Area Moment - Accuracy question

Rhino
1

I have a quick question concerning the error values on the AreaMoments command.

I’m working on a script calculating section properties (Inertia).

If I draw a planar surface that is 152.4 x 406.4, I get an Ixx about the centroid of 852441960. This matches exactly the results of a hand calculation (= b.h^3/12).

But if I draw a slightly different surface that is 152.4 x 406.422, I get an Ixx about the centroid of 852580707. Which is different than the hand calculation = 852580405. The error is bout 301 mm4. In absolute terms, it isn’t significant at all.

What I find confusing is the output from Rhino suggests the error is +/- 0.1, which is wildly off. I imagine the error is in model units?

The actual error is on the order of .000035%, so perhaps the +/-0.1 is a percentage?

Best,

Tom

2

I get 852580405 for the moment of inertia about the centroid for a planar surface 152.4 x 406.422. Tested with a planar surface with centroid at the origin, and a planar surface with centroid at an arbitrary location. The error compared to your hand calculation is 0.
AreaMomentDC01.3dm (2.4 MB)

Surface with centroid at world origin:
Area = 61938.7128 (+/- 1e-05) square millimeters
Area Centroid = 2e-14,-4.02753668e-16,0 (+/- 3.2e-14,1e-25,0)
Area Moments:
First Moments
x: 1e-09 (+/- 2e-09)
y: -2e-11 (+/- 1e-20)
z: 0 (+/- 0)
Second Moments
xx: 852580405 (+/- 0.1)
yy: 119881140 (+/- 0.1)
zz: 0 (+/- 0)
Product Moments
xy: -4.26614173e-08 (+/- 4.7e-08)
yz: 0 (+/- 0)
zx: 0 (+/- 0)
Area Moments of Inertia about World Coordinate Axes
Ix: 119881140 (+/- 0.1)
Iy: 852580405 (+/- 0.1)
Iz: 972461545 (+/- 0.1)
Area Radii of Gyration about World Coordinate Axes
Rx: 43.9940905 (+/- 1e-08)
Ry: 117.323926 (+/- 1e-07)
Rz: 125.301171 (+/- 1e-07)
Area Moments of Inertia about Centroid Coordinate Axes
Ix: 119881140 (+/- 0.1)
Iy: 852580405 (+/- 0.1)
Iz: 972461545 (+/- 0.1)
Area Principal Moments of Inertia about Centroid and Principal Axes
I1: 119881140 , Direction ( 1, 0 ,0)
I2: 852580405 , Direction ( 0, 1 ,0)
I3: 972461545 , Direction ( 0, 0 ,1)
Area Radii of Gyration about Centroid Coordinate Axes
Rx: 43.9940905 (+/- 1e-08)
Ry: 117.323926 (+/- 1e-07)
Rz: 125.301171 (+/- 1e-07)

Surface with centroid at -184.891641,225.18477,0
Area = 61938.7128 (+/- 1e-05) square millimeters
Area Centroid = -184.891641,225.18477,0 (+/- 1e-07,1e-07,0)
Area Moments:
First Moments
x: -11451950.3 (+/- 0.01)
y: 13947654.8 (+/- 0.01)
z: 0 (+/- 0)
Second Moments
xx: 2.96995029e+09 (+/- 1)
yy: 3.26068058e+09 (+/- 1)
zz: 0 (+/- 0)
Product Moments
xy: -2.57880479e+09 (+/- 1)
yz: 0 (+/- 0)
zx: 0 (+/- 0)
Area Moments of Inertia about World Coordinate Axes
Ix: 3.26068058e+09 (+/- 1)
Iy: 2.96995029e+09 (+/- 1)
Iz: 6.23063087e+09 (+/- 1)
Area Radii of Gyration about World Coordinate Axes
Rx: 229.442064 (+/- 1e-07)
Ry: 218.974479 (+/- 1e-07)
Rz: 317.164757 (+/- 1e-07)
Area Moments of Inertia about Centroid Coordinate Axes
Ix: 119881140 (+/- 0.1)
Iy: 852580405 (+/- 0.1)
Iz: 972461545 (+/- 0.1)
Area Principal Moments of Inertia about Centroid and Principal Axes
I1: 119881140 , Direction ( 1, 0 ,0)
I2: 852580405 , Direction ( 0, 1 ,0)
I3: 972461545 , Direction ( 0, 0 ,1)
Area Radii of Gyration about Centroid Coordinate Axes
Rx: 43.9940905 (+/- 1e-08)
Ry: 117.323926 (+/- 1e-07)
Rz: 125.301171 (+/- 1e-07)