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Engineering LibreTexts

11: Fundamental Concepts in Structural Plasticity

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  • Plastic properties of the material were already introduced briefly earlier in the present notes. The critical slenderness ratio of column is controlled by the yield stress of the material. The subsequent buckling of column in the plastic range requires the knowledge of the hardening curve. These two topics were described in Chapter 8. In Chapter 9 the concept of the ultimate strength of plates was introduced and it was shown that the yield stress is reached first along the supported or clamped edges and the plastic zones spread towards the plate center, leading to the loss of stiffness and strength. In the present lecture the above simple concepts will be extended and formalized to prepare around for the structural applications in terms of the limit analysis. There are five basic concepts in the theory of plasticity:

    • Yield condition
    • Hardening curve
    • Incompressibility
    • Flow rule
    • Loading/unloading criterion

    All of the above concept will first be explained in the 1-D case and then extended to the general 3-D case.