of potential applications in the more general range of structural
engineering is given in Table 1 Each case is located in a given column which can be
characterized by one two or three capital letters The meaning of the letters is L for lightness
C for corrosion resistance F for functionality according to the previous definitions The
combination of these properties identifies the reasons why the use of aluminium alloys can be
particularly suitable and even competitive with respect to steel
Design of Aluminium Structures
3 Aluminium alloys for structural use
Aluminium is not just one material but it gives rise to a family of different groups of alloys
whose mechanical properties widely vary from one group to another and also within each
group itself From the point of view of the technological use the aluminium alloys can be
grouped into eight series according to the American Association classification the first of the
four digits characterizing the main alloying element and the other three the secondary ones
Mazzolani 1985b 1994 2003 a b
1000 Series Pure aluminium
In this series the aluminium percentage is very high 98 8 to 99 percent It can be used in low
stressed structures under form of plates Electrical and chemical industries use this series for
cables and tanks due to the high corrosion resistance of the aluminium itself Its elastic limit
is very low f0 2 30 Nmm 2 but its ductility is excellent being the ultimate elongation t 30
to 40 percent If the material is cold worked the strength can increase up to f0 2 100 Nmm 2
whereas the ductility is drastically reduced t 3 to 4 percent
2000 Series Aluminium Copper alloys
These alloys are generally produced under form of profiles plates and pipes When submitted
to heat treatment elastic limit f0 2 can increase up to 300 Nmm 2 with a sufficient ductility
being t 10 percent Since the corrosion resistance of these alloys is not very high it is
necessary to protect them especially when used in a corrosive environment Because of their
bad weldability they are not very popular in structural engineering Basically they are used in
aeronautical industry with riveted connections
3000 Series Aluminium Manganese alloys
These alloys cannot be heat treated and they have a slightly higher strength than pure
aluminium by keeping a very high ductility which allows very hard cold forming processes
for increasing strength They are corrosion resistant Specific applications are panels and
trapezoidal sheeting for roofing systems
4000 Series Aluminium Silicon alloys
The properties of these alloys are similar to those of the 3000 series However they are not
often used except for welding wires
5000 Series Aluminium Magnesium alloys 5000 series
Even though these alloys cannot be heat treated their mechanical properties could be higher
than those corresponding to the 1000 3000 e 4000 series The strength can be increased when
they are cold worked being the elastic limit f0 2 up to 200 Nmm 2 and the ductility still quite
high t up to 10 percent The corrosion resistance is also high especially in marine
environment when the amount of Mg is less than 6 percent These alloys are often used in
welded structures since their strength is not drastically reduced in the heat affected zone
6000 Series Aluminium Silicon Magnesium alloys
By means heat treatment the strength of these alloys is increased up to f0 2 250 Nmm 2 with
a quite good ductility being t up to 12 percent These alloys are corrosion resistant They are
particularly suitable for extrusion but also rolled sections as well as tubes can be produced
These alloys are used either in welded structures and in bolted or riveted connections
Federico M Mazzolani
7000 Series Aluminium Zinc alloys
These alloys are produced under form of both extruded and rolled heat treated profiles They
can be subdivided into two sub families depending upon the percentage of copper as the third
alloying element
AlZnMg alloys reach a remarkable strength being the elastic limit f0 2 greater than 250
Nmm 2 with a quite good ductility t 10 percent They are also corrosion resistant These
alloys are generally used in structural applications because they are particularly suitable in
welded structures owing to their self tempering behaviour which allows to recover the initial
strength in the heat affected zone
AlZnMgCu alloys are the highest resistance alloys after heat treatment reaching f0 2
500 Nmm 2 conversely they have low weldability and are not corrosion resistant
because of the presence of copper therefore requiring protection by plating or painting
8000 Series Aluminium Iron Silicon alloys
This series is preferably used as material for packaging but due to its advantages in
fabrication it finds more and more application in building industry especially for facades
4 Comparing Aluminium with Steel
There are many reasons for the selection of a material for structural applications but the
