Closed-form solutions for torsion analysis of structural beams considering web-flange junctions fillets

In this paper, an effective semi-analytical method is presented for torsion analysis of structural beams with various kinds of junctions such as T, I, H, E and + beams. A fairly simple but precise formulation based on analytical and accurate numerical solutions is presented for evaluating the shearing stress at critical points and computing the torsional rigidity of a member under torsion. The problem is formulated based on Prandtl's stress function. The cross-section is decomposed into several segments, including straight, curved, end, and junction segments. The torsion problem is solved in each segment separately. Standard junction segments are analyzed using the finite element method with a fine mesh. Other segments are analyzed by analytical methods. Closed-form expressions in terms of geometrical parameters are found for the shearing stresses at critical points of each segment. The torsional rigidity of the cross section is also expressed by a closed-form expression. The presented formulations can be used for analysis of a wide range of thin- to moderately thick-walled complicated sections.