To kick of this series, please read our blog: Difference Between Lateral Torsional Buckling & Torsion.
Torsion has proven to be more complex than many initially assume. Not only does it manifest in distinct forms—St. Venant torsion and Warping torsion—but it also introduces various load effects, including axial, shear, and bending stresses. Adding to this complexity is the fact that torsional behavior depends heavily on the profile of the member in question. Thin-walled and open sections (e.g., I, C, and Z profiles) are particularly susceptible to torsion. Consequently, if a member is subjected to torsion, it must be analyzed carefully. Unfortunately, these calculations are far from straightforward.
For open sections, St. Venant torsion can often be disregarded per EN 1993-1-1:2005, simplifying matters somewhat. However, key properties are still required to evaluate torsional and warping effects effectively. These include:
- G – Shear Modulus of Elasticity of the material (also Shear Modulus)
- J – Torsional constant of the cross-section (geometric property)
- E – Modulus of Elasticity of the material (also Young’s Modulus)
- Cw – Warping constant of the cross-section (geometric property)
Let’s break down how to obtain these values for a given member and material:
- G – This is, as mentioned, material specific. This value can be obtained as one would the E value. It can also be calculated quite easily: G = E/[2x(1+µ)] with µ being the Poisson’s Ratio. The Shear Modulus for S355JR steel is 77GPa.
- J – This value can be obtained from the SAISC Red Book profile/cross-section tables. If you have an unlisted profile, you can use Prokon’s Prosec module to calculate this value.
- E – This value is obtained through easy research and is usually easily obtained through the use of an internet browser.
These parameters are essential for determining C, a dimensionless coefficient related to torsional or flexural-torsional buckling behavior. Smaller values of C are generally beneficial for slender members, as warping stiffness plays a critical role in stability. Conversely, larger C values are more favorable for compact members, where torsional stiffness governs. The formula for C is as follows:
For slender or long members, smaller C values are typically advantageous because warping effects are critical, and higher warping stiffness improves stability. For short or compact sections, larger C values can be more favorable because torsional stiffness is often the limiting factor.
Although, initially, it is very hard to distinguish between the two, torsional stiffness is governed by J (torsional constant) and G (shear modulus), whereas warping stiffness is governed by Cw (warping constant) and E (Young’s modulus). Key differences are summed up below:
Interestingly, open sections tend to have low torsional stiffness and rely heavily on warping resistance for stability. To enhance these properties:
- For improved torsional stiffness, increase wall thickness to boost J.
- For enhanced warping stiffness, add stiffeners, bracing, or modify the member’s profile.
In Part 2, we will explore the workflow outlined in EN 1993-1-1:2005. We aim to understand these parameters further and learn how to apply these workflows effectively, ultimately mastering this challenging yet essential aspect of structural engineering.
