Chapter 1
INTRODUCTION

1.1 GENERAL

1.1.1 Aims of the book

The aim of the present book is threefold:

1. - To provide designers with practical guidance and tools for the design of steel and composite joints;
2. - To point out the importance of structural joints on the response of steel and composite structures and to show how the actual behaviour of joints may be incorporated into the structural design and analysis process;
3. - To illustrate the possibilities of producing more economical structures using the new approaches offered in Eurocode 3 and Eurocode 4 as far as structural joints are concerned.

The organisation of the book reflects the belief that, in addition to the sizing of the members (beams and columns), consideration should also be given to the joint characteristics throughout the design process. This approach, despite the novelty it may present to many designers, is shown to be relatively easy to integrate into everyday practice using present day design tools.

Hence the present book addresses design methodology, structural analysis, joint behaviour and design checks, at different levels:

1. - Presentation and discussion of concepts;
2. - Practical guidance and design tools.

1.1.1.1 The traditional common way in which joints are modelled for the design of a frame

Generally speaking, the process of designing building structures has been up to now made up of the following successive steps:

1. - Frame modelling including the choice of rigid or pinned joints;
2. - Initial sizing of beams and columns;
3. - Evaluation of internal forces and moments (load effects) for each ultimate limit state (ULS) and serviceability limit state (SLS) load combination;
4. - Design checks of ULS and SLS criteria for the structure and the constitutive beams and columns;
5. - Iteration on member sizes until all design checks are satisfactory;
6. - Design of joints to resist the relevant members end forces and moments (either those calculated or the maximum ones able to be transmitted by the actual members); the design is carried out in accordance with the prior assumptions (frame modelling) on joint stiffness.

This approach was possible since designers were accustomed to considering the joints to be either pinned or rigid only. In this way, the design of the joints became a separate task from the design of the members. Indeed, joint design was often performed at a later stage, either by other personnel or by another company.

Recognising that most joints have an actual behaviour which is intermediate between that of pinned and rigid joints, Eurocode 3 and Eurocode 4 offer the possibility to account for this behaviour by opening up the way to what is presently known as the semi-continuous approach. This approach offers the potential for achieving better and more economical structures.

1.1.1.2 The semi-continuous approach

The rotational behaviour of actual joints is well recognised as being often intermediate between the two extreme situations, i.e. rigid or pinned.

In sub-chapter 1.2, the difference between joints and connections will be introduced. For the time being, examples of joints between one beam and one column only will be used.

Let us now consider the bending moments and the related rotations at a joint (Fig. 1.1):

Figure 1.1 - Classification of joints according to stiffness

When all the different parts in the joint are sufficiently stiff (i.e. ideally infinitely stiff), the joint is rigid, and there is no difference between the respective rotations at the ends of the members connected at this joint (Fig. 1.1a). The joint experiences a single global rigid-body rotation which is the nodal rotation in the commonly used analysis methods for framed structures.

Should the joint be without any stiffness, then the beam will behave just as a simply supported beam, whatever the behaviour of the other connected member(s) (Fig. 1.1b). This is a pinned joint.

For intermediate cases (non-zero and non-infinite stiffness), the transmitted moment will result in a difference ? between the absolute rotations of the two connected members (Fig. 1.1c). The joint is semi-rigid in these cases.

The simplest way for representing this concept is a rotational (spiral) spring between the ends of the two connected members. The rotational stiffness Sj of this spring is the parameter that links the transmitted moment Mj to the relative rotation ?, which is the difference between the absolute rotations of the two connected members.

When this rotational stiffness Sj is zero, or when it is relatively small, the joint falls back into the pinned joint class. In contrast, when the rotational stiffness Sj is infinite, or when it is relatively high, the joint falls into the rigid joint class. In all the intermediate cases, the joint belongs to the semi-rigid joint class.

Figure 1.2 - Modelling of joints (case of elastic global analysis)

For semi-rigid joints the loads will result in both a bending moment Mj and a relative rotation ? between the connected members. The moment and the relative rotation are related through a constitutive law depending on the joint properties. This is illustrated in Figure 1.2 where, for the sake of simplicity, an elastic response of the joint is assumed in view of the structural analysis to be performed (how to deal with non-linear behaviour situations will be addressed later on, especially in chapter 2).

It shall be understood that the effect, at the global analysis stage, of having semi-rigid joints instead of rigid or pinned joints is to modify not only the displacements, but also the distribution and magnitude of the internal forces throughout the structure.

As an example, the bending moment diagrams in a fixed-base simple portal frame subjected to a uniformly distributed load are given in Figure 1.3 for two situations, where the beam-to-column joints are respectively either pinned or semi-rigid. The same kind of consideration holds for deflections.

Figure 1.3 - Elastic distribution of bending moments in a simple portal frame

1.1.1.3 The merits of the semi-continuous approach

Both the Eurocode requirements and the desire to model the behaviour of the structure in a more realistic way leads to the consideration of the semi-rigid behaviour when necessary.

Many designers would stop at that basic interpretation of Eurocode 3 and Eurocode 4 and hence would be reluctant to confront the implied additional computational effort involved. Obviously a crude way to deal with this new burden will be for them to design joints that will actually continue to be classified as being either pinned or fully rigid. However such properties will have to be proven at the end of the design process; in addition, such joints will certainly be found to be uneconomical in a number of situations.

It shall be noted that the concept of rigid and pinned joints still exists in Eurocode 3 and Eurocode 4. It is accepted that a joint which is almost rigid or, on the contrary, almost pinned, may still be considered as being truly rigid or truly pinned in the design process. How to judge whether a joint can be considered as rigid, semi-rigid or pinned depends on the comparison between the joint stiffness and the beam stiffness, which latter depends on the second moment of area and length of the beam.

The designer is strongly encouraged to go beyond this "all or nothing" attitude. Actually it is possible, and therefore of interest, to consider the benefits to be gained from the semi-rigid behaviour of joints. Those benefits can be brought in two ways:

1. The designer decides to continue with the practice of assuming - sometimes erroneously - that joints are either pinned or fully rigid. However, Eurocode 3 and Eurocode 4 require that proper consideration be given to the influence that the actual behaviour of the joints has on the global behaviour of the structure, i.e. on the precision with which the distribution of forces and moments and the displacements have been determined. This may not prove to be easy when the joints are designed at a late stage in the design process since some iteration between global analysis and design checking may be required. Nevertheless, the following situations can be foreseen:
   1. - So that a joint can be assumed to be rigid, it is common practice to introduce, for instance, column web stiffeners in a beam-to-column joint. Eurocode 3 and Eurocode 4 now provide the means to check whether such stiffeners are really necessary for the joint to be both rigid and have sufficient resistance. There are practical cases where they are not needed, thus permitting the adoption of a more economical joint design.
   2. - When joints assumed to be pinned are later found to have fairly significant stiffness (i.e. to be semi-rigid), the designer may be in a position to reduce beam sizes. This is simply because the moments carried out by the joints reduce the span moments and deflections in the beams.
2. The designer decides to give consideration, at the preliminary design stage, not only to the properties of the members but also to those of the joints. It will be shown that this new approach is not at all incompatible with...