Forces and Free-Body Diagrams: From Loads to Equilibrium

Mechanical Engineering · CHAPTER 1 / 5

Level: introductory undergraduate · Study session: 15–20 minutes including practice.

Learning outcome: Draw a system boundary, identify external forces, and solve static equilibrium.

Before you begin: Basic algebra, SI units and a willingness to sketch the problem.

1. Understand the idea

A free-body diagram isolates one object. Replace each support by its reaction force and represent weight at the centre of mass. Choose axes before resolving forces. Static equilibrium requires zero resultant force and zero resultant moment; zero force alone does not prevent rotation.

2. Write the model

ΣFx = 0; ΣFy = 0; ΣM = 0

Define the symbols from the worked case before substituting values. Keep units consistent, record the assumptions and round only after the calculation.

3. Follow a worked example

A simply supported 4 m beam carries a 600 N point load 1 m from the left support. Taking moments about the left support gives RB × 4 = 600 × 1, so RB = 150 N and RA = 450 N.

4. Explore the model

Figure: calculated teaching cases; straight segments connect sampled points, not experimental observations. Read exact values below.

Illustrative scenario sweep — synthetic educational data
Load position x (m)	Left reaction (N)	Right reaction (N)
1	450	150
2	300	300
3	150	450

Move the same load from x=1 to x=3 m. The reactions exchange values while their sum remains 600 N.

5. Reproduce it yourself

Copy the input cases into Excel or a notebook and name each quantity and unit.
Recalculate each result from the stated equation or rule. For qualitative cases, explain the state or partition decision instead.
Change one input, predict the direction of change, then calculate again.
Write one sentence explaining where the model stops being valid.

6. Check your understanding

For the same beam, what are the reactions for a load at x=2 m?

Reveal the answer and check your work

RA = RB = 300 N.

Compare your result, units and reasoning. If they differ, return to the equation and test the worked case first.

7. Common mistake

Do not include internal forces on a diagram of the complete beam.

Further study and academic note

Explore the discipline reference and further learning resources. This is an original IIMEEE introductory teaching note with synthetic examples; it is not a peer-reviewed research result or a professional design specification. Figures were constructed from the listed teaching cases. Resource links support further study and do not imply endorsement.