Abstract An approximate analytical approach to the torsion of thin-walled beams of open cross-section with influence of shear is presented. It is assumed that the normal stresses in the cross-section contour direction are small compared to the normal stresses in the beam longitudinal direction that can be ignored in the stress–strain relations. The stresses and displacements are obtained in the closed analytical form. It is assumed that transverse load can be reduced to moments of torsion only, with respect to the cross-section shear centre. The beam will be subjected to torsion, with respect to the shear centre, i.e. the principal cross-section sectorial coordinate, in the case of cross-sections with two axes of symmetry; to torsion and bending in the case of cross-sections with one axes of symmetry and to torsion, bending and tension in the case of general cross-sections. An illustrative example of beam with one axis of symmetry is given.
[1]
G. Cowper.
The Shear Coefficient in Timoshenko’s Beam Theory
,
1966
.
[2]
C. F. Kollbrunner,et al.
Torsion in Structures
,
1970
.
[4]
S. Timoshenko,et al.
LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars
,
1921
.
[5]
S. Timoshenko,et al.
X. On the transverse vibrations of bars of uniform cross-section
,
1922
.
[6]
S U Bhat,et al.
A FORMULATION OF THE SHEAR COEFFICIENT OF THIN-WALLED PRISMATIC BEAMS
,
1985
.
[7]
V. Vlasov.
Thin-walled elastic beams
,
1961
.
[8]
A. Gjelsvik,et al.
The Theory of Thin-Walled Bars
,
1981
.
[9]
T. M. Roberts,et al.
Influence of shear deformation on restrained torsional warping of pultruded FRP bars of open cross-section
,
2001
.