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 |
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δi |
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Following expression is used for cells:
Where is: | D |
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Ω |
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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 |
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ω |
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δ |
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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 |
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ω |
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