Stresses and Strains

  • Steen Krenk
  • Jan Høgsberg


In structural elements like beams and frames, statics and equilibrium are formulated in terms of section forces and moments. The section forces and moments represent the accumulated effect of local force distributions expressed in terms of so-called stresses. Similarly the deformation of structural elements is expressed in terms of e.g. extension and curvature. These deformations lead to deformation at the local level inside the structural element, and these deformations are expressed in terms of strain. The mechanics of deformable bodies is called continuum mechanics and is based on the notion of a state of the material at each individual point of the body expressed in terms of stresses and strains. Some simple states of stresses and strains have been introduced for bars, beams and columns already. This chapter gives a general presentation of stresses and strains within a material body. The relation between the stresses and strains depends on the particular material under consideration and is governed by the so-called constitutive relations of the material, e.g. linear elasticity. While the present chapter lays the ground by defining general properties of stresses and strains, the following chapter gives a brief description of linear elastic material behavior, and presents some commonly used criteria for material failure. The presentation is deliberately kept at the level of a complement to the theory of structures.


Principal Stress Stress Component Axial Strain Virtual Work Strain Component 
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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTechnical University of DenmarkKongens LyngbyDenmark

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