A Comparative Study of “Elastic-Plastic” and “Plastic-Plastic” Design of Steel Frames

The design of metallic structures is governed by construction standards such as the Eurocodes, developed in the 80s with the aim of harmonizing design and calculation procedures in Europe. As far as industrial halls are concerned, there is a lack of detailed recommendations about the methods to use for the calculation of internal forces. Several design methods exist, taking into account – or not – the existence of plastic hinges and the redistribution of internal forces.
One of these methods, which is used by the majority of continental European structural engineers, is based on a global elastic analysis of the structure and is sometimes called “The French method”. It considers that both the structure and the cross sections behave elastically, with no plastic hinges, and thus no redistribution of internal forces. The Eurocodes then allow the plastic cross-sectional resistance to be considered within the results of the elastic global analysis, on the condition that the section class is a class 1 or class 2 (one could also talk about “Elastic-Plastic” design). This method thus considers that failure happens at the birth of the first hinge. If the section class is a class 3 or 4, one will talk about the ‘Elastic-Elastic” design.
Another method, not usually used in continental Europe, is nevertheless particularly developed by the British Standards and some other Anglo-Saxon standards: it is based on a plastic analysis of the structure in order to calculate the internal forces, and is sometimes called "The British method”. It takes advantage of the possible redistribution of internal forces, considering the rotation due to the formation of plastic hinges (one could also talk about “Plastic-Plastic” design).
The “Plastic-Plastic” design does not consider that failure appears at the formation of the first hinge. Indeed, the approach consists in applying the load incrementally and assumes that the structural elements behave elastically until one of their cross sections reaches the maximum value of the plastic moment capacity. This results in a redistribution of the moments, without necessarily reaching a collapse mechanism.
The “Elastic-Plastic” design will usually lead to heavier and thus more expensive structures. However, when deflections govern design rather than ultimate resistance, there is less advantage in using “Plastic-Plastic” design, as far as it allows larger deflections.
In this work, a comparative study was performed, considering a large range of industrial halls. The study is based on the development of software which allows the determination of different collapse loads given by each method. The study was also performed using commercial software based on shell elements. Finally, a deformation criterion was introduced to evaluate the effective usefulness of the “Plastic-Plastic” design.
This paper will thus compare both methods (“Elastic-Plastic” and “Plastic-Plastic”) and summarize the advantages and disadvantages they provide, for a large range of steel frames.