# How a non uniform force, converted to an equivalent point force acts on an object.

#### jot_dain

Hello all

I am trying to understand how a non uniform force, converted to an equivalent point force acts on an object.

I was hoping I could get the communities opinion on the following sketch I have made:- In Diagram A have a non uniform force that is being applied to my shape.
The centre of mass & centroid are the same location as the density of the material is uniform.

In Diagram B I have calculated the X,Y,Z position of the force distribution shown in blue.
I now have 2 x centroids, one for my shape and one for my force distribution.

In Diagram C I have projected the centroid of my force distribution onto my shape shown in yellow.
If I converted my non uniform distributed load into an equivalent point load then would it be correct to say that the point force would act at the projected centroid (yellow) and not the centroid of my shape.

Is this correct?

#### Woody

Yes.
I personally would not have thought to describe the force distribution as a three dimensional shape as you have,
(I would have used a more abstract weighted average)
But your method is a good way of visualising the problem, and it gives the correct answer.

• jot_dain

#### jot_dain

Yes.
I personally would not have thought to describe the force distribution as a three dimensional shape as you have,
(I would have used a more abstract weighted average)
But your method is a good way of visualising the problem, and it gives the correct answer.
Woody

Thank you, I needed to clear up the doubt in my mind.

Thanks.