Introduction - The Behaviour and Design of Steel Structures to EC3 - page 23

the designer usually relies on a design code or specification for this information.
The strength of the isolated statically determinate members is fully discussed in
Chapters 2-7 and 10.
For a statically determinate structure, the principles of static equilibrium are
used in the structural analysis to determine the member forces and moments, and
thestiffnessandstrengthofeachmemberarethendeterminedinthesamewayas
for statically determinate members.
1.6.3 Analysis of statically indeterminate structures
Astatically indeterminate structure can be approximately analysed if a sufficient
number of assumptions are made about its behaviour to allow it to be treated as
if determinate. One method of doing this is to guess the locations of points of
zero bending moment and to assume there are frictionless hinges at a sufficient
numberoftheselocationsthatthememberforcesandmomentscanbedetermined
by statics alone. Such a procedure is commonly used in the preliminary analysis
of a structure, and followed at a later stage by a more precise analysis. However,
astructuredesignedonlyonthebasisofanapproximateanalysiscanstillbesafe,
providedthestructurehassufficientductilitytoredistributeanyexcessforcesand
moments. Indeed, the method is often conservative, and its economy increases
withtheaccuracyoftheestimatedlocationsofthepointsofzerobendingmoment.
More commonly, a preliminary analysis is made of the structure based on the
linear elastic computer methods of analysis [42, 43], using approximate member
stiffnesses.
Theaccurateanalysisofstaticallyindeterminatestructuresiscomplicatedbythe
interaction between members: the equilibrium and compatibility conditions and
the constitutive relationships must all be used in determining the member forces
and moments. There are a number of different types of analysis which might be
made, and some indication of the relevance of these is given in Figure 1.15 and
in the following discussion. Many of these can only be used for two-dimensional
frames.
For many structures, it is common to use a first-order elastic analysis which is
basedonlinearelasticconstitutiverelationshipsandwhichignoresanygeometrical
non-linearities and associated instability problems.The deformations determined
by such an analysis are proportional to the applied loads, and so the principle of
superposition can be used to simplify the analysis. It is often assumed that axial
andsheardeformationscanbeignoredinstructureswhoseactionispredominantly
flexural, and that flexural and shear deformations can be ignored in structures
whosememberforcesarepredominantlyaxial.Theseassumptionsfurthersimplify
the analysis, which can then be carried out by any of the well-known methods
[25-27],forwhichmanycomputerprogramsareavailable[44,45].Someofthese
programs can be used for three-dimensional frames.
However, a first-order elastic analysis will underestimate the forces and
momentsinandthedeformationsofastructurewheninstabilityeffectsarepresent.