Second moment of inertia1/22/2024 ![]() To sum up, the formula for finding the moment of inertia of a rectangle is given by I=bd³ ⁄ 3, when the axis of rotation is at the base of the rectangle. H is the depth and b is the base of the rectangle. In this case, the formula for the moment of inertia is given as, The variables are the same as above, b is the width of the rectangle and d is the depth of it.įormula when the axis is passing through the centroid perpendicular to the base of the rectangle When the axis is passing through the base of the rectangle the formula for finding the MOI is, The formula for finding the MOI of the rectangle isĭ = depth or length of the rectangle Formula when the axis is passing through the base of the rectangle When the axis of rotation of a rectangle is passing through its centroid. Formula when the axis is passing through the centroid Let us see when we change the axis of rotation, and then how the calculation for the formula changes for it. Therefore, the equation or moment of inertia of a rectangular section having a cross-section at its lower edge as in the figure above will be, Similar to mathematical derivations, as we found the MOI for the small rectangular strip ‘dy’ we’ll now integrate it to find the same for the whole rectangular section about the axis of rotation CD. If we see the area of a small rectangular strip having width ‘dy’ will beĪnd the moment of inertia of this small area dA about the axis of rotation CD according to a simple moment of inertial formula which is And after finding the moment of inertia of the small strip of the rectangle we’ll find the moment of inertia by integrating the MOI of the small rectangle section having boundaries from D to A. ![]() Involvement of this ‘dy’ will make the assumptions and calculations easier. Now, let us find the MOI about this line or the axis of rotation CD.Īlso, consider a small strip of width ‘dy’ in the rectangular section which is at a distance of value y from the axis of rotation. Consider the line or the edge CD as the axis of rotation for this section. Where b is the width of the section and d is the depth of the section. Consider a rectangular cross-section having ABCD as its vertices. ![]()
0 Comments
Leave a Reply.AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |