# Design of Steel Structures Questions and Answers – Behaviour and Ultimate Strength of Plates and Possible Failure Modes

This set of Design of Steel Structures online quiz focuses on “Behaviour and Ultimate Strength of Plates and Possible Failure Modes”.

1. What is the fundamental path in graph?
a) line along load axis up to P > Pcr
b) line along load axis up to P < Pcr
c) line along load axis up to P = Pcr
d) line along load axis up to P ≥ Pcr

Explanation: If axial load verses lateral displacement is plotted, we get a line along the load axis up to P=Pcr, this is called fundamental path.

2. Which of the following is true about secondary path?
a) lateral displacement increases indefinitely at constant load
b) lateral displacement decreases indefinitely at constant load
c) lateral displacement remains same at constant load
d) lateral displacement increases indefinitely and decreases at constant load

Explanation: When the axial load reaches the Euler bucking load, the lateral displacement increases indefinitely at constant load. This is called secondary path, which bifurcates from fundamental path at the buckling load.

3. Which of the following statement is true?
c) secondary path for a plate is unstable
d) secondary path for a plate is stable

Explanation: The secondary path shows that plate can carry loads higher than elastic critical load. The secondary path for a plate is stable.

4. What is apparent modulus of elasticity?
a) ratio of average strain carried by plate to average stress
b) ratio of average stress carried by plate to average strain
c) product of average strain carried by plate to average stress
d) product of average stress carried by plate to average strain

Explanation: Elastic post-buckling stiffness is measured in terms of apparent modulus of elasticity, E*. It is the ratio of average stress carried by plate to average strain. In most of the cases, the value of E* is in the range 0.408 – 0.5 E and may be approximately taken as 0.5E.

5. The effective width of hot-rolled and welded plates is given by
a) be/b = α √(fy/fcr)
b) be/b = α √(fcr x fy)
c) be/b = α √(fcr +fy)
d) be/b = α √(fcr/fy)

Explanation: The effective width of hot-rolled and welded plates is given by be/b = α √(fcr/fy), where α is the parameter that indicates the inclusions of influence of initial curvatures and residual stress. Generally α=0.65.
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6. The effective width of cold-formed steel sections is given by
a) be/b = (fcr/fy)[1-0.22√(fcr/fy)].
b) be/b = (fcr/fy)[1+0.22√(fcr/fy)].
c) be/b = (fy/fcr)[1-0.22√(fcr/fy)].
d) be/b = (fcr/fy)[1+0.22√(fy/fcr)].

Explanation: The effective width based on tests on cold-formed steel sections is given by be/b = (fcr/fy)[1-0.22√(fcr/fy)]. This formula was first adopted in AISC specification for light gauge cold-formed sections.

7. Which of the following is true about local buckling?
a) failure occurs by twisting of one or more individual elements of member
b) failure occurs by buckling of one or more individual elements of member
c) failure occurs by both buckling and twisting of one or more individual elements of member
d) cannot be prevented by selecting suitable width-to-thickness ratio of elements

Explanation: Local buckling is failure which occurs by buckling of one or more individual elements of member. It can be prevented by selecting suitable width-to-thickness ratio of elements.

a) yield stress + area of cross section
b) yield stress – area of cross section
c) yield stress / area of cross section
d) yield stress x area of cross section

Explanation: When length of column is relatively small and its component elements are prevented from local buckling, then column will be able to attain its full strength or squash load (squash load = yield stress x area of cross section).

9. What is overall flexural buckling?
a) failure occurs by excessive deflection in plane of weaker principal axis
b) failure occurs by excessive deflection in plane of stronger principal axis
c) failure occurs by twisting of member
d) failure caused by seismic load

Explanation: Overall flexural buckling is failure which occurs by excessive deflection caused by bending or flexure, about axis corresponding to weaker principal axis(minor) – one with smallest radius of gyration, largest slenderness ratio.

10. Which of the following is true about torsional buckling?
a) failure occurs by bending about shear centre in longitudinal axis
b) failure occurs when torsional rigidity of member is greater than bending rigidity
c) standard hot rolled shapes are not susceptible to torsional buckling
d) it cannot occur with doubly symmetric cross section

Explanation: In torsional buckling, failure occurs by twisting about shear centre in longitudinal axis. It occurs when torsional rigidity of member is appreciably smaller than bending rigidity. It can occur only with doubly symmetric cross section with very slender cross sectional elements. Standard hot rolled shapes are not susceptible to torsional buckling.

11. Which of the following is not a solution for torsional buckling?
a) increasing length of members subjected to torsion
b) by careful arrangement of members
c) by providing bracing to prevent lateral movement and twisting
d) box section fabricated by adding welding side plates to ISHB sections

Explanation: Torsional buckling can be prevented by careful arrangement of members, by providing bracing to prevent lateral movement and twisting. In situations where torsion is expected either a box section fabricated by adding welding side plates to ISHB sections or by shortening box section fabricated by adding welding side plates to ISHB sections becomes the solution.

12. Flexural torsional buckling cannot occur in ________
a) unsymmetrical members
b) cross section with one axis of symmetry
c) cross section with no axis of symmetry
d) doubly symmetric members

Explanation: Flexural torsional buckling is a combination of flexural and torsion buckling. The member bends and twists simultaneously. It can occur only with open sections that have unsymmetrical cross section – both with one axis of symmetry(eg: channels, double angled shapes) and those with no axis of symmetry (eg: unequal leg single angles). Since the shear centre and centroid coincide with each other, doubly symmetric or point symmetric open sections are not subjected to flexural torsional buckling. Close sections are also immune to flexural torsional buckling.

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