![]() The cross-section shown is not axisymmetric about its x-axis due to the thickness at the bottom ( t 2) being larger than at the top ( t 1). An example of a non-axisymmetric hollow rectangle is shown in the following figure: If the hollow rectangular tube is designed such that it is not axisymmetric about one (or both) axis, it is necessary to utilize the parallel axis theorem to evaluate the moment of inertia about the axis running through the centroid of the cross-section. Calculating The Moment Of Inertia For A Non-Axisymmetric Hollow Rectangle In that case, when calculating the interior dimensions, it will be necessary to use the top and bottom thickness for determining the interior height and the side thickness for determining the interior width. The moment of inertia about the y-axis is calculated as follows: Variation Of Calculation With Different ThicknessesĪlthough the cross-section may be axisymmetric about both axes, the thickness of the top and bottom may be different from that of the two sides. Calculate the moment of inertia about the x-axis:.Calculate the interior dimensions of the rectangular tube:.The moment of inertia about the x-axis is calculated using the following steps: Take a hollow rectangular tube with the following dimensions as an example to demonstrate calculating the moments of inertia: Where t is the thickness of the rectangle, with SI units of mm.Ī graphical representation of these dimensions is shown in the following figure:īecause the thickness t remains constant around the entire rectangle, the structure is axisymmetric about both its x-axis and its y-axis. The interior dimensions of the rectangle are calculated as follows: h h is the interior height of the rectangle, with SI units of mm.b h is the interior width of the rectangle, with SI units of mm.h is the exterior height of the rectangle, with SI units of mm.b is the exterior width (base) of the rectangle, with SI units of mm.I y is the moment of inertia about the y-axis, with SI units of mm 4.I x is the moment of inertia about the x-axis, with SI units of mm 4.Calculation Of The X-Axis Moment Of InertiaĬalculating The Moment Of Inertia For A Hollow Rectangle That Is Axisymmetricįor a rectangular tube or hollow rectangle that is symmetric about both its x-axis and its y-axis, the equations for its moments of inertia are:.Calculation Of The Y-Axis Moment Of Inertia.Calculating The Moment Of Inertia For A Non-Axisymmetric Hollow Rectangle. ![]() ![]() ![]() Variation Of Calculation With Different Thicknesses.Calculating The Moment Of Inertia For A Hollow Rectangle That Is Axisymmetric. ![]()
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