Polar Moment of Inertia - Weld Treated As line

[maramos]

I'm doing a torsion weld calc on a pipe and cant figure out why the polar moment of Inertia formula (Jw) for a weld treated as a line is different than the standard polar moment of inertia formula for a circle.
In my text book, the polar moment of Inertia (J) of a circle (with axis on CG)is J=Iy+Ix.
For a 4" pipe I calculate (J) as 25.133in^4 using the textbook formula.
Using formula taken from the attached sheet Jw = 50.26in^4
Why are these two values different? Jw = 2xJ

Thanks in advance for the help.

 

[SnTMan]

maramos, sometimes called the unit properties, they do not contain info about the weld size, thus can be easily tabulated. Note the units, they are one (length unit) short, i.e. in^3 instead of in^4. To get the polar monent from the unit polar moment, multiply the unit moment by the weld leg (h) and by 0.707 (sin or cos 45 deg) to account for the throat dimension. J = 0.707 * h * Jw.

Odd this question should come up, I had a weld torsion problem this morning myself and dug out the old Shigley and Miske to refresh.

Regards,

Mike

 

[SnTMan]

maramos, maybe I have taken you wrong, I can't seem to get your numbers. Apologies if so.

 

[wannabeSE]

The units for the polar moment of intertia of lines (rather than areas) are length[sup]3[/sup].
I[sub]x[/sub] = I[sub]y[/sub] = πR[sup]3[/sup] = πD[sup]3[/sup]/8
I[sub]x[/sub] + I[sub]y[/sub] = πD[sup]3[/sup]/4

 

[desertfox]

Try this:-