determinant issue is that the product must be affordable i e its cost must be acceptable to the
customer Generally aluminium is attractive in many applications because of a favourable
life cycle cost which is given by the sum of the initial cost of the finished product the cost of
operating or maintaining the product over its life and the cost of disposing of or recycling it
after its useful life In addition aluminium has sustained and increased its use in many fields
partly because the prince for aluminium relative to that for steel overall has decreased
gradually over the 100 year life of the aluminium industry
A comprehensive comparison with steel not only in term of cost is important in order to
clearly identify the conditions under which and the field of application where aluminium
alloys can be competitive
The main pre requisities of aluminium are Mazzolani 1985 b 1994 1999b 2003 a b
Lightness The specific weight is 2700 kgm 3 equal to one third that of steel
Corrosion resistance The exposed surface of aluminium combines with oxygen to
form a thin inert aluminium oxide film which blocks further oxidation Contrary steel
must be always corrosion protected in any kind of environment
From the point of view of mechanical resistance as it has been emphasized in the previous
Section 3 aluminium alloys series form a big family of materials where the elastic limit
widely varies from 30 Nmm 2 pure aluminium to 500 Nmm 2 AlZnMgCu alloy and the
ultimate elongation in many cases but not always lies in a suitable or at least acceptable
range for structural applications
Table 2 shows a summary comparison among some aluminium alloys extrusions one work
hardened 5083 F two heat treated 6063 T6 and 7020 T6 and the most commonly used mild
steels for hot rolled sections S235 S275 and S355 The main mechanical properties are
compared here elastic limit f0 2 or yield stress fy ultimate strength ft Young s modulus
E ultimate elongation t specific weight and thermal elongation coefficient
Design of Aluminium Structures
From the comparison of the two typical stress strain curves it can be observed that Figure 7
Both materials behave linear elastically with a different slope of the curve up to the
elastic limit f0 2 for aluminium and the yield stress fy for steel this part of the curve basically
covers the working range of structures the only difference between the two materials being
the slope of the curve
After the elastic range aluminium alloys have a continuous strain hardening behaviour
which is not preceded by a perfectly plastic branch corresponding to yielding plateau as for
The ultimate deformation for aluminium alloys is lower around 8 12 than the one of
steel greater than 20
The ft f0 2 ratio for aluminium alloys is normally lower that the one of steel depending on the
degree of hardening
A generalized relationship for aluminium alloys is the so called Ramberg Osgood law
Mazzolani 1994
E is the Young s modulus and f0 2 is the elstic limit at a residual strain of 0 2
The exponent n of the Ramberg Osgood law is given by
where f0 1 is the stress at a residual strain of 0 1
Depending on the ratio f0 2 f0 1 which characterises the knee of the curve the values of
n are useful to classify aluminium alloys from the point of view of the strain hardening rate of
the stress strain behaviour
In fact when the ratio f0 2 f0 1 tends to 1 the exponent n tents to infinity and the Ramberg
Osgood law represents the mild steel behaviour Contrary n 1 provides a linear elastic
behaviour Intermediate values of n express the different behaviours of aluminiumn alloys by
means of decreasing values of n as far as the rate of strain hardening increases
An effective interpretation of structural materials by means of the exponent n of the Ramberg
Osgood law is given in Figure 8 as a function of the f0 2 f0 1 ratio where aluminium alloys are
identified by means of the classical Sutter s classes In general it can be observed that this
law can be suitably used also to represent all round type metallic material i e stainless steel
An important parameter for comparing structural materials is the ratio f0 between strength
and specific weight being the reference strength f0 equal to fy for steel and to f0 2 for
aluminium alloys This ratio multiplied by 105 cm is about 3 to 4 5 for mild steels whereas
it can vary from 8 to 17 for aluminium alloys giving a good forfaitary index of the material
utilization which is extraordinary advantageous for aluminium alloys
However it is not always possible to completely take advantage of this structural benefit
offered by aluminium alloys especially when the material is loaded in compression because
due to the smaller value of the Young s modulus the instability phenomena are more likely to
occur than in steel structures and therefore more dangerous
