# Shear deformations

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Shear deformation should normally be taken into account, since there are these deformations. For comparison with other calculations the shear deformations can be ignored. For nonlinear shaft model the shear deformations should be considered to improve convergence.

There are different options available. Either a fixed value can be entered. Usually 1/1.1 is used for cylinders. The options ‘according Cowper’ and ‘according Hutchinson’ are also considering an inner diameter for hollow shafts and the Poisson number of the material. [Hutchinson](bibliography.md#hutchinson_2001) considers higher order terms in his formula than [Cowper](bibliography.md#cowper_1966):

- Hutchinson (Circular Cross Section):   
$k = \frac{6(1+\nu)^2}{7+12\nu+4\nu^2}$

- Hutchinson (Hollow Circular Cross Section):   
$k = \frac{6(a^2+b^2)^2(1+\nu)^2}{7a^4 + 34a^2b^2+7b^4+\nu (12a^4+48a^2b^2 + 12b^4) + \nu^2(4a^4 + 16a^2b^2 + 4b^4)}$  
  
where 'b' is the outer radius, 'a' the inner radius and 'ν' the Poisson’s ratio.

- Cowper (Circular Cross Section):   
$k = \frac{6(1+\nu)}{7+6\nu}$

- Cowper (Hollow Circular Cross Section):   
$k = \frac{6(1+\nu)(1+m^2)^2}{(7+6\nu)(1+m^2)^2+(20+12\nu)m^2}$  
  
where $m=b/a$ is the ratio of inner to outer radius and 'ν' the Poisson’s ratio.