H1Doubly and singly symmetric members subjected to flexure and axial force

H1.1 Doubly and Singly Symmetric Members Subjected to Flexure and Compression

The interaction of flexure and compression in doubly symmetric members and singly symmetric members constrained to bend about a geometric axis (x and/or y) shall be limited by Equations H1-1a and H1-1b.

User Note: Section H2 may be used in lieu of the provisions of this section.

• (a) When $\frac{P_{r}}{P_{c}} \geq 0.2$

(H1-1a)

• (b) When $\frac{P_{r}}{P_{c}}<0.2$

(H1-1b)

where

• $\begin{aligned} P_{r} & =\text { required compressive strength, determined in accordance with Chapter C, } \\ & \text { using LRFD or ASD load combinations, kips (N) }\end{aligned}$

• $P_{c}=$ available compressive strength, $\phi_{c} P_{n}$ or $P_{n} / \Omega_{c}$, determined in accordance with Chapter E, kips (N)

• $M_{r}=$ required flexural strength, determined in accordance with Chapter C, using LRFD or ASD load combinations, kip-in. (N-mm)

• $M_{c}=$ available flexural strength, $\phi_{b} M_{n}$ or $M_{n} / \Omega_{b}$, determined in accordance with Chapter F, kip-in. (N-mm)

• $x \quad=$ subscript relating symbol to major-axis bending

• y = subscript relating symbol to minor-axis bending

User Note: All terms in Equations H1-1a and H1-1b are to be taken as positive.

H1.2 Doubly and Singly Symmetric Members Subjected to Flexure and Tension

The interaction of flexure and tension in doubly symmetric members and singly symmetric members constrained to bend about a geometric axis (x and/or y) shall be limited by Equations H1-1a and H1-1b,

where

• $P_{r}=$ required tensile strength, determined in accordance with Chapter C, using LRFD or ASD load combinations, kips (N)
• $P_{c}=$ available tensile strength, $\phi_{t} P_{n}$ or $P_{n} / \Omega_{t}$, determined in accordance with Chapter D, kips (N)

For doubly symmetric members, $C_{b}$ in Chapter F is permitted to be multiplied by $\sqrt{1+\frac{\alpha P_{r}}{P_{e y}}}$ when axial tension acts concurrently with flexure,

where

(H1-2)

• $\alpha=1.0$ (LRFD); $\alpha=1.6$ (ASD)
• $E \quad=$ modulus of elasticity of steel
• = 29,000 ksi (200 000 MPa)
• $I_{y}=$ moment of inertia about the y-axis, in. ${ }^{4}\left(\mathrm{~mm}^{4}\right)$
• $\begin{aligned} L_{b} & =\text { length between points that are either braced against lateral displacement } \\ & \text { of the compression flange or braced against twist of the cross section, in. }^{4} \\ & \text { (mm }^{4}\end{aligned}$

H1.3 Doubly Symmetric Rolled Compact Members Subjected to Single-Axis Flexure and Compression

For doubly symmetric rolled compact members, with the effective length for torsional buckling less than or equal to the effective length for y-axis flexural buckling, $L_{c z} \leq L_{c y}$, subjected to flexure and compression with moments primarily about their major axis, it is permissible to address the two independent limit states, in-plane instability and out-of-plane buckling or lateral-torsional buckling, separately in lieu of the combined approach provided in Section H1.1,

where

• $L_{c y}=$ effective length for buckling about the $y$-axis, in. (mm)

$L_{c z}=$ effective length for buckling about the longitudinal axis, in. (mm)

For members with $M_{r y} / M_{\mathrm{cy}} \geq 0.05$, the provisions of Section H1.1 shall be followed.

• (a) For the limit state of in-plane instability, Equations H1-1a and H1-1b shall be used with $P_{c}$ taken as the available compressive strength in the plane of bending and $M_{c x}$ taken as the available flexural strength based on the limit state of yielding.
• (b) For the limit state of out-of-plane buckling and lateral-torsional buckling

where

• $\begin{aligned} C_{b} & =\text { lateral-torsional buckling modification factor determined from Section } \\ & \text { F1 }\end{aligned}$
• $M_{c x}=$ available lateral-torsional strength for major-axis flexure determined in accordance with Chapter F using $C_{b}=1.0, \mathrm{kip} \cdot \mathrm{in} .(\mathrm{N}-\mathrm{mm})$
• $P_{\mathrm{cy}}=$ available compressive strength out of the plane of bending, kips (N)

User Note: In Equation H1-3, $C_{b} M_{c x}$ may be larger than $\phi_{b} M_{p x}$ (LRFD) or $M_{p x} / \Omega_{b}$ (ASD). All variables in Equation H1-3 are to be taken as positive. The yielding resistance of the beam-column is captured by Equations H1-1a and H1-1b.