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, 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.
 Â
 Â
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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