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Torsion and warping
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TECHNICAL FEATURE // TORSION AND WARPING
Restrained warping for the torsion of thin-wall open sections is not included in most commonly used frame analysis programs. Almost all frame programs in practice use St-Venant torsion theory ignoring the effects of restrained warping.
It is important to note that the torsional stiffness of an open section is function of the warping end conditions as well as the location of the torsional load. Thus, the distribution of the forces in the structure having members resisting torsion may differ whether this option is enabled or disabled. A subdivided continuous member needs to be specified as a physical member to get the continuity effect of warping along the member.
In addition to shear stresses, some members carry torque by axial stresses. This is called warping torsion. This happens when the cross-section wants to warp, i.e., displace axially, but is prevented from doing so during twisting of the beam. In other words, the section tends to resist torsion by out of plane bending of the flanges.
For solid and thin-wall closed sections (square, rectangular and circular tubes) these effects are often negligible. However, for thin-wall open sections restrained warping is often dominant. To include the effect of restrained warping we need to know the torsion constant J and the warping constant Cw which are geometric properties of the cross-section. For open shapes (I, C, Z, T, L, built-up …) the following equation may be used to evaluate the influence of the warping.
In addition to shear stresses, some members carry torque by axial stresses. This is called warping torsion. This happens when the cross-section wants to warp, i.e., displace axially, but is prevented from doing so during twisting of the beam. In other words, the section tends to resist torsion by out of plane bending of the flanges.
For solid and thin-wall closed sections (square, rectangular and circular tubes) these effects are often negligible. However, for thin-wall open sections restrained warping is often dominant. To include the effect of restrained warping we need to know the torsion constant J and the warping constant Cw which are geometric properties of the cross-section. For open shapes (I, C, Z, T, L, built-up …) the following equation may be used to evaluate the influence of the warping.
where
G Shear modulus of elasticity of the material
J Torsional constant for the cross section
E Modulus of elasticity of the material
Cw Warping constant for the cross-section
For axisymmetric cross-sections and thin-walled cross-sections with straight parts that intersect at one point such as X-shaped, T-shaped, and L-shaped cross-sections pure torsion will generally dominate over warping stresses. In these cases, torsional loads are carried by pure torsional shear stresses (St-Venant torsion) regardless of the boundary conditions.
G Shear modulus of elasticity of the material
J Torsional constant for the cross section
E Modulus of elasticity of the material
Cw Warping constant for the cross-section
For axisymmetric cross-sections and thin-walled cross-sections with straight parts that intersect at one point such as X-shaped, T-shaped, and L-shaped cross-sections pure torsion will generally dominate over warping stresses. In these cases, torsional loads are carried by pure torsional shear stresses (St-Venant torsion) regardless of the boundary conditions.
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