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Wednesday, 28 June 2017

END CONDITIONS FOR LONG COLUMNS

In our previous topics, we have seen some important concepts such as Assumptions made in the Euler’s column theory, Difference between column and strut, Difference between long columns and short columns and Failure of a column with the help of our previous posts.

Today we will see here one very important topic in strength of material i.e. End conditions for long columns with the help of this post.

We will first understand here the basic concept of columns and after that we will figure out the end conditions for long columns.

What is column?

Column is basically defined as a vertical member of a structure and it will be subjected with vertical compressive load. Line of action of compressive load will pass through the axis of the column or sometime also parallel to the axis of the column.

In simple, a member of structure will be termed as column if it is vertical and it’s both ends are fixed rigidly and also subjected with axial vertical compressive load.

Example

Vertical structural member between roof and floor could be considered as the best example of column.

As we have discussed that in case of failure of long column, we will not consider the direct compressive stress because direct compressive stress will be negligible as compared to the bending stress developed in the column due to the application of axial compressive load.

Therefore, we can say here that long columns will fail only because of buckling or bending stress developed in the column. Long column is basically defined as the column in which the ratio of effective length of the column to the least lateral dimension of the column is more than 12.

End conditions for long columns

We will discuss and analyze following four types of end conditions for long columns as mentioned here.

Both ends of the long column are hinged
One end of the long column is fixed and other end of the long column is free
Both ends of the long column are fixed
One end of the long column is fixed and other end of the long column is hinged

Let us see here the deflection and slope for above various types of end conditions for long columns

End condition of long column is hinged end: Deflection will be zero
End condition of long column is free end: Deflection will not be zero
End condition of long column is fixed end: Deflection and slope, both will be zero

Do you have suggestions? Please write in comment box.

We will now discuss "Sign conventions" used for bending of long columns 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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