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.
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Chapter 4 addresses combined bending and extension.
See Chapter 4.
Named after the Swiss Jacob Bernoulli (1654–1705), from a famous family of mathematicians and physicists.
Inhomogeneous cross-sections are covered in Chapter 9.
Remember that the bar will not bend (curve) if there is no bending, but only extension.
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.
Chapter 3 addresses the location of the centroid in further detail.
The order of the differential equation is determined by the highest derivative.
Field boundaries (locations) are indicated by a sub-index and the fields (regions) are indicated by an upper index.
See also Volume 1, Section 4.3.1.
Remember that the upper index is used to indicate the members.
The normal force N is initially unknown here.
The displacement u is initially unknown here.
The formal definition also leads to a consistent tensor notation, which is out of the scope of this volume.
See Volume 1, Section 1.3.2.
See Volume 1, Section 3.3.1.
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(2007). Bar Subject to Extension. In: Engineering Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5763-2_2
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DOI: https://doi.org/10.1007/978-1-4020-5763-2_2
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