# Internal Force: Definition & Examples

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• 0:04 What Are Internal Forces?
• 0:55 Equilibrium
• 2:37 Sign Convention
• 3:12 Numerical Example
• 3:51 Lesson Summary
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Lesson Transcript
Instructor
Ali Motamedi

Ali received his MSc degree in Civil Engineering and PhD degree in Risk Management. He has been teaching engineering and analytics courses for several years.

Expert Contributor
Christianlly Cena

Christianlly has taught college physics and facilitated laboratory courses. He has a master's degree in Physics and is pursuing his doctorate study.

In this lesson you will learn what the internal forces are and what they do in a structure member such as pole, beam and column. We also review the commonly used sign convention and solve a numerical example to understand how to calculate an internal force in a structure member.

## What are Internal Forces?

Internal forces are produced from the external forces acting on structure members such as poled, beamd or columnd. Generally, we have three types of internal forces: axial, dhear and moment. Axial force, sometimes called 'normal force,' is a compression or tension force acting aligned with the extension of a structure member. Shear force is a force acting in a direction perpendicular to the alignment of the member. Moment force, lastly, is a turning result of a force multiplied by the distance from its acting location to the turning point. The number of these components varies in one-dimensional, two-dimensional and three-dimensional cases. Now the questions are what each of these components do and how to calculate these internal forces.

## Equilibrium

When a structure member such as a pole, beam or column is in equilibrium, it means that it isn't moving as it is supposed to be. Therefore, the combination or resultant of all the external forces applied to the member equals zero. In fact, the internal forces maintain the equilibrium of a structure member in different directions.

### 1D Case

In the simplest example, let's consider a pole in a building structure (1D case). Depending on the applied external loading, this pole can be in either tension or compression. Now, what if the pole is cut from left to right of an arbitrary size (it's called a free body diagram)? Since the pole is not moving, as we discussed, the resultant of all the applied forces, including the external and internal forces, still needs to equal zero (see Figure 1).

### 2D Case

We will have the same concept in a 2D case with a beam. Since we assume that the beam is fixed and not moving, the resultant of all applied forces from different directions equal zero (see Figure 2).

### 3D Case

Similar to the 1D case example, cutting the beam from left or right of an arbitrary size and section will result in a combination of external and internal forces with zero resultant (see Figure 3).

In the 3D case, we will need more force components to maintain the equilibrium: one axial and two shears, one twisting and two bending moments.

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## Crossword Puzzle on Internal Force

### Directions

This crossword puzzle touches on the definition and examples of internal force. Complete the crossword by filling in a word that fits each of the given clues. To do this, you have two options: (1) draw the crossword puzzle (shown below) using a colored pen on a sheet of paper or (2) right click to save the image and print it. With a pencil and an eraser, neatly write your answers in the boxes provided. For comparison, an answer key is also included at the end of the section.

### Across

2. When a structure is not moving, the resultant of all the applied forces must be equal to _____.

5. This force acts in a direction perpendicular to the alignment of the structure member.

6. In a 3D case, a bending moment has a _____ sign when it's creating concave upward rotation on the section.

8. In the 3D case, the shear force will have a positive sign when it creates a _____ rotation.

9. It is the turning force, or torque, which results from the force multiplied by the distance from its acting location to the turning point.

10. It is generally defined as a force (such as compression force) acting along the extension of a structure member.

### Down

1. A _____ diagram is an arbitrary section of the structure member.

3. Internal forces maintain the _____ in a structure member in axial, radial and rotational directions.

4. This is another term for the axial force.

7. It is a force produced from the external forces acting on structure members.

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