G2I-shaped members and channels

This section addresses the determination of shear strength for I-shaped members and channels. Section G2.1 is applicable for webs with and without transverse stiffeners. Alternatively, Sections G2.2 and G2.3 are permitted to be used for webs with transverse stiffeners.

G2.1 Shear Strength of Webs

The nominal shear strength, $V_{n}$, is

$V_{n}=0.6 F_{y} A_{w} C_{v 1}$

(G2-1)

where

$\begin{aligned} F_{y} & =\text { specified minimum yield stress of the type of steel being used, ksi (MPa) } \\ A_{w} & =\text { area of web, the overall depth times the web thickness, } d t_{w}, \text { in. }^{2}\left(\mathrm{~mm}^{2}\right)\end{aligned}$

(a) For webs of rolled I-shaped members with $h / t_{w} \leq 2.24 \sqrt{E / F_{y}}$ $\phi_{v}=1.00$ (LRFD) $\Omega_{v}=1.50$ (ASD)

and

(G2-2)

where

$\begin{aligned} E & =\text { modulus of elasticity of steel } \\ & =29,000 \mathrm{ksi}(200000 \mathrm{MPa}) \\ h & =\text { clear distance between flanges less the fillet at each flange, in. (mm) } \\ t_{w} & =\text { thickness of web, in. (mm) }\end{aligned}$

User Note: All current ASTM A6/A6M W, S, and HP shapes except W44×230, W40×149, W36×135, W33×118, W30×90, W24×55, W16×26, and W12×14 meet the criteria stated in Section G2.1(a) for $F_{y}=50 \mathrm{ksi}(345 \mathrm{MPa})$.

• (b) For all other I-shaped members and channels
• (1) The web shear strength coefficient, $C_{\mathrm{v} 1}$, is determined as follows:

(i) When $h/t_{w}\leq1.10\sqrt{k_{v}E/F_{y}}$ $C_{v1}=1.0$ (G2-3)

where $h$ = for built-up welded sections, the clear distance between flanges, in. (mm) = for built-up bolted sections, the distance between fastener lines, in. (mm)

(ii) When $h/t_{w}>1.10\sqrt{k_{v}E/F_{y}}$ $C_{v1}=\frac{1.10\sqrt{k_{v}E/F_{y}}}{h/t_{w}}$ (G2-4)

• (2) The web plate shear buckling coefficient, $k_{\mathrm{v}}$, is determined as follows:
• (i) For webs without transverse stiffeners

$k_{y}=5.34$

(ii) For webs with transverse stiffeners $k_{v}$ : $=5+\frac{5}{(a/h)^{2}}$ (G2-5) $=5.34$ when $a/h\ >3.0$

where

$a=$ clear distance between transverse stiffeners, in. (mm)

User Note: $C_{v 1}=1.0$ for all ASTM A6/A6M W, S, M, and HP shapes except M12.5×12.4, M12.5×11.6, M12×11.8, M12×10.8, M12×10, M10×8, and M10×7.5, when $F_{y}=50 \mathrm{ksi}(345 \mathrm{MPa})$.

G2.2 Shear Strength of Interior Web Panels with $a / h \leq 3$ Considering Tension Field Action

The nominal shear strength, $V_{n}$, is determined as follows:

(a) When $h / t_{w} \leq 1.10 \sqrt{k_{y} E / F_{y}}$

(G2-6)

(b) When $h / t_{w}>1.10 \sqrt{k_{\mathrm{v}} E / F_{\mathrm{y}}}$ (1) When $2 A_{w} /\left(\left.A_{f c}+A_{f t}\right)\right) \leq 2.5, h / b_{f c} \leq 6.0$, and $h / b_{f t} \leq 6.0$

(1) When $2 A_{w} /\left(A_{f c}+A_{f t}\right) \leq 2.5, h / b_{f c} \leq 6.0$, and $h / b_{f t} \leq 6.0$

(G2-7)

(2) Otherwise

(G2-8)

where

the web shear buckling coefficient, $C_{\mathrm{v} 2}$, is determined as follows:

When $h / t_{w} \leq 1.10 \sqrt{k_{v} E / F_{y}}$

(G2-9)

(ii) When $1.10 \sqrt{k_{\mathrm{y}} E / F_{\mathrm{y}}} < h / t_{\mathrm{w}} \leq 1.37 \sqrt{k_{\mathrm{y}} E / F_{\mathrm{y}}}$

(G2-10)

(iii) When $h / t_{w}>1.37 \sqrt{k_{y} E / F_{y}}$

(G2-11)

$\begin{aligned} A_{f c} & =\text { area of compression flange, in. }^{2}\left(\mathrm{~mm}^{2}\right) \\ A_{f t} & =\text { area of tension flange, in. }^{2}\left(\mathrm{~mm}^{2}\right) \\ b_{f c} & =\text { width of compression flange, in. (mm) } \\ b_{f t} & =\text { width of tension flange, in. (mm) } \\ k_{v} & \text { is as defined in Section G2.1(b)(2) }\end{aligned}$

The nominal shear strength is permitted to be taken as the larger of the values from Sections G2.1 and G2.2.

User Note: Section G2.1 may predict a higher strength for members that do not meet the requirements of Section G2.2(b)(1).

