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... for cables

Figure 14.19

Figure 14.19 Hartsuijker & Welleman (2006)

The differential equation for equilibrium relations for cables is based on the infinitesimal small loaded cables:

leading to :

qz=dVdx{q_z} = - \frac{{{\rm{d}}V}}{{{\rm{d}}x}}
V=Hdzdx{V} = H\frac{{{\rm{d}}z}}{{{\rm{d}}x}}

This is treated in chapter 14.1.3 of the book Engineering Mechanics Volume 1 Hartsuijker & Welleman, 2006.

References
  1. Hartsuijker, C., & Welleman, J. W. (2006). Engineering mechanics: Volume 1: Equilibrium. In Engineering Mechanics: Volume 1: Equilibrium. Springer Dordrecht. 10.1007/978-1-4020-5483-9