5.5:
Two Force Member
Consider a lamp hanging vertically from the arms with its upper end clamped.
If the arm member is isolated and the two forces act at two points, A and B, with no load in between, it is called a two-force member. Here, the nature of the forces is either tensile or compressive.
For the two-force member to be in equilibrium, the forces FA and FB must be equal in magnitude but opposite in direction.
To satisfy the condition for the moment equilibrium, FA and FB must have the same line of action.
Generally, a two-force member can have multiple forces acting on points A and B that are represented as the resultant force at points A and B.
If the magnitude and direction of the force on one side are known, the force on the other side can be calculated. This reduces the number of unknowns from the equilibrium equation.
The two-force member is not necessarily straight; it can be bent or curved and is used to analyze the structure of trusses, frames, and machines.
5.5:
Two Force Member
The equilibrium of a two-force body is a particular case that is often encountered in practical applications. A two-force body is a rigid body that is subjected to only two external forces. For such a body to be in equilibrium, the two forces must have the same magnitude, the same line of action, and the opposite direction.
Consider any of the shown plates subjected to two forces, F1 and F2, that act at points A and B, respectively. If the plate is in equilibrium, then the sum of the moments of F1 and F2 about any axis must be zero. Summing the moments about point A, we can show that the moment of F2 must be zero. As a result, its line of action must pass through point A. Similarly, summing the moments about point B, we can show that the line of action of F1 must pass through point B. This means that both forces have the same line of action—the line joining A and B.
Furthermore, it can be shown that the two forces have the same magnitude and opposite directions. This can be seen from the equations ΣFx = 0 and ΣFy = 0, where the forces cancel each other out.
When several forces act at points A and B, the forces acting at A can be replaced by their resultant F1, and their resultant F2 can replace those acting at B. A two-force body can be generally defined as a rigid body subjected to forces acting at only two points. It is important to note that, in any case, the resultants F1 and F2 must have the same line of action, the same magnitude, and the opposite direction to ensure the equilibrium of the body.
Suggested Reading
- Hibbeler, R.C. (2016). Engineering Mechanics ‒ Statics and Dynamics. Hoboken, New Jersey: Pearson Prentice Hall. Pp 230.
- Beer, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. and Self, B.P. (2019). Vector Mechanics for Engineers ‒ Statics and Dynamics. New York: McGraw-Hill. Pp 195.