E3Flexural buckling of members without slender elements

This section applies to nonslender-element compression members, as defined in Section B4.1, for elements in axial compression.

User Note: When the torsional effective length is larger than the lateral effective length, Section E4 may control.

The nominal compressive strength, $P_{n}$, shall be determined based on the limit state of flexural buckling:

(E3-1)

The nominal stress, $F_{n}$, is determined as follows:

(a) When $\frac{L_{c}}{r} \leq 4.71 \sqrt{\frac{E}{F_{y}}}$ (or $\frac{F_{y}}{F_{e}} \leq 2.25$ )

(E3-2)

(b) When $\frac{L_{c}}{r}>4.71 \sqrt{\frac{E}{F_{y}}}$ (or $\frac{F_{y}}{F_{e}}>2.25$ )

(E3-3)

where

$A_{g}=$ gross area of member, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$

• E = modulus of elasticity of steel, ksi (MPa)
• = 29,000 ksi (200 000 MPa)

$F_{e}=$ elastic buckling stress determined according to Equation E3-4; or as specified in Appendix 7, Section 7.2.3(b); or through an elastic buckling analysis, as applicable, ksi (MPa)

(E3-4)

$\begin{aligned} F_{y} & =\text { specified minimum yield stress of the type of steel being used, ksi (MPa) } \\ r & =\text { radius of gyration, in. (mm) }\end{aligned}$

User Note: The two inequalities for calculating the limits of applicability of Sections E3(a) and E3(b), one based on $L_{c} / r$ and one based on $F_{y} / F_{e}$, provide the same result for flexural buckling.