FG Baustatik, Stahlbau, FEM
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Engineering structures exposed to high temperature environment exhibit time dependent behaviour due to time dependent material behaviour. In order to avoid full inelastic analyses, simplified inelastic analysis methods are desirable.
The concept of elastic follow-up was introduced to allow determination of quantities serving as measure for life assessment of structures subjected to creep conditions without performing full time dependent structural analyses. Various simplified methods are described in the literature to estimate enhancement of creep strain and of creep damage arising from the fact that so-called secondary stresses caused by displacement-controlled loading do not necessarily relax with time in the same way as stresses do that are caused by strain-controlled loading, but rather show some characteristics of stress-controlled loading.
After providing a definition of elastic follow-up, the fundamental principles of elastic follow-up are compiled. A parameter "q" is introduced as a measure of elastic follow-up and is derived for some examples. Effects of non-uniform temperature distribution are discussed as well as effects resulting from multiaxial stress states. A number of methods to quantify elastic follow-up by simplified methods adopted by design codes or proposed in the literature are reviewed for general structures (Part I) and for piping (Part II).
Engineering structures subjected to high cyclic straining necessitating fatigue analysis play an important role in many industries. If the proportionality limit of the material is exceeded, nonlinearity of the material behaviour is to be taken into account. The structural response can then be calculated using either rigorous inelastic analysis methods, where stresses and strains are calculated on a step-by-step basis throughout a given load history, or by employing simplified methods of analysis. In the latter case a plastic strain range enhancement factor Ke is often used to obtain an elastic-plastic strain range based on fictitious elastic stress analyses.
Plastic behaviour of simple academic and practical structures is investigated to identify the basic features which determine the factor Ke:
(a) geometry of the structure
(b) kind of loading
(c) load level
(d) material behaviour.
The factor Ke is quantified for different geometries and kinds of loading. Parameter studies are performed to quantify the effects of load level, material models and hardening characteristics.
The background of some factors Ke established in Nuclear Design Codes or proposed in the literature is reviewed.
The behaviour of plastic structures can be attributed to global, localised and multiaxiality effects. Global structural effects comprise uniform reduction and redistribution of section forces and moments due to plasticity, including redistribution of stress across a section. Localised effects are concentrated to a very small volume of the material not affecting section forces and moments (e.g. notch effects). Multiaxiality effects arise from different Poisson's ratio associated with elastic and plastic behaviour.
Emphasis is laid on global structural effects rather than localised effects due to notches and fillets. Therefore structures exhibiting geometric stiffness discontinuities are considered to be "smooth" in the sense that the specific geometry of the transition between parts of different stiffnesses is disregarded.