Torsion (mechanics)

Which describes the rotation of twist of a component, resulting from the action of a torsional moment. If you try to twist a rod with a lever that acts on these ( in addition to any shear force ), a torsional moment.

The torsion T is derived from the force F on the lever multiplied by the length r of the lever used for this purpose:

The resulting torsion ( twist angle) of the rod results from the torsional moment T divided by the torsional moment of inertia, which describes the size and shape of the rod cross -section, and the shear modulus G, multiplied by the rod length L:

For circular cross -sections and for closed- circular cross -sections, the torsional moment of inertia is equal to the polar moment of area. Other cross-sections for the calculation of the Torsionsträgheitsmoments is possible only in special cases, in closed form. In addition, in determining in many cases of importance, whether it is verwölbungsfreie cross-sections, and whether or not the warping is disabled or not.

The shear stress in the rod arises from the torsional moment T divided by the polar moment of resistance:

The maximum shear stress occurs at the edge, or at the maximum radius in the observed cross section. on.

This shear stress must not be greater than the maximum allowable shear stress of the material to be used:

In case of excessive torsion deformation of a wave from the elastic range into the plastic range proceeds, for example, and eventually leads to breakage.

Torsion without warping

For uniform cross -sections which satisfy the conditions that the product of wall thickness and radius on the run variables are constant, and that it is a closed profile, incurred for the twist is no tension in the longitudinal direction and thus no warping of the cross section. This phenomenon met such as a circular cylinder of constant wall thickness. This case of torsion is called Neubersche shell. Note, however, that the linear elasticity theory holds, which means that only small deformations, small distortion and no plastic deformation is allowed. In addition, the load should be present in the form of a voltage applied to the longitudinal axis of the torsional moment.

Twist with unobstructed warping ( Saint- Venant )

Pure twist, also called Saint- Venant torsion allows unimpeded movement of the cross -section points in the longitudinal direction (Z direction ) of the profile. This is known as an unobstructed warping of the cross section. The cross-sectional shape perpendicular to the Z - direction is retained ( small deformations). It is believed that the Querschnittsverwölbung is independent of the position of the cross section and can be adjusted freely. It uses a quasi tricks to make twisting profiles, in effect, that have a circular cross-section. They can not be construed as Neubersche shell. However, it must be firmly clamped in such a profile, it must be free standing in the room and it is applied a torque to both sides. This ensures that no normal stresses occur along the profile, although individual points may move in the longitudinal direction of the profile.

The inner torsion is constant along the length of the rod and has the size of the external torsional moment. We also talk about primary torsion.

The largest torsional shear stress can be found in the smallest wall thickness ( theory of thin-walled closed hollow profiles and thin-walled open sections ).

Warping torsion

Warping torsion occurs when

• The warping of the twisted rod cross -section at support points, is hindered, for example by end plates.
• By changes in cross section and thus variable torsional stiffness and changing Einheitsverwölbung of Staff
• As well as by variable torsion if the resulting torsional moment in the rod is not constant (eg by a Streckentorsionsmoment )
• If no wölbfreier cross section is present or a wölbfreier cross section by forcing another rotational axis gets forced upon its shear center warpage.

It also occurs when the torsional attacks within the rod length. It corresponds to a twisting of the rod disabling local stress state through a support condition. Mathematically, one can imagine the warping torsion as a St. Venant torsion with additional statically indeterminate longitudinal stresses in the bearing point, which must be sufficiently large that the support condition, for example, longitudinal displacement equal to zero, are met.

The internal torque of the rod then splits into two portions. A portion comes from the pure torsion, the second component is produced by the warping disabled.

In full sections, the proportion of Wölbmomentes is due to the relatively low warpage usually small, it is appropriate to disregard the rule. However, for thin-walled sections, they must be considered.

In thin-walled cross-sections in addition to the contact St.Venantschen shear stresses ( the so-called Primary Torsionsschubspannungen ) additional secondary thrust (also called Wölbschubspannungen ) and WölbNormalspannungen, which result from a warp of the cross section prevented from above-mentioned reasons. For closed thin-walled sections such as cold-formed hollow sections, these stresses and the resulting deformations, however, usually remain small compared to the voltages from the pure torsion. In general, no consideration of warping torsion is required for these cross sections. However, borderline cases must be considered, taking into account the cross-sectional deformation at very thin-walled cross-sections in the calculation.

The Wölbnormalspannungen spread evenly over the cross section.

The twist is not constant over the length of the rod, because of the influence of the warping torsion with increasing distance from the bearing point at which the warping of the cross section is disabled is reduced. Therefore, the length of the rod of the Wölbnormalspannungen are not constant.

Retro - and anteversion

If this segment is twisted with respect to its longitudinal axis forward, it is called anteversion. If there is a rearward rotation, it is called retroversion. In humans is the femur, the femur, such an example. Here, the femoral head and neck is rotated with respect to the longitudinal axis of the femur to the front.

Application Examples

The effect of torsion found in many areas of application:

• Torsion pendulum as a time standard in watches
• Henry Cavendish used in 1798 to measure a gravitational balance of the gravitational constant. This results in a balance between torsional force of the suspension wire and gravity sets.
• Coil spring
• Torsion bar spring in vehicle
• Torsionsgeschütz, antique artillery weapon
• Torsion test for material testing
• Spanish winch for tensioning
• Wring out ( pre-dry ), for example, laundry, mop or hair