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Cross-sectional characteristics

Following characteristics are calculated:

Warping coordinate

The warping coordinate is doubled area circumscribed by the radius vector between defined pole and point on the centre line of the branch. The values are modified in cells due to the effect of constant shear flow.

Main warping coordinate

The warping coordinate φ is considered as a main coordinate ω, if the beginning is selected in that way, that following formula is valid:

It means that the warping coordinate of whole cross-section is equal to 0.

The warping coordinate depends on the pole position. Usually, poles in the centre of gravity or in the shear centre are used.

The rigidity moment in simple torsion

The rigidity moment in simple torsion is calculated for open branches with the help of this expression:

Where is:

li

  • The length of i-sector

δi

  • The thickness of i-sector

Following expression is used for cells:

Where is:

D

  • The parameter dependent on the shear flow in the cell

Ω

  • The area surrounded by the centre line of the cell multiplied by two

Shear centre

The shear centre is a point, through which goes the resultant of inner shear forces in the cross-section. If the resultant of external transverse forces goes also through this point, the bending of the member does not cause the torsional stresses. The warping characteristics are calculated relatively to this point very often.

Warping constant

The warping constant is necessary for calculation of shear stress in warping. It is calculated according to the expression

Where is:

s

  • The centre line of cross-section

ω

  • The main warping coordinate

δ

  • The sector thickness

Warping moment of inertia

The warping moment of inertia describes the stiffness in warping. It is necessary for calculation the normal stress induced by warping. It is calculated using expression

Where is:

A

  • The cross-sectional area

ω

  • The main warping coordinate

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