Abstract

The evaluation of the maximum level of load that any 2D framed structure can undergo, before plastic collapse or buckling, is addressed in this paper. The analytical approach, based on a beam element with elastic behaviour except on its ends, uses an incremental approach to determine when changes appear due to plastic behaviour. When the combination of axial force and bending moment in any cross-section reaches the plastic function, that section is considered to yield suddenly and relative displacements can appear because of the yielding. The model includes the traditional plastic hinge, which only considers relative rotation due to the effect of the bending moment. The sequential loading and yielding reduces the stiffness and stability of the frame, which is computed and compared with the classic plastic methods of analysis.

Abstract

Many complex engineering structures, e.g. blades of wind turbines and helicopters, are beamlike and non-prismatic. They may be tapered, twisted and curved in their unstressed state, undergo large displacements of the centre-line, and cross-sectional warping in and out of plane. For their structural modeling, an approach based on beam elements can be the best compromise between computational efficiency and accuracy, but classical beam models (see, for example, the monumental Love's treatise) may not be sufficient. Better results may be obtained by exploiting geometrically exact and asymptotic approaches. This paper proposes a physical-mathematical model for the aforementioned non-prismatic structures. Analytical results obtained for small warping and strain fields are presented and compared to the results obtainable from nonlinear 3D-FEM analyses.