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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:

  1. When λw ≤ 0.8

    τb= fyw⁄√3

  2. When 0.8 < λw < 1.2

    τb= [1 - 0.8(λw - 0.8) ](fyw⁄√3)

  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
Parent topic: D8.A.2 Design Process