This set of Design of Steel Structures Multiple Choice Questions & Answers (MCQs) focuses on “Local Buckling of Plates”.

1. Buckling occurs to members or elements mainly subjected to ________

a) seismic forces

b) tensile forces

c) compressive forces

d) shear forces

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Explanation: Buckling may be defined as structural behavior in which mode of deformation develops in direction or plane perpendicular to that of bending which produces it. Such deformation changes rapidly with increase in magnitude of applied loading. It occurs mainly members or elements that are subjected to compressive forces.

2. The critical stress of infinite plate having width b and thickness t loaded by compressive forces acting on simply supported sides is given by

a) (kπ^{2}E)/ [12(1-μ^{2})(b/t)].

b) (kπ^{2}E)/ [12(1-μ^{2})(b/t)^{2}].

c) (kπ^{2}E)/ [12(1+μ^{2})(b/t)].

d) (kπ^{2}E)/ [12(1+μ^{2})(b/t)^{2}].

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Explanation: The critical stress of infinite plate having width b and thickness t loaded by compressive forces acting on simply supported sides is given by

f

_{cr}= (kπ

^{2}E)/ [12(1-μ

^{2})(b/t)

^{2}],

where μ is Poisson’s ratio of material, b/t is width-to-thickness ratio of plate, k is buckling coefficient and E is Young’s modulus of rigidity of material. The value of coefficient k depends on constraints along non-loaded edges of plate.

3. Which of the following statement is correct?

a) stiffened elements are supported along one edge perpendicular to axial stress

b) un-stiffened elements are supported along one edge perpendicular to axial stress

c) stiffened elements are supported along one edge parallel to axial stress

d) un-stiffened elements are supported along one edge parallel to axial stress

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Explanation: Unstiffened elements are supported along one edge parallel to axial stress (eg : legs of single angles, flanges of beams, and stems of T-section). Stiffened elements are supported along both the edges parallel to axial stress (eg: flanges of square and rectangular hollow sections, perforated cover plates, and webs of I-sections and channel sections).

4. Lowest value of buckling coefficient for simply supported plates is _____

a) 4.0

b) 2.0

c) 5.0

d) 3.0

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Explanation: The lowest value of buckling coefficient for simply supported plates is 4.0. The buckilng stress depends upon buckling coefficient.

5. The buckling stress f_{cr} varies _____

a) inversely as plate slenderness or width-to-thickness ratio

b) directly as plate slenderness or width-to-thickness ratio

c) inversely as square of plate slenderness or width-to-thickness ratio

d) directly as square of plate slenderness or width-to-thickness ratio

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Explanation: The buckling stress f

_{cr}varies inversely as square of plate slenderness or width-to-thickness ratio, √(f

_{y}/f

_{cr}) = (b/t)√{(f

_{y}/ E)[12(1-μ

^{2})/(π

^{2}k)]} .

6. The buckling coefficient for thin flat plate free along one longitudinal edge is given by

a) k = 0.425 + (b/a)

b) k = 0.425 + (b/a)^{2}

c) k = 0.425 + (a/b)^{2}

d) k = 0.425 – (b/a)^{2}

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Explanation: For a thin plate simply supported along both transverse edged and one longitudinal edge and free along the other longitudinal edge, the buckling coefficient can be approximated by k = 0.425 + (b/a)

^{2}.

7. The elastic buckling stress of thin flat plate of length L, depth d and thickness t simply supported along four edges and loaded by shear stresses distributed uniformly along its edges is given by

a) f_{cr} = kπ^{2}E / [12(1-μ^{2})(d/t)^{2}].

b) f_{cr} = kπ^{2}E / [12(1+μ^{2})(d/t)^{2}].

c) f_{cr} = kπ^{2}E / [12(1-μ^{2})(d/t)].

d) f_{cr} = kπ^{2}E / [12(1+μ^{2})(d/t)].

View Answer

Explanation: The elastic buckling stress f

_{cr}of thin flat plate of length L, depth d and thickness t simply supported along all four edges and loaded by shear stresses distributed uniformly along its edges is given by f

_{cr}= kπ2E / [12(1-μ

^{2})(d/t)

^{2}], where buckling coefficient can be approximated by k=5.35 + 4(d/L)

^{2}, when L ≥ d and k = 5.35(d/L)2 + 4, when L ≤ d.

8. The elastic buckling stress for thin flat plate of length L, depth d and thickness t simply supported along four edges and loaded by bending stress distribution is given by

a) f_{cr} = π^{2}E/k[12(1-μ^{2})(d/t)^{2}].

b) f_{cr} = π^{2}E/k[12(1+μ^{2})(d/t)^{2}].

c) f_{cr} = kπ^{2}E/[12(1+μ^{2})(d/t)^{2}].

d) f_{cr} = kπ^{2}E/[12(1-μ^{2})(d/t)^{2}].

View Answer

Explanation: The elastic buckling stress for thin flat plate of length L, depth d and thickness t simply supported along all four edges and loaded by bending stress distribution, which varies linearly across its width is given by f

_{cr}= kπ

^{2}E/[12(1-μ

^{2})(d/t)

^{2}], where buckling coefficient k depends on aspect ratio L/d and the number of buckles along the plate.

9. Which of following statement is correct?

a) elastic buckling stress may be decreased by using longitudinal stiffeners

b) elastic buckling stress may be decreased by using intermediate stiffeners

c) elastic buckling stress may be increased by using intermediate transverse stiffeners

d) elastic buckling stress is not affected by intermediate or longitudinal stiffeners

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Explanation: The elastic buckling stress may be increased by using intermediate transverse stiffeners (which will decrease the aspect ratio L/d, thus increasing the value of buckling coefficient), or by using longitudinal stiffeners to decrease the depth-thickness ratio.

10. Match the following values of limiting b/t or d/t ratio for various cases

Plates (b/t))√(fy /250) or (d/t)√(fy /250) i. Simply supported plates A) 17.5 ii. Long plate elements in shear B) 131.4 iii. Long plate elements free along one longitudinal edge C) 81.9 iv. Long plate elements in bending D) 53.8

a) i-A, ii-B, iii-C, iv-D

b) i-D, ii-C, iii-A, iv-B

c) i-C, ii-D, iii-B, iv-A

d) i-D, ii-C, iii-B, iv-A

View Answer

Explanation: i) For simply supported plates, if material ceases to be linearly elastic at yield stress f

_{y}, the width-to-thickness ratio b/t is given by (b/t)√(f

_{y}/250) = 53.8

ii) For long plate elements simply supported along both transverse edges and one longitudinal edge and free along other longitudinal edge, elastic buckling stress is equal to yield stress if (b/t)√(f

_{y}/250) = 17.5

iii) The elastic buckling stress is equal to yield stress in shear τy = f

_{y}/√3 when (d/t)√(f

_{y}/250) = 81.9

iv) For long plates elements simply supported along four edges and loaded by bending stress distribution, limiting ratio d/t may be given as (d/t)√(f

_{y}/250) = 131.4.

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