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The term 'collapse' is often used to refer to the sudden loss of structural integrity and does not distinguish between the two major categories leading to structural failure: (a) material failure or (b) structural instability due to loss of structural stiffness within the elastic limit of the material. The term 'buckling' is often reserved specifically for the latter category. At an elementary level, predicting material failure may be accomplished using linear finite element analysis. The strains and corresponding stresses obtained from this analysis may be compared to design stress (or strain) allowables anywhere within the structure. If the finite element solution indicates regions where these allowables are exceeded, it is assumed that material failure has occurred. Design allowables are based on experimentally-derived material strengths and usually include a safety margin. This type of analysis will give an adequate prediction for statically determinate metallic structures undergoing small deformations. If the structure is statically indeterminate, as indeed the majority of practical structures are, the analyst may want to assess the evolution of material failure. The load at which material failure initiates may be significantly lower than that which leads to eventual collapse. The analyst may also want to know the nature of this failure progression, that is, is it gradual or does it occur rapidly? Material failure may be the result of plasticity in metallic structures or fracture, which is a more prevalent form of failure in brittle materials such as ceramics or carbon-fibre reinforced plastics. The structure may also undergo large deformations before or during material failure and it is therefore apparent that the presence of geometric and material non-linearities requires more
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