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How to Draw and Analyse Free Body Diagrams (FBDs)

In this free engineering tutorial we shall review:

  1. What is a Free Body Diagram (FBD)

  2. Steps to draw a Free Body Diagram

  3. Representing supports in Free Body Diagrams

  4. Examples of Free Body Diagrams

What is a Free Body Diagram (FBD)

A free-body diagram is a sketch of a body, a portion of a body, or two or more bodies completely isolated from all other bodies. It shows the external forces and couples acting on the system (drawn carefully with respect to location, direction and magnitude). The forces may result from externally applied pushes or pulls, from gravity forces such as the bodies own weight, from forces exerted by other bodies and must include reactions from any supports.

The free-body diagram is one of the most important steps in the solution of problems in engineering.

Steps to Draw a FBD

1. Decide which body or combination of bodies is to be isolated.

2. Draw the boundary which isolates the body from all surrounding bodies and supports.

3. Add all known forces as vector arrows showing position and direction and with magnitude (including units) written alongside. Include the weight of the bodies where appreciable. Unknown forces should have the magnitude and direction represented by a symbol. If the sense (i.e. + or - direction) is unknown assume the positive direction. The calculations will give a negative value for the force if wrong.

4. Draw the co-ordinate axes.

5. Put on essential dimensions but do not clutter the diagram with unnecessary information.

Supports for FBDs

Structures that interact with the ground can be modelled with different types of 'supports'.

Types of Supports for Free Body Diagrams

In the diagram above, the top row shows the structure and the bottom row shows the FBD.

For the simple joints shown there is a reaction Ry due to the presence of the surface reaction force pushing upwards on the structure – this is the reaction force due to the weight of the structure acting down. Rx is present because we know that if we try to push the structure in the x direction there will be a resistance of some sort.

Roller Supports for Free Body Diagrams

In the diagram above, the top row shows the structure and the bottom row shows the FBD.

In each case the structure is either on a roller (frictionless wheel) or in the centre a frictionless table. Correspondingly, there is no resistance in the x-direction, hence there is no need for a reaction force, Rx in this case. Ry is still present to represent the reaction force upwards due to the weight of the structure.