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Daily Dose 041 | Statics
How to solve Free Body Diagram reactions?
Knowing how to solve Free Body Diagram reactions will play a major role in your upcoming FE Exam.
Not only will you see them in Statics – but Dynamics and Mechanics of Materials, amongst others, rely heavily on understanding how to set up and solve FBDs.
Free Body Diagrams are fundamental to so much of what we do as engineers and…
Many will struggle – but you can’t afford to.
In this video, we will break it all down, showing you exactly how to go about setting up and solving for the reactions of a Free Body Diagram, faster and with a lot less stress on the FE Exam.
Key Definition
What is a FREE BODY DIAGRAM?
A FREE BODY DIAGRAM (FBD) is a graphical illustration used to visualize the applied forces, movements, and resulting reactions on a body in a given condition.
This is the foundation of many of the engineering problems we work. FREE BODY DIAGRAMS depict a body or connected bodies with all the applied forces, moments, and reactions which act on the geometry of interest.
The FBD may consist of multiple internal members (such as a truss), or be a compact body (such as a beam). In more complex real-world situations, a series of FREE BODY DIAGRAMS may be necessary to determine a solution.
In nutshell, we will use FREE BODY DIAGRAMS in almost all ENGINEERING MECHANICS problems to help us visualize the forces and moments applied to a body, allowing us to calculate the resulting reactions
The Process
So how can we set up and solve Free Body Diagram reactions?
The biggest factor in solving a Free Body Diagram problem is having a keen ability to visualize and set them up – fast.
Here are some tips:
- Identify the object
- Isolate the object
- Identify external forces
- Represent forces as vectors
- Choose a coordinate system
- Resolve forces into components
- Include acceleration (if applicable)
- Review and double-check
Clearly identify the object for which you want to create a free body diagram. This could be a physical object or a specific point in a system.
Mentally or visually isolate the object from its surroundings. Imagine removing the object from its environment, leaving only the forces acting on it.
Identify and locate all the external forces acting on the object. These forces can include gravity, applied forces, friction, tension, normal force, etc. Take into account the direction and magnitude of each force.
Draw arrows to represent the forces acting on the object. The length and direction of the arrows should correspond to the magnitude and direction of the forces, respectively. Label each arrow with the name of the force it represents.
Select a convenient coordinate system that aligns with the object’s motion or symmetry. Common choices include Cartesian coordinates (x, y) or polar coordinates (r, θ). This will help you break down forces into their respective components later.
If needed, break down any angled forces into their horizontal and vertical components. Use trigonometry (such as sine and cosine functions) to determine the magnitudes of these components.
If the object is accelerating, such as in the case of Newton’s second law, include an arrow representing the acceleration vector. The direction of this arrow should align with the direction of acceleration.
Ensure that you have accurately represented all the forces and their directions. Check for any missing forces or errors in vector representation.
Creating a free body diagram may take practice, but through a few sets and reps, you will become more efficient.
Check out the video and see how we can go about solving this type of problem in the most efficient manner.
As always, with Love, Prepineer