G2.3 Shear Strength of End Web Panels with $a / h \leq 3$ Considering Tension Field Action

• (a) The nominal shear strength for I-shaped members with equal flange areas in the end panel, $V_{n}$, is

(G2-12)

where

(G2-13)

$F_{\mathrm{yw}}=$ specified minimum yield stress of the web material, ksi (MPa)

• $M_{p f}=$ plastic moment of a section composed of the flange and a segment of the web with the depth, $d_{e}$, kip-in. (N-mm)

$M_{p m}=\operatorname{smaller}$ of $M_{p f}$ and $M_{p s t}$, kip-in. (N-mm)

• $M_{p s t}=$ plastic moment of a section composed of the end stiffener plus a length of web equal to $d_{e}$ plus the distance from the inside face of the stiffener to the end of the beam, except that the distance from the inside face of the stiffener to the end of the beam shall not exceed $0.84 t_{w} \sqrt{E / F_{y}}$ for calculation purposes, kip-in. (N-mm)
• (i) When $C_{v 2} \leq 0.8$

(G2-14)

• (ii) When $C_{v 2}>0.8$

(G2-15)

The flexural stress in the tension flange, $\alpha M_{r} / S_{x t}$, in the end panel shall not be larger than $0.35 F_{y}$,

where

$\alpha=1.0$ (LRFD); $\alpha=1.6$ (ASD)

• (b) The nominal shear strength for I-shaped members with unequal flange areas shall be determined by analysis.

User Note: An approach for I-shaped members with unequal flange areas is discussed in the Commentary.

G2.4 Transverse Stiffeners

For transverse stiffeners, the following shall apply.

• (a) Transverse stiffeners are not required where $h / t_{w} \leq 2.54 \sqrt{E / F_{y}}$, or where the available shear strength provided in accordance with Section G2.1 for $k_{y}=5.34$ is greater than the required shear strength.
• (b) Transverse stiffeners are permitted to be stopped short of the tension flange, provided bearing is not needed to transmit a concentrated load or reaction. The weld by which transverse stiffeners are attached to the web shall be terminated not less than four times nor more than six times the web thickness from the near toe of the web-to-flange weld or web-to-flange fillet. When stiffeners are used, they shall be detailed to resist twist of the compression flange.
• (c) Bolts connecting stiffeners to the girder web shall be spaced not more than 12 in. (300 mm) on center. If intermittent fillet welds are used, the clear distance between welds shall not be more than 16 times the web thickness nor more than 10 in. (250 mm).

(d) $\left(b / t\right)_{s t} \leq 0.56 \sqrt{\frac{E}{F_{y s t}}}$ (G2-16)

(e) $I_{s t} \geq I_{s t 2}+\left(I_{s t 1}-I_{s t 2}\right) \rho_{w}$ (G2-17)

where

• $\begin{aligned} F_{y s t} & =\text { specified minimum yield stress of the stiffener material, ksi (MPa) }\end{aligned}$
• $\begin{aligned} I_{s t} & =\text { moment of inertia of the transverse stiffeners about an axis in the web } \\ & \text { center for stiffener pairs, or about the face in contact with the web plate } \\ & \text { for single stiffeners, in. }^{4}\left(\mathrm{~mm}^{4}\right)\end{aligned}$
• $\begin{aligned} I_{s t 1} & =\text { minimum moment of inertia of the transverse stiffeners required for } \\ & \text { development of the full shear post-buckling resistance of the stiffened } \\ & \text { web panels, } V_{r}=V_{c 1}, \text { in. }^{4}\left(\mathrm{~mm}^{4}\right)\end{aligned}$

(G2-18)

• $\begin{aligned} I_{s t 2} & =\text { minimum moment of inertia of the transverse stiffeners required for } \\ & \text { development of the web shear buckling resistance, } V_{r}=V_{c 2}, \text { in. }^{4}\left(\mathrm{~mm}^{4}\right)\end{aligned}$

(G2-19)

• $\begin{aligned} V_{c 1} & =\text { available shear strength calculated with } V_{n} \text { as defined in Section G2.1 or } \\ & \text { G2.2, as applicable, kips (N) }\end{aligned}$
• $\begin{aligned} V_{c 2} & =\text { available shear strength, kips (N), calculated with } V_{n}=0.6 F_{y} A_{w} C_{v 2}\end{aligned}$
• $\begin{aligned} V_{r} & =\text { required shear strength in the panel being considered, kips (N) }\end{aligned}$
• $\begin{aligned} b_{p} & =\text { smaller of the dimensions } a \text { and } h, \text { in. (mm) }\end{aligned}$

$\left(b / t\right)_{s t}=$ width-to-thickness ratio of the stiffener

$\rho_{s t} \quad=$ larger of $F_{y w} / F_{y s t}$ and 1.0

$\begin{aligned} \rho_{w} & =\text { maximum shear ratio, } \frac{V_{r}-V_{c 2}}{V_{c 1}-V_{c 2}} \geq 0 \text { within the web panels on each side } \\ & \text { of the transverse stiffener }\end{aligned}$

User Note: $I_{s t}$ may conservatively be taken as $I_{s t 1}$. Equation G2-18 provides the minimum stiffener moment of inertia required to attain the web shear postbuckling resistance according to Sections G2.1 and G2.2, as applicable. If less post-buckling shear strength is required, Equation G2-17 provides a linear interpolation between the minimum moment of inertia required to develop web shear buckling and that required to develop the web shear post-buckling strength.