About Moments of Inertia (AutoCAD Mechanical Toolset)

With the AMINERTIA command, you can calculate the moment of inertia of closed contours.

Closed contours are contours that can be hatched using the AutoCAD HATCH command (not the BHATCH command).

Moment of inertia

When you start the AMINERTIA command, you are prompted to select a cross section. The cross section you select must be a closed contour. AutoCAD Mechanical toolset fills the area, and you are asked if the filled area is the area you want to be analyzed.

In the next step, the program draws the principal axes, 1 and 2, for the moment of inertia and performs the moment of inertia calculation. The following results are displayed:

• X and Y coordinates of the center of gravity of the cross section.
• Moment of inertia (I1 and I2) along the 1 and 2 axes.
• Angle between the horizontal line and the 1 axis, for which I1 is always the greater moment of inertia.

In the final stage of the calculation, you specify the direction of the load forces. The direction of the load forces influences the result of the effective moment of inertia. Make also sure that the load forces you specify must be acting in the same plane. The following values are displayed.

• Effective moment of inertia that corresponds to the load direction you selected.
• Angle of deflection.
• Maximum distance from the neutral line to the border of the extension side.
• Minimum distance from the neutral line to the border of the compression side.

The moment of inertia block, which is a table containing the results of the moment of inertia calculation, is displayed and can be inserted anywhere in the drawing.

Note: If you change the contour of the cross section, a new calculation of the moment of inertia is carried out automatically and the moment of inertia block is also updated.

Moment of inertia block

The moment of inertia block is a value table containing the results of the moment of inertia calculation.

Attributes of the moment of inertia block are as follows:

Block title	Name of the block.
I1	Moment of inertia along the first main axis.
I2	Moment of inertia along the second main axis.
Sc	Distance of the outermost fiber in compression from the neutral axis.
St	Distance of the outermost fiber in tension from the neutral axis.
A	Area of the cross section.

Moment of inertia for circular or rectangular cross sections

To calculate the moment of inertia for cross sections of cylinders, hollow cylinders, rectangular prisms, or hollow rectangular prisms, you can use the AMINERTIAPROF or AMINERTIA command.

Each command uses different algorithms for calculating the moment of inertia. The procedure for calculating the moment of inertia for the same cross section varies by commands:

• With the AMINERTIA command, you select the cross section in the drawing and specify the direction of the load force before starting the moment of inertia calculation.
• With the AMINERTIAPROF command, you only specify the dimension values for the selected cross section to obtain the moment of inertia.

The AMINERTIA command can be used on complex objects; it delivers accurate results. The AMINERTIAPROF command can be used only on the types of cross sections mentioned previously; the values it delivers can vary up to 0.1% from the values obtained with the AMINERTIA command. These deviations, however, do not have any impact on subsequent calculations.