Mass moment of inertia is a mass property with units of mass*length^2. Section modulus is a cross-section property with units of length^3. Section modulus and mass moment of inertia are entirely different properties altogether. Therefore, the equation for maximum bending stress becomes: Since the stress is greatest at the farthest distance from the neutral axis, section modulus combines both the area moment of inertia and the maximum distance from the neutral axis into one term: Where σ is the stress in the beam, y is the distance from the neutral axis passing through the centroid, and I is the area moment of inertia. Section modulus and area moment of inertia are closely related, however, as they are both properties of a beam’s cross-sectional area.Īrea moment of inertia can be used to calculate the stress in a beam due to an applied bending moment at any distance from the neutral axis using the following equation:
Area moment of inertia: a geometric cross-sectional property (also known as second moment of area).There are two cases in which the term “moment of inertia” is used: What is the difference between moment of inertia and section modulus? It is very rare that a section would be allowed to yield, and so plastic section modulus is rarely used. Plastic section modulus, however, is used when a material is allowed to yield and plastically deform.
This is the most common usage, because it deals with materials that are within their elastic limit, or stresses less than the yield strength. When the term section modulus is used, it is typically referring to the elastic modulus. What is the difference between section modulus and plastic modulus?
#Moment of inertia of a circle beam section software
For that reason, it’s common to use specialized software to calculate the section modulus in these instances. This can be a very difficult integration to perform with a high level of accuracy for an irregular shape. Therefore, the section modulus of an irregular shape can be defined by L = the perpendicular distance from the element to the neutral axis passing through the centroid The definition of moment of inertia isĭA = the area of an element of the cross-sectional area of the irregular shape Recall that the section modulus is equal to I/y, where I is the area moment of inertia. How do you find the section modulus of an irregular shape?Įven if a shape does not have a pre-defined section modulus equation, it’s still possible to calculate its section modulus.