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Steel Designers' Manual - 6th Edition (2003)
Chapter 9
Introduction to manual and
computer analysis
by RANGACHARI NARAYANAN
9.1 Introduction
The analysis of structures consists essentially of mathematical modelling of the
response of a structure to the applied loading. Such models are based on idealizations
of the structural behaviour of the material and of the components. They are,
therefore, imperfect to a larger or smaller degree, depending upon the extent of
inaccuracy built into the assumptions in modelling. This is not to imply that the
calculations are meaningless, rather to emphasize the fact that the assessment of
structural responses is the best estimate that can be obtained in the light of the
assumptions implicit in the modelling of the system. Some of these assumptions
are necessary in the light of inadequate data; others are introduced to simplify the
calculation procedure to economic levels.
There are several idealizations introduced in the modelling process.
• Firstly, the physical dimensions of the structural components are idealized.
For example, skeletal structures are represented by a series of line elements and
joints are assumed to be of negligible size. The imperfections in the member
straightness are ignored or at best idealized.
• Material behaviour is simplified. For example, the stress–strain characteristic
is assumed to be linearly elastic, and then perfectly plastic. No account is taken
of the variation of yield stress along or across the member. The influence of
residual stresses due to thermal processes (such as hot rolling and flame cutting),
as well as that due to cold working and roller straightening, is ignored.
• The implications of actions which are included in the analytical process itself
are frequently ignored. For example, the development of local plasticity at
connections or possible effects of change of geometry causing local instability
are rarely, if ever, accounted for in the analysis.
However, it must be recognized that the design loads employed in assessing structural
response are themselves approximate. The analysis chosen should therefore
be adequate for the purpose and should be capable of providing the solutions at an
economical cost.
The fundamental concepts employed in mathematical modelling are discussed
next.
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