Section Modulus is also referred to as the ** Polar Modulus** or the

**. It is denoted by**

*Torsional Sectional Modulus**Z*

_{p}. Along with these, there are two more definitions also there to discuss. So let’s discuss this topic in more detail.

(FYI: *We discuss this topic more in terms of circular shafts, If you are looking for other cross-sections, you may understand the topic at least here, later you can apply for the desired section you would like)*

## Section Modulus

Section Modulus is the geometric property of the given cross-section of any shaft or beam structures. It is the direct measure of the strength of the shaft section or the beam section. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Section modulus is defined as the ratio of polar moment of inertia to the radius of the shaft or the distance from the neutral axis to the outer fibres.

The common way of calculating Section_Modulus for a shaft requires is its diameters even if it is a solid or hollow shaft. If it is a beam (Square/rectangle in shape) then it will require the moment of inertia and the distance of the outer fibres from its neutral axes.

Following is the formula to calculate the section_modulus for the solid shaft

Where d is the diameter of the shaft.

If it is the hollow shaft then

On the other hand, there are two types of section moduli, The Elastic Section_Modulus, and the Plastic Section_Modulus.

The ** Elastic Section Modulus** has the same definition as the above-mentioned formula where it should be used for the materials which behave elastically under loading.

whereas the ** Plastic Section Modulus** used for the materials which have plastic behaviour as a dominant character.

The formula for the plastic section_modulus is defined as the sum of the product of the area of cross-section on each side of the plastic neutral axis and the distance from the local centroids of the areas to the plastic neutral axis.

## Conclusion

We have discussed the definition of the Section_Modulus and written the formulas to calculate it for the solid shaft and also defined what is the Elastic and the Plastic Section Moduli. If you have any further thoughts on this topic, let us know in the comment section below.

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