By LE Sanchis
Provides a unique method of set idea that's totally operational. This strategy avoids the existential axioms linked to conventional Zermelo-Fraenkel set conception, and gives either a beginning for set conception and a pragmatic method of studying the topic.
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Extra info for Set Theory-An Operational Approach
Safe actions: In gross plastic deformation design checks, an action is called safe if it is not larger than the corresponding limit analysis action or, in other words, if it is enclosed by the set of limit analysis actions. In structural stability design checks, an action is called safe if it is not larger than the smallest bifurcation action or snap-through action, depending on the instability mode. Design models: The design model is a physical or mathematical model of the structure used in determining the effects of actions (EN 13445-3 Annex B).
It takes considerable effort to produce a structural material that is initially isotropic in its inelastic response. e. constitutive laws that are independent of material orientation. In the various design models two types of constitutive laws are used: linear-elastic constitutive laws and linear-elastic ideal-plastic constitutive laws, with specific yield condition and associated flow law. e. an (unbounded) linear relationship exists between stress and strain, which is in cases of thermal stress problems generalized to include the strain due to temperature changes.
Self-stresses: A stress field is called a self-stress field if it is statically admissible for vanishing imposed forces, in the interior of the structure and at each point of the surface with dynamic boundary conditions. e. surface tractions in points with kinematic boundary conditions, need not be zero, but must be in (global) equilibrium with imposed actions. To avoid further confusion: This designation, used consistently here, is called self-equilibrating stress field in EN 13445-3. Unfortunately the two designations are not clearly distinguished in the literature, causing much confusion.