Some thoughts about Torsion
It is rather straight forward to analyze torsion of a thick-walled or closed thin-walled profile (e.g. an axle or a tube). The shear stress (τ) can be assessed by dividing the torsional moment (M ) with the torsional resistance (W ). The magnitude of the shear stress caused by torsion is independent of the length of the profile and the shear stress flow is closed, Figure 1. Each cross-section of the profile remains plane after torsion. This is called torsion according to Saint-Venant.
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Figure 1. Torsion according to Saint-Venant.
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The torsion of an open thin-walled profile (which often is the case when it comes to welded structures) is different and more complex.
As an example, study the I-beam in Figure 2. The torsional moment will be transmitted by two forces (F = M /h), acting in opposite direction at the flanges. These forces will be the cause of bending moments in the upper and lower flange, which in turn will result in normal stresses (σ ) in the flanges. The magnitude of the normal stresses are depending on the length (L). The longer L in Figure 2, the higher the normal stresses σ . Cross sections of the profile will not be plane after torsion. This is called Warping or Non-uniform torsion.
At least two parallel sheets are required to transfer the torsional moment as warping. The sheets need to be steered or supported somewhere, e.g. by welding the beam to a rigid surface, as indicated in Figure 2. If those demands are not met, for example in the case of an angular section or just a plane sheet, the profiles are extremely poor for transmitting torsional moments and should not be used for that purpose.
Based on experience, the normal stresses easily become high, even for seemingly modest torsional moments. Torsion of thin-walled open sections should therefore, if possible, be avoided.
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One smart way of avoiding torsional moments in a beam is to make sure that the forces act through the Shear Center (SC). The Shear Center is defined as being the point where forces can act without the beam rotating.
In Figure 3, Shear Center and Center of Gravity (CG) are defined for an I-beam and for an U-beam.
NOTE: The Shear Center location far outside the web of the U-beam. To avoid torsion of the section, all forces must act through SC.
Figure 2. Torsion of an open thin-walled
profile.
Figure 3. Center of Gravity (CG) and Shear Center (SC).
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