Warping

Warping refers to the deformation of cross sections in the direction of the bar axis in the torsion of rods . The reason is the camber-changing voltages caused by the warping torsion arise. In contrast to the Saint-Venant torsion , the cross-sectional shape perpendicular to the longitudinal axis is not retained. In particular, the corner points of the deformed profile no longer lie in one plane.

Warping of the I-profile under a torsional moment . In the unloaded profile on the left, the orange-colored end points are all in the plane that is spanned by the orange rectangle. The profile on the right is twisted counterclockwise at its front end and clockwise at its rear end due to the torsional moment. Due to the twisting of the profile, the four outer corner points move from their original position on the light gray line to a new position that is no longer in the original plane. Note: Contrary to the visual impression, the surfaces of the upper and lower chords of the I-profile are not at an angle to one another. Only the corner points move. In reality, the upper, lower chord and web would be forced into a spiral shape if the profile was twisted, but this is not shown here. ${\displaystyle M_{\mathrm {T} }}$

${\displaystyle M_{\mathrm {T} }}$

With the exception of certain arch-free cross-sections, all cross-sectional shapes warp under torsion.

Warping-free cross-sections

In the case of arch-free cross-sections, only one rotation of the cross- sections is assumed . The arch-free cross-sections include:

• Circular and circular ring cross-sections
• Closed polygon cross-sections with constant wall thickness , the wall center lines of which form circular tangents . This also includes all regular polygons such as square and equilateral triangle and, as a special form, the circle.
• Closed polygonal cross-sections with constant wall thickness on each side . This is e.g. B. a rectangle with two short thin-walled and two long thick-walled sides. In general, the following conditions must be met for a corner:, where the wall thickness and the distance to the axis of rotation are designated. ${\displaystyle m}$ ${\displaystyle m-1}$ ${\displaystyle r_{1}t_{1}=r_{2}t_{2}=\cdots =r_{m}t_{m}}$ ${\displaystyle t_{i}}$ ${\displaystyle r_{i}}$
• Open, thin-walled profiles with cross-sections that are composed of solid rectangles and whose wall center lines all intersect at one point. The individual wall thicknesses can be different here. These are z. B. X, T and L profiles. The 2 narrow rectangles from which z. B. an L-profile is constructed, span a plane and do not move the cross-section in the case of torsion in a third dimension.

See also

• Torsional torsional buckling

Individual evidence

1. ↑ Questions and answers on lightweight construction from Professor Schürmann , Chapter 3, Question 17, Student, 2006