Question

The ratio of the effective length of column and the minimum radius of gyration of its cross-sectional area is known-
1. Buckling factor
2. Slenderness ratio
3. Crippling ratio
4. None of the above

Answer 1

Correct Answer - Option 2 : Slenderness ratio

Explanation:

Slenderness ratio:

• It is the ratio of the effective length of a column and the least radius of gyration of its cross-section.
• It is used extensively for finding out the design load as well as in classifying various columns in short/intermediate/long.

\(\lambda = \frac{{{L_e}}}{{{k_{min}}}}\)

\(k = \sqrt {\frac{I}{A}}\)

Leffective = Effective length of the column

kmin = minimum radius of gyration

I = Moment of Inertia

A = Area of the cross-section

Sectional Modulus (Z): 

• It is the ratio of moment of inertia (I) of the beam cross-section about the neutral axis to the distance (ymax) of extreme fiber from the neutral axis,  \(Z = \frac{I}{y_{max}}\)
• The section modulus (Z) of the cross-sectional shape is significant in designing beams.
• It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.

• The unit of the Section modulus is mm3.

Modulus of rigidity or shear modulus:

• The ratio of shear stress to the corresponding shear strain within the elastic limit is known as Modulus of Rigidity or Shear Modulus.
• It is denoted by C or G or N.

\(\therefore C\left( {or\;G\;or\;N} \right) = \frac{{Shear\;stress}}{{Shear\;strain}} = \frac{\tau }{\phi }\)