bending moment of inertia for multiple step shaft
bending moment of inertia for multiple step shaft
(OP)
I created a shaft with 3 steps and using CAD program I was able to find out the Ix, Iy, Iz on the shaft.
L1/D1 = 2"/5"
L2/D2 = 4"/7"
L3/D3 = 3"/6"
density (rho) = 0.283 lb/in3
From CAD, I got Ix = 65.74 Lb-in2 and Iy = Iz = 785.7 lb-in2
How do I get Iy and Iz analytically? I was able to get Ix by summing up rho*L*pi*D^4/32 for all sections, but this doesn't work for Iy and Iz.
L1/D1 = 2"/5"
L2/D2 = 4"/7"
L3/D3 = 3"/6"
density (rho) = 0.283 lb/in3
From CAD, I got Ix = 65.74 Lb-in2 and Iy = Iz = 785.7 lb-in2
How do I get Iy and Iz analytically? I was able to get Ix by summing up rho*L*pi*D^4/32 for all sections, but this doesn't work for Iy and Iz.





RE: bending moment of inertia for multiple step shaft
i think Iy (and Iz) are based on the plan view of the shaft (like areas of D*L) about the center of mass of the shaft ?
Quando Omni Flunkus Moritati
RE: bending moment of inertia for multiple step shaft
RE: bending moment of inertia for multiple step shaft
Quando Omni Flunkus Moritati
RE: bending moment of inertia for multiple step shaft
Ix = m*D^2/8
Iy = Iz = m/48*(3*D^2+4*L^2)
For Ix, I can calculate each section separately and sum all the sections to obtain the Ix for the entire shaft. I can't do that for Iy and Iz.
RE: bending moment of inertia for multiple step shaft
Quando Omni Flunkus Moritati
RE: bending moment of inertia for multiple step shaft
V(x) = Int {w(x)}dx
M(x) = Int {V(x)}dx
Slope(x) = Int {M(x)}dx / [E*I(x)]
displacement y(x) = Int{Slope(x)}dx
Note that I(x) denotes I varying... different in the three regions.
Sorry if I missed your point and am rambling about irrelevant and obvious things.
=====================================
(2B)+(2B)' ?
RE: bending moment of inertia for multiple step shaft
Your software has calculated the rotational moment of inertia, as if it were a 3 dimensional flywheel. That's fine and dandy, if you are designing 3 dimensional flywheels.
I suspect from the thread title you are interested in the bending behaviour of your shaft considered as a beam, in which case the software has led you up the proverbial garden path, taken you into the wood shed, and is about to have its wicked way with you.
So go back to elastic beam theory. If you describe the problem you need solving, I expect somebody here can help.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: bending moment of inertia for multiple step shaft
you've posted an expression of mass moment of a cylinder about the y- (and z-) axis through the centroid of the cylinder (i think so) or through the base (i could look up mass moments of inertia but i don't feel inclined to) ? just summing the x-axis mass moments for the individual cylinders works because they share the same x-axis and it's through the CG of the assembly, but doesn't work for y- and z- 'cause these axes are not colinear (they're parallel). Research parallel axes theorem.
alternatively, since he can't do (or recognise) the simple parallel axis maybe he doesn't ??
Quando Omni Flunkus Moritati
RE: bending moment of inertia for multiple step shaft
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: bending moment of inertia for multiple step shaft