Introduction - The Behaviour and Design of Steel Structures to EC3 - page 22

of the response of the structure can be obtained. The basis for this process is the
knowledgeofthematerialbehaviour,andthisisusedfirsttoanalysethebehaviour
oftheindividualmembersandjointsofthestructure.Thebehaviourofthecomplete
structure is then synthesised from these individual behaviours.
The methods of structural analysis are fully treated in many textbooks
[e.g. 25-27],andsodetailsofthesearenotwithinthescopeof this topic. However,
some discussion of the concepts and assumptions of structural analysis is neces-
sarysothatthedesignercanmakeappropriateassumptionsaboutthestructureand
make a suitable choice of the method of analysis.
In most methods of structural analysis, the distribution of forces and moments
throughout the structure is determined by using the conditions of static equilib-
rium and of geometric compatibility between the members at the joints.The way
in which this is done depends on whether a structure is statically determinate
(inwhichcasethecompletedistributionofforcesandmomentscanbedetermined
by statics alone), or is statically indeterminate (in which case the compatibility
conditionsforthedeformedstructuremustalsobeusedbeforetheanalysiscanbe
completed).
An important feature of the methods of structural analysis is the constitutive
relationships between the forces and moments acting on a member or connection
anditsdeformations.Theseplaythesameroleforthestructuralelementasdothe
stress-strainrelationshipsforaninfinitesimalelementofastructuralmaterial.The
constitutiverelationshipmaybelinear(forceproportionaltodeflection)andelastic
(perfectrecoveryonunloading),ortheymaybenon-linearbecauseofmaterialnon-
linearities such as yielding (inelastic), or because of geometrical non-linearities
(elastic) such as when the deformations themselves induce additional moments,
as in stability problems.
It is common for the designer to idealise the structure and its behaviour so as
to simplify the analysis.Athree-dimensional frame structure may be analysed as
the group of a number of independent two-dimensional frames, while individual
members are usually considered as one-dimensional and the joints as points. The
joints may be assumed to be frictionless hinges, or to be semi-rigid or rigid. In
some cases, the analysis may be replaced or supplemented by tests made on an
idealised model which approximates part or all of the structure.
1.6.2 Analysis of statically determinate members
and structures
For an isolated statically determinate member, the forces and moments acting on
thememberarealreadyknown,andthestructuralanalysisisonlyusedtodetermine
the stiffness and strength of the member. A linear elastic (or first-order elastic)
analysis is usually made of the stiffness of the member when the material non-
linearities are generally unimportant and the geometrical non-linearities are often
small. The strength of the member, however, is not so easily determined, as one
or both of the material and geometric non-linearities are most important. Instead,