# Difference Between Plastic Modulus and Moment of Inertia

** Plastic Modulus vs Moment of Inertia**

A plastic modulus is the short term for a plastic section modulus. A plastic section modulus, in turn, is one of the classifications of a section modulus, a geometric property for a given cross section. A plastic modulus is used in the field of structural engineering, specifically in the design of beams or flexural members in every level or any fiber.

The plastic modulus is a formula that is used for materials where there is the presence of dominance or irreversible plastic behavior. It is used to calculate the plastic moment or the full capacity of the cross section. In this context, “plastic” is a term that refers to the type of deformation which beams are prone to. The formula is applied to various geometric shapes like rectangles, squares, full and hollow circles, as well as I-beams. There are various formulas for each shape and material.

The main formula for the plastic modulus is equal to the sum of all the areas of the cross sections on each side of the PNA. The sum is multiplied by the distance from local androids of two areas. As a formula, it is dependent on the material’s location of the plastic neutral axis or PNA. In an equation, the plastic modulus is represented by the letter “Z.”

On the other hand, the moment of inertia is also called a mass moment of inertia, rotational inertia, or polar amount of inertia. It is covered in the field of classical mechanics also known as physics. Basically, the moment of inertia is the force needed for an object to change speeds. Moment of inertia measures an object’s resistance to factors that involve changes in its angular rotation or acceleration.

“Low moment of inertia” means that the object requires a small amount of inertia to change course while objects with a high moment of inertia require a lot more force and difficulty to change their speed.

Like the plastic modulus, the moment of inertia is also a mathematical formula and is represented by a letter. In this case, the letter “I” is used to represent the concept. Moment of inertia equals the product of the body or object’s mass and the square of the object’s distance from its axis of rotation.

The concept was first introduced by Leonard Euler, a Swiss mathematician in 1730 under his book, called Theoria Motus Corporum Solidorum Seu Rigidorum or Theory of the Motion of Solid or Rigid Bodies.

There are many practical applications under the moment of inertia. It is used in car manufacturing and also in sports like golf, baseball, and diving.

Summary:

1.Both the moment of inertia and plastic modulus are fundamental concepts in their fields. Also, both concepts can be expressed as mathematical equations. As equations, they are represented by a single letter followed by a formula to calculate and applied to a certain situation.

2.Moment of inertia is a concept under the field of physics while plastic modulus falls under the study of structural engineering.

3.Another difference between the two studies is evident in their equation form in terms of representation. The moment of inertia is represented by the letter “I” while the plastic modulus is also expressed by a single letter, this time by the letter “Z.”

4.Both concepts require an object or a material. In plastic modulus, the main concern is the point of deformation while the focus of moment of inertia is the speed of a particular object.

5.Moment of inertia is not a property because it refers to the force needed to change speeds. It can be classified as a low moment of inertia or high moment of inertia. On the other side, a plastic modulus is a type of section modulus. Plastic modulus is a property of the cross section and not of the material.

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