Formulas: HSS Subjected to Combined Torsion, Shear, Flexure, and Axial Force

Equation C-H3-6

Several interaction equation forms have been proposed in the literature for load combinations that produce both normal and shear stresses. In one common form, the normal and shear stresses are combined elliptically with the sum of the squares (Felton and Dobbs, 1967):

Equation C-H3-7

In a second form, the first power of the ratio of the normal stresses is used:

Equation C-H3-8

The latter form is somewhat more conservative, but not overly so (Schilling, 1965), and this is the form used in this Specification:

where

the terms with the subscript $r$ represent the required strengths, and the ones with the subscript $c$ are the corresponding available strengths. For this edition of the Specification, provisions have been explicitly given for biaxial bending and shear. Normal effects due to flexural and axial load effects are combined linearly and then combined with the square of the linear combination of flexural and torsional shear effects. When an axial compressive load effect is present, the required flexural strength, $M_{r}$, is to be determined by second-order analysis. When normal effects due to flexural and axial load effects are not present, the square of the linear combination of flexural and torsional shear effects underestimates the actual interaction. A more accurate measure is obtained without squaring this combination.

Found in

• MEMBERS SUBJECTED TO TORSION AND COMBINED TORSION, FLEXURE, SHEAR, AND/OR AXIAL FORCE