4 / 14
Calculation of Shear Areas and Torsional Constant using the Boundary Element Method with Scada Pro
4
2. Calculation of torsional constant
Torsion is a load in which a transverse force is applied at a distance from the reference
axis of the bar, creating in this way a torque vector
t
M
having the reference axis of the bar
direction. Torsion in bar elements is created when the plane of the external load does not
pass through the shear center S of their cross-section. It is also known that the deformation
of a bar with non-circular cross-section subjected to twisting moment, consists of a rotation
of the cross-section about the torsional axis of the bar and a torsional warping of the cross-
section (Img.2.1b)
.
Simple torsional support (forked)
(a)
(b)
Img. 2.1. Free torsional warping of a rectangular cross-section.
When the torsional warping of the cross-section of the member is not restrained
(Img.2.1a) the applied twisting moment is undertaken from the Saint-Venant shear stresses
[2.1]. In this case the angle of twist per unit length remains constant along the bar and the
torsion is characterized as
uniform
.
Img. 2.2. Nonuniform torsion of bars due to internal loading and boundary conditions.