# Strength of Materials Questions and Answers – Euler’s Theory at Critical Load with Effective Length

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This set of Strength of Materials online test focuses on “Euler’s Theory at Critical Load with Effective Length”.

1. _____________ of column mainly depends upon end conditions.
b) Slenderness ratio
d) Effective length

Explanation: The effective length of a column with given end conditions is a length of an equivalent column of the same material and cross section with hinged ends. The effective length of the column mainly depends upon end conditions.

2. The hinged end is also known as ___________
a) Fixed end
b) Pinned end
c) Rigid end
d) Free end

Explanation: In hinged end case, the end is fixed in position only (but the direction is free). The deflection in the case of this end is zero. (y = 0). It is also known as “Pinned end”.

3. Long columns fail due to ____________
a) Direct stress
b) Buckling stress
c) Lateral stress
d) Tensile stress

Explanation: In long columns, direct stress is very small compared to the bending stresses. The long column commonly fails because of bending stress.
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4. In short columns, the slenderness ratio is less than __________
a) 32
b) 64
c) 56
d) 28

Explanation: The short column fails primarily due to direct stress. In short columns, the buckling stresses are very small compared to direct stresses. The short column is a column whose slenderness ratio is less than 32.

5. For ___________ columns, the slenderness ratio is more than 32 and less than 120.
a) Long
b) Short
c) Average
d) Medium

Explanation: Medium column is a column which fails either due to direct stress or buckling stress. For medium columns, the slenderness ratio is more than 32 and less than 120. For medium columns, the length is more than 8 times but less than 30 times their least lateral dimension.

6. Radius of gyration is denoted by __________
a) k
b) g
c) y
d) s

Explanation: The ratio of square root of the moment of inertia (I) to the cross sectional area(A) is called “radius of gyration”. It is denoted by “k” or “r”.
K = (I/A)1/2.

7. The __________ is the distance between Centres to centre of effective lateral ends.
a) Mean length
b) Stripped length
c) True length
d) Actual length

Explanation: The actual length of a column is defined as the distance between the centre to centre of effective lateral restraints (L).

8. The slenderness ratio is the ratio of effective length to least ______________
b) Actual length
d) Factor of safety

Explanation: The ratio of effective length to the least radius of gyration (k) is called the slenderness ratio. For good design purpose, the slenderness ratio should be as small as possible to an extent.

9. Which of the following is also known as the working load?

Explanation: A column and Strut can never be subjected to critical load and the column is subjected to less than a critical load. This load is phenomenally known as safe load or working load.

10. Factor of safety is a ratio of crippling load to __________ load.

Explanation: The ratio of crippling load to the safe load of a column is called a factor of safety.
• The safe load is obtained by dividing the critical load by a number (called factor of safety).

11. At ___________ load, the column is said to have developed an elastic instability.
a) Safe
b) Working
c) Factored
d) Crippling

Explanation: The load at which the column just buckles is called crippling load. The column is said to have developed an elastic instability, at this load. The buckling of a column takes place along least radius of gyration or least moment of inertia.

12. The value of _________ is relatively high for short columns.

Explanation: The load at which the column just bents or buckles is called buckling load or critical load or crippling load. The value of buckling load is low for long columns and relatively high for short columns.

13. The slenderness ratio is ________ to critical stress.
a) Directly proportional
b) Inversely proportional
c) Equal
d) Transverse

Explanation: As the slenderness ratio increases, the permissible stress or critical stress reduces. Consequently, the load carrying capacity also reduces. In this way, the slenderness ratio behaves inversely proportional to the critical stress induced.

14. For a given material length, end conditions and equal area the shape of the column which is most efficient as per Euler’s is _________
a) Square
b) Circular
c) I section
d) Tubular

Explanation: As the radius of gyration will be least along the major axis of cross section. For example rectangular column along y-axis; for a given area, the tubular section will have a maximum radius of gyration. It is more efficient than any other section.

15. What is the rankines constant for cast iron?
a) 1/2000
b) 1/2400
c) 1/1600
d) 1/1800

Explanation: Rankines constant for cast iron is 1/ 1600.

Material Rankine’s Constant
Wrought Iron 1/9000
Cast Iron 1/1600
Timber 1/750

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