This set of Design of Steel Structures Multiple Choice Questions & Answers (MCQs) focuses on “Web Panel subjected to Shear”.

1. The shear capacity of web comprises of strength

a) before onset of buckling strength only

b) post buckling strength only

c) before onset of buckling strength and post buckling strength

d) compression strength

View Answer

Explanation: The shear capacity of web comprises of strength before onset of buckling strength and post buckling strength. strength before onset of buckling is contributed because of elastic behaviour wherein stresses are entirely elastic and the only requirement for the stiffeners is to keep the web flat.

2. What will happen when d/tw is sufficiently low?

a) web will yield under buckling before shear

b) web will yield under shear before buckling

c) web will not yield under shear

d) web will not yield under both shear and buckling

View Answer

Explanation: When d/tw ratio is sufficiently low, the elastic critical stress increases above the value of yield shear stress and the web will yield under shear before buckling.

3. The nominal shear strength according to simple post-critical method is given by

a) A_{v}

b) A_{v}τ_{b}

c) τ_{b}

d) A_{v} /τ_{b}

View Answer

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

_{n}= Avτb, where A

_{v}= area of web, τ

_{b}= shear stress corresponding to web buckling.

4. The value of τb in the nominal shear strength equation according to simple post-critical method is given by

a) f_{yw} / √ λ_{w}

b) f_{yw}/λ_{w}

c) f_{yw}/λ_{w}²

d) f_{yw}/(√3 λ_{w}²)

View Answer

Explanation: The value of τb in the nominal shear strength equation according to simple post-critical method is given by τ

_{b}= f

_{yw}/√3 for λ

_{w}≤0.8, [1-0.8(λ

_{w}-0.8)](f

_{yw}/√3) for 0.8 < λw<1.2, f

_{yw}/(√3 λ

_{w}²) for λ

_{w}≥1.2, where f

_{yw}is yield strength of web, λ

_{w}is non-dimensional web slenderness ratio for shear buckling stress.

5. The value of non-dimensional web slenderness ratio in the nominal shear strength equation according to simple post-critical method is given by

a) √(f_{yw}/(√3τ_{cr,e}))

b) (f_{yw}/(√3τ_{cr,e}))

c) (f_{yw}/(τ_{cr,e}))

d) (f_{yw}/(√3τ_{cr,e}))^{2}

View Answer

Explanation: The value of non-dimensional web slenderness ratio in the nominal shear strength equation according to simple post-critical method is given by λ

_{w}=√(f

_{yw}/(√3τ

_{cr,e})), where f

_{yw}is yield strength of web, τ

_{cr,e}is elastic critical shear stress of the web.

6. The elastic critical shear stress of the web is given by

a) k_{v}π^{2}/[12(1+μ^{2})(d/t_{w})^{2}].

b) k_{v}π^{2}E/[12(1+μ^{2})(d/t_{w})^{2}].

c) k_{v}π^{2}E/[12(1-μ^{2})(d/t_{w})^{2}].

d) k_{v}E/[12(1-μ^{2})(d/t_{w})].

View Answer

Explanation: The elastic critical shear stress of the web is given by τ

_{cr,e}= k

_{v}π

^{2}E/[12(1-μ

^{2})(d/t

_{w})

^{2}], where E is elastic modulus, μ is Poisson’s ratio, k

_{v}is constant which depends on spacing of transverse stiffeners and depth of web.

7. The value of k_{v} in the elastic critical shear stress equation for c/d < 1 is given by

a) 4.0 – [5.35/(c/d)].

b) 4.0 + [5.35/(c/d)^{2}].

c) 5.35 + [4/(c/d)^{2}].

d) 5.35 – [4/(c/d)].

View Answer

Explanation: The value of k

_{v}in the elastic critical shear stress equation is given by k

_{v}= 5.35 when transverse stiffeners are provided only at supports, k

_{v}= 4.0 + [5.35/(c/d)

^{2}] for c/d < 1.0, k

_{v}= 5.35 + [4/(c/d)

^{2}] for c/d ≥ 1.0, where c and d are spacing of transverse stiffeners and depth of web respectively.

8. Which of the following conditions are true when tension field method is used?

a) it is based on pre-buckling strength

b) c/d < 1.0

c) it may not be used for webs with intermediate stiffeners

d) it may be used for webs with intermediate stiffeners

View Answer

Explanation: The tension field method, based on the post-shear buckling strength, may be used for webs with intermediate transverse stiffeners at supports, provided the panels adjacent to the panel angle tension field action or the end posts provide anchorage for the tension field and is c/d>1.0.

9. What is the value of nominal shear strength according to tension field method?

a) A_{v}τ_{b}

b) 0.9w_{tf}t_{w}f_{v}sinφ

c) A_{v}τ_{b} – 0.9w_{tf}t_{w}f_{v}sinφ

d) A_{v}τ_{b} + 0.9w_{tf}t_{w}f_{v}sinφ

View Answer

Explanation: In tension field method, the nominal shear strength is given by V

_{n}= A

_{v}τ

_{b}+ 0.9w

_{tf}t

_{v}sinφ, where A

_{v}is area of web, τ

_{b}is buckling strength or shear stress corresponding to web buckling, f

_{v}is yield strength of tension field which depends on inclination of tension field, w

_{tf}is the width of tension field, t

_{w}is width of web.

