## General Mechanical

#### Force distribution

• m.caragiuli
Subscriber

Hi,

just a question to avoid doubts. I have a body (I call it main) correctly connected to multiple bodies. I apply a force load on its face so the load is distributed on its volume and is transmitted and distributed over the other bodies. If I probe the reaction force at one of the multiple bodies (call it secondary body) connected to the main body I get a vector pointing in the opposite direction of the distributed force load and the magnitude should balance a portion of the applied force load. But if I want to know the force load vector on that secondary body is it correct to invert the sign of the x y and z component of the reaction force probed? Please refer to the following picture for better understanding.

Thank you!

• peteroznewman
Subscriber

The sum of all the Y components of the reaction forces across all legs should equal the negative of the Y component of the force load.  The same for the X and Z components.

• m.caragiuli
Subscriber

Hi Peter,

I know that if there are three bodies the sum of Y1 Y2 Y3 reaction forces across each body should equal the magnitude of the applied force and be of opposite sign and the same for X and Z components. Maybe the histogram I did before was not complete, however if there is only one body, is it correct to find out the force distribution on that body by chaging the sign of all the three components of the reaction force, making it opposite?

• peteroznewman
Subscriber

It doesn't matter how many bodies.  Each component of the applied load must be equal and opposite to the sum of the components of the reaction forces.

• m.caragiuli
Subscriber

Why not? If there is only one body where I probe the reaction force  its components should be  equal and opposite to the components of the applied load. I don't understand what is wrong..I'm interested in the force distribution on that body, since I don't know how the applied load distributes I was wondering if by analysing the components of the reaction force on that body I could find out the magnitude on each direction, but that would be a force which opposes to the applied load, not the load distribution itself...and in order to find out this load distribution it would be necessary to change the sign of the reaction force. Hope to be clear.

Applied load is a force which is applied on a body and distributes in a certain manner. Reaction force is how the body reacts to the applied load and its components can be different from the ones of the applied load if there are multiple bodies since the load in the latter case is distributed on a wider area.

Is this wrong?

Thanks for the help

• peteroznewman
Subscriber

If you have three legs of a stool, and a load is placed on the seat, then each leg takes some load. The reaction force at each leg shows you how much each leg is carrying.  The sum of the three legs equals the load (by component), in the opposite direction.

• m.caragiuli
Subscriber

Hi Peter,

Thanks for your answears. Just one thing taking the exemple of the stool..The rection force, as you said, at each leg reports the amount of load each leg is carrying. However if I look at the sign of the components of the reaction force I can understand the direction towards which the leg opposes to the movement due to the load, right? Thus, if I want to know the direction towards which the leg is supposed to be moved due to the applied load I think it would be sufficient to consider the vector of reaction force with opposite direction (thus the components x y and z have an opposite sign). Does it make sense for you?

• peteroznewman
Subscriber

Yes, that is correct. Reaction Forces are the forces the floor (not modeled) is applying to the stool to keep it in equilibrium. If the forces are all pushing up, then the stool is stable and there is compressive stress in all legs. If one of the reaction forces is pointing down, that means that leg would need to be nailed to the floor and there are tensile stresses in that leg.