8.4Shear

8.4.1.1

The shear area may be calculated as given below:

I and channel sections:

Major Axis Bending:

Hot-Rolled — $h t_{\mathrm{w}}$

Welded $\quad-d t_{\mathrm{w}}$

Minor Axis Bending:

Hot-Rolled or Welded — 2b $t_{f}$ Rectangular hollow sections of uniform thickness: Loaded parallel to depth (h) — $A h /(b+h)$ Loaded parallel to width (b) — $A b /(b+h)$ Circular hollow tubes of uniform thickness $— 2 A / \pi$ Plates and solid bars — $A$ where

$A=$ cross-section area,

$\begin{aligned} b & =\text { overall breadth of tubular section, breadt } \\ & \text { of I-section flanges, }\end{aligned}$

$d \quad=$ clear depth of the web between flanges

$h \quad=$ overall depth of the section

$\begin{aligned} t_{\mathrm{f}} & =\text { thickness of the flange, and } \\ t_{\mathrm{w}} & =\text { thickness of the web. }\end{aligned}$

NOTE — Fastener holes need not be accounted for in plastic design shear strength calculation provided that:

$A_{\mathrm{vn}} \geq\left(f_{\mathrm{y}} / f_{\mathrm{u}}\right)\left(\gamma_{\mathrm{ml}} / \gamma_{\mathrm{m} 0}\right) A_{\mathrm{v}} / 0.9$

If $A_{\mathrm{vn}}$ does not satisfy the above condition, the effective shear area may be taken as that satisfying the above limit. Block shear failure criteria may be verified at the end connections. Section 9 may be referred to for design strength under combined high shear and bending.

8.4.2.1

Resistance to shear buckling shall be verified as specified, when

$\frac{d}{t_{\mathrm{w}}}>67 \epsilon$ for a web without stiffeners, and

$>67 \varepsilon \sqrt{\frac{K_{\mathrm{v}}}{5.35}}$ for a web with stiffeners

where

$K_{\mathrm{v}}=$ shear buckling coefficient (see 8.4.2.2), and

$\varepsilon=\sqrt{250 / f_{y}}$

8.4.2.2

Shear buckling design method.

The nominal shear strength, $V_{\mathrm{n}}$, of webs with or without intermediate stiffeners as governed by buckling may be evaluated using one of the following methods:

a) Simple post-critical method — The simple post critical method, based on the shear buckling strength can be used for webs of I-section girders, with or without intermediate transverse stiffener, provided that the web has transverse stiffeners at the supports. The nominal shear strength is given by:

$V_{\mathrm{n}}=V_{\mathrm{cr}}$

where

$\begin{aligned} V_{\mathrm{cr}} & =\text { shear force corresponding to web } \\ & \text { buckling }\end{aligned}$

$=A_{\mathrm{v}} \tau$

where

$\tau_{\mathrm{b}}=$ shear stress corresponding to web buckling, determined as follows:

1. when $\lambda_{\mathrm{w}} \leq 0.8$ $\tau_{\mathrm{b}}=f_{\mathrm{yw}} / \sqrt{3}$

2. when $0.8<\lambda_{\mathrm{w}}<1.2$ $\tau_{\mathrm{b}}=\left[1-0.8\left(\lambda_{\mathrm{w}}-0.8\right)\right]\left(f_{\mathrm{yw}} / \sqrt{3}\right)$

3. when $\lambda_{\mathrm{w}} \geq 1.2 \quad \tau_{\mathrm{b}}=\mathrm{f}_{\mathrm{yw}} /\left(\sqrt{3} \lambda_{\mathrm{w}}^{2}\right)$ where

$\begin{aligned} \lambda_{w} & =\text { non-dimensional web slendernes } \\ & \text { ratio for shear buckling stress } \\ & \text { given by: }\end{aligned}$

$\lambda_{\mathrm{w}}=\sqrt{f_{\mathrm{yw}} /\left(\sqrt{3} \tau_{\mathrm{cr}, \mathrm{c}}\right)}$

