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Thursday, 29 June 2017

SIGN CONVENTIONS FOR BENDING MOMENT FOR A COLUMN

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

Today we will see here one very important topic in strength of material i.e. Sign conventions used for bending of the columns with the help of this post.

We will figure out here the sign conventions used for bending of the columns as we will use this concept during calculation based on the bending of column and strut.

So let us see here the following sign conventions used for bending of the columns

Bending moment with positive sign

Bending moment which will tend to bend the column with its convexity towards its initial central line will be considered as positive.

Let us consider we have one column whose initial central line is displayed here by AB. Once axial compressive load will be applied on column, there will be developed one bending moment and it will try to bend the column.

Let us consider here that column is bending, under the action of bending moment developed by axial compressive load, with taking shape of AC or AD as we have displayed here in following figure.
Bending moment, developed by the axial compressive load, producing such type of curvature will be considered as positive.

Bending moment with negative sign

Bending moment which will tend to bend the column with its concavity towards its initial central line will be considered as negative.

Let us consider we have one column whose initial central line is displayed here by AB. Once axial compressive load will be applied on column, there will be developed one bending moment and it will try to bend the column.
  
Let us consider here that column is bending with taking shape of ACB or ADB as we have displayed here in following figure.
Bending moment, developed by the axial compressive load, producing such type of curvature will be considered as negative.

Do you have suggestions? Please write in comment box.

We will now derive the expression of crippling load when both the ends of the column are hinged, 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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