This set of Advanced Design of Steel Structures Questions and Answers focuses on “Design Strength of Laterally Unsupported Beams – II”.

1. Imperfection factor for rolled section is

a) 0.1

b) 0.21

c) 2.1

d) 4.9

View Answer

Explanation: Imperfection factor for rolled section is 0.21. The imperfection factor takes into account all the relevant defects in real structure when considering buckling, geometric imperfections, eccentricity of applied loads and residual stresses. It depends on the buckling curve.

2. Imperfection factor for welded section is

a) 4.9

b) 0.21

c) 2.1

d) 0.49

View Answer

Explanation: Imperfection factor for welded section is 0.49. The imperfection factor depends on the buckling curve and takes into account all the relevant defects in real structure when considering buckling, geometric imperfections, eccentricity of applied loads and residual stresses.

3. Non-dimensional slenderness ratio is given by

a) λ_{LT} = √(β_{b}Z_{p}f_{y}/M_{cr})

b) λ_{LT} = √(β_{b}Z_{p}f_{y}M_{cr})

c) λ_{LT} = √(β_{b}Z_{p}/M_{cr})

d) λ_{LT} = √(β_{b}Z_{p}f_{y})

View Answer

Explanation: Non-dimensional slenderness ratio is given by λ

_{LT}= √(β

_{b}Z

_{p}f

_{y}/M

_{cr}), where β

_{b}= 1 for plastic and compact sections, β

_{b}= Ze/Z

_{p}for semi-compact sections, Ze = elastic section modulus, Z

_{p}= plastic section modulus, M

_{cr}is elastic critical moment.

4. The check for non- dimensional slenderness ratio is given by

a) λ_{LT} = 2.4 √(Zef_{y}/M_{cr})

b) λ_{LT} > 2 .4 √(Zef_{y}/M_{cr})

c) λ_{LT} ≤ 1.2 √(Zef_{y}/M_{cr})

d) λ_{LT} ≥ 1.2 √(Zef_{y}/M_{cr})

View Answer

Explanation: The non- dimensional slenderness ratio is given by λ

_{LT}= √(β

_{b}Z

_{p}f

_{y}/M

_{cr}). The check for it is given by λ

_{LT}≤ 1.2 √(Zef

_{y}/M

_{cr}), where Ze = elastic section modulus, M

_{cr}is elastic critical moment.

5. Which of the following relation is correct?

a) λ_{LT} = √(f_{y}/f_{cr,b})

b) λ_{LT} = f_{y}/f_{cr,b}

c) λ_{LT} = (f_{y}/f_{cr,b})^{2}

d) λ_{LT} = √(f_{y} f_{cr,b})

View Answer

Explanation: λ

_{LT}= √(β

_{b}Z

_{p}f

_{y}/M

_{cr}) = √(f

_{y}/f

_{cr,b}), where β

_{b}= 1 for plastic and compact sections, β

_{b}= Ze/Z

_{p}for semi-compact sections, Ze = elastic section modulus, Z

_{p}= plastic section modulus, M

_{cr}is elastic critical moment, f

_{cr,b}is extreme compressive elastic buckling stress.

6. The elastic critical moment is given by

a) M_{cr} = β_{b} f_{cr,b}

b) M_{cr} = β_{b}Z_{p} / f_{cr,b}

c) M_{cr} = β_{b}Z_{p}

d) M_{cr} = β_{b}Z_{p} f_{cr,b}

View Answer

Explanation: The elastic critical moment is given by M

_{cr}= √{[π

^{2}EI

_{y}/ L

^{2}M

_{LT}][ GIt + (π

^{2}EIw/L

^{2}

_{LT})]} = β

_{b}Z

_{p}f

_{cr,b}, I

_{y}= moment of inertia about minor axis, Iw = warping constant, It = St. Venant’s constant, G = Shear modulus.

7. Warping constant in elastic critical moment is given by

a) (1+β_{f})β_{f} I_{y} h^{2}_{f}

b) (1-β_{f})β_{f} I_{y} h^{2}_{f}

c) β_{f} I_{y} h^{2}_{f}

d) (1-β_{f})/β_{f} I_{y} h^{2}_{f}

View Answer

Explanation: Warping constant in elastic critical moment is given by Iw = (1-β

_{f})β

_{f}I

_{y}h

^{2}

_{f}, where β

_{f}is ratio of moment of inertia of compression flange to sum of moments of inertia of compression and tension flanges, I

_{y}= moment of inertia about minor axis, h

_{f}= centre-to-centre distance between flanges.

8. St. Venant’s constant is given by

a) ∑b_{i}t_{i}^{2}/3

b) ∑b_{i}t_{i}^{2}

c) ∑b_{i}t_{i}^{3}/3

d) ∑b_{i}t_{i}

View Answer

Explanation: St. Venant’s constant is given by It = ∑b

_{i}ti3/3. For open section (e.g. I -section) : It = 2bft3f/3 + bft3w/3.

9. The value of f_{cr,b} is given by

a) f_{cr,b} = [1.1π^{2}E/(L_{LT}/r_{y})^{2}]{1+1/20[(L_{LT}/r_{y})/(h_{f}/t_{f})]^{2}}

b) f_{cr,b} = [1.1π^{2}E/(L_{LT}/r_{y})]{1-1/20[(L_{LT}/r_{y})/(h_{f}/t_{f})]}

c) f_{cr,b} = [1.1π^{2}E/(L_{LT}/r_{y})^{2}]{1+1/20[(L_{LT}/r_{y})/(h_{f}/t_{f})]^{2}}^{0.5}

d) f_{cr,b} = [1.1π^{2}E/(L_{LT}/r_{y})^{2}]{1-1/20[(L_{LT}/r_{y})/(h_{f}/t_{f})]^{2}}^{0.5}

View Answer

Explanation: The value of f

_{cr,b}is given by f

_{cr,b}= [1.1π

^{2}E/(L

_{LT}/r

_{y})

^{2}]{1+1/20[(L

_{LT}/r

_{y})/(h

_{f}/t

_{f})]

^{2}}

^{0.5}, where r

_{y}= radius of gyration about weaker axis, L

_{LT}= effective length for lateral-torsional buckling, t

_{f}= thickness of flange, h

_{f}= centre-to-centre distance between flanges.

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