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If the crushing stress in the material of a mild steel column is 3300 kg/cm2. Euler’s formula for crippling load is applicable for slenderness ratio equal to/greater than
- a)40
- b)50
- c)60
- d)80
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If the crushing stress in the material of a mild steel column is 3300 ...
For Euler’s formula to be applicable the critical stress must not exceed the proportional limit.
Now crushing stress in mild steel
= 3300 kg/cm2
= 330 N/mm2
But stress at proportional limit in mild steel
= 250 M/mm2
Euler’s buckling stress
λ = 88.55 ≈ 89
Thus slenderness ratio should be more than or equal to 89 ideally. Option (d) is the most close one.
Now crushing stress in mild steel
= 3300 kg/cm2
= 330 N/mm2
But stress at proportional limit in mild steel
= 250 M/mm2
Euler’s buckling stress
λ = 88.55 ≈ 89
Thus slenderness ratio should be more than or equal to 89 ideally. Option (d) is the most close one.
Most Upvoted Answer
If the crushing stress in the material of a mild steel column is 3300 ...
's formula for the critical buckling load of a long column is given by:
P = (π²EI)/(l²)
where P is the critical buckling load, E is the modulus of elasticity, I is the moment of inertia, and l is the length of the column.
Assuming the column is a solid cylinder with diameter d and length L, the moment of inertia can be calculated as:
I = (πd⁴)/64
Substituting these values and solving for P, we get:
P = (π² x 2.1 x 10^6 x (πd⁴)/64)/(L²)
where we have assumed a modulus of elasticity of 2.1 x 10^6 kg/cm2 for mild steel.
Simplifying this expression, we get:
P = (1.64 x 10^8 x d⁴)/(L²)
To find the maximum length of the column that can withstand the critical buckling load without exceeding the crushing stress, we can equate the critical buckling load to the load that produces the crushing stress:
P = (π/4) x d² x 3300
Equating this with the expression for P above and solving for L, we get:
L = (1.64 x 10^8 x d²)/(3300 x 4)
Simplifying this expression, we get:
L = 12,485 x d²
Therefore, the maximum length of the column that can withstand the critical buckling load without exceeding the crushing stress is proportional to the square of the diameter of the column. For example, if the diameter of the column is 10 cm, the maximum length would be:
L = 12,485 x 10² = 1,248,500 cm = 12,485 m = 12.5 km (approx.)
P = (π²EI)/(l²)
where P is the critical buckling load, E is the modulus of elasticity, I is the moment of inertia, and l is the length of the column.
Assuming the column is a solid cylinder with diameter d and length L, the moment of inertia can be calculated as:
I = (πd⁴)/64
Substituting these values and solving for P, we get:
P = (π² x 2.1 x 10^6 x (πd⁴)/64)/(L²)
where we have assumed a modulus of elasticity of 2.1 x 10^6 kg/cm2 for mild steel.
Simplifying this expression, we get:
P = (1.64 x 10^8 x d⁴)/(L²)
To find the maximum length of the column that can withstand the critical buckling load without exceeding the crushing stress, we can equate the critical buckling load to the load that produces the crushing stress:
P = (π/4) x d² x 3300
Equating this with the expression for P above and solving for L, we get:
L = (1.64 x 10^8 x d²)/(3300 x 4)
Simplifying this expression, we get:
L = 12,485 x d²
Therefore, the maximum length of the column that can withstand the critical buckling load without exceeding the crushing stress is proportional to the square of the diameter of the column. For example, if the diameter of the column is 10 cm, the maximum length would be:
L = 12,485 x 10² = 1,248,500 cm = 12,485 m = 12.5 km (approx.)
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If the crushing stress in the material of a mild steel column is 3300 kg/cm2. Euler’s formula for crippling load is applicable for slenderness ratio equal to/greater thana)40b)50c)60d)80Correct answer is option 'D'. Can you explain this answer?
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