Formulas: flexural buckling of members without slender elements

Equation E3-1

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

P_{n}=F_{n} A_{g}

Formula 2

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

\frac{L_{c}}{r} \leq 4.71 \sqrt{\frac{E}{F_{y}}}

Formula 3

\frac{F_{y}}{F_{e}} \leq 2.25

Equation E3-2

F_{n}=\left(0.658 \frac{F_{y}}{F_{c}}\right) F_{y}

Formula 5

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

\frac{L_{c}}{r}>4.71 \sqrt{\frac{E}{F_{y}}}

Formula 6

\frac{F_{y}}{F_{e}}>2.25

Equation E3-3

F_{n}=0.877 F_{e}

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)

Found in

FLEXURAL BUCKLING OF MEMBERS WITHOUT SLENDER ELEMENTS