Torsion on cylinder described differentially

[MicroCosmos]

Hi all,

In this article, page 7 - 3 there is a drawing of a Cylinder suffering Torsion. In the next page it says:
ftp://www.bauwesen.fh-muenchen.de/Bauwesen/Konrad/Baustatik_1/Festigkeitslehre/kap07.pdf

γ⋅dx = r⋅dϑ

From my observations i come to tan γ=s/x ; tan ϑ=s/r ; therefore x⋅tan γ = r⋅tan ϑ
But how to understand/find it the way its written? I want to learn how to read those relations differentially.

Thanks in advance!

 

[Spinnor]

Hi all,

In this article, page 7 - 3 there is a drawing of a Cylinder suffering Torsion. In the next page it says:
ftp://www.bauwesen.fh-muenchen.de/Bauwesen/Konrad/Baustatik_1/Festigkeitslehre/kap07.pdf

γ⋅dx = r⋅dϑ

From my observations i come to tan γ=s/x ; tan ϑ=s/r ; therefore x⋅tan γ = r⋅tan ϑ
But how to understand/find it the way its written? I want to learn how to read those relations differentially.

Thanks in advance!

This may not help, take a uniform cylinder of length L, free of torsion, and draw a straight line on the cylinder so that the line is parallel to the axis of the cylinder. Now apply equal and opposite torques to the ends of the cylinder. The straight line is now a helix ( or at least part of a helix). The amount of twist per length of the cylinder is a constant as it is with a helix. I don't think the tan function comes into play?

 

[MicroCosmos]

Im sorry, i forgot to say that in my equations, "s" is a part of the circumference where the Torsion is being applied. x is the lengh of the cylinder, r the radius.
It may be a correct way of thinking about it, but i don't see how this is going to help. Is γ⋅dx = r⋅dϑ the formula of an helix?

Not sure if i just got it. For every step in x direction we get a step in ϑ, that is proportional to γ, and inverse proportional to r? Am i missing something?