H3Members subjected to torsion and combined torsion, flexure, shear, and/or axial force

H3.1 Round and Rectangular HSS Subjected to Torsion

The design torsional strength, $\phi_{T} T_{n}$, and the allowable torsional strength, $T_{n} / \Omega_{T}$, for round and rectangular HSS according to the limit states of torsional yielding and torsional buckling shall be determined as follows:

(H3-1)

where

$C=\mathrm{HSS}$ torsional constant, in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$

The critical stress, $F_{c r}$, shall be determined as follows:

(a) For round HSS, $F_{c r}$ shall be the larger of

and

Figure description:

• Formula (H3-2b: $F_{cr} = \frac{0.60E}{(D/t^{3/2}}$
• Condition: $F_{cr}$ shall not exceed $0.6F_y$
• Key Entities:
  • $F_{cr}$: Critical stress
  • $E$: Modulus of elasticity
  • $D$: Outside diameter of round HSS
  • $t$: Design wall thickness
  • $F_y$: Specified minimum yield stress

but shall not exceed $0.6 F_{y}$,

where

$D=$ outside diameter, in. (mm)

$L=$ length of member, in. (mm)

$t \quad=$ design wall thickness defined in Section B4.2, in. (mm)

(b) For rectangular HSS

(1) When $h / t \leq 2.45 \sqrt{E / F_{y}}$

(H3-3)

(2) When $2.45 \sqrt{E / F_{\mathrm{y}}} < h / t \leq 3.07 \sqrt{E / F_{\mathrm{y}}}$

(H3-4)

(3) When $3.07 \sqrt{E / F_{y}}<h / t \leq 260$

(H3-5)

where

$h=$ flat width of longer side, as defined in Section B4.1b(d), in. (mm)

User Note: The torsional constant, C, may be conservatively taken as:

For round HSS: $C=\frac{\pi(D-t)^{2} t}{2}$

For rectangular HSS: $C=2(B-t)(H-t) t-4.5(4-\pi) t^{3}$

H3.2 HSS Subjected to Combined Torsion, Shear, Flexure, and Axial Force

When the required torsional strength, $T_{r}$, is less than or equal to $20 \%$ of the available torsional strength, $T_{c}$, the interaction of torsion, shear, flexure, and axial force for HSS may be determined by Section H1 and the torsional effects may be neglected. When $T_{r}$ exceeds $20 \%$ of $T_{c}$, the interaction of torsion, shear, flexure, and/or axial force shall be limited, at the point of consideration, by

(H3-6)

where

$V_{r} / V_{c}$ shall be taken as the larger value for the x- or y-axis and

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

• $\begin{aligned} P_{c} & =\text { available tensile or compressive strength, } \phi P_{n} \text { or } P_{n} / \Omega \text {, determined in } \\ & \text { accordance with Chapter D or E, kips (N) }\end{aligned}$

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

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

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

• $\begin{aligned} V_{c} & =\text { available shear strength, } \phi_{v} V_{n} \text { or } V_{n} / \Omega_{v} \text {, determined in accordance with } \\ & \text { Chapter G, kips (N) }\end{aligned}$

• $\begin{aligned} T_{r} & =\text { required torsional strength, determined in accordance with Chapter C, } \\ & \text { using LRFD or ASD load combinations, kip-in. (N-mm) }\end{aligned}$

• $\begin{aligned} T_{c} & =\text { available torsional strength, } \phi_{T} T_{n} \text { or } T_{n} / \Omega_{T} \text {, determined in accordance } \\ & \text { with Section H3.1, kip-in. (N-mm) }\end{aligned}$

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

• y = subscript relating symbol to minor-axis bending

User Note: All terms in Equations H3-6 are to be taken as positive.

H3.3 Non-HSS Members Subjected to Torsion and Combined Stress

The available torsional strength for non-HSS members shall be the lowest value obtained according to the limit states of yielding under normal stress, shear yielding under shear stress, or buckling, determined as follows:

$\phi_{T}=0.90$ (LRFD) $\quad \Omega_{T}=1.67$ (ASD)

• (a) For the limit state of yielding under normal stress

(H3-7)

(b) For the limit state of shear yielding under shear stress

(H3-8)

• (c) For the limit state of buckling

(H3-9)

where

$F_{c r}=$ buckling stress for the section as determined by analysis, ksi (MPa)