Strength of massive tubular members in bending
Research Team: Dr Adam Sadowski
Funding: Funded by EU RFCS in collaboration with the University of Edinburgh, Technical University of Delft, Karlsruhe Institute of Technology, University of Thessaly, ArcelorMittal and BAM Infraconsult bv.
Due for completion in 2014.
Spiral welded carbon steel tubes are often used as primary load-bearing members in 'combined walls' where, together with sheet piling, they offer a significantly increased resistance against flexure. The practical range of geometries for the diameter to thickness ratio D/t of such 'Combitubes' is approximately 50 to 150. Consequently, these may be designed for bending either as 'thin tubes' using beam theory and a global stress resultant criterion (bending moment) according to EN 1993-1-1 (2003) or as 'thick shells' using shell theory and a local stress criterion according to EN 1993-1-6 (2007).
Unfortunately, the differences in the design philosophy between these two standards have resulted in a substantial and unnecessary discrepancy between the provisions of both standards for tubes in this D/t range. In particular, the 'local stress criterion' in the hand design rules of EN 1993-1-6 may lead to uneconomical designs for Combitubes because it is unable to deal with conditions where substantial parts of the tube wall have yielded before buckling, unless the stress state is uniform which it is not under global bending.
The aim of the project is thus to draw up safe and economical design rules for tubes in bending, based on an extensive programme of experimental and numerical studies.
A significant part of the project involves the testing of several full-scale spiral welded Combitube specimens under global bending, together with detailed imperfection surveys obtained by laser scanning of the exterior surface of the tubes and tensile testing of material specimens taken at different orientations with respect to the spiral weld.
The results of the bending tests used to validate the nonlinear finite element models. The spiral imperfections are modelled using specially developed meshing tools (Fig. 1) for an accurate representation of the helical geometry. The vast amounts of data obtained in the laser imperfection surveys are subject to an extensive numerical analysis to extract 'characteristic imperfections' relating to the spiral weld process (Fig. 2). The results of the tensile tests are subject to statistical analyses to identify any meaningful relationships between various post-yield material properties, in particular those regarding strain hardening.
Running in parallel is a wide-ranging computational parametric study of the strength of tubes in bending. It is of particular interest to know how the bending resistance is affected by buckling, plastic collapse, geometric nonlinearity (due to ovalisation - Fig. 3), material plasticity, strain hardening, geometric imperfections, residual stresses caused by the spiral welding process, local loads, construction details and material anisotropy.
The results are currently being characterised as capacity curves (Fig. 4) for implementation as design recommendations for Combitubes and cylindrical shells in bending generally. An amendment to the EN 1993-1-6 European Standard on the buckling of metal shells has already been approved on the basis of this research.
Several journal and conference papers are in preparation, and the following have already been published:
- Sadowski A.J. & Rotter J.M. (2013) "Solid or shell finite elements to model thick cylindrical tubes and shells under global bending". International Journal of Mechanical Sciences, 74, 143-153
- Sadowski A.J. & Rotter J.M. (2013) "On the relationship between mesh and stress field orientations in linear stability analyses of thin plates and shells". Finite Elements in Analysis and Design, 73C, 42-54