MI properties for a standard shapes can be obtained from a list of table or standard formula. But for irregular shapes and nonstandard sizes, the sectional properties are not readily available. This Presentation is about a tool that allows you to draw any shape and then calculate geometric and inertial properties for any arbitrary shape. Geometric and MI properties of any regular/ standard shape can also be predicted.

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AREA
LITE/PRO
Area Moment of Inertia Calculator
by apps.atoa.com

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Bending Cross Sectional Shape vs
Load = 1000 N
Same Material
Same Support
Same weight
=
Cost
Deflection
=
Performance
5 mm vs 30 mm
6X better
?
Area moment of Inertia
1.46 mm4 vs 0.22 mm4

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Bending Cross Sectional Shape vs
Higher Area MI
=
Better Flexural loading performance

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Area Moment of Inertia app
Why?
• Area, principal or 2nd moment of inertia
(MI) is the sectional properties of 2D shapes
• Useful for structural mechanics and
dynamics and s critical for bending stiffness
and strength
• MI properties for a standard shapes can be
obtained from a table or standard formulas.
• But for irregular shapes and nonstandard
sizes, the sectional properties are not
readily available.
• This tool allows you to draw any shape and
calculate geometric and inertial properties.
Standard Shapes
Arbitrary Shapes

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Area Moment of Inertia App
Theory
• A general formula for the moments of
arbitrary shape bounded by straight
lines is derived leveraging Green’s
theorem for transforming domain to
boundary integrals. This formula is
implemented as an algorithm for
computing inertial properties of
arbitrary shapes.
• Moment of inertia is calculated w.r.t
the centroid. Ix cg and Iy cg
Arbitrary Cross sections
(e.g. corroded I beam Section)
A dx dy A  y dx dy x I  y dx dy xx
2
;
;
;

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areaMILite Tutorial
•Draw by tapping the vertexes
•Tap areaMI to calculate MI
•Default draw window size is 2 mm &snap size is 0.2 mm.
Change defaults by tapping settings.
Select a convenient Unit.
Drag and drop vertex to modify Shape
Edit the X,Y coordinates of the vertex
Set the size to the maximum from nano meter (10-9) to giga meter (10+9).
•Tips:
Draw and then edit by tap or X, Y input.
Boundary should not cross each other.
For irregular shapes use maximum points
X

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Area Moment of Inertia APP for Android OS Validation and Verification

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Prediction Comparison
MI of each sections were predicted by
1.Analytical Method: Theory of Elasticity/ Roark's Formulas.
2.Numerical Method: Numerical Integration solver/ Comsol Multiphysics.
3.ATOA Area MI app.
Following 5 common sections are compared (Analytical vs Numerical vs Area MI app).
Rectangular - Section
T - Section
I - Section
C - Section
Circular - Section
Following 2 artery sections are also compared (Numerical vs Area MI app).
Aileron Aero Profile
Eroded I-Beam Cross section

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Rectangular section

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T- Section

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I - Section

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C - Section

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Circular Section

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Aileron aero Profile

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Eroded I-Beam Crossection

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Comparison of Results
•For straight line profiled geometry the prediction accuracy is very high.
•For curved boundary the accuracy can be improved by increasing the number of vertex.
•But for arbitrary shapes such as corroded or damaged members, custom built sections, 3D printed shapes, complex designs, Area MI lite is the only app which will help to cross sectional area and principal Moment of inertia, Ix and Iy.

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Lite vs Pro
areaMILite
areaMIPro
To download your apps and for more Visit
apps.atoa.com
•Free
•Maximum Number of Vertex 24
•Properties: A, Ix, Iy
•Open Section: No
•Composite Section: No
•Import Export data: No
•Share DWG/Results: No
•Paid
•Maximum Number of Vertex 1000+
•Properties: A Cx Cy Ix Iy Ixy Z
•Open Section: Yes
•Composite Section: Yes
•Import Export data: Yes
•Share DWG/Results: Yes