Thrust flow

In construction , technical mechanics and strength theory, the shear flow  is the course of the shear forces from transverse forces or torsional moments in the cross section of a component . It has the unit of measurement N / m ( Newtons per meter), i.e. H. Force per length. ${\displaystyle T(s)}$

The resulting sum of the shear flows gives the vector of the shear forces Q in terms of magnitude and direction :

${\displaystyle \int _{s}T(s)\cdot \mathrm {d} s={\vec {Q}}}$

with the running coordinate s, which is related to the center of gravity of the cross-sectional area .

Thin-walled components

In the case of thin-walled components ( profiles ), the shear stress distribution and thus also the shear flow can be assumed to be constant over the component thickness : ${\displaystyle \tau (s)}$ ${\displaystyle t}$

${\displaystyle {\begin{alignedat}{2}t&\ll s_{\mathrm {max} }\\\Rightarrow \tau &=\tau (s)&&\neq \tau (t)\\\Rightarrow T&=T(s)=\tau (s)\cdot t(s)&&\neq T(t)\end{alignedat}}}$

In this case the shear flow runs parallel to the component edge.

The shear flow at the profile centerline is:

${\displaystyle {\begin{aligned}T_{0}&=\tau _{0}\cdot t_{0}\\\Leftrightarrow T(s=0)&=\tau (s=0)\cdot t(s=0)\end{aligned}}}$

In addition:

${\displaystyle T(s)=T_{0}-Q\cdot {\frac {S(y)}{I}}}$

With:

• ${\displaystyle S(y)}$the static moment
• ${\displaystyle I}$the area moment of inertia .

The thrust flow is constant in a thin-walled, closed cross-section that is subjected to torsion . This can be  calculated from the torsional moment using Bredt's first formula .

Individual evidence

1. ↑ Russel C. Hibbeler: Technische Mechanik 2 Strength Theory , 8th Edition, Pearson Germany, Munich 2013, ISBN 978-3-86894-126-5 .