7th DoF (warping) - Stress results

Introduction

New result items and several changes in present results are in "3D stresses" and "1D stresses" - stresses concerning 1D beams, if the warping (the 7th DoF) is activated in the project.

Normal stress - σ_x - change

The described change is applicable for "basic magnitudes" within "1D stresses" and also "3D stresses".

The total normal stress in 1D beam is considered as summary of following:

where indexes "N", "My", "Mz" and "Mw" determine, which internal force is contributing to normal stress in the 1D beam section: normal force, two bending moments along y and z axes, and bimoment respectively. Apparently, if the bimoment "Mw" is present (7th DoF is activated), the change in the total normal stress is caused by this part. An example of normal stress caused (only) by bimoment is provided in the figure below.

Shear stress from torsion - τ_tor - change

Noted as "τ_tor" within "basic magnitudes" of the "1D stresses", and noted as "τ_tor (1D)" within the "basic magnitudes" of the "3D stresses".

If the 7th DoF is activated, "τ_tor" is derived from the primary torsional moment "M_xp"

If the 7th DoF is NOT activated, "τ_tor" is derived from the torsional moment M_x.

An example is provided below.

Shear stress from warping - τ_w - new entity

Noted as "τ_w" within "basic magnitudes" of the "1D stresses", and noted as "τ_w (1D)" within the "basic magnitudes" of the "3D stresses".

If the 7th DoF is activated, "τ_w" is derived from the secondary torsional moment "M_xs"

If the 7th DoF is NOT activated, "τ_w" is not present at all.

An example is provided below.

Total shear stress - τ_tot - change

The described change is applicable for "principal magnitudes" within "1D stresses" and also "3D stresses".

The total shear stress in 1D beam is considered as summary of following:

where indexes "Vy", "Vz" determine, which internal force is contributing to the shear stress in the 1D beam section: two shear forces along local y and z axes of the beam section. "τ_tor" and "τ_w"are explained above. If the 7th DoF is activated, there is a change in "τ_tor" and "τ_w" is newly present, hence the change in "τ_tot". An example is provided in the figure below.

Other items

As far as there are changes in σ_x and τ_tot if the 7th DoF is activated, there are expected to be differences also in corresponding stresses derived from these values, e.g. equivalent von misses stress σ_E, etc. All these changes are explicitly not summarized here.