Diagramming Structural Forces
Definition
Force Diagram
A force diagram (or free-body diagram) shows all the forces acting on a structure or object. These include applied loads, reactions at supports, and internal forces like tension and compression.
Note
Copy this link and watch this video to understand how to draw and interpret force diagrams: https://youtu.be/29YPIvj1zjc?si=aM2lJ5vTk6lhNWFv
Key Principles
- Forces are vectors: They have both magnitude and direction.
- Forces in the same direction add up.
- Forces in opposite directions are subtracted.
- Resultant Force is the overall effect of all forces acting on an object.
- E.g. If one horse pulls a cart with 4 N and another with 3 N in the same direction → Resultant = 7 N
- If opposing (tug of war): 4 N left – 3 N right → Resultant = 1 N left
Note
Static Equilibrium
A structure is in equilibrium when:
- Σ Vertical Forces = 0
- Σ Moments = 0
If an object isn’t moving, the resultant force = 0 N.
Tip
When creating a force diagram, always start by identifying all the forces acting on the structure, including external loads and internal reactions.
Example
A 100 N load sits in the middle of a 2 m beam supported at both ends.
Step 1: Diagram
- Draw a horizontal beam with supports at both ends.
- Show a 100 N downward force in the centre.
Step 2: Calculate support reactions
- Load is symmetric → Each support carries 50 N upward
- Σ Forces = 50 N + 50 N – 100 N = 0 N
Tip
Forces vs Acceleration
- Use Newton's 2nd Law if movement is involved:
- $\text{Force (F)} = \text{Mass (m)} \times \text{Acceleration (a)}$
- If acceleration = 0, then the resultant force = 0 N (balanced).
- If unbalanced, the object will accelerate in the direction of the resultant force.
Common Mistake
- Forgetting to include support reactions
- Misjudging direction (e.g. drawing all forces down)
- Confusing moment with force