10. The value of fv in the nominal shear strength according to tension field method is given by

a) [f_{yw}^{2}+3 τ_{b}^{2}+Ψ^{2}]^{0.5}+Ψ

b) [f_{yw}^{2}-3 τ_{b}^{2}+Ψ^{2}]^{0.5}-Ψ

c) [f_{yw}^{2}-3 τ_{b}^{2}-Ψ^{2}] -Ψ

d) [f_{yw}^{2}+3 τ_{b}^{2}+Ψ^{2}]+Ψ

View Answer

Explanation: The value of f

_{v}in the nominal shear strength according to tension field method is given by f

_{v}= [f

_{yw}

^{2}-3 τ

_{b}

^{2}+Ψ

^{2}]

^{0.5}-Ψ , where f

_{yw}is yield stress of web, τ

_{b}is buckling strength or shear stress corresponding to web buckling, Ψ is a parameter which depends on inclination of tension field and buckling strength.

11. What is the expression for Ψ in the f_{v} for nominal shear strength according to tension field method is given by

a) 1.5 τ_{b} sin2φ

b) sin2φ

c) 1.5 τ_{b}

d) 1.5 τ_{b} /sin2φ

View Answer

Explanation: The value of Ψ in the f

_{v}for nominal shear strength according to tension field method is given by Ψ =1.5 τ

_{b}sin2φ, where τb is buckling strength or shear stress corresponding to web buckling, φ is inclination of tension field which depends on depth of web and spacing of stiffeners.

12. The inclination of tension field is

a) tan(c/d)

b) tan(d/c)

c) tan^{-1}(c/d)

d) tan^{-1}(d/c)

View Answer

Explanation: The inclination of tension field is given by φ = tan

^{-1}(d/c), where d is depth of web and c is spacing between stiffeners. The change in angle of inclination of tension field affects the width and yield strength of tension field.

13. Which of the following is an expression for width of tension field?

a) w_{tf} = d sinφ + (c-s_{c}-s_{t})cosφ

b) w_{tf} = d cosφ + (c-s_{c}-s_{t})sinφ

c) w_{tf} = d cosφ – (c+s_{c}-s_{t})sinφ

d) w_{tf} = d sinφ – (c+s_{c}-s_{t})cosφ

View Answer

Explanation: The width of tension field in the tension field action method is given by w

_{tf}= d cosφ + (c-s

_{c}-s

_{t})sinφ, where d is depth of beam, φ = inclination of tension field = tan

^{-1}(d/c), c is spacing between stiffeners, s

_{c}and s

_{t}are anchorage lengths of tension field along the compression and tension flanges respectively and depends on reduced plastic moment capacity, inclination of tension field, thickness of web and yield stress of web.

14. The anchorage length of tension field is

a) s = (2 sinφ)(M_{fr}/f_{yw}t_{w})^{0.5}

b) s = (2/ sinφ)(M_{fr}/f_{yw}t_{w})

c) s = (2/ sinφ)(M_{fr}/f_{yw}t_{w})^{0.5}

d) s = (2/ sinφ)(M_{fr}f_{yw}t_{w})

View Answer

Explanation: The anchorage length of tension field is s = (2/ sinφ)(M

_{fr}/f

_{yw}t

_{w})

^{0.5}where φ = inclination of tension field = tan

^{-1}(d/c), c is spacing bet

_{w}een stiffeners, d is depth of beam, M

_{fr}is reduced plastic moment capacity of the respective flange plate, f

_{yw}is yield stress of web and t

_{w}is thickness of web. The anchorage length should be less than or equal to spacing bet

_{w}een stiffeners.

15. Which of the following expression for reduced plastic moment capacity is correct?

a) M_{fr} = 0.25b_{f}t_{f}^{2}f_{yf} {1-[N_{f}/( b_{f}t_{f}f_{yf}/γ_{m0})^{2}]}

b) M_{fr} = b_{f}t_{f}f_{yf} {1-[N_{f}/( b_{f}t_{f}f_{yf}/γ_{m0})]}

c) M_{fr} = 0.25b_{f}t_{f} {1+[N_{f}/( b_{f}t_{f}f_{yf}/γ_{m0})]}

d) M_{fr} = 0.25b_{f} {1+[N_{f}( b_{f}t_{f}f_{yf}γ_{m0})^{2}]}

View Answer

Explanation: The reduced plastic moment capacity of respective flange plate is calculated after accounting for axial force in flange, due to overall bending and any external axial force in the cross section. It is given by M

_{fr}= 0.25b

_{f}t

_{f}

^{2}f

_{yf}{1-[N

_{f}/( b

_{f}t

_{f}f

_{yf}/γ

_{m0})

^{2}]}, where b

_{f}and t

_{f}are width and thickness of flange respectively, f

_{yf}is yield stress of flange and N

_{f}is the axial force in flange.

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