1
Introduction
1.1 An Unsolved Problem
Steel connection analysis and checking is one of the most complex problems in structural engineering, and even though we use very powerful computing tools, it is still generally done using very simplistic approaches.
From the point of view of a typical structural engineer, the problem to solve is to design and check nodes,1 not single connections, i.e. a number of connections between a number of different members - maybe tens or even hundreds of load combinations, inclined member axes, and generic stress states. In a typical 3D structure there may be several tens of such nodes (Figure 1.1), or maybe even hundreds, which may be similar, or may be different from one another; identifying nodes that are equal is one of the problems that the designer has to face in order to reduce the number of different possible solutions, and in order to get a rational design. However, this problem of detecting equal nodes has not been sufficiently researched, and there are currently no tools that are able to properly solve this issue.
Figure 1.1 A possible node of a 3D structure.
If posed with the due generality, the problem of checking 3D nodes of real structures has not been solved by automatic computing tools. Also, because a general method of tackling all these problems is apparently still lacking, usually a few "cooking recipes" have been used to solve a limited number of typical, recurring (2D assimilated) nodes. Indeed, it often happens that true, real world nodes have to be analyzed by such recipes, despite the fact that the basic hypotheses needed to apply these recipes do not always hold true. This poses a serious problem because although these "cooking recipes" have been widely used, in the past few years they have been applied to 3D structures designed using computer tools, in the non-linear range, perhaps in seismic areas, and with the aim of reducing the weight of steel.
The effects of such oversimplification have already been seen in many structures where steel connections have failed, especially in seismic areas (e.g. Booth 2014), but even in non-seismic areas (e.g. White et al. 2013, Bruneau et al. 2011). Generally speaking, it is well known that connections are one of the most likely points of weakness of steel structures, one of the most cumbersome to design - indeed one of the least designed - and one of the least software-covered in structural engineering.
This book describes the research efforts made by the author since 1999 to tackle these issues, and it proposes a general set of methods to deal with these problems (see Section 1.6 for more details).
1.2 Limits of Traditional Approaches
1.2.1 Generality
Traditional approaches to connection design have been extensively used for many years, and are still widely used. Usually they imply several simplifying hypotheses, which are needed in order to apply them in by hand computation. The equivalent of by hand computation is today a "simple spreadsheet" often written very quickly for each given job. As with every other form of calculus, they are prone to serious errors (slips and lapses - see Reason 1990 for a general study of human error, and Rugarli 2014 for a discussion on validation of structural models; for spreadsheets programming errors, see the European Spreadsheet Risk Interest Group web site).
There are several possible design situations where the use of traditional approaches is completely justified. These approaches are rooted in the traditional 1D or 2D design. The use of 2D design needed intense by hand computation or the use of graphic tools up to the 1970s; at that time there was no need and no specific legal requirements for checking tens or may be hundreds load combinations, and safety factors were much higher than those used nowadays. When dealing with such situations, today - for example simple determined structures under elementary actions - the use of traditional approaches is still useful. So, it would not be sensible to exclude them completely. Indeed, they will never lose their utility, especially as one of several possible cross-checking tools that can be used to detect possibly unsound designs.
However, in current design practice, we almost always use 3D methods of analysis applied to highly redundant structures, sometimes in the plastic range, automatic computerized checks, with minimum weight often being a must, and safety factors have been reduced to their minimum. (Currently the material safety factor for limit state design is 1.0 in Eurocode 3. The load safety factor for dead loads is lower than that valid for live loads. The maximum loads are applied with a reduction factor ? to take into account the reduced probability of contemporary occurrence. All these practices were not, as such, in traditional designs, which means that they used higher safety factors.)
In summary, while traditional design of structures was often simple, 2D, and was designed by making extensive use of safe-side envelopes both for loads and for resistance, today things are not so easy; indeed, they are much more complex. While virtually all design steps have been semi-automated (modeling, checking members, drawing them, and even cutting them into true 3D pieces by means of computer numerical control, CNC), the checking of connections has remained at the traditional level, more or less upgraded to the modern era by the use of spreadsheets and dedicated, ad hoc software.
As mentioned, several simplifications are widely used in traditional approaches. The following sections will briefly summarize them.
1.2.2 Member Stress State Oversimplification
Members in highly redundant 3D structures are often nonsymmetrical (such as in industrial plants or architects' innovative designs), and under the effect of combined load cases, they are always loaded in the most general way. If they are not: (a) fully hinged at both extremities, (b) straight, and (c) with no transverse load applied, they will in general exhibit all six internal forces components: an axial force, two shears, one torque and two bending moments, referred to the principal axes of the member cross-section.
Idealizing the connection in such a way that some member internal forces components are considered zero at the connection is still a widely used practice. While this is justified when the connections are specifically conceived with that aim, this is unjustified for connections that are not so designed. In a typical moment resisting frame (MRF) ideally designed to work in a plane, beam-to-column connections that must transfer bending and shear in one plane (and axial force) will always transfer the bending and the shear also in the other plane - and of course torque. So the internal forces to deal with are not three, but six. Sometimes it is said that the torque and out-of-plane bending are avoided by "the concrete slab", or by something equivalent, but often the concrete slab does not exist or cannot be considered a true restraint, or its true effect is questionable.
A simple beam hinged at an extremity (e.g. Figure 1.2), will transfer the shear, and will not transfer bending moment if the connection is light and does not use flanges, but it will also transfer the axial force and, if any, the shear in the other direction. However, textbooks usually refer to "shear connections" and only recently, under the flag of "robust design" (a replacement for correct design) has this axial force finally - sometimes, in some textbooks, - been considered (e.g. the Green Books by SCI).
Figure 1.2 Flexible end plate connection ("shear" connection).
This systematic neglect of some internal forces which have, however, been computed introduces a clear mismatch in the design process. Simply, load paths are interrupted (Figure 1.3) and the corresponding forces are thrown away: recalling the variational crimes of the finite element literature, this can be called a connection-design crime, more specifically an equilibrium crime. Usually no one cares, and no one mention it.
Figure 1.3 Traditional design applied to computerized analysis: no way for the load path.
1.2.3 Single Constituent Internal Combined Effects Linearization
Not only are some components of member internal stress states thrown away, but the remaining components are tackled one at a time, as if the connection were loaded only by a single member internal force component. The typical example is the axial force plus (one) bending moment loading condition, for beam-to-column connection or for a base plate. As already pointed out, this loading condition is itself usually the result of a connection-design crime. However, several possible combinations of N and M can be applied to the connection (two infinities), leading to an infinite number of possible stress states. This is usually tackled by computing the limit for the axial force, Nlim, and for the bending moment, Mlim, as if they were acting alone, and then the mutual interaction is computed by simply drawing a straight line in the (N, M) plane. So the design...
