Keywords: plastic analysis, aluminium alloys, ductility, rotational capacity, strain hardening, internal forces redistribution.

Since the fifties, several authors have pointed out that the most economical and rational structural design can be achieved using plastic analysis methods. In fact, although linear elasticity theory may be appropriate for the computation of stresses and strains under working loads, it is relatively meaningless as a measure of the structural collapse. On the basis of such a consideration, plastic analysis methods, able to define the resources of a system beyond the elastic range, were formulated for civil structures [1]. In case of structures constituted by elastic-perfectly-plastic material, at the collapse (when finite deformations of at least a part of the structure can occur without any change in the loads) the internal bending moment distribution remains constant as the structures deform. If the characteristics of the bending moment distribution at collapse are defined, the classical theorems of limit analysis can be applied [2].

The main advantage of this methodology of analysis is its relative simplicity. In fact, a rigorous method of analysis of structures loaded beyond the elastic limit should be based on an incremental procedure by using a discretized model. However, such an approach would be excessively burdensome and not compatible with practical applications. For this reason, simpler methods, based on the concept of concentrated plasticity are commonly adopted for the collapse analysis of structures. These methods, which are tie tightly to the hypothesis of elastic-perfectly-plastic material, have shown a satisfying precision in the prediction of the bearing capacity of steel structures. In fact, in this case the material ductility allows the full development of the plastic mechanism and the relationship is actually characterised by a stress plateau without any significant strain hardening [3,4], so that the load evaluated through the plastic hinge method may be assumed as a reliable estimation of the actual collapse load [5]. In the last years, an international scientific interest has been posed on strain hardening materials and in particular on the aluminium alloys. Simple supported and continuous beams, multibay rectangular frames and single or multibay pitched-roof portals are familiar examples of structural applications of these materials. Their behaviour in the post-elastic range is remarkably different as respect to steel for two basic reasons: on one hand there is the strain hardening of the material (usually ignored in case of steel) which constitutes an important mechanical feature of these materials and, on the other hand, the limited available ductility of considered alloy which, contrarily to the steel, can constitute a limitation to the full development of the collapse mechanism. It is worthy to note that the mechanical properties of the material can be remarkably different for the several tempers available and far enough from the elastic-perfectly plastic schematisation [5]. The continuous stress-strain relationship poses an interesting question regarding the possibility about the extension of the limit analysis theorems, and in particular, the plastic hinge method, to aluminium alloy structures. This method is based on the assumption that, under proportional load conditions, concentrated plastic zones will form progressively up to transform the structure or its part in a kinematic mechanism. Therefore, the ultimate load of an indeterminate structure is defined in relation to the failure mechanism associated to the development of a certain number of plastic hinges. But, a complete mechanism can be placed on only if formed plastic hinges provide the required plastic rotation. In other words, to allow the full redistribution of bending moments, the first formed plastic hinges should be able to rotate without significant strength degradation.

In this paper, the results of an extensive numerical analysis devoted to the evaluation of the inelastic behaviour of aluminium alloy beams are presented. For simple structural systems as continuous beams, which are representative of the structural applications of aluminium alloys, the flexural ductilities (available and required), which must be compared when plastic analysis is carried out, are evaluated. The parametric analysis is performed by using a numerical model implemented in the implicit FE code ABAQUS/Standard [6] and calibrated against experimental tests. The obtained results have allowed, on the hand an assessment of the influence of mechanical (strain hardening) and geometrical (shape factor and flexural continuity) parameters on the required rotational capacity and, on the other hand, a comparison with the available rotational capacity depending on the material ductility. On the basis of this results, a stress multiplier () which, on the basis of the available material ductility, amplifies (or reduces) the elastic limit and, therefore, the bearing capacity of the structure evaluated by applying the plastic hinge method, has been proposed. Further analyses should be performed to provide a numerical expression for this coefficient and to verify the applicability to other structural schemes (e.g. frames).

1

P.G. Hodge. "Plastic analysis of Structures". McGraw, 1959.

2

W. Prager. "Introduction to Plasticity". Addison-Wesley, 1959.

3

B.G. Neal. "The plastic methods of structural analysis", 3rd ed. Chapman & Hall, 1977.

4

J. Lubliner. "Plasticity Theory". Macmillan, 1990.

5

F.M. Mazzolani. "Aluminium alloy structures", 2nd ed. Chapman & Hall, 1995.

6

Hibbitt, Karlsson, Sorensen, Inc. "ABAQUS/Standard", v6.1. Pawtucket, RI, USA, 2001.

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