Columns and Struts Questions and Answers

Q: Slenderness ratio of a column is the ratio of its :

The slenderness ratio is length to its radius of gyration.The slenderness ratio is the effective length of the column divided by its least radius of gyration, \(\lambda = l_{e}/k_{min}\), with \(k = \sqrt{I/A}\). It decides whether a column fails by crushing (short columns) or by buckling (long columns), and it appears directly in Euler's critical stress \(\pi^{2}E/\lambda^{2}\).Length over least lateral dimension is a rough measure used in RCC codes to classify columns as short or long, but it is not the slenderness ratio. The maximum lateral dimension is the wrong dimension altogether, and lateral dimension over radius of gyration has no length in it.

21.

Slenderness ratio of a column is the ratio of its :

A.Length to its maximum lateral dimension
B.Lateral dimension to radius of gyration
C.Length to its least lateral dimension
D.Length to its radius of gyration

Exam Year(s)

RSMSSB JE - 2025, RSMSSB - 2025,

Answer: D

The slenderness ratio is length to its radius of gyration.

The slenderness ratio is the effective length of the column divided by its least radius of gyration, \(\lambda = l_{e}/k_{min}\), with \(k = \sqrt{I/A}\). It decides whether a column fails by crushing (short columns) or by buckling (long columns), and it appears directly in Euler's critical stress \(\pi^{2}E/\lambda^{2}\).

Length over least lateral dimension is a rough measure used in RCC codes to classify columns as short or long, but it is not the slenderness ratio. The maximum lateral dimension is the wrong dimension altogether, and lateral dimension over radius of gyration has no length in it.

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22.

According to Euler's formula, the bending load 'P' for a column of length 'l' with both ends hinged (I = least moment of inertia of the section of the column, E = Young's modulus of the material ) of the column is :

A.\(\frac{4\pi^{2}EI}{l^{2}}\)
B.\(\frac{2\pi^{2}EI}{l}\)
C.\(\frac{\pi^{2}EI}{4l^{2}}\)
D.\(\frac{\pi^{2}EI}{l^{2}}\)

Exam Year(s)

RSMSSB JE - 2025, RSMSSB - 2025,

Answer: D

For a column with both ends hinged, the Euler load is \(\frac{\pi^{2}EI}{l^{2}}\).

Euler's formula is \(P = \frac{\pi^{2}EI}{l_{e}^{2}}\), where the effective length \(l_{e}\) depends on the end conditions. With both ends hinged (pinned), the column bends in a single half sine wave and \(l_{e} = l\).

The other options are other end conditions or errors. With both ends fixed, \(l_{e} = l/2\), giving \(\frac{4\pi^{2}EI}{l^{2}}\). With one end fixed and the other free, \(l_{e} = 2l\), giving \(\frac{\pi^{2}EI}{4l^{2}}\). \(\frac{2\pi^{2}EI}{l}\) is dimensionally wrong; the fixed-hinged case is \(\frac{2\pi^{2}EI}{l^{2}}\).

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