A bending moment and the resulting internal tensile and compressive stresses needed to ensure the beam is in equilibrium.Īs we can see in the diagram, there is some central plane along which there are no tensile or compressive stresses. These stresses exert a net moment to counteract the loading moment, but exert no net force so that the body remains in equilibrium. When an object is subjected to a bending moment, that body will experience both internal tensile stresses and compressive stresses as shown in the diagram below.
Bending Stresses and the Second Area Moment On this page we are going to focus on calculating the area moments of inertia via moment integrals. Just as with centroids, each of these moments of inertia can be calculated via integration or via composite parts and the parallel axis theorem. Moments applied about the x and y axis represent bending moments, while moments about the z axis represent a torsional moments. The moments of inertia for the cross section of a shape about each axis represents the shape's resistance to moments about that axis. Moments about the x and y axes would tend to bend an object, while moments about the z axis would tend to twist the body. The moment of inertia about each axis represents the shapes resistance to a moment applied about that respective axis. Specifically, the area moment of inertia refers to the second, area, moment integral of a shape, with I xx representing the moment of inertia about the x axis, I yy representing the moment of inertia about the y axis, and J zz (also called the polar moment of inertia) representing the moment of inertia about the z axis.
Area moments of inertia are used in engineering mechanics courses to determine a bodies resistance to bending loads or torsional loads.
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