Further observations regarding aluminium alloy structures have to be pointed out
The structures made of aluminium alloys are more sensitive to thermal variations because
the coefficients of thermal expansion of this metal is twice the one of steel this fact has to
be taken into account particularly when designing support apparatus
Federico M Mazzolani
Contrary residual stresses produced by constraining thermal deformations are about 30
percent lower than those in steel structures because they are proportional to the product
Aluminium alloy structural components can be manufactured by rolling extrusion casting
and drawing processes The extrusion process is of particular interest as it allows
fabrication of profiles of any shape Figure 1 contrary to steel whose shapes are
standarized being limited by the hot rolling process
5 International research and codification
Owing to the increasing use of aluminium alloys in construction several countries have
published specifications for the design of aluminium structures It is due to the efforts of the
ECCS Committee for Aluminium Structures and of its working groups that the first edition of
the European Recommendations for Aluminium Alloy Structures became available in 1978
Mazzolani 1978 1981a These Recommendations represent the first international attempt to
unify computational methods for the design of aluminium alloy constructions in civil
engineering and in other applications by using a semi probabilistic limit state methodology
Immediately after during the eighties the UK BS 8118 Italian UNI 8634 Atzori
Mazzolani 1983 Swedish SVR French DTU German DIN 4113 and Austrian ON
specifications have been published or revised
In the last decade the Aluminium Association Recommendations in USA have been up dated
and the ultimate limit state design has been introduced beside the traditional allowable stress
design A new edition of the Canadian Code has been recently set up on the bases of an ISO
technical document produced by the Committee TC 167
Since 1970 the ECCS Committee on Aluminium Alloy Structures has carried out extensive
studies and research in order to investigate the mechanical properties of materials their
imperfections and their influence on the instability of members Mazzolani Valtinat 1987
On the basis of these data for the first time the aluminium alloy members have been
characterized as industrial bars in accordance with the current trends of the safety
principles in metallic structures Mazzolani 1974 Mazzolani Frey 1977 De Martino et
al 1985 Mazzolani 1980 see Section 7
Among the research programs in this fields undertaken with the cooperation and support of
several European countries buckling tests on extruded and welded built up members were
carried out at the University of Li ge in cooperation with the University of Naples and the
Experimental Institute for Light Metals of Novara Italy Gatto et al 1979 Mazzolani
The use of ad hoc simulation methods which allow all the geometrical and mechanical
properties together with their imperfections to be taken into account has led to satisfactory
results in the study of the instability phenomena of columns and beam columns The analysis
of these experimental and numerical results demonstrated the major differences between the
behaviour of steel and aluminium In particular the buckling curves Mazzolani 1981b
Mazzolani Frey 1983 Mazzolani Piluso 1990 valid for extruded and welded bars with
different cross sections and different alloys have been defined and they have been used in
many national and international Codes including ISO and Eurocode
During the 80 s the extension of the principles of plastic design has been successfully done
Mazzolani 1984 Mazzolani et al 1985 Cappelli et al 1987 The main results have been
utilized also in the preparation of Eurocode 9
In the last decade the research reached satisfactory levels also in other fields such as the local
buckling of thin plates and its interaction with the global behaviour of the bar the instability
Design of Aluminium Structures
of two dimensional elements plates stiffened plates web panels and the post buckling
problems of cylindrical shells Mandara Mazzolani 1989 1990 Mazzolani et al 2003a b
Mazzolani Mandara 2004
A new field of interest for structural application has been investigated in the composite
aluminium concrete system Encouraging results have been obtained but not sufficient for a
codification Bruzzese et al 1989 1991
6 The main features of Eurocode 9
The unavoidable complexity of a code on Aluminium Structures is essentially due to both the
nature of the material itself much more critical and less known than steel which involves
the solution of difficult problems and demands careful analysis In this case the need for the
code to be educational as well as informative and not only normative has been particularly
determinant Mazzolani 1998a 1999a
