Polar Moment of Inertia for extruded rectangular tubing
Polar Moment of Inertia for extruded rectangular tubing
(OP)
Can anyone remind me the equation or steer me to an immediate resource for the Polar Moment of Inertia of extruded retangular tubes for figuring total shear loading at the Neutral Axis for a rectangular hollow tube with a torsional load?
Cheers!
Cheers!





RE: Polar Moment of Inertia for extruded rectangular tubing
Wes C.
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RE: Polar Moment of Inertia for extruded rectangular tubing
back transcribing from a spreadsheet, ie there may be errors
2*t^2(a-t)^2(b-t)^2/(at+bt-2*t^2)
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
RE: Polar Moment of Inertia for extruded rectangular tubing
I don't have Roark's - it "took a walk" on me.
Ah, can I assume "a" = height above the Neutral Axis, "b" = width across the Neutral Axis, and "t" is the material wall thickness?
Chris
RE: Polar Moment of Inertia for extruded rectangular tubing
Ixx = b*a^3/12-(b-2t)*(a-2t)^3/12
= (2a^2t(3b+a)-12at^2(a+b)+8t^3(b+3a-2t))/12
Iyy = a*b^3/12-(a-2t)*(b-2t)^3/12
= (2b^2t(3a+b)-12bt^2(a+b)+8t^3(a+3b-2t))/12
RE: Polar Moment of Inertia for extruded rectangular tubing
simplify polar moment = [(a+b-6t)*(a+b)^2+16t^2*(a+b-t)]*t/6
RE: Polar Moment of Inertia for extruded rectangular tubing
t/6*[3*(a+b-2t)(a-t)(b-t)+(a-t)^3+(b-t)^3]
RE: Polar Moment of Inertia for extruded rectangular tubing
RE: Polar Moment of Inertia for extruded rectangular tubing
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
RE: Polar Moment of Inertia for extruded rectangular tubing
shear stress of a closed section due to torque is T/(2[A]t), where [A] is the enclosed area of the tube (a-t)(b-t).
tho' the reference to "neutral axis" is abit confusing
RE: Polar Moment of Inertia for extruded rectangular tubing
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
RE: Polar Moment of Inertia for extruded rectangular tubing
comparing your formula and mine yours has extra terms that amount to (a-t)(b-t)/(a+b-2t). for the couple of tests i did this is greater than 1 (and got bigger as the section got thinner), something like 2. this would give lower stresses, no ?
RE: Polar Moment of Inertia for extruded rectangular tubing
A reasonable rule of thumb is that you'll only see 60% of the theoretical stiffness near the joint (say 10*a) if you use squarish tubes and butt joints. Good joint design can take that up to 90-95%.
It is almost impossible to manually estimate the stiffness of sections that are re-entrant or generally weird, such as are used in cars. A good example of that is using a light foam to stiffen a steel structure. At first sight it is ridiculous, but the foam stabilises the flat surfaces in the section and provides a measurable improvement in performance.
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.