RESULTANT OF A SYSTEM OF FORCES ACTING ON A BODY

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.

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, F₃and 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.

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Further we will find out, in our next post, reactions at support and connection in engineering mechanics.