![]() Using this information, the location of the x-axis of the overall shape can be calculated using the following equation: ![]() To determine the distance between the two axes, it is necessary to divide the shape of the tube into individual pieces, as shown in the following: d is the distance from the arbitrary axis to the axis through the centroid, with units of in.A is the area of the tube, with units of in 2.I’ is the moment of inertia about an arbitrary axis that is parallel to the axis through the centroid.To calculate the moment of inertia about the x-axis, it is necessary to use the parallel axis theorem, which is applied via the following equation: For example, if the bottom wall thickness is larger than the top wall thickness, the tube will not be symmetric about the x-axis. Previously, rectangular tubes that were symmetric about the x-axis and the y-axis were discussed. In the event that the wall thicknesses are not the same, the moment of inertia equations are changed as follows: Example Calculation For Rectangular Tube With Different Thicknessesįor a rectangular tube with the same width and height as the previous example but with t 1 equal to 10 in and t 2 equal to 5 in, the moments of inertia are: Moment Of Inertia For Unsymmetric Rectangular Tube Such a tube is shown in the following image: In practical engineering applications, a rectangular tube with different thicknesses on the sides and the top and bottom may be used. Taking a rectangular tube with a width of 30 in, a height of 50 in, and a thickness of 5 in, the moments of inertia are calculated as follows: Moment Of Inertia For Rectangular Tube With Different Thickness Similarly, the moment of inertia about the y-axis is calculated as follows: Example For A Rectangular Tube I x is the moment of inertia about the x-axis, with units of in 4.t is the thickness of the tube, with units of in.h is the height of the tube, with units of in.w is the width of the tube, with units of in.To calculate the moment of inertia about the x-axis, the following equation is used: Unlike a circular tube, the moment of inertia of a rectangular tube is different about the x-axis than about the y-axis. The moment of inertia of a rectangular tube is a function of the width, w, and height, h, of the tube and the tube thickness, t, as shown in the following figure: Taking a circular tube with an outer radius of 20 in and an inner radius of 18 in, the moment of inertia is calculated as follows: Rectangular Tube Moment Of Inertia ![]() In the case of a typical circular tube, the moment of inertia about the x-axis will be equal to that about the y-axis, and both will pass through the centroid of the tube. I is the moment of inertia, with units of in 4.r i is the inner radius, with units of in.r o is the outer radius, with units of in. ![]() To calculate the moment of inertia for a circular tube, the following equation is used: ![]() The moment of inertia of a circular tube is a function of the outer radius, r o, and the inner radius, r i, as shown in the following figure:Īlternatively, the outer diameter and the wall thickness, t, may be given, where the thickness is simply the outer radius minus the inner radius. In optimizing an engineering design, choosing the dimensions of the tube to withstand expected loads can help minimize the overall weight of the tube, which can reduce costs. A tube with a higher moment of inertia will resist those forces and moments better than a tube with a lower moment of inertia, which means that there will be less bending stress in the tube. Regardless of the shape of the tube, the moment of inertia is used in engineering design to determine how the tube will respond to forces and moments that cause bending. Example Calculation For Unsymmetric Rectangular Tube.Moment Of Inertia For Unsymmetric Rectangular Tube.Example Calculation For Rectangular Tube With Different Thicknesses.Moment Of Inertia For Rectangular Tube With Different Thickness. ![]()
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