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:
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Nominal Plastic Shear Resistance
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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:
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When subjected to pure shear:
τab = 0.40 · Fy
-
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