We have started a new
topic in our previous post i.e. engineering mechanics. We have seen
there the basics of engineering mechanics such as concept
of force system, principle
of transmissibility of forces and its limitations, classification
of force system, body
force and surface force, moment
of a force, Varignon’s
theorem, concept
of a couple and how to draw free body diagrams in engineering mechanics. Â
Also
read Â
Now, we will be
interested here to understand the resultant of the forces acting on a body with
the help of this post. We will see here how to find out the resultant of forces
acting on a body.
Resultant of the forces acting on a body
This topic i.e. the resultant
of the forces acting on a body is very important and will be used in solving
the various types of problems in engineering mechanics, therefore we need to
understand it precisely how to determine the resultant of the forces acting on
a body.
So let us consider a body
as displayed here in following figure. Let us assume that there are multiple
forces i.e. F1, F2, F3 and F4 acting
on the body and these forces are having with different line of action and in
different directions as displayed here in the figure.
Now question is this how
to find out the resultant of these forces acting on the body. What we need to
do in order to find out the resultant of these forces acting on body? Let us
see here.
We will translate these
forces to a point P. The point P would be usually the mass point. We must note
it here that we can not simply translate these forces to the point P as in
doing so the external effect of these forces will be changed.
In order to maintain the
external effect of these forces on the body, we need to introduce a couple for
each force translated to the point P.
Let us assume that the
perpendicular distances of the point P from the line of action of these forces
are d1, d2, d3 and d4.
Therefore by keeping in
mind the sense of rotation of these forces and sign convention for couple of a
force, we will write here the equation for resultant moment of these forces and
it will be as displayed here.
Now, we can translate
these forces to the point P with introduction of net moment of these forces as
displayed here in following figure.
Now we will use the
principle of vector addition of forces and we will find out the resultant of
these forces acting on the body.
Therefore, we have seen
here that any force system acting on a body could be converted in to a
resultant force and a resultant moment.
This principle of determination
of resultant of the forces acting on a body will be applicable in both statics
and dynamics.
Therefore, we have seen
here how to find out the resultant of multiple forces acting on a body in engineering
mechanics with the help of this post.Â
Do you have any
suggestions? Please write in comment box and also drop your email id in the
given mail box which is given at right hand side of page for further and
continuous update from www.hkdivedi.com.Â
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Further we will find out,
in our next post, reactions at support and connection in engineering mechanics.  Â
Reference:Â Â
Engineering Mechanics, By
Prof K. RameshÂ
Image courtesy:
Google Â
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