Z axis Moment of Inertia for L shape
Z axis Moment of Inertia for L shape
(OP)
Does anyone know how to calculate the Z axis Moment of Inertia for a L-shape?
Thanks in advance
Thanks in advance
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Z axis Moment of Inertia for L shape
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Z axis Moment of Inertia for L shapeZ axis Moment of Inertia for L shape(OP)
Does anyone know how to calculate the Z axis Moment of Inertia for a L-shape?
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RE: Z axis Moment of Inertia for L shape
Anyway, once you get the product of inertia use varying values of theta (O) in the equation:
Ix(cos^2(O))+ Iy(sin^2(O))-2Ixy(sin(O)(cos(O)) until you get the max value. This is the max I. Then subtract this value from Ix+Iy and this will give you Imin.
RE: Z axis Moment of Inertia for L shape
The principal moments of inertia for an unsymmetrical shape can be found in "Elements of Strength of Materials" by Timoshenko and McCullough as follows:
Imax/Imin = (Ix + Iy)/2 +/- {[(Ix - Iy)/2]^2 + Ixy^2)^0.5
They can also be found by using a Mohr's circle.
Best regards,
BA
RE: Z axis Moment of Inertia for L shape
RE: Z axis Moment of Inertia for L shape
Best regards,
BA
RE: Z axis Moment of Inertia for L shape
EdR
P.S. Use the same axis location used to get the moments of inertia if you are going to compute the principal values...If not the transfer theorm for products of inertia is Ixy = Icg + xbar*ybar*A
RE: Z axis Moment of Inertia for L shape
I'm attaching my example calc.
RE: Z axis Moment of Inertia for L shape
actually it works much like Mohr's circle ... it's easy enought to calc Ixx and Iyy (x^2*dA) then Ixy is just x*y*dA ... plot the two points (Ixx, Ixy) and (Iyy, -Ixy), draw the circle, and get Imax and Imin (where Ixy = 0).
RE: Z axis Moment of Inertia for L shape
RE: Z axis Moment of Inertia for L shape