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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.

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