The ENV edition of Eurocode 9 Design of Aluminium Structures 1998 was composed by
three documents Part 1 1 General rules Part 1 2 Structural fire design and Part 2
Structures susceptible to fatigue
For an explicit request of the European Aluminium Association EAA two new items have
been added in the conversion phase cold formed sheeting and shell structures as the
Aluminium Industry is particularly interested in both these fields of applications
The PTs for the conversion phase from ENV to EN started to work in 2001 on the basis of the
remarks collected in the meantime This phase will end in 2005 and the final version of
Eurocode 9 will be composed by five documents
Part 1 1 General rules
Part 1 2 Additional rules for fire design
Part 1 3 Additional rules for structures susceptible to fatigue
Part1 4 Supplementary rules for cold formed sheeting
Part 1 5 Supplementary rules for shell structures
Contrary to the others Eurocodes Eurocode 9 consist in one Part only which is split in one
basic document General rules and four specific documents which are related to the basic
one No mention to specific types of structures like in steel i e bridges towers tanks
but just general items which are applicable not only to the range of the so called Civil
Engineering but more widely to any kind of structural applications including the
Transportation Industry
The preparation of the Eurocode 9 has been based on the most significant results which has
been achieved in the field of aluminium alloy structures without ignoring the previous
activities developed within ECCS and in the revision of outstanding codes like BS 8118
The ECCS method for column buckling has been utilised also in EC9 with just some small
editorial changes It is based on the use of two buckling curves a and b which cover
extruded profiles made of heat treated and work hardened alloys respectively Mazzolani
1994 1995a
In general checks for beams columns and beam columns have been provided considering the
specific features of aluminium alloys Mazzolani Valtinat 1992
For welded profiles the lowering effects of heat treated zones have been taken into account
by means of appropriate reduction factors This method was based on the experimental
evidence which allowed to characterise the aluminium alloy members as industrial bars see
An innovative issue of Eurocode 9 Part 1 1 General Rules is given by the introduction for
the first time in a structural aluminium code of the analysis of the inelastic behaviour starting
Federico M Mazzolani
from the cross section up to the structure as a whole Mandara Mazzolani 1995 Mazzolani
Piluso 1995 De Matteis et al 1999b Mazzolani et al 1999b
The classification of cross section has been done on the basis of experimental results which
come from an ad hoc research project supported by the main representatives of the
European Aluminium Industry which provided the material for specimens
The output has been the set up of behavioural classes based on the b t slenderness ratio
according to an approach qualitatively similar to the one used for steel but with different
extension of behavioural ranges which have been based on the experimental evidence
Mazzolani et al 1996a 1999a 2000a 2001b 2003c and confirmed by numerical
simulation Mazzolani et al 1997c De Matteis et al 2001c 2002a see Section 8
The evaluation of the resistance of cross sections has been introduced in an unitary way with
specific reference to the limit states which the behaviour of the four classes are concerned to
see Section 9
For members of class 4 slender sections the check of local buckling effect is done by means
of a new calculation method which is based on the effective thickness concept Three new
buckling curves for slender sections has been assessed considering both heat treated and
work hardened alloys together with welded and non welded shapes Landolfo Mazzolani
1995 1998 Mazzolani et al 1997a 1998 see Section 10 This method represents the basic
starting point for the detailed treatment of cold formed sheeting as given in Part 1 4
Supplementary rules for cold formed sheeting
The problem of the evaluation of internal actions has been faced by considering several
models for the material constitutive law from the simplest to the most sophisticated which
give rise to different degrees of approximation The global analysis of structural systems in
inelastic range plastic strain hardening has been based on a simple method which is similar
to the well known method of plastic hinge but considers the typical parameters of aluminium
alloys like absence of yielding plateau continuous strain hardening behaviour limited
ductility of some alloys Mazzolani 1994 see Section 11
The importance of ductility on local and global behaviour of aluminium structures has been
emphasised due to the sometime poor values of ultimate elongation and a new ad hoc
