In our previous topics, we have seen some important concepts such as basic concept of eccentric loading , Assumptions made in the Euler’s column theory and difference between long column and short column with the help of our previous posts.

Today we will see here one very important topic in strength of material i.e. slenderness ratio of column and its importance with the help of this post.

### Slenderness ratio of column

Slenderness ratio of column is basically defined as the ratio of effective length of the column to the least radius of gyration. Slenderness ratio will be given in numbers because it is one ratio and hence slenderness ratio will not have any unit.

Slenderness ratio is usually displayed by Greek letter λ
Slenderness ratio = Effective length of the column/ Least radius of gyration

### Importance of Slenderness ratio

In designing of structure, slenderness ratio plays a very important role. Columns are classified on the basis of slenderness ratio.

For long column, Slenderness ratio will be more than 45
For short column, Slenderness ratio will be less than 45

Strength of column is also dependent over the slenderness ratio. With increase in slenderness ratio, column will have more tendencies to buckle. Hence, compressive strength of column decreases with increase in Slenderness ratio.

In simple, we can say that slenderness ratio of the column will be indirectly proportional to the compressive strength of the column. A column with lower slenderness ratio will have more capability to bear higher compressive load and will have more resistance against buckling.

### Some important definitions in respect of slenderness ratio

We have already discussed here the basic concept of slenderness ratio and now we must have to understand here its two parameters i.e. Effective length of the column and radius of gyration.

### Effective length of the column

Effective length of a given column is basically defined as the distance between successive points of inflection or points of zero movement. Effective length of the column will be dependent over the end conditions of the given column.

Radius of gyration of a body or a given lamina is basically defined as the distance from the given axis up to a point at which the entire area of the lamina will be considered to be concentrated.

We can also explain the radius of gyration about an axis as a distance that if square of distance will be multiplied with the area of lamina then we will have area moment of inertia of lamina about that given axis.
I = A.k2
Where, k is the radius of gyration of the given column
A is area of cross-section of the column
I =  Area moment inertia of the given column

Do you have suggestions? Please write in comment box.

We will now discuss the limitations of Euler’s formula, in the category of strength of material, in our next post.

### Reference:

Strength of material, By R. K. Bansal