Bar Subject to Extension

A bar is a body of which the two cross-sectional dimensions are considerably smaller than the third dimension, the length. A bar is one of the most frequently used types of structural members. To understand something about the behaviour of bar type structures, it is first necessary to understand the behaviour of a single bar. This chapter addresses the case of a bar subject to extension. We talk of extension when the (straigh t) bar rem ains straight after deformation and does not bend.


Normal Force Engineering Mechanic Constitutive Relationship Axial Stiffness Dead Weight 
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  1. Chapter 4 addresses combined bending and extension.Google Scholar
  2. See Chapter 4.Google Scholar
  3. Named after the Swiss Jacob Bernoulli (1654–1705), from a famous family of mathematicians and physicists.Google Scholar
  4. Inhomogeneous cross-sections are covered in Chapter 9.Google Scholar
  5. Remember that the bar will not bend (curve) if there is no bending, but only extension.Google Scholar
  6. In the notation “ Nx ” the index x indicates that the normal force N acts along the x axis. Since it is the convention to let the normal force apply at the bar axis and to select the x axis there, the index is generally omitted. In this section we are also using a coordinate system for which the x axis does not coincide with the member axis. Therefore the index x is temporarily used.Google Scholar
  7. Chapter 3 addresses the location of the centroid in further detail.Google Scholar
  8. The order of the differential equation is determined by the highest derivative.Google Scholar
  9. Field boundaries (locations) are indicated by a sub-index and the fields (regions) are indicated by an upper index.Google Scholar
  10. See also Volume 1, Section 4.3.1.Google Scholar
  11. Remember that the upper index is used to indicate the members.Google Scholar
  12. The normal force N is initially unknown here.Google Scholar
  13. The displacement u is initially unknown here.Google Scholar
  14. The formal definition also leads to a consistent tensor notation, which is out of the scope of this volume.Google Scholar
  15. See Volume 1, Section 1.3.2.Google Scholar
  16. See Volume 1, Section 3.3.1.Google Scholar

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© Springer 2007

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