# Understanding Deflection Of A Simply Supported Beam Formula

These days, many of us are familiar with the concept of deflection of a simply supported beam formula. This is because it is used in many engineering applications and is found in various books and articles. In this article, we will take a closer look at what this formula is and how it works.

The deflection of a simply supported beam formula is used to calculate the deflection of a beam at any point along its length. It is based on the concept of deflection, which is the displacement of a beam from its original position due to the applied load or force. The formula is based on the principle of virtual work and it is used to obtain the displacement of the beam along its length.

The formula for calculating the deflection of a simply supported beam is as follows:
$$\Delta = \frac{-F \cdot L^3}{3EI}$$
Where, Δ represents the deflection of the beam, F represents the applied force, L represents the length of the beam, E represents the modulus of elasticity of the material, and I represents the second moment of area of the beam.

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## How to Use the Deflection of a Simply Supported Beam Formula

Using this formula is simple, as all you need to do is to enter the values of the parameters into the formula. The first step is to determine the value of the applied force (F). This can be done by using a strain gauge or by using a load cell. Once you have the value of the applied force, you can then proceed to calculate the value of the deflection.

The next step is to calculate the value of the length of the beam (L). This can be done by measuring the length of the beam and then entering the value into the formula. Once you have the value of the length of the beam, you can then proceed to calculate the value of the modulus of elasticity (E) of the material. This can be done by consulting the material’s datasheet.

The next step is to calculate the value of the second moment of area (I). This can be done by using the polar moment of inertia formula and then entering the value into the formula. Once you have the value of the second moment of area of the beam, you can then proceed to calculate the value of the deflection.

## Advantages & Disadvantages of Deflection of a Simply Supported Beam Formula

The main advantage of using the deflection of a simply supported beam formula is that it is easy to use and is accurate. It is also very useful in determining the displacement of a beam along its length. This makes it ideal for use in engineering applications.

The main disadvantage of the deflection of a simply supported beam formula is that it is not applicable for beams with complex shapes. This is because the formula does not take into account the shape of the beam and does not account for the effects of different materials used in the beam.

## Example of Deflection of a Simply Supported Beam Formula

To illustrate how to use the deflection of a simply supported beam formula, let’s consider the following example. Suppose we have a beam with a length of 10 meters and an applied load of 25 kN. The modulus of elasticity of the material is 210 GPa and the second moment of area of the beam is 0.2 m4.

Using the deflection of a simply supported beam formula, we can calculate the deflection of the beam as follows:
$$\Delta = \frac{-F \cdot L^3}{3EI} = \frac{(-25 \cdot 10^3) \cdot 10^3}{3 \cdot 210 \cdot 10^9 \cdot 0.2} = 0.095 \text{ m}$$
Therefore, the deflection of the beam is 0.095 m.

## Conclusion

In conclusion, the deflection of a simply supported beam formula is an important tool for engineers and can be used to calculate the deflection of a beam at any point along its length. It is based on the concept of virtual work and takes into account the modulus of elasticity, the second moment of area, and the applied force. While it is easy to use and is accurate, it is not applicable for beams with complex shapes.