Қолданған күштер мен моменттердің схемалық кескіні

Diagram showing applied forces and moments on a physical body

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. Sometimes in order to calculate the resultant force graphically the applied forces are arranged as the edges of a polygon of forces or force polygon (see ).

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.

In an analysis, a free body diagram is used by summing all forces and moments (often accomplished along or about each of the axes). When the sum of all forces and moments is zero, the body is at rest or moving and/or rotating at a constant velocity, by Newton's first law. If the sum is not zero, then the body is accelerating in a direction or about an axis according to Newton's second law.

Determining the sum of the forces and moments is straightforward if they are aligned with coordinate axes, but it is more complex if some are not. It is convenient to use the components of the forces, in which case the symbols ΣFx and ΣFy are used instead of ΣF (the variable M is used for moments). Forces and moments that are at an angle to a coordinate axis can be rewritten as two vectors that are equivalent to the original (or three, for three dimensional problems)—each vector directed along one of the axes (Fx) and (Fy).

A simple free body diagram, shown above, of a block on a ramp, illustrates this. All external supports and structures have been replaced by the forces they generate. These include:
mg: the product of the mass of the block and the constant of gravitation acceleration: its weight. N: the normal force of the ramp. Ff: the friction force of the ramp. The force vectors show the direction and point of application and are labelled with their magnitude. It contains a coordinate system that can be used when describing the vectors. Some care is needed in interpreting the diagram. The normal force has been shown to act at the midpoint of the base, but if the block is in static equilibrium its true location is directly below the centre of mass, where the weight acts because that is necessary to compensate for the moment of the friction. Unlike the weight and normal force, which are expected to act at the tip of the arrow, the friction force is a sliding vector and thus the point of application is not relevant, and the friction acts along the whole base.

In the case of two applied forces, their sum (resultant force) can be found graphically using a parallelogram of forces. To graphically determine the resultant force of multiple forces, the acting forces can be arranged as edges of a polygon by attaching the beginning of one force vector to the end of another in an arbitrary order. Then the vector value of the resultant force would be determined by the missing edge of the polygon. In the diagram, the forces P1 to P6 are applied to the point O. The polygon is constructed starting with P1 and P2 using the parallelogram of forces (vertex a). The process is repeated (adding P3 yields the vertex b, etc.). The remaining edge of the polygon O e represents the resultant force R.

In dynamics a kinetic diagram is a pictorial device used in analyzing mechanics problems when there is determined to be a net force and/or moment acting on a body. They are related to and often used with free body diagrams, but depict only the net force and moment rather than all of the forces being considered. Kinetic diagrams are not required to solve dynamics problems; their use in teaching dynamics is argued against by some in favor of other methods that they view as simpler. They appear in some dynamics texts but are absent in others.