Abstract
The problem of bi-axial bending and cyclic bi-axial bending has been examined analytically and experimentally. The specific problem of a cantilever subjected to cycles of horizontal deflection with a sustained vertical load was investigated for circular and square cross-section beams. The stress-strain curves representing initial and cyclic material properties were modelled mathematically and incorporated in a "finite element" analysis computer program. A research rig was developed together with a data acquisition system which enabled the loads and deflection to be monitored throughout the cyclic process.The validity of simplifying assumptions such as using the simplified curvature equations and ignoring any rotation of the neutral surface was evaluated together with the movement of the neutral surface for non-circular sections in bi-axial plastic bending.
The changing material properties resulting from the cyclic process was modelled and the computer program was able to follow the loading history of each elemental fibre in the beam, update the material properties within each cycle and from cycle to cycle. A comparison of experimental results and theoretical predictions showed that accurate modelling of the material properties was necessary for good results in the first quarter cycle when the plastic strains are small. It was easier to model cyclic material behaviour due to the absence of elastic behaviour on stress reversal, and the theoretical predictions of deflections and loads in the steady state cyclic condition were good. The computer program identified elements which unloaded during bending due to rotation of the neutral surface. It was shown that their effect was small for the range of strains examined but if the strain range was increased the unloading process should be included in any analysis. The method of analysis adopted also allowed the strain distribution throughout the beam to be evaluated at all stages of loading.
| Date of Award | 1986 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | S. J. Harvey (Supervisor) & P. J. Hancell (Supervisor) |