Relationships between load and de ection, stress, and strain are initially linear. After a certain magnitude of applied load, the behavior of the beam or column becomes nonlinear. For example, dead load or self weight analysis is usually linear. When response of the member under a higher load, as observed in the laboratory, shows second or third degree nonlinearity of load de ection or stress-strain relationships, the analysis is no longer straight forward. Also, signi cant changes in geometry of the structure can result in overstress, cracking or yielding of material. Geometric nonlinearity: Examples are load de ection characteristics of suspension cables, long span trusses, and slender columns (P-Delta effect). Tied arches and trusses are not designed to undergo large de ections. In other structures long spans and heavy loads may lead to nonlinear load-de ection behavior of members. Hence, analysis should correspond to a series of unique loads under which the deformed structure is in equilibrium and has geometric compatibility. Material non-linearity: When analysis is based on plastic deformation of certain materials, material nonlinearity is considered. Nonlinear analysis is required when studying post-elastic
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Build Your Own Elec tric Vehicle
Part I:
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