Prerequisites

Methods of analysis of steel structures

Read Lecture

Related lectures

Local buckling

Read Lecture

Restrained beams part 1

Read Lecture

Frames

Read Lecture

Cross-section classification

OBJECTIVE

To describe the classification of cross-sections and explain how this controls the application of the methods of analysis given in Eurocode 3 [1].

RELATED WORKED EXAMPLES

Worked example 7.1: Methods of Analysis of Steel Structures

SUMMARY

The analysis methods used are primarily dependent upon the geometry of the cross-section and especially on the width to thickness ratio of the elements which make it up.

The lecture describes how sections are classified as plastic, compact, or semi-compact and gives the limiting proportions of the elements by which these classifications are made.

1. INTRODUCTION

When designing a structure and its components, the designer must decide on an appropriate structural model. The choice of model effects:

  • the analysis of the structure, which is aimed at the determination of the stress resultants (internal forces and moments), and
  • the calculation of the cross-section resistance.

Thus, a model implies the use of a method of analysis combined with a method of cross-section resistance calculation.

There are several possible combinations of methods of analysis and methods of cross-section calculation, for the ultimate limit state, involving either an elastic or plastic design approach; the possible combinations are listed in Table 1.

Table 1 Ultimate limit state design - definition of design models

Model

Method of global analysis
(calculation of internal forces and moments)

Calculation of member
cross-section resistance

I

II

III

IV

Plastic

Elastic

Elastic

Elastic

Plastic

Plastic

Elastic

Elastic plate buckling


Model I is related to plastic design of structures. Full plasticity may be developed within cross-sections, i.e. the stress distribution corresponds to a fully rectangular block so that plastic hinges can form. These have suitable moment rotation characteristics giving sufficient rotation capacity for the formation of a plastic mechanism as the result of moment redistribution in the structure.

For a structure composed of sections which can achieve their plastic resistance but do not have sufficient rotation capacity to allow for a plastic mechanism in the structure, the ultimate limit state must refer to the onset of the first plastic hinge. Thus, in Model II, the internal forces are determined using an elastic analysis and are compared to the plastic capacities of the corresponding cross-sections. For statically determinate systems, the onset of the first plastic hinge produces a plastic mechanism; both methods I and II should thus give the same result. For statically indeterminate structures, Model II, in contrast to Model I, does not allow moment redistribution.

When the cross-sections of a structure cannot achieve their plastic capacity, both analysis and verification of cross-sections must be conducted elastically. The ultimate limit state, according to Model III, is achieved when yielding occurs at the most stressed fibre. Sometimes yielding in the extreme fibre cannot even be attained because of premature plate buckling of one component of the cross-section; in such cases, the above ultimate limit state should apply only to effective cross-sections (Model IV).

It is obviously not possible to have a model where a plastic method of analysis is combined with an elastic cross-section verification. Indeed, the moment redistribution which is required by the plastic analysis cannot take place without some cross-sections being fully yielded.

Read more