Formulas: Classification of Sections for Local Buckling

Formula 1

The maximum limit of 0.76 corresponds to $F_{c r}=0.69 E / \lambda^{2}$ , which was used as the local buckling strength in earlier editions of both the ASD and LRFD Specifications.

F_{c r}=0.69 E / \lambda^{2}

Formula 2

Because of web-flange interactions, it is possible to get $k_{c}<0.42$ from the $k_{c}$ formula.

k_{c}<0.42

Formula 3

If $h / t_{w}>5.70 \sqrt{E / F_{y}}$ , use $h / t_{w}=5.70 \sqrt{E / F_{y}}$ in the $k_{c}$ equation, which corresponds to the 0.35 limit.

h / t_{w}>5.70 \sqrt{E / F_{y}}

Formula 4

h / t_{w}=5.70 \sqrt{E / F_{y}}

Formula 5

Excluding the use of round HSS with $D / t>0.45 E / F_{y}$ was also recommended in Schilling (1965).

D / t>0.45 E / F_{y}

Formula 6

The values of the limiting ratios, $\lambda_{p}$ and $\lambda_{r}$ , specified in Table B4.1b are similar to those in the 1989 Specification for Structural Steel Buildings-Allowable Stress Design and Plastic Design (AISC, 1989) and Table 2.3.3.3 of Galambos (1978), except that $\lambda_{p}=0.38 \sqrt{E / F_{y}}$ , limited in Galambos (1978) to determinate beams and to indeterminate beams when moments are determined by elastic analysis, was adopted for all conditions on the basis of Yura et al.

\lambda_{p}=0.38 \sqrt{E / F_{y}}

Formula 7

Since 2005, the $\lambda_{p}$ limit for webs in rectangular HSS flexural members (Case 19 in Table B4.1b) has been reduced from $\lambda_{p}=3.76 \sqrt{E / F_{y}}$ to $\lambda_{p}=2.42 \sqrt{E / F_{y}}$ based on the work of Wilkinson and Hancock (1998, 2002).

\lambda_{p}=3.76 \sqrt{E / F_{y}}

Formula 8

\lambda_{p}=2.42 \sqrt{E / F_{y}}

Equation C-B4-1

F_{c r}=k \frac{\pi^{2} E}{12\left(1-\nu^{2}\right)}\left(\frac{t}{b}\right)^{2}

Found in

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