Center of thrust

Sketch of shear centers

The shear center point , also called the center of the transverse force or torsional rest point, is the point of a profile cross-section through which the resultant of the transverse forces must pass in order to achieve a torsion -free force or to exert no torsion on the cross-section.

All forces that act on the profile from a lateral direction are understood as transverse forces. The simplest example is the load that acts on a jacked U-beam. The opposite of the transverse force is the longitudinal force that acts on the profile surface in the longitudinal axis of the profile strand or parallel to it.

The center of shear coincides with the center of gravity for full profiles . In the case of thin-walled cross-sections, on the other hand, the influence of the edge zones is great, so that the shear stresses follow the profile because only tangential stresses can occur on a free surface. The shear stresses, which are to a certain extent directed by the profile course, can, depending on the profile, generate a moment on the center of gravity. The shear center is the point at which the moment disappears as a result of these shear stresses. With double-symmetrical profiles (e.g. I-profiles) the shear center point is identical to the center of gravity. With thin-walled, star-shaped profiles, the shear center is at the intersection. For profiles with only one axis of symmetry, it lies on this axis , but does not coincide with the center of gravity. In the case of U-profiles, for example, it is opposite the center of gravity outside of the profile cross-section.

The formula for calculating the shear center of simple symmetrical thin cross-sections is:

${\displaystyle \ Q\times r_{M}={\int _{}{}}{\tau }{(s)\times r(s)t(s)ds}}$

Where:

${\displaystyle Q}$: Shear force

${\displaystyle r_{M}}$: Lever arm of the transverse force to the center

${\displaystyle \tau (s)}$: Shear stress in the section

${\displaystyle r(s)}$: Lever arm of the shear stress to the bending axis

${\displaystyle t(s)}$: Thickness of the section.

Information on the position of the shear center point for profile cross-sections that are not centrally or doubly symmetrical are often only valid under the assumption of a thin-walled profile. Specifications for thick-walled profiles require complicated calculations.

literature

• Karl-Eugen Kurrer : History of Structural Analysis. In search of balance , Ernst and Son, Berlin 2016, pp. 580–588, ISBN 978-3-433-03134-6 .