In physics and engineering, a free body diagram (FBD; also called a force diagram) is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which act on the body(ies). The body may consist of multiple internal members (such as a truss), or be a compact body (such as a beam). A series of free bodies and other diagrams may be necessary to solve complex problems.
Purpose
Free body diagrams are used to visualize forces and moments applied to a body and to calculate reactions in mechanics problems. These diagrams are frequently used both to determine the loading of individual structural components and to calculate internal forces within a structure. They are used by most engineering disciplines from Biomechanics to Structural Engineering. In the educational environment, a free body diagram is an important step in understanding certain topics, such as statics, dynamics and other forms of classical mechanics.
Features
A free body diagram is not a scaled drawing, it is a diagram. The symbols used in a free body diagram depends upon how a body is modeled.
Free body diagrams consist of: A simplified version of the body (often a dot or a box) Forces shown as straight arrows pointing in the direction they act on the body Moments are shown as curves with an arrow head or a vector with two arrow heads pointing in the direction they act on the body One or more reference coordinate systems By convention, reactions to applied forces are shown with hash marks through the stem of the vector
The number of forces and moments shown depends upon the specific problem and the assumptions made. Common assumptions are neglecting air resistance and friction and assuming rigid body action.
In statics all forces and moments must balance to zero; the physical interpretation is that if they do not, the body is accelerating and the principles of statics do not apply. In dynamics the resultant forces and moments can be non-zero.
Free body diagrams may not represent an entire physical body. Portions of a body can be selected for analysis. This technique allows calculation of internal forces, making them appear external, allowing analysis. This can be used multiple times to calculate internal forces at different locations within a physical body.
For example, a gymnast performing the iron cross: modeling the ropes and person allows calculation of overall forces (body weight, neglecting rope weight, breezes, buoyancy, electrostatics, relativity, rotation of the earth, etc.). Then remove the person and show only one rope; you get force direction. Then only looking at the person the forces on the hand can be calculated. Now only look at the arm to calculate the forces and moments at the shoulders, and so on until the component you need to analyze can be calculated.
Modeling the body
A body may be modeled in three ways:
a particle. This model may be used when any rotational effects are zero or have no interest even though the body itself may be extended. The body may be represented by a small symbolic blob and the diagram reduces to a set of concurrent arrows. A force on a particle is a bound vector. rigid extended. Stresses and strains are of no interest but rotational effects are. A force arrow should lie along the line of force, but where along the line is irrelevant. A force on an extended rigid body is a sliding vector. non-rigid extended. The point of application of a force becomes crucial and has to be indicated on the diagram. A force on a non-rigid body is a bound vector. Some use the tail of the arrow to indicate the point of application. Others use the tip.
Example: A body in free fall
Consider a body in free fall in a uniform gravitational field. The body may be
a particle. It is enough to show a single vertically downward pointing arrow attached to a blob. rigid extended. A single arrow suffices to represent the weight W even though calm gravitational attraction acts on every particle of the body. non-rigid extended. In non-rigid analysis, it would be an error to associate a single point of application with the gravitational force.
What is included
An FBD represents the body of interest and the external forces acting on it.