Non-uniform torsion of open-section members considering cross-sectional curvatures

Abstract

An analytical solution for torsional analysis of constrained open-section members, which can estimate the variation of the axial displacement, the normal and shearing stresses along the beam and across the cross section, is important and is the main goal of this article. A new formulation for constrained torsional analysis of open-section members is presented. In the formulation, cross sections with curved corners can be analyzed. The cross section is decomposed into some straight and curved segments with uniform thickness. This decomposition makes it possible to solve the governing equations in each segment analytically. The method can predict the stress concentration at reentrant corners of the cross section with an acceptable accuracy. Specific formulas for channel beams and tubes with a longitudinal slot are also derived. Accuracy of the presented method is verified by comparing the obtained results with the three-dimensional finite element method solutions with a fine mesh. Numerical investigations show that the obtained formulas give relatively accurate results for thin to moderately thick-walled open cross sections.

Torsional analysis of hollow members with sandwich wall

“…Similarly, by using equations ( 18), (23), and (24b), the constants c 4 , c 5 , and c 6 in terms of q are found as follows…”

“…Integration constants in terms of shear flow can be obtained similar to the previous case. For this end, the shearing stresses from equation ( 9) through (12) are substituted in equations ( 20) and ( 21), and then combined with equation ( 18); however, q 0 1j , q 0 2j , and q 0 3j are replaced with q 1j , q 2j , and q 3j in equation (23). One can find shearing stresses in terms of q in straight segments by substituting integration constants from equation ( 22) into equations ( 9) to (11) as follows…”

“…The proposed method is devoted to uniform (Saint Venant) torsion only. The nonuniform torsion analysis of homogenous members can be performed analytically for thin-walled [21,22] and moderately thick-walled sections [23]. Several numerical methods for nonuniform torsion analysis of nonhomogeneous members have been presented too [24][25][26][27].…”