---
title: "Principle of transmissibility and limitations"
subject: "Applied Mechanics"
chapter: 3
key: "semester_1/applied_mechanics:transmissibility-limitations"
source: https://www.bctengineer.com/q/semester_1/applied_mechanics/transmissibility-limitations
site: BCT Engineering
---

# Principle of transmissibility and limitations

Applied Mechanics · Chapter 3: Forces acting on particle and rigid body

- Asked in: 2068 Shrawan, 6 marks
- Video: [Principle of Transmissibility of Forces II Fundamental of Mech Engg II Mechanics](https://www.youtube.com/watch?v=fD_juM3wrDo) — Shailendra's Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/transmissibility-limitations
- Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-3

## Question

Explain principles of transmissibility and its limitations.

## Short answer

The principle states that the external effect of a force on a rigid body is unchanged if it slides along its line of action. Limitations: it applies only to rigid bodies for external effects, cannot move a force off its line or across joints, and is invalid for internal stress analysis.

## Answer

#### Principle of transmissibility
The external effect of a force on a rigid body (its tendency to move or rotate the body) remains unchanged if the force is moved to any other point on its line of action, provided its magnitude and direction are kept. So a force is a **sliding vector**: its line of action matters, not its point of application.

**Example:** a cart pulled by a rope with force F at the front, or pushed with the same force F at the back along the same line, moves in the same way. In terms of moments, the moment of F about any point O is F × d, and d (the perpendicular distance to the line of action) is the same wherever F is applied along its line.

```text
   F ---->  o-----------o  <---- F      (same line of action,
   A        B           C               same effect on a rigid body)
```

#### Limitations
1. It holds **only for rigid bodies**. For a deformable body, shifting a force changes the internal stresses and deformation.
   - A bar pulled by two equal forces at its ends is in tension. If both forces are slid to the opposite ends, the bar is in compression, although the external effect (equilibrium) is the same.
2. It is valid only for the **external effect**. It cannot be used to find internal forces such as axial force, shear force or bending moment, as these change when the point of application changes.
3. It cannot be used to move a force **off its line of action**. Moving a force to a parallel line needs an added couple of moment F × d.
4. It applies only within one rigid body. A force cannot be slid off the body, or past a hinge or joint into another connected member, because that changes how the load is transferred.
5. It cannot be used in strength of materials or in finding internal forces in structural analysis, where the actual point of loading governs the stresses.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does the principle of transmissibility say about a force on a rigid body?
   A. Its external effect is unchanged if moved along its line of action
   B. Its effect is unchanged if moved to any parallel line
   C. Its effect depends on its point of application
   D. Its effect is zero when moved
   Answer: A. A force is a sliding vector: the line of action matters, not the point. (Key point: Sliding vector)

2. Why does the principle fail for deformable bodies?
   A. Sliding the force changes internal stresses and deformation (e.g. tension becomes compression)
   B. Deformable bodies have no equilibrium
   C. The force magnitude changes
   D. Moments become zero
   Answer: A. A bar pulled at its ends is in tension, but with both forces slid to opposite ends it is compressed. (Key point: Rigid body only)

3. Can transmissibility be used to find axial force, shear force or bending moment?
   A. No, it only preserves external effects
   B. Yes, as these are external
   C. Only axial force
   D. Only bending moment
   Answer: A. Internal forces depend on where the load actually acts. (Key point: Internal forces)

4. What is needed to move a force to a parallel line?
   A. Add a couple of moment F × d
   B. Nothing
   C. Double the force
   D. Reverse its direction
   Answer: A. Transmissibility is only along the line of action; off the line, a couple is required. (Key point: Off line of action)

## Related in Applied Mechanics

- [Principle of transmissibility; resultant on plate ABCD](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Atransmissibility-resultant-plate-abcd) — Applied Mechanics, chapter 3

## Related in other subjects

- [Principle of superposition, example and limitations](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aprinciple-of-superposition-limitations) — Strength of Materials, chapter 1
- [Management vs administrative principles](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Aprinciples-management-compare) — Construction Management, chapter 10
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- [Sine bar principle, setting and error](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Asine-bar-setting-and-error) — Metrology, chapter 5