ADVANCED STRENGTH OF MATERIALS UNIT :3

UNIT : 3 Columns
1) Define Column
The vertical compression member whose lateral dimensions are small when compared to
its length and if either ends are fixed (or) one hinged is known as Column.
2) Define Strut
A structural member whose lateral dimensions are small when compared to its length
and subjected to compressive force is known as Strut.
3) What are the types of Stresses causes for failure in a column?
Direct compressive stress
Buckling Stresses
Combined of Direct compressive stress and Buckling Stresses
4) Define Slenderness ratio
The ratio of length of a member to its least radius of gyration is known as Slenderness
ratio.
5) List out the factors which affect the strength of a column
Slenderness ratio
End conditions
6) Define Buckling
A long column when subjected to direct load deflects in lateral direction is known as
Buckling.
7) Define Critical load
Critical load is defined as the load at which the column is in neutral equilibrium.
8) What are the assumptions followed in Euler’s equation
1. The material of the column is homogenous.
2. The section of the column is uniform through out.
3. The column initially straight and loaded axially.
4. The effect of the direct axial stress is neglected.
5. The column fails by buckling only.

9) List out the end conditions in Euler’s theory
i. One end free and other end fixed
ii. Both ends are fixed
iii. Both ends are hinged
iv. One end fixed and other end hinged
10) What are the limitations of Euler’s theory?
1. It is not valid for steel column having slenderness ratio<80.
2. It does not take the direct stress. But in case of load it can withstand compression only.
11) What is beam column?
Column having transverse load in addition to the axial compressive load is termed as beam
column.
Ex: Engine Shaft, Wing of an air craft
12) Define thick cylinders
Thick cylinders are vessels, containing fluid under pressure and whose wall thickness is not
small (t≥d/20)
13) What are the assumptions followed in Lame’s equation
1. The material of the column is homogenous.
2. Plane section is perpendicular to the longitudinal axis of the cylinder remain plane
after the application of internal pressure.
3. The material is stressed with in the limit.
4. All the fibres of the material are free to expand or contract independent without
being constrained by the adjacent fibres.
14) State the variation of hoop’s stress in a thick cylinder
The hoop’s stress is maximum at the inner circumference and minimum at the outer
circumference of a thick cylinder.
15) How can you reduce hoop’s stress in a thick cylinder?
The hoop’s stress in a thick cylinder can be reduced by shrinking one cylinder over another
cylinder.
16) What are thin cylinders?
Thin cylinders are vessels, containing fluid under pressure and whose wall thickness is less than
1/15(or) 1/20 of its internal diameter.
17) Define buckling factor
Buckling factor is the relation between equivalent length and minimum radius of gyration.
18) Define safe load
It is the load to which a column is actually subjected to and is well below the buckling load.
Safe load = buckling load
Factor of safety
19) Write Euler’s general formula for finding buckling load
P = π^2EI
L^2
Where,
P = buckling load
L= equivalent length
20) Write Lame’s equation to find out stress in a thick cylinder
Radial stress = σr = b - a
R^2
Circumferential (or) hoops stress = σc = b + a
R^2