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... for extension

The differential equation for kinematic relations for extension is based on a displaced the infinitesimal small beam:

leading to :

ϵ=−dudx{\epsilon} = - \frac{{{\rm{d}}u}}{{{\rm{d}}x}}
(1)

This is treated in chapter 2.2.1 of the book Engineering Mechanics Volume 2 Hartsuijker & Welleman, 2007.

References
  1. Hartsuijker, C., & Welleman, J. W. (2007). Engineering Mechanics: Volume 2: Stresses, strains and displacements. Springer Netherlands. 10.1007/978-1-4020-5763-2
Activities
Kinematic relations
Activities
... for bending