C-G3G3 Single angles and tees

Shear stresses in single-angle members and tee stems are the result of the gradient of the bending moment along the length (flexural shear) and the torsional moment.

For angles, the maximum elastic stress due to flexural shear is

$f_{v}=\frac{1.5 V_{b}}{b t}$ (C-G3-1)

where $V_{b}$ is the component of the shear force parallel to the angle leg with width $b$ and thickness $t$. The stress is constant throughout the thickness and it should be calculated for both legs to determine the maximum. The coefficient 1.5 is the calculated value for equal-leg angles loaded along one of the principal axes. For equal-leg angles loaded along one of the geometric axes, this factor is 1.35 . Factors between these limits may be calculated conservatively from $V_{b} Q / I t$ to determine the maximum stress at the neutral axis. Alternatively, if only flexural shear is considered, a uniform flexural shear stress in the leg of $V_{b} / b t$ may be used due to inelastic material behavior and stress redistribution.

If the angle is not laterally braced against twist, a torsional moment is produced equal to the applied transverse load times the perpendicular distance, $e$, to the shear center, which is at the point of intersection of the centerlines of the two legs. Torsional moments are resisted by two types of shear behavior: pure torsion (St. Venant torsion) and warping torsion (Seaburg and Carter, 1997). The shear stresses due to restrained warping are small compared to the St. Venant torsion (typically less than $20 \%$ ) and they can be neglected for practical purposes. The applied torsional moment is then resisted by pure shear stresses that are constant along the width of the leg (except for localized regions at the toe of the leg), and the maximum value can be approximated by

(C-G3-2)

where

A = area of angle, in.² (mm²)

= torsional constant [approximated by $\Sigma\left(b t^{3} / 3\right)$ when precomputed value is unavailable], in. ${ }^{4}\left(\mathrm{~mm}^{4}\right)$

$M_{T}=$ torsional moment, kip-in. (N-mm)

For a study of the effects of warping, see Gjelsvik (1981). Torsional moments from laterally unrestrained transverse loads also produce warping normal stresses that are superimposed on the bending stresses. However, because the warping strength of single angles is relatively small, this additional bending effect, just like the warping shear effect, can be neglected for practical purposes.