Engr Help

Equipollent Force Systems

Key Concept: Two force systems are said to be equipollent if they have the same

resultant force (ΣF) and the same resultant moment (ΣM_p) with respect to any

point P. You can think of equipollent as meaning equivalent.

In a Nut Shell:

Engineering structures carry many types of loads including concentrated forces,

distributed forces (i.e. wind loading), torques (i.e. torque wrench), and combinations

of loads.

Of note, a force system can be reduced to a single resultant force for the following

cases.

a. Concurrent (passing through the same point) forces with no couples

b. Coplanar forces with couples perpendicular the plane of the forces

c. Parallel forces with couples perpendicular to the forces

In the most general case of a system with forces and couples, the force system can

always be reduced to a “screwdriver” – a single force and couple. Think of an actual

screwdriver where you apply both a torque and a thrust force to secure a screw.

To illustrate two equipollent force systems consider the 12 ft beam with the two

distributed loads shown. Replace this force system having the two distributed loads

with an equivalent one with only concentrated loads.