Formulas: Doubly and Singly Symmetric Members Subjected to Flexure and Compression

Equation C-H1-1

\frac{f_{a}}{F_{a}}+\frac{C_{m} f_{b}}{\left(1-\frac{f_{a}}{F_{e}^{\prime}}\right) F_{b}} \leq 1.0

\frac{P}{P_{y}}+\frac{8}{9} \frac{M_{p c}}{M_{p}}=1 \quad \text { for } \frac{P}{P_{y}} \geq 0.2

\frac{P}{2 P_{y}}+\frac{M_{p c}}{M_{p}}=1 \quad \text { for } \frac{P}{P_{y}}<0.2

For $0 \leq \frac{P}{P_{y}} \leq \frac{t_{w}\left(d-2 t_{f}\right)}{A}$ (for the plastic neutral axis in the web)

0 \leq \frac{P}{P_{y}} \leq \frac{t_{w}\left(d-2 t_{f}\right)}{A}

\frac{M_{p c}}{M_{p}}=1-\frac{A^{2}\left(\frac{P}{P_{y}}\right)^{-}}{4 t_{w} Z_{x}}

For $\frac{t_{w}\left(d-2 t_{f}\right)}{A}<\frac{P}{P_{y}} \leq 1$ (for the plastic neutral axis in the flange)

\frac{t_{w}\left(d-2 t_{f}\right)}{A}<\frac{P}{P_{y}} \leq 1

\left.\frac{M_{p c}}{M_{p}}=\frac{A\left(1-\frac{P}{P_{y}}\right)}{2 Z_{x}}\right|_{d-\frac{A\left(1-\frac{P}{P_{y}}\right)}{2 b_{f}}}

For major-axis bending, an equation approximating the average yield strength of wide-flange shapes when $P \geq 0.15 P_{y}$ is given as

P \geq 0.15 P_{y}

\frac{M_{p c}}{M_{p}}=1.18\left(1-\frac{P}{P_{y}}\right) \leq 1

When $P<0.15 P_{y}, M_{p c}$ may be taken as $M_{p}$ .

P<0.15 P_{y}, M_{p c}

The normalized equations corresponding to the beam-column with length effects included are shown as Equation C-H1-5:

\frac{P_{u}}{P_{n}}+\frac{8}{9} \frac{M_{u}}{M_{n}}=1 \quad \text { for } \frac{P_{u}}{P_{n}} \geq 0.2

\frac{P_{u}}{2 P_{n}}+\frac{M_{u}}{M_{n}}=1 \quad \text { for } \quad \frac{P_{u}}{P_{n}}<0.2