method for the evaluation of rotation capacity for members in bending has been set up
Mazzolani Piluso 1995 De Matteis et al 1999b 2002a see Section 12
For the behaviour of connections a new classification system has been proposed according to
strength stiffness and ductility Mazzolani et al 1996b De Matteis et al 1999a see
Section 13
Based on the experimental evidence on monotonic and cyclic test a new method for the
strength evaluation of T stub connections has been set up and introduced in Part 1 1
Mazzolani et al 2000b De Matteis et al 1999c 2001a b 2002b 2003
The new Part 1 5 Supplementary rules for shell structures dealing with shell structures has
been built up by following the same format of the similar document in EC3 but the
calculation method are based on appropriate buckling curves which are obtained by the
experimental evidence on aluminium shells Mandara Mazzolani 1989 1990 Mazzolani et
al 2003 a b Mazzolani Mandara 2004
Fire Design is a transversal subject for all Eurocodes dealing with structural materials and it is
located in Part 1 2 Additional rules for fire design For Aluminium Structures it has been
codified for the first time according to the general rules which assess the fire resistance on the
bases of the three criteria Resistance R Insulation I and Integrity E
As it is well known aluminium alloys are generally less resistant to high temperatures than
steel and reinforced concrete Nevertheless by introducing rational risk assessment methods
the analysis of a fire scenario may in some cases result in a more beneficial time temperature
relationship and thus make aluminium more competitive and the thermal properties of
Design of Aluminium Structures
aluminium alloys may have a beneficial effect on the temperature development in the
structural component Mazzolani 1994
The knowledge on the fatigue behaviour of aluminium joints has been consolidated during the
last 30 years Mazzolani 1994 In 1992 the ECCS Recommendations on Fatigue Design of
Aluminium Alloy Structures have been published representing a fundamental bases for the
development of Eurocode 9 Mandara et al 1992 Mazzolani Grillo 1995 It was decided
to characterise Part 1 3 Additiona lrules for structures susceptible to fatigue of EC9 in
general way giving general rules applicable to all kind of structures under fatigue loading
conditions with respect to the limit state of fatigue induced fracture It has been done contrary
to steel for which Part 2 is dealing with bridges only Three design methods has been
introduced
Safe life design
Damage tolerant design
Design assisted by testing
The following basic groups of detail categories have been considered
non welded details in wrought and cast alloys
members with transverse welded attachments
members with longitudinal welded attachments
welded joints between members
crossing welds built up beams
mechanically fastened joints
adhesively bonded joints
The use of finite elements and the guidance on assessment by fracture mechanism have been
suggested for stress analysis
The importance of quality control on welding has been particularly emphasised in general and
specific reference to pr EN 1090 Execution of steel and aluminium structures has been
taken into consideration
7 Characterization of industrial bar
The results of the imperfection measurements have been used to calibrate the simulation
methods which were used for the evaluation of the load carrying capacity of members
Mazzolani 1994
Summing up the aluminium alloys bars due to their fabrication process are affected by the
following types of geometrical and mechanical imperfections characterizing the industrial
bar Mazzolani 1995a
a geometrical imperfections
Out of straightness of aluminium extruded bars is usually less severe than in steel being
limited by the value of about L 2000 in case of welded bars this value decreases to
Variations of dimension are present in the extruded tubes where the scatter in thickness
reaches 9 percent in case of welded double T profiles the eccentricity of the webs in the
weak axis direction reaches the value of L 1600 but when added to initial out of
straightness never overcomes the value of L 1000 which can be considered as an upper
bound to be used in calculations
b mechanical imperfections
Residual stresses in the extruded profiles of any shape whatever the heat treatment have
very low values so they have a very small effect on load bearing capacity and for practical
purposes they can be neglected On the contrary they are not negligible in welded profiles
Federico M Mazzolani
where the elastic limit of the welding metal is reached near the welds So their influence
must be taken into account in checking stability even if in average the residual stress
distribution in aluminium alloy is less severe than in steel
Distribution of mechanical properties can be considered highly homogeneous in extruded
