Formulas: Doubly Symmetric Rolled Compact Members Subjected to Single-Axis Flexure and Compression

Formula 1

interaction equations for out-of-plane resistance for the case of a W27×84 (W690×125) beam-column, $L_{b}=10 \mathrm{ft}(3.1 \mathrm{~m})$ and $F_{y}=50 \mathrm{ksi}(345 \mathrm{MPa})$ , subjected to a linearly varying major-axis moment with zero moment at one end and maximum moment at the other end $\left(C_{b}=1.67\right)$ .

\left(C_{b}=1.67\right)

Equation C-H1-6

\left(\frac{M_{u}}{C_{b} \phi_{b} M_{n x}\left(C_{b}=1\right)}\right)^{-1} \leq\left(1-\frac{P_{u}}{\phi_{c} P_{n y}}\right)\left(1-\frac{P_{u}}{\phi_{c} P_{e z}}\right)

Formula 3

Equation H1-3 is obtained by substituting a lower bound of 2.0 for the ratio of the elastic torsional buckling resistance to the out-of-plane nominal flexural buckling resistance, $P_{e z} / P_{n y}$ , for W-shape members with $L_{c y}=L_{c z}$ .

L_{c y}=L_{c z}

Formula 4

The 2005 AISC Specification (AISC, 2005b) assumed an upper bound, $P_{e z} / P_{n y}=\infty$ , in Equation C-H1-6 in the development of Equation H1-3 which led to some cases where the out-ofplane strength was overestimated.

P_{e z} / P_{n y}=\infty

Formula 5

In addition, the fact that the nominal out-of-plane flexural resistance term, $C_{b} M_{n x}\left(C_{b}=1\right)$ , may be larger than $M_{p}$ was not apparent in the 2005 AISC Specification.

C_{b} M_{n x}\left(C_{b}=1\right)

Found in

DOUBLY AND SINGLY SYMMETRIC MEMBERS SUBJECTED TO FLEXURE AND AXIAL FORCE