![]() ![]() 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: Mass moment of inertia or polar moment of inertia: resistance of a mass to changes in rotational velocity. ![]() 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? 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. Therefore, the required section modulus to achieve a safety factor of 2 in bending is calculated as shown below:įor this example problem, the required section modulus is 6.67 in3. Rearrange the equation from the beginning of this post into the following form:Ī36 steel is equal to the yield stress of 36,000 psi. Calculate the required section modulus with a factor of safety of 2. Consider the following example:Ī beam made from A36 steel is to be subjected to a load of 120,000 lbf-in. The required section modulus can be calculated if the bending moment and yield stress of the material are known. Y = the distance from the neutral axis to the outside edge of a beam What is the required section modulus? I = the area moment of inertia (or second moment of area) The general formula for elastic section modulus of a cross section is: The elastic section modulus of C-channel is calculated from the following equation: ![]()
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