profiles and therefore ignored On the contrary in case of welded shapes the distribution is
strongly influenced by the technological treatment giving rise to different lowering effect
near the weld In case of work hardened alloys the decrease of strength is about 10 percent
but in case of heat treated alloys it reaches 40 50 percent Near the weld three regions can
be identified having different stress strain curves
unaffected parent metal
partially affected parent metal
heat treated zones around the weld metal HAZ
For the heat treated zones HAZ in welded sections the actual distribution of the proof
stress must be therefore considered in the evaluation of load bearing capacity by means
of appropriate models
The lowering effects due to HAZ on the load carrying capacity of aluminium alloy welded
members have been carefully taken into account in EC9 in both strength and stability
8 Classification of cross sections
The behaviour of members strictly depends on the shape of the cross section and therefore
the model to be used in structural analysis must be related to the capability of members to
reach a given limit state such as
a elastic buckling limit state characterised by the onset of local instability phenomena in
the compressed parts of the section
b elastic limit state corresponding to the attainment of the proof stress in the most stressed
fibres of the cross section
c plastic limit state corresponding to the complete yielding of the cross section under the
hypothesis of elastic perfectly plastic material
d collapse limit state corresponding to the actual full strength of the cross section
considering hardening effects
These limit states definition corresponds to the one of steel sections in EC3 In EC9 it was
decided to keep the same definition already well known for steel by quantifying the
behavioural ranges in different way according to the experimental evidence
Therefore in Eurocode 9 with reference to the above limit states aluminium cross sections
are divided in four classes Figure 9
Class 1 ductile sections which develop all the collapse resistance without any problem of
local buckling and with the full exploitation of the hardening properties of material until the
ultimate value of deformation depending on the type of alloy limit state d
Class 2 compact sections which are capable to develop the plastic ultimate resistance
without full exploitation of the hardening properties of material which is prevented by the
onset of plastic instability phenomena limit state c
Class 3 semi compact sections which are capable to develop the elastic limit resistance
only without getting into inelastic range owing to instability phenomena which prevent the
development of important plastic deformations giving rise substantially to a scarsely ductile
behaviour limit state b
Class 4 slender sections whose behaviour is governed by the occurring of local buckling
phenomena which produce a reduction of the effective resistant section without plastic
Design of Aluminium Structures
deformations giving rise to a remarkably brittle behaviour limit state a
Figure 9 shows the generalised force F versus displacement D curves corresponding to the
above defined behavioural classes
As reference parameter to decide which class a given cross section belongs to the b t ratio is
conventionally assumed like in steel but with different values
The following limits have been assumed in Eurocode 9
class 1 b t 11
class 2 11 b t 16
class 3 16 b t 22
class 4 b t 22
They are based on the experimental evidence coming from an ad hoc research programme
on hollow rectangular and square sections channels and angles Mazzolani et al 1996a
1999a 2000a 2001b 2003c
Figure 10 shows the normalised stress strain curves from stub column tests on hollow
sections belonging to the four behavioural classes and Figure 11 identifies the b t ratios
corresponding to the boundary of the four classes as given above
Eurocode 3 gives the values of the slenderness parameters 1 2 3 being
0 5 which identify the limits of the four classes considering the presence of
welds and the type of alloy being basically class A for heat treated alloys having n 10 and
class B for non heat treated alloys having n 10 see Table 3
These values allow the classification of parts of cross section which can be internal or
outstand The evaluation of the parameter b as a function of the b t ratio of each per t is given
by means of appropriate formulae which take also into account the stress gradient and the
different local buckling modes
9 Resistance of cross sections
9 1 Evaluation of ultimate axial load
The load bearing capacity of cross sections under axial compression excluding overall
buckling phenomena of the member can be evaluated with reference to the above mentioned
limit states and the corresponding behavioural classes Mazzolani 1998b
The value of axial load for a given limit state can be expressed by the generalized formula
