Strength of Materials - Columns
1.Define: Column and strut.
A column is a long vertical slender bar or vertical member, subjected to an axial compressive load and fixed rigidly at both ends.
A strut is a slender bar or a member in any position other than vertical, subjected to a compressive load and fixed rigidly or hinged or pin jointed at one or both the ends.
2. What are the types of column failure?
1. Crushing failure:
The column will reach a stage, when it will be subjected to the ultimate crushing stress, beyond this the column will fail by crushing The load corresponding to the crushing stress is called crushing load. This type of failure occurs in short column.
2. Buckling failure:
This kind of failure is due to lateral deflection of the column. The load at which the column just buckles is called buckling load or crippling load or critical load. This type of failure occurs in long column.
3. What is slenderness ratio ( buckling factor)? What is its relevance in column?
It is the ratio of effective length of column to the least radius of gyration of the cross sectional ends of the column.
Slenderness ratio = l eff / r
l eff = effective length of column r = least radius of gyration
Slenderness ratio is used to differentiate the type of column. Strength of the column depends upon the slenderness ratio, it is increased the compressive strength of the column decrease as the tendency to buckle is increased.
4. What are the factors affect the strength column?
Strength of the column depends upon the slenderness ratio, it is increased the compressive strength of the column decrease as the tendency to buckle is increased.
2. End conditions: Strength of the column depends upon the end conditions also.
5.Differentiate short and long column
6.What are the assumptions followed in Euler's equation?
1. The material of the column is homogeneous, isotropic and elastic.
2. The section of the column is uniform throughout.
3. The column is initially straight and load axially.
4. The effect of the direct axial stress is neglected.
5. The column fails by buckling only.
7. What are the limitations of the Euler's formula?
1. It is not valid for mild steel column. The slenderness ratio of mild steel column is less than 80.
2. It does not take the direct stress. But in excess of load it can withstand under direct compression only.
8. Write the Euler's formula for different end conditions.
1. Both ends fixed.
2. Both ends hinged
3. One end fixed ,other end
4. One end fixed, other end
L = Length of the column
9. Define: Equivalent length of the column.
The distance between adjacent points of inflection is called equivalent length of the column. A point of inflection is found at every column end, that is free to rotate and every point where there is a change of the axis. ie, there is no moment in the inflection points. (Or)
The equivalent length of the given column with given end conditions, is the length of an equivalent column of the same material and cross section with hinged ends , and having the value of the crippling load equal to that of the given column.
10. What are the uses of south well plot? (column curve).
The relation between the buckling load and slenderness ratio of various column is known as south well plot.
The south well plot is clearly shows the decreases in buckling load increases in slenderness ratio.
It gives the exact value of slenderness ratio of column subjected to a particular amount of buckling load.
11. Give Rakine's formula and its advantages.
P R = Rakine's critical load
f C = yield stress
A = cross sectional area
a = Rakine's constant
= effective length
r = radius of gyration
In case of short column or strut, Eul er's load will be very large. Therefore, Euler's formula is not valid for short column. To avoid this limitation, Rankine's formula is designed. The Rankine's formula is applicable for both long and short column.
12. Write Euler's formula for maximum stress for a initially bent column?
? max = P /A + ( M max / Z )
Where, P = axial load
A = cross section area PE = Euler's load
a = constant
Z = section modulus
13. Write Euler's formula for maximum stress for a eccentrically loaded column?
Where, P = axial load
A = cross section area PE = Euler's load
e = eccentricity
Z = section modulus EI = flexural rigidity
14. What is beam column? Give examples.
Column having transverse load in addition to the axial compressive load are termed as beam column.
Eg : Engine shaft, Wing of an aircraft.
15. Define buckling factor and buckling load.
Buckling factor : It is the ratio between the equivalent length of the column to the minimum radius of gyration.
Buckling load : The maximum limiting load at which the column tends to have lateral displacement or tends to buckle is called buckling or crippling load. The buckling takes place about the axis having minimum radius of gyration, or least moment of inertia.
16. Define safe load.
It is the load to which a column is actually subjected to and is well below the buckling load. It is obtained by dividing the buckling load by a suitable factor of safety (F.O.S).
Safe load = Buckling load / Factor of safety
17. Write the general expressions for the maximum bending moment, if the deflection curve equation is given.
BM = - EI ( d 2y / dx 2 )
18. Define thick cylinders.
Thick cylinders are the cylindrical vessels, containing fluid under pressure and whose wall thickness is not small. (t ³d/20)
19. State the assumptions made in Lame's theory.
i) The material is homogeneous and isotropic.
ii) Plane sections perpendicular to the longitudinal axis of the cylinder remain plane after the application of internal pressure.
iii) The material is stressed within the elastic limit.
iv) All the fibres of the material are to expand or contract independently without being constrained by the adjacent fibres.
20. Write Lame's equation to find out stesses in a thick cylinder.
Radial stress = sr = b - a r2
Circumferential or hoop stress = sc = b + a r2
21. State the variation of hoop stress in a thick cylinder.
The hoop stress is maximum at the inner circumference and minimum at the outer circumference of a thick cylinder.
22. How can you reduce hoop stress in a thick cylinder.
The hoop stress in thick cylinders are reduced by shrinking one cylinder over another cylinder.
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