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

1. What is lateral torsional buckling?

a) buckling of beam loaded in plane of its weak axis and buckling about its stronger axis accompanied by twisting

b) buckling of beam loaded in plane of its strong axis and buckling about its weaker axis accompanied by twisting

c) buckling of beam loaded in plane of its strong axis and buckling about its weaker axis and not accompanied by twisting

d) buckling of beam loaded in plane of its weak axis and buckling about its stronger axis and not accompanied by twisting

View Answer

Explanation: The buckling of beam loaded in plane of its strong axis and buckling about its weaker axis accompanied by twisting (torsion) is called as torsional buckling. The load at which such beam buckles can be much less than that causing full moment capacity to develop.

2. Critical bending moment capacity of a beam undergoing lateral torsional buckling is a function of

a) does not depend on anything

b) pure torsional resistance only

c) warping torsional resistance only

d) pure torsional resistance and warping torsional resistance

View Answer

Explanation: Critical bending moment capacity of a beam undergoing lateral torsional buckling is a function of pure torsional resistance and warping torsional resistance.

3. Elastic critical moment is given by

a) (π/L){√[(EI_{y}GI_{t}) + (πE/L)^{2}I_{w}I_{y}]}

b) (π/L){√[(EI_{y}GI_{t}) – (πE/L)^{2}I_{w}I_{y}]}

c) (π/L){√[(EI_{y}GI_{t}) + (πE/L) I_{w}I_{y}]}

d) (π/L){ [(EI_{y}GI_{t}) – (πE/L)^{2}I_{w}I_{y}]}

View Answer

Explanation: Elastic critical moment is given by M

_{cr}= (π/L){√[(EI

_{y}GI

_{t}) + (πE/L)2I

_{w}I

_{y}]}, where EI

_{y}= flexural rigidity(minor axis), GI

_{t}= torsional rigidity, I

_{t}= St.Venant torsion constant, I

_{w}= St.Venant warping constant, L = unbraced length of beam subjected to constant moment in plane of web.

4. Lateral torsional buckling is not possible to occur if

a) moment of inertia about bending axis is twice than moment of inertia out of plane

b) moment of inertia about bending axis is greater than moment of inertia out of plane

c) moment of inertia about bending axis is equal to or less than moment of inertia out of plane

d) moment of inertia about bending axis is equal to or greater than moment of inertia out of plane

View Answer

Explanation: I

_{t}is not possible for lateral torsional buckling to occur if moment of inertia of section about bending axis is equal to or less than moment of inertia out of plane.

5. Limit state of lateral torsion buckling is not applicable to

a) square shapes

b) doubly symmetric I shaped beams

c) I section loaded in plane of their webs

d) I section singly symmetric with compression flanges

View Answer

Explanation: Lateral torsional buckling is applicable to doubly symmetric I shaped beams, I section loaded in plane of their webs, I section singly symmetric with compression flanges. I

_{t}is not possible for lateral torsional buckling to occur if moment of inertia of section about bending axis is equal to or less than moment of inertia out of plane. So, limit state of lateral torsion buckling is not applicable for shapes bent about their minor axis for shapes with Iz ≤ I

_{y}or for circular or square shapes.

6. Which of the following assumptions were not made while deriving expression for elastic critical moment?

a) beam is initially undisturbed and without imperfections

b) behaviour of beam is elastic

c) load acts in plane of web only

d) ends of beam are fixed support

View Answer

Explanation: The following assumptions were made while deriving expression for elastic critical moment: (i) beam is initially undisturbed and without imperfections, (ii) behaviour of beam is elastic,(iii) beam is loaded with equal and opposite end moments in plane of web, (iv) load acts in plane of web only, (v) ends of beam are simply supported vertically and laterally, (vi) beam does not have residual stresses.

7. For different loading conditions, the equation of elastic critical moment is given by

a) M_{cr} = c_{1} (EI_{y}GI_{t}) γ

b) M_{cr} = c_{1} [(EI_{y}GI_{t})^{2}] γ

c) M_{cr} = c_{1} [√(EI_{y}GI_{t})] γ

d) M_{cr} = c_{1} (EI_{y} /GI_{t}) γ

View Answer

Explanation: For different loading conditions, the equation of elastic critical moment is given by M

_{cr}= c

_{1}[√(EI

_{y}GI

_{t})] γ, where c

_{1}= equivalent uniform moment factor or moment coefficient, EI

_{y}= flexural rigidity(minor axis), GI

_{t}= torsional rigidity, γ = (π/L){√[1 + (πE/L)

^{2}I

_{w}I

_{y}]}, I

_{t}= St.Venant torsion constant, I

_{w}= St.Venant warping constant, L = unbraced length of beam subjected to constant moment in plane of web.

8. Which of the following is not true about moment coefficient?

a) for torsionally simple supports the moment coefficient is greater than or equal to unity

b) for torsionally simple supports the moment coefficient is less than unity

c) moment coefficient accounts for the effect of differential moment gradient on lateral torsional buckling

d) it depends on type of loading

View Answer

Explanation: The moment coefficient accounts for the effect of differential moment gradient on lateral torsional buckling and depends on type of loading. For torsionally simple supports the moment coefficient is greater than or equal to unity.

9. √EI_{y}GI_{t} depends on

a) shape of beam only

b) material of beam only

c) shape and material of beam

d) does not depend on anything

View Answer

Explanation: √EI

_{y}GI

_{t}depends on shape and material of beam, where = flexural rigidity(minor axis), GI

_{t}= torsional rigidity.

10. Which of the following is true?

a) sections with greater lateral bending and torsional stiffness have great resistance to bending

b) sections with lesser lateral bending and torsional stiffness have great resistance to bending

c) sections with greater lateral bending and torsional stiffness have less resistance to bending

d) lateral instability of beam cannot be reduced by selecting appropriate shapes

View Answer

Explanation: Lateral instability of beam can be reduced by selecting appropriate shapes. Sections with greater lateral bending and torsional stiffness have great resistance to bending.

11. In the equation M_{cr} = c_{1} [√(EI_{y}GI_{t})] γ, γ depends on

a) load on beam

b) shape of beam

c) material of beam

d) length of beam

View Answer

Explanation: In the equation M

_{cr}= c

_{1}[√(EI

_{y}GI

_{t})] γ, c

_{1}varies with loading and support conditions, [√(EI

_{y}GI

_{t})] varies with material properties and shape of beam and γ varies with length of beam.

12. Which of the following is true?

a) long shallow girders have high warping stiffness

b) short and deep girders have very low warping resistance

c) long shallow girders have low warping stiffness

d) short and shallow girders have very low warping resistance

View Answer

Explanation: Short and deep girders have very high warping stiffness while long shallow girders have low warping stiffness or resistance.

13. Elastic critical moment for long shallow girders is given by

a) (π/L){√(EI_{y}GI_{t})}

b) (πL){√(EI_{y}GI_{t})}

c) (π/L){√(EI_{y} /GI_{t})}

d) (πL){√(EI_{y} /GI_{t})}

View Answer

Explanation: Long shallow girders have low warping stiffness or resistance. So, elastic critical moment for long shallow girders is given by (π/L){√(EI

_{y}GI

_{t})}, where EI

_{y}= flexural rigidity(minor axis), GI

_{t}= torsional rigidity, L = unbraced length of beam subjected to constant moment in plane of web.

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