fd the design value of strength f 0 2 m
A the net cross sectional area
Nj a correction factor given in Table 4 depending on the assumed limit state
where Aeff is the effective cross sectional area evaluated accounting for local buckling
phenomena When welded sections are involved a reduced value Ared of the net cross
sectional area shall be used evaluated by accounting for HAZ
In case of flexural buckling the ultimate resistance is given by
is the reduction factor for the relevant buckling mode
k is a factor to allow for the weakening effects of longitudinal welding
The non dimensional buckling curves are given in Figure 12 where curve 1 is used for heat
treated alloys class A and curve 2 for work hardened alloys class B
Federico M Mazzolani
9 2 Evaluation of ultimate bending moment
The load bearing capacity of cross sections under bending moment can be evaluated with
reference to the above mentioned limit states and the corresponding behavioural classes
Mazzolani 1998b
The value of bending moment for a given limit state can be expressed by the generalized
fd the design value of strength f 0 2 m
W the elastic section modulus
Mj a correction factor given in Table 5 depending on the assumed limit state where
n f0 2 in daNmm 2 is the exponent of Ramberg Osgood law representing the material
behaviour see Section 4
5 and 10 are the generalized shape factors corresponding to ultimate curvature values
u 5 el and 10 el respectively being el the elastic limit curvature the value 5 or 10 is
assumes considering the ductility of the alloy
0 is the geometrical shape factor
Z is the plastic section modulus
Weff is section resistance modulus evaluated accounting for local buckling phenomena
When welded sections are involved reduced value Wred and Zred of section resistance and
plastic modulus shall be used evaluated by accounting for HAZ
10 The approach for slender sections
The effect of local buckling in slender members section class 4 is allowed for by replacing
the true section by an effective one which is obtained by using a local buckling coefficient c
to factor down the thickness of any slender element that is wholly or partly in compression
The coefficient c is provided through curves as a function of the factor being a
slenderness parameter which depends both on b t ratio and stress gradient for the element
concerned and 250 f0 2 0 5
Three design curves Figure 13 have been proposed referring to the following cases
Landolfo Mazzolani 1998
Curve a unwelded elements in heat treated alloy class A n 10
Curve b welded elements in heat treated alloy class A n 10 and unwelded plates in non
heat treated alloy class B n 10
Curve c welded elements in non heat treated alloy class B n 10
According to EC9 a preliminary distinction between internal and outstand elements gives rise
to the design curves expressed in the general form
c 1 with 3 see Section 8
being c1 and c2 two coefficients whose values are approximately given in Table 6
Design of Aluminium Structures
This methodology based on the reduced thickness approach is applied to typical cold formed
sheetings in Part 1 4 Figure 14
11 Evaluation of internal actions
Some indications regarding the methods of global analysis both elastic and plastic to be used
in the calculation of structures are provided in EC9
Elastic global analysis relies on the assumption that the stress strain relationship of the
material is linear up to failure independently of the stress level This assumption may be kept
for both first order and second order analysis even when the resistance of the cross sections is
evaluated according to its ultimate load bearing capacity in post elastic range In order to take
into account the plastic moment redistribution within the structure the peak elastic moment
can be increased or decreased by up to 15 provided the new internal forces and moments
remain in equilibrium and the cross section have sufficient ductility to allow for the plastic
redistribution For this reason all members where the moments are reduced must have Class
1 or at least Class 2 cross section When such conditions are fulfilled then elastic global
analysis can be used in all cases
For more refined calculation elastic global analysis may be also applied by assuming that the
stress strain relationship of the material is not linear the value of the instantaneous tangent
modulus depending on the stress level but the exploitation of the inelastic behaviour of
material can be allowed just for members having cross section of Class 1 or Class 2
The characterization of the law of the material must take into account the actual strain
hardening behaviour of the alloy To this purpose Eurocode 9 Annex B gives some
analytical models from the more simple piecewise bi or three linear with and without
hardening see Figure 15 to more sophisticated continuous models according to the
