second moment of area

I - the second moment of area about the neutral axis x.

The participants were also asked to minimize the polar second moment of area of the total shape.

I is the second moment of area of the cross-section in metres to the fourth power.

The critical load is directly proportional to the second moment of area of the cross section.

It is often easier to derive the second moment of area with respect to its centroidal axis, .

However, it may be necessary to calculate the second moment of area with respect to a different, parallel axis, say the axis.

This article is about the geometrical property of an area, termed the second moment of area.

In other words, the second moment of area of "missing" parts are considered negative for the method of composite shapes.

It is identical to the second moment of area J for concentric circular tube, or round solid shafts only.

Summing the second moments of area for the triangular segments in a counterclockwise fashion yields:

Note that is the elastic modulus and that is the second moment of area of the beam's cross-section.

A stiffer beam (high modulus of elasticity and high second moment of area) produces less deflection.

The stiffness of a structural element of a given material is the product of the material's Young's modulus and the element's second moment of area.

The parallel axes rule also applies to the second moment of area (area moment of inertia) for a plane region D:

Developments of the planimeter can establish the position of the first moment of area (center of mass), and even the second moment of area.

Tensile and compressive stresses increase proportionally with bending moment, but are also dependent on the second moment of area of the cross-section of the structural element.

The second moment of area is typically denoted with either an for an axis that lies in the plane or with a for an axis perpendicular to the plane.

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.

For instance, consider the bending of a thin-walled tube: the second moment of area is inversely related to the stress in the tube wall, i.e. stresses are lower for larger values.

If instead of force, the area of the figure or mass of the body is considered, it is called the second moment of area or second moment of mass.

Thus the second moment of area will vary approximately as the inverse of the density squared, and performance of the beam will depend on Young's modulus divided by density squared.

Note that the ultimate strength of a beam in bending depends on the ultimate strength of its material and its section modulus, not its stiffness and second moment of area.

The second moment of area for any simple polygon on the XY-plane can be computed in general by summing contributions from each triangular segment of the polygon (method of composite shapes).

The car has 50:50 front-rear weight distribution, and a low second moment of area that is achieved by mounting the engine behind the front axle and the fuel tank ahead of the rear axle.