Enter all but one of the applied force, length of the shaft, modulus of elasticity of the material, and moment of inertia of the shaft into the calculator to determine the deflection; this calculator can also evaluate any of the variables given the others are known.

## Shaft Deflection Formula

The following formula is used to calculate the deflection of a shaft:

D = (F * L^3) / (3 * E * I)

Variables:

- D is the deflection of the shaft
- F is the applied force
- L is the length of the shaft
- E is the modulus of elasticity of the material
- I is the moment of inertia of the shaft

To calculate the deflection of a shaft, multiply the applied force by the cube of the length of the shaft. Divide the result by 3 times the modulus of elasticity of the material times the moment of inertia of the shaft.

## What is a Shaft Deflection?

Shaft deflection refers to the degree to which a structural element is displaced under a load. It is a critical factor in mechanical engineering and structural design, as excessive deflection can lead to failure of the component or the entire system. In the context of a rotating shaft, such as in an engine or transmission, deflection can cause misalignment, vibration, and increased wear on bearings and other components. This can result in decreased performance, increased maintenance costs, and potential catastrophic failure. Therefore, engineers must carefully consider and calculate expected shaft deflection during the design process to ensure the integrity and longevity of the system. Factors influencing shaft deflection include the material properties of the shaft, the magnitude and direction of the applied load, the length of the shaft, and the method of support at the ends of the shaft.

## How to Calculate Shaft Deflection?

The following steps outline how to calculate the Shaft Deflection.

- First, determine the applied load (F) in Newtons.
- Next, determine the length of the shaft (L) in meters.
- Next, determine the modulus of elasticity (E) in Pascal.
- Next, determine the moment of inertia (I) in meters^4.
- Next, gather the formula from above = δ = (F * L^3) / (3 * E * I).
- Finally, calculate the Shaft Deflection.
- After inserting the variables and calculating the result, check your answer with the calculator above.

**Example Problem : **

Use the following variables as an example problem to test your knowledge.

applied load (F) = 500 N

length of the shaft (L) = 0.5 m

modulus of elasticity (E) = 2.1 x 10^11 Pa

moment of inertia (I) = 1.5 x 10^-6 m^4