Effective Length and Slenderness Ratio

Q. For a circular column having its ends hinged, the slenderness ratio is 160. The 1/d ratio of the column is

1. 80
2. 57
3. 40
4. 20

Q. When a column is fixed at both ends corresponding Euler's criterion load is

1. $\frac{{\pi }^{2}EI}{L^2}$
2. $\frac{2{\pi }^{2}EI}{L^2}$
3. $\frac{3{\pi }^{2}EI}{L^2}$
4. $\frac{4{\pi }^{2}EI}{L^2}$

Q. If the crushing stress in the material of a mild steel column is $3300kg/c{m}^2$. Euler's Formula for crippling load is applicable for slenderness ratio equal to/greater than

1. $40$
2. $50$
3. $60$
4. $80$

Q. The slenderness ratio of a compression member in the context of Rankine's formula is defined as

1. $\frac{\text{Length}}{\text{Least lateral dimension}}$
2. $\frac{\text{Effective length}}{\text{Least radius of gyration}}$
3. $\frac{\text{Effective length}}{\text{Least lateral dimension}}$
4. $\frac{\text{Length}}{\text{Least radius of gyration}}$

Q. A column has a rectangular cross-section of 10mm$\times$ 20 mm and a length of 1 m. The slenderness ratio of the column is close to

1. 200
2. 346
3. 477
4. 1000

Q. The effective length of a column of length L fixed against rotation and translation at one end is

1. 0.5 L
2. 0.7 L
3. 1.414 L
4. 2 L

Q. For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is

1. 1
2. 2
3. 4
4. 8

Q. The minimum axial compressive load, P required to initiate buckling for a pinned slender column with bending stiffness EI and length L is

1. $P=\frac{{\pi }^{2}EI}{4L^2}$
   
2. $P=\frac{{\pi }^{2}EI}{L^2}$
   
3. $P=\frac{3{\pi }^{2}EI}{4L^2}$
   
4. $P=\frac{4{\pi }^{2}EI}{L^2}$
   

Q. A steel column, pinned at both ends, has a buckling load of 200 kN. If the column is restrained against lateral movement at its mid-height, its buckling load will be

1. 200 kN
2. 283 kN
3. 400 kN
4. 800 kN