Forces and Moments MET 2214 Statics MET 2214

Forces and Moments MET 2214 Statics (MET 2214) Prof. S. Nasseri

Moments and Forces Part 5 Statics (MET 2214) Prof. S. Nasseri

Equivalent system An equivalent system is: A system in which forces and couple moments acting on a body are simplified to a single resultant force and couple moment acting at a specified point O. Consider the figure below in which point O is on the line of action of the force: F is applied at A (Fig. a). It is needed to move the force F to point O (keeping the external effects on the body constant). Imagine we apply +F and –F at O (Fig. b). As +F at A and –F at O are cancelled out, hence +F is applied at O (Fig. c). Statics (MET 2214) Prof. S. Nasseri

Equivalent system Now if point O is not on the line of action of the force: Force F is applied at A (Fig. a) and OA does not pass through the line of action of F. It is needed to move force F to O (keeping the external effects on the body constant). In this case: Apply +F and –F at O (Fig. b), then +F at A and –F at O create a couple moment (M = r x F). M is a free vector, so remember that it can be applied on any point P (Fig. c) So, F is applied at O and also a moment M is produced (Fig. c). Statics (MET 2214) Prof. S. Nasseri

Example 1 The weights of the various components of the truck are shown. Replace this system of forces by an equivalent resultant force and couple moment acting at point A. Statics (MET 2214) Prof. S. Nasseri

Example 2 Replace the force and couple moment system by an equivalent force and couple moment acting at point P. Solution: -60 cos 30 N P -60 sin 30+ (-140)N Statics (MET 2214) Prof. S. Nasseri -51. 96 N 73 P -170 N

Example 2 60 cos 30 N Moment due to horizontal component of 60 N 8 m P 60 sin 30 N Moment due to vertical component of 60 N 4 m P P Moment due to the force 140 N 15 m 140 N P Statics (MET 2214) Prof. S. Nasseri 40 Nm

Example 3 Replace the two wrenches and the force, acting on the pipe assembly, by an equivalent resultant force and couple moment acting at point O. Solution: Statics (MET 2214) Prof. S. Nasseri

Example 3 Statics (MET 2214) Prof. S. Nasseri

Example 3 Statics (MET 2214) Prof. S. Nasseri