# D8.A.2.5 Shear

The design capacities of the section against shear force in major- and minor-axis directions are evaluated as per section 8.4 of the code, taking care of the following phenomena:

• Nominal Plastic Shear Resistance

• Resistance to Shear Buckling

Shear area of the sections are calculated as per sec. 8.4.1.1. The full cross-sectional area is considered as the shear area for a solid rod section.

Nominal plastic shear resistance is calculated as per sec. 8.4.1.

Among shear buckling design methods, Simple post-critical method is adopted as per sec. 8.4.2.2(a).

## Working Stress Design

The actual shear stress is determined about the major and minor axes, respectively:

τbY = FY / AY

τbZ = FZ / AZ

The permissible shear stress is determined as:

1. When subjected to pure shear:

τab = 0.40 · Fy

2. When subjected to shear buckling:

τab = 0.70 · Vn · Av

where
 Vn = Nominal Shear Strength as per Clause 8.4.2.2.(a) = Vcr = τb · Av Av = AY or AZ, whichever is appropriate, with reference to Clause 8.4.1.1.

Shear buckling must be checked when (d/ tw) > 67 · ϵw for webs without stiffener or (d/tw) > 67 · ϵw · √(Kv/5.35) for webs with stiffeners.

where
 d = Clear Depth of Web between Flanges. tw = Thickness of Web. ϵw = √ ( 250 / Fy ) Fy = Yield Strength of Web, specified using the FYLD parameter. Kv = Shear Buckling Coefficient: = 5.35, when transverse stiffeners are provided only at supports. = 4.0 + 5.35 / (c/d)2 for (c/d) < 1.0 = 5.35 + 4.0 / (c/d)2 for (c/d) ≥ 1.0 c = Spacing of Transverse Stiffeners μ = Poisson’s Ratio τb = Shear Stress corresponding to Web-buckling: = Fy / √3, when, λw ≤ 0.8 = ( 1 – 0.8 · (λw - 0.8) ) · (Fy / √3) when, 0.8 < λw < 1.2 = Fy / (√3 · λw 2 ) when, λw ≥ 1.2 τcr,e = The Elastic Critical Shear Stress of the Web

τcr,e = (Kv · π2 · E) / (12 · (1 – μ2 ) · (d/tw)2 )

where
 λw = Non-dimensional Web Slenderness Ratio for Shear Buckling Stress. λw = [Fy / (√3 · τcr,e)]1/2

## Slender Sections

Slender sections should be verified against shear buckling resistance if d/tw > 67 · ε for web without stiffeners or if it exceeds 67 · ε · √(Kv⁄5.35) for a web with stiffeners.

Design methods for resistance to shear buckling are described in clause 8.4.2.2 of IS:800-2007 code.

Vn = Vcr

where
 Vcr = shear force corresponding to web buckling= Av · τb τb = shear stress corresponding to web buckling, determined as follows: When λw ≤ 0.8 τb= fyw⁄√3 When 0.8 < λw < 1.2 τb= [1 - 0.8(λw - 0.8) ](fyw⁄√3) When λw ≥ 1.2 τb= fyw⁄((√3 λw 2 ) ) λw = non-dimensional web slenderness ratio or shear buckling stress, given by: = [ fyw⁄(√3 τcr,e )]1/2 τcr,e = elastic critical shear stress of the web = (kv·π2·E)/[12·(1 - μ2 ) (d⁄tw)2] μ = Poisson’s ratio Kv = 5.35 when transverse stiffeners are provided only at supports = 4.0 + 5.35/(c/d)2 for c/d < 1.0 = 5.35 + 4.0/(c/d)2 for c/d ≥ 1.0 c = spacing of transverse stiffeners d = depth of the web