250+ TOP MCQs on Web Panel Subjected to Shear and Answers

Design of Steel Structures Multiple Choice Questions 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
Answer: c
Clarification: 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
Answer: b
Clarification: 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_vτ_b
c) τ_b
d) A_v /τ_b
Answer: b
Clarification: 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_w²
d) f_yw/(√3 λ_w²)
Answer: d
Clarification: 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 < λwyw/(√3 λ_w²) 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
Answer: a
Clarification: 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_vπ²/[12(1+μ²)(d/t_w)²].
b) k_vπ²E/[12(1+μ²)(d/t_w)²].
c) k_vπ²E/[12(1-μ²)(d/t_w)²].
d) k_vE/[12(1-μ²)(d/t_w)].
Answer: c
Clarification: The elastic critical shear stress of the web is given by τ_cr,e = k_vπ²E/[12(1-μ²)(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)].
Answer: b
Clarification: 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
Answer: d
Clarification: 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_vτ_b
b) 0.9w_tft_wf_vsinφ
c) A_vτ_b – 0.9w_tft_wf_vsinφ
d) A_vτ_b + 0.9w_tft_wf_vsinφ
Answer: d
Clarification: In tension field method, the nominal shear strength is given by V_n = A_vτ_b + 0.9w_tftf_vsinφ, 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_yw²+3 τ_b²+Ψ²]^0.5+Ψ
b) [f_yw²-3 τ_b²+Ψ²]^0.5-Ψ
c) [f_yw²-3 τ_b²-Ψ²] -Ψ
d) [f_yw²+3 τ_b²+Ψ²]+Ψ
Answer: b
Clarification: The value of f_v in the nominal shear strength according to tension field method is given by f_v = [f_yw²-3 τ_b²+Ψ²]^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
Answer: a
Clarification: 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)
Answer: d
Clarification: 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
Answer: b
Clarification: 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_ywt_w)^0.5
b) s = (2/ sinφ)(M_fr/f_ywt_w)
c) s = (2/ sinφ)(M_fr/f_ywt_w)^0.5
d) s = (2/ sinφ)(M_frf_ywt_w)
Answer: c
Clarification: The anchorage length of tension field is s = (2/ sinφ)(M_fr/f_ywt_w)^0.5 where φ = inclination of tension field = tan^-1(d/c), c is spacing bet_ween 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_ween stiffeners.

15. Which of the following expression for reduced plastic moment capacity is correct?
a) M_fr = 0.25b_ft_f²f_yf {1-[N_f/( b_ft_ff_yf/γ_m0)²]}
b) M_fr = b_ft_ff_yf {1-[N_f/( b_ft_ff_yf/γ_m0)]}
c) M_fr = 0.25b_ft_f {1+[N_f/( b_ft_ff_yf/γ_m0)]}
d) M_fr = 0.25b_f {1+[N_f( b_ft_ff_yfγ_m0)²]}
Answer: a
Clarification: 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_ft_f²f_yf {1-[N_f/( b_ft_ff_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.