$\mathrm{t}_{\mathrm{cr}, \mathrm{e}}=$ the elastic critical shear stress of the

$\operatorname{web}=\frac{K_{\mathrm{y}} \pi^{2} E}{12\left(1-\mu^{2}\right)\left[d / t_{\mathrm{w}}\right]^{2}}$

where

$\mu \quad=$ Poisson's ratio, and

$K_{y}=5.35$ when transverse stiffeners are provided only at supports

$=4.0+5.35 /(c / d)^{2}$ for $c / d<1.0$

• $\begin{aligned} & =5.35+4.0 /(c / d)^{2} \text { for } c / d \geq 1.0 \\ & \text { where } c, d \text { are the spacing of } \\ & \text { transverse stiffeners and depth of } \\ & \text { the web, respectively. }\end{aligned}$
• b) Tension field method — The tension field method, based on the post-shear buckling strength, may be used for webs with intermediate transverse stiffeners, in addition to the transverse stiffeners at supports, provided the panels adjacent to the panel under tension field action, or the end posts provide anchorage for the tension fields and if $c / d \geq 1.0$, where $c$, $d$ are the spacing of transverse stiffeners and depth of the web, respectively.

In the tension field method, the nominal shear resistance, $V_{\mathrm{n}}$, is given by:

$V_{\mathrm{n}}=V_{\mathrm{tf}}$

where

$V_{\mathrm{if}}=\left[A_{\mathrm{v}} \tau_{\mathrm{b}}+0.9 w_{\mathrm{if}} t_{\mathrm{w}} f_{\mathrm{v}} \sin \phi\right] \leq V_{\mathrm{p}}$

where

• τb = buckling strength, as obtained from 8.4.2.2(a)

$\begin{aligned} f_{\mathrm{y}} & =\text { yield strength of the tension field } \\ & \text { obtained from }\end{aligned}$

$=\left[f_{\mathrm{yw}}^{2}-3 \tau_{\mathrm{b}}^{2}+\psi^{2}\right]^{0.5}-\psi$

$\psi=1.5 \tau_{\mathrm{b}} \sin 2 \phi$

$\begin{aligned} \phi & =\text { inclination of the tension field } \\ & =\tan ^{-1}\left(\frac{d}{-}\right)\end{aligned}$

$\begin{aligned} w_{\mathrm{tf}} & =\text { the width of the tension field, given } \\ & \text { by: }\end{aligned}$

$=d \cos \phi+\left(c-s_{\mathrm{c}}-s_{\mathrm{t}}\right) \sin \phi$

$f_{\mathrm{yw}}=$ yield stress of the web

• $d \quad=$ depth of the web
• c = spacing of stiffeners in the web
• τb = shear stress corresponding to buckling of web 8.4.2.2(a)

$s_{\mathrm{c}}, s_{\mathrm{t}}=$ anchorage lengths of tension field along the compression and tension flange respectively, obtained from:

$s=\frac{2}{\sin \phi}\left[\frac{M_{\mathrm{fr}}}{f_{\mathrm{yw}} t_{\mathrm{w}}}\right]^{0.5} \leq c$

where

$M_{\mathrm{fr}}=$ reduced plastic moment capacity of the respective flange plate (disregarding any edge stiffener) after accounting for the axial force, $N_{\mathrm{f}}$ in the flange, due to overall bending and any external axial force in the cross-section, and is calculated as:

$M_{\mathrm{fr}}=0.25 b_{\mathrm{f}} t_{\mathrm{f}}^{2} f_{\mathrm{yf}}\left[1-\left\{N_{\mathrm{f}} /\left(b_{\mathrm{f}} t_{\mathrm{f}} f_{\mathrm{yf}} / \gamma_{\mathrm{m} 0}\right)\right\}^{2}\right]$

where

$b_{\mathrm{f}}, t_{\mathrm{f}}=$ width and thickness of the relevant flange respectively

= yield stress of the flange