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.

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 Î»

Slenderness ratio is usually displayed by Greek letter Î»

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 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.

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**

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.

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.k

^{2}
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 want the detailed post based on radius of gyration? Click here.

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.

Do you want the detailed post based on radius of gyration? Click here.

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

Image
Courtesy: Google

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