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All questions of Euler's Theory of Columns for Mechanical Engineering Exam
The resultant cuts the base of a circular column of diameter ‘d’ with an eccentricity equal to one-fourth of 'd'. The ratio between the maximum compressive stress and the maximum tensile stress is- a)3
- b)4
- c)5
- d)Infinity
Correct answer is option 'A'. Can you explain this answer?
The resultant cuts the base of a circular column of diameter ‘d’ with an eccentricity equal to one-fourth of 'd'. The ratio between the maximum compressive stress and the maximum tensile stress is
a)
3
b)
4
c)
5
d)
Infinity
 | Simran Saha answered |
For a solid circular section, the maximum eccentricity for no tension is d/8.
The stress
for e = d/4
The minus sign is due to opposite nature of forces.
The stress
for e = d/4
The minus sign is due to opposite nature of forces.
A column of length 2.4 m area of cross-section 2,000 mm2 andmoment of inertia of Ixx = 720 x 104 mm4 and Iyy = 80 x 104 mm4 is subjected to buckling load. Both the ends of the column are fixed. What is the slenderness ratio of column?- a)120 .
- b)80
- c)60
- d)40
Correct answer is option 'C'. Can you explain this answer?
A column of length 2.4 m area of cross-section 2,000 mm2 andmoment of inertia of Ixx = 720 x 104 mm4 and Iyy = 80 x 104 mm4 is subjected to buckling load. Both the ends of the column are fixed. What is the slenderness ratio of column?
a)
120 .
b)
80
c)
60
d)
40
 | Rajat Sen answered |
Slenderness ratio of column is given by,
A hollow circular column of internal diameter 'd' and external diameter '1.5 d’ is subjected to compressive load. The maximum distance of the point of application of load from the centre for no tension is- a)d/8
- b)13d/48
- c)d/4
- d)13d/96
Correct answer is option 'B'. Can you explain this answer?
A hollow circular column of internal diameter 'd' and external diameter '1.5 d’ is subjected to compressive load. The maximum distance of the point of application of load from the centre for no tension is
a)
d/8
b)
13d/48
c)
d/4
d)
13d/96
| | Lekshmi Rane answered |
Euler’s formula for a mild steel long column hinged at both end is not valid for slenderness ratio- a)greater than 80
- b)less than 80
- c)greater than 180
- d)greater than 120
Correct answer is option 'B'. Can you explain this answer?
Euler’s formula for a mild steel long column hinged at both end is not valid for slenderness ratio
a)
greater than 80
b)
less than 80
c)
greater than 180
d)
greater than 120
| | Lekshmi Rane answered |
Hence, when the slenderness ratio is less than this limit for mild steel columns , Euler’s formula will not be valid.
A rectangular bar as shown in the figure below carries a tensile load of 1 kN as shown in the figure. Under this load the maximum value of stress over the mean value will increase by
- a)20%
- b)40%
- c)60%
- d)80%
Correct answer is option 'C'. Can you explain this answer?
A rectangular bar as shown in the figure below carries a tensile load of 1 kN as shown in the figure. Under this load the maximum value of stress over the mean value will increase by
a)
20%
b)
40%
c)
60%
d)
80%
| | Srestha Khanna answered |
Mean value of stress,
Maximum intensity of stress
∴ Increase in stress
Maximum intensity of stress
∴ Increase in stress
For the case of slender column of length 'l’ and flexural rigidity EI built in at its base and free at the top, the Euler's buckling load is- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
For the case of slender column of length 'l’ and flexural rigidity EI built in at its base and free at the top, the Euler's buckling load is
a)
b)
c)
d)
| | Pallabi Bajaj answered |
Euler’s buckling load,
For a column fixed at base and free at the top,
∴
For a column fixed at base and free at the top,
∴
Rankine-GordonTormulafor buckling is valid for- a)long columns
- b)short columns
- c)short and long columns
- d)very long columns
Correct answer is option 'C'. Can you explain this answer?
Rankine-GordonTormulafor buckling is valid for
a)
long columns
b)
short columns
c)
short and long columns
d)
very long columns
| | Anmol Menon answered |
Rankine-Gordon Formula for buckling is valid for short and long columns.
Explanation:
Buckling is a phenomenon in which a slender column experiences a sudden, drastic lateral deflection under a compressive load. Buckling is a common problem in structural engineering, and it is important to predict the critical buckling load of a column to prevent failure of the structure. The Rankine-Gordon formula is a widely used method for predicting the critical buckling load of a column.
The Rankine-Gordon formula is valid for both short and long columns. The formula is given as follows:
Pcr = (π²EI)/(KL)²
Where:
Pcr = Critical buckling load
E = Modulus of elasticity of the material
I = Moment of inertia of the cross-section of the column
K = Effective length factor
L = Length of the column
For short columns, the effective length factor K is less than or equal to 1.0, and for long columns, K is greater than 1.0. Therefore, the Rankine-Gordon formula can be used for both short and long columns by appropriately selecting the effective length factor.
In conclusion, the Rankine-Gordon formula is a useful tool for predicting the critical buckling load of a column. It is valid for short and long columns, and the effective length factor K can be adjusted accordingly.
Explanation:
Buckling is a phenomenon in which a slender column experiences a sudden, drastic lateral deflection under a compressive load. Buckling is a common problem in structural engineering, and it is important to predict the critical buckling load of a column to prevent failure of the structure. The Rankine-Gordon formula is a widely used method for predicting the critical buckling load of a column.
The Rankine-Gordon formula is valid for both short and long columns. The formula is given as follows:
Pcr = (π²EI)/(KL)²
Where:
Pcr = Critical buckling load
E = Modulus of elasticity of the material
I = Moment of inertia of the cross-section of the column
K = Effective length factor
L = Length of the column
For short columns, the effective length factor K is less than or equal to 1.0, and for long columns, K is greater than 1.0. Therefore, the Rankine-Gordon formula can be used for both short and long columns by appropriately selecting the effective length factor.
In conclusion, the Rankine-Gordon formula is a useful tool for predicting the critical buckling load of a column. It is valid for short and long columns, and the effective length factor K can be adjusted accordingly.
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