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Hi, I've been always using eq. I=Pi*(D^4-d^4)/64 to find moment of inertia of a pipe. Recently I've seen that moment can be in different directions, and then it is expressed differently. So what is the difference between Ixy and Iz?
i think you are using product of Inertia- see moment of Inertia represented as a Tensor -about an axis which is not fixed in the body.So what is the difference between Ixy and Iz?
You apparently are talking about the second moment of area of the pipe, at least, that's what your formula calculates.Hi, I've been always using eq. I=Pi*(D^4-d^4)/64 to find moment of inertia of a pipe. Recently I've seen that moment can be in different directions, and then it is expressed differently. So what is the difference between Ixy and Iz?
The second moment of area is used primarily to calculate the bending stress in a beam, so Iz would have no use for that calculation, assuming that the cross section of the pipe lies in the x-y plane.OK, thank you! I understand that it is a confusing question, let's say z in the vertical axis. I wanted to see your opinions on this one, as I didn't see the difference between body's moment of inertia in different axes...
If you are using dynamic equations, there could possibly be a mix of area moments of inertia and mass moment of inertia for the different sections of pipe. If the piping assembly is fixed so that there are no gross rotations about a fixed point, then you are probably dealing just with area moments of inertia.Right, I see now. I want to calculate displacement in pipe using dynamic eq. [M]{U''}+[C]{U'}+[K]{U}={F}, where U is displacement, and U' and U'' are its derivateves. M, C, K are matrices of mass, damping and stiffness. Matrices are defined, and some of the expressions contain Ixy and Iz (area moment of inertia). Actually axes are as in the drawing, so I assume that Iy=Iz, and Ix = 0?
View attachment 96807
OK, it became a bit more clear, thank you very much for your input.If you are using dynamic equations, there could possibly be a mix of area moments of inertia and mass moment of inertia for the different sections of pipe. If the piping assembly is fixed so that there are no gross rotations about a fixed point, then you are probably dealing just with area moments of inertia.
The stiffness matrices K will require the area moments of inertia, while the mass matrix M will generally require only the masses of the individual elements.
Because the stiffness matrices K will presumably be assembled from individual elements, the area moments of inertia will probably be referred to some local element coordinate system, so it would be unwise to specify the values of the individual element inertias until this point is established.