Ramberg Osgood law see Figure 16
Plastic global analysis may be used only when member cross sections satisfy requirements
specified for Class 1 cross sections and provided that the aluminium alloy has sufficient
ductility Cross section of Class 2 3 and 4 are not allowed For Class 1 cross sections the
check of the deformation capacity is required in relation to the ductility demand of the
structural scheme
Plastic analysis may be carried out by assuming for the material the following behavioural
Rigid Perfectly plastic
Elastic Perfectly plastic
Inelastic Perfectly plastic
The three models differ each other by the assumption made on the material behaviour in the
elastic range which can be either rigid elastic or inelastic When it is assumed to be rigid
then elastic deformations of cross sections members and foundations may be neglected and
all plastic deformations are assumed to be concentrated at plastic hinge location It can be
used when the elastic pre collapse deformations are comparatively small and their magnitude
is not so relevant as to involve second order effects
In the elastic perfectly plastic analysis the behaviour of material is assumed to be linear up to
a limit level of stress corresponding to the yielding As a consequence of this the behaviour
of the cross sections can be generally assumed to be elastic plastic as well at least for small
values of the geometrical shape factor 1 2 As a consequence of this it is possible to
assume that the plastic deformations are concentrated in correspondence of the plastic hinge
Federico M Mazzolani
location The transition from elastic to plastic range will be more or less gradual depending on
both load condition and section shape
A more generality can be achieved if the elastic branch of the material law is assumed to be
non linear as in the third one of the above cases Accordingly the non linear behaviour of
sections is considered in the evaluation of the deformation occurring in a given member
before the formation of the plastic hinge For this method a discretized F E M approach is
recommended in order to closely represent the non linear behaviour of the structure
In addition the effect of strain hardening can be taken into account by substituting the
horizontal plastic branch with an increasing one evaluated according to the hardening feature
of the alloy The following options are covered
Rigid Hardening
Elastic Hardening
Generically inelastic
Rigid and elastic hardening analyses are quite similar to the corresponding rigid and elastic
plastic ones in the sense that they are based on a concentrated plasticity model relying on the
concept of plastic hinge The main difference stands in the evaluation of the post elastic
response which depends on the hardening feature of the alloy as well as on its available
ductility For this reason the analysis is assumed to be concluded when a given limit value of
deformation is reached in the material
In the most general case of structural analysis called Generically inelastic both material
and sections are idealized according to their actual stress strain and generalized force
displacement relationship respectively The transition from the elastic to the plastic range is
gradual and the achievement of the ultimate limit state is defined by the attainment of a given
limit values of strength or deformation Contrary to the all previous cases the Generically
inelastic approach cannot adopt the simple concentrated plasticity idealization based on the
concept of plastic hinge but should use refined discretized approaches e g F E M
simulation to display the whole of its accuracy in the prediction of structural inelastic
For practical purpose Eurocode 9 in Annex E gives a simple approach for plastic analyses for
structures whose collapse occurs due to the attainment of ultimate deformation in a certain
number of sections It is a plastic hinge method for continuous beams very familiar in steel
which is based on the elastic perfectly plastic behaviour of material
The ultimate moment is defined as
M u f 0 2 W
is an appropriate correction factor
is the generalized shape factor taking into account the material hardening effect and
depending on the ductility feature of the alloy
The values of have been evaluated on the bases of a parametric analyses in which the
approximate plastic hinge method has been compared with the results of the application of a
discretized method Figure 17
The evaluation of ductility demand is conventionally given by considering two limits values
for the curvature u based on the ultimate tensile deformation
u 5 e for brittle alloys 4 u 8
u 10 e for ductile alloys u 8
Figure 18 shows the values of as a function of the above limit curvatures the geometrical
shape factor 0 and the exponent np of the Ramberg Osgood law in plastic range


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