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Shear stress due to torsion

The St. Venant and warping torsion is considered during the analysis. For St. Venant torsion, the shear stress τt is calculated for torsional moment Tt. Following expression is used for open cross-sections:

Where is:

Tt

  • The torsional moment

It

  • The rigidity moment in St.Venant torsion

t

  • The thickness of the plate in the considered point

The stress τt for closed cross-sections is given by the expression

Where is:

Tt

  • The torsional moment

Ωt

  • The area bounded by the centre lines of plates increased by a factor of two

t

  • The thickness of the plate in the considered point

For warping torsion, the shear stress τω is calculated for torsional moment Tω using following formula:

Where is:

Tω

  • The torsional moment

Sω

  • The warping constant in the considered point

Iω

  • The sectional moment of inertia

t

  • The thickness of the plate in the considered point

The shear stress is verified according to the following expression:

Where is:

fy

  • The yield strength

γM0

  • The partial safety factor

The values of shear resistance VRd,y and VRd,z are reduced due to torsion for combination of shear forces and torsional moments. The reduction is based on following expression

for I- and U-profiles and

for other cross-sections.

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