Resultant of a system of forces!!

[chz]

Let us say we have a plate subjected to a system of forces like a moment, vertical forces.The resultant of the system of forces which is a single equivalent vertical force lies outside the plate.How can this be interpreted physically, i.e. the resultant lying outside the body??

 

[vonlueke]

Weld an imaginary rigid bar to the plate at the centroid of the vertical forces such that the free end of the bar extends to the location of the force and moment resultant. Apply your resultant force to the tip of the rod. If the plate is a rigid body, this resultant force simultaneously applies to the plate a total vertical force and total moment mathematically equivalent to the total force and total moment of the original system of forces.

 

[poetix99]

It's worth noting that the resultant force could not be outside of the physical confines of the body (at least for shapes that don't fold back on themselves) UNLESS there are moments acting upon the body.

 

[chz]

Does this mean that the moment to which the plate was subjected to need be from an external source and not the result of forces which are acting directly over the plate?

 

[Flareman]

All the forces on the plate are really external.
The single force principle assumes that you can put a simple point force at one place to balance and restrain the motion of your plate, like putting your finger on one side of the plate. If you do this at the edge of the plate, and the plate twists away under your finger because the twisting (moment) forces are too high, then the point of application of the single load is outside your plate and you need to apply a moment by gripping with your thumb as well, to restrain it. The moment you apply is equivalent to the distant force x the distance away from the plate edge. Does that help?

 

[vonlueke]

chz: Answer: No. If the moment induced by the vertical forces themselves happens to be high enough, the resultant force could be outside the plate. (And notice this doesn't contradict poetix99's statement.)

 

[poetix99]

I don't mean for this to become circular, but here goes:

For rigid bodies, any distribution of (discrete) forces can be equivalently expressed as a resultant force acting through the center of mass, and a moment, also acting at the center of mass. This gives only the equivalent net force and torque on the body; stress distributions through the body are NOT equivalent, of course.

Alternatively, a “resultant” force could be shown acting at an appropriate distance from the center of mass in order to include the effects of the above-mentioned moment, which then disappears. I think that this is the configuration you ended up with. There is no reason that this resultant force might not be outside of the confines of the rigid body; it simply depends on the original force vectors.

 

[vtl]

Joint the plate wilh an extend beam or connection.

Location of force to apply so that plate wont move.