On the gradient of the yield plateau in structural carbon steels

New design methodologies are being developed to allow stocky steel members to attain and exceed the full plastic condition. For theoretical validation, such methods require a characterisation of the uniaxial stress-strain behaviour of structural steel beyond an idealised elastic-plastic representation. However, the strain hardening properties of carbon steels are not currently guaranteed by the standards or by any steel manufacturer. Assumptions must thus be made on what values of these properties are appropriate, often based on limited information in the form of individual stress-strain curves. There is very little consistency in the choices made. This paper first illustrates, using an example elastic-plastic finite element calculation, that a stocky tubular structure can attain the full plastic condition at slendernesses comparable with those defined in current standards and supported by experiment when using only a very modest level of strain hardening, initiated at first yield. It is then hypothesised that the yield plateau in the stress-strain curve for structural carbon steels, classically treated as flat and with zero tangent modulus, actually has a small but statistically significant positive finite gradient. Finally, a robust set of linear regression analyses of yield plateau gradients extracted from 225 tensile tests appears to support this hypothesis, finding that the plateau gradient is of the order of 0.3% of the initial elastic modulus, consistent with what the finite element example suggests is sufficient to reproduce the full plastic condition at experimentally-supported slendernesses.