VIDEO: Calculating the moment of deviation in mechanics

What the moment of deviation actually is

• First of all, it is important to know that the moment of deviation or centrifugal moment or secondary moment of inertia called, is a physical quantity which measures the attempt to determine the axis of rotation of a rotating body change.
• So there is always a moment of deviation when a body does not rotate around any of its main axes of inertia. The moments of deviation, like moments of inertia in general, can be related to the inertia tensor can be ascribed, with the moment of deviation itself as a secondary diagonal element of the inertia tensor consider is.
• From a mathematical point of view, this can be calculated using the formula Ixy = integral over A of x and y. However, in order to be able to solve this formula and actually calculate the moment of inertia, you should know and pay attention to a few things.

What you should consider when calculating

In general, it should be helpful to proceed according to the following scheme.

1. For example, in the first step, if not specified, you can determine the area of ​​the concrete bodies and, if necessary, calculate their total area from this. This should represent basic mathematical knowledge, which should be more or less easy for almost everyone.
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2. In the second step, you finally determine the center of gravity of the specific area or areas, if this was not specified. The calculation of the center of gravity is easier to accomplish especially when the volume center point lies on the axis of symmetry of the body. So the center of gravity of point symmetrical figures is simply the center of symmetry.
3. Finally, for the third step, you can look up the Izo for the 3 bodies in tables and Calculate accordingly - for a rectangle, this can be done using the formula (b * h³) 12, for example accomplish.
4. Finally it comes to the calculation of Iz, which should generally be Izo + Steiner share.
5. For the Steiner part itself you should remember the following formula: Distance to the center of gravity in the square * area (y² * A).
6. It is also worth knowing that the moment of deviation is 0 when the coordinate system passes through the centroid. In such a case, with a moment of deviation of zero, you only need Steiner's part to solve the formula. If you know that, you may end up saving yourself steps 1 to 6.

Ultimately, you should definitely have the formula collection to hand for determining the deviation moment. A run-of-the-mill solution for calculating moments of deviation can basically not be given here. A concrete solution proposal can only be made with the concrete task. In this sense, it should be said at the end - good luck!