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The second moment of area, also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis. The unit of dimension of the second moment of area is length to fourth power, L 4 , and should not be confused with the mass moment of inertia .
The second moment of area for the entire shape is the sum of the second moment of areas of all of its parts about a common axis. This can include shapes that are "missing" (i.e. holes, hollow shapes, etc.), in which case the second moment of area of the "missing" areas are subtracted, rather than added.
The above formula is for the xy plane passing through the center of mass, which coincides with the geometric center of the cylinder. If the xy plane is at the base of the cylinder, i.e. offset by d = h 2 , {\displaystyle d={\frac {h}{2}},} then by the parallel axis theorem the following formula applies:
In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members.Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness.
Simply put, the polar moment of area is a shaft or beam's resistance to being distorted by torsion, as a function of its shape. The rigidity comes from the object's cross-sectional area only, and does not depend on its material composition or shear modulus. The greater the magnitude of the second polar moment of area, the greater the torsional ...
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
A is the cross-sectional area of the flow, P is the wetted perimeter of the cross-section. More intuitively, the hydraulic diameter can be understood as a function of the hydraulic radius R H, which is defined as the cross-sectional area of the channel divided by the wetted perimeter. Here, the wetted perimeter includes all surfaces acted upon ...
The area of the side is known as the lateral area, L. An open cylinder does not include either top or bottom elements, and therefore has surface area (lateral area) = The surface area of the solid right circular cylinder is made up the sum of all three components: